Abstract: Investigating the mechanisms underlying the genesis and conduction of electrical excitation in the atria at physiological and pathological states is of great importance. To provide knowledge concerning the mechanisms of excitation, we constructed a biophysical detailed and anatomically accurate computer model of human atria that incorporates both structural and electrophysiological heterogeneities. The three-dimensional geometry was extracted from the visible female dataset. The sinoatrial node (SAN) and atrium, including crista terminalis (CT), pectinate muscles (PM), appendages (APG) and Bachmann's bundle (BB) were segmented in this work. Fibre orientation in CT, PM and BB was set to local longitudinal direction. Descriptions for all used cell types were based on modifications of the Courtemanche et al. model of a human atrial cell. Maximum conductances of Ito, IKr and ICa,L were modified for PM, CT, APG and atrioventricular ring to reproduce measured action potentials (AP). Pacemaker activity in the human SAN was reproduced by removing IK1, but including If, ICa,T, and gradients of channel conductances as described in previous studies for heterogeneous rabbit SAN. Anisotropic conduction was computed with a monodomain model using the finite element method. The transversal to longitudinal ratio of conductivity for PM, CT and BB was 1:9. Atrial working myocardium (AWM) was set to be isotropic. Simulation of atrial electrophysiology showed initiation of APs in the SAN centre. The excitation spread afterwards to the periphery near to the region of the CT and preferentially towards the atrioventricular region. The excitation extends over the right atrium along PM. Both CT and PM activated the right AWM. Earliest activation of the left atrium was through BB and excitation spread over to the APG. The conduction velocities were 0.6ms-1 for AWM, 1.2ms-1 for CT, 1.6ms-1 for PM and 1.1ms-1 for BB at a rate of 63bpm. The simulations revealed that bundles form dominant pathways for atrial conduction. The preferential conduction towards CT and along PM is comparable with clinical mapping. Repolarization is more homogeneous than excitation due to the heterogeneous distribution of electrophysiological properties and hence the action potential duration.
Abstract: Elucidation of the cellular basis of arrhythmias in ion channelopathy disorders is complicated by the inherent difficulties in studying human cardiac tissue. Thus we used a computer modeling approach to study the mechanisms of cellular dysfunction induced by mutations in inward rectifier potassium channel (Kir)2.1 that cause Andersen-Tawil syndrome (ATS). ATS is an autosomal dominant disorder associated with ventricular arrhythmias that uncommonly degenerate into the lethal arrhythmia torsade de pointes. We simulated the cellular and tissue effects of a potent disease-causing mutation D71V Kir2.1 with mathematical models of human ventricular myocytes and a bidomain model of transmural conduction. The D71V Kir2.1 mutation caused significant action potential duration prolongation in subendocardial, midmyocardial, and subepicardial myocytes but did not significantly increase transmural dispersion of repolarization. Simulations of the D71V mutation at shorter cycle lengths induced stable action potential alternans in midmyocardial, but not subendocardial or subepicardial cells. The action potential alternans was manifested as an abbreviated QRS complex in the transmural ECG, the result of action potential propagation failure in the midmyocardial tissue. In addition, our simulations of D71V mutation recapitulate several key ECG features of ATS, including QT prolongation, T-wave flattening, and QRS widening. Thus our modeling approach faithfully recapitulates several features of ATS and provides a mechanistic explanation for the low frequency of torsade de pointes arrhythmia in ATS.
Abstract: In this work, a new framework is presented that is suitable to solve the cardiac bidomain equation efficiently using the scientific computing library PETSc. Furthermore, the framework is able to modularly combine different ionic channels and is flexible enough to include arbitrary heterogeneities in ionic or coupling channel density. The ability of this framework is demonstrated in an example simulation in which the three-dimensional electrophysiological heterogeneity was adjusted in order to get a positive T-wave in the body electrocardiogram (ECG).
Abstract: Simulations of the electrophysiological behavior of the heart improve the comprehension of the mechanisms of the cardiovascular system. Furthermore, the mathematical modeling will support diagnosis and therapy of patients suffering from heart diseases. In this paper, the chain of modeling of the electrical function in the heart is described. The components are explained briefly, namely modeling of cardiac geometry, reconstructing the cardiac electrophysiology and excitation propagation. Additionally, the mathematical methods allowing to implement and solve these models are outlined. The three recently more investigated cases atrial fibrillation, ischemia and long-QT syndrome are described and show how cardiac modeling can support cardiologists in answering their open questions.
Abstract: Atrial arrhythmias are frequently treated using catheter ablation during electrophysiological (EP) studies. However, success rates are only moderate and could be improved with the help of personalized simulation models of the atria. In this work, we present a workflow to generate and validate personalized EP simulation models based on routine clinical computed tomography (CT) scans and intracardiac electrograms. From four patient data sets, we created anatomical models from angiographic CT data with an automatic segmentation algorithm. From clinical intracardiac catheter recordings, individual conduction velocities were calculated. In these subject-specific EP models, we simulated different pacing maneuvers and measurements with circular mapping catheters that were applied in the respective patients. This way, normal sinus rhythm and pacing from a coronary sinus catheter were simulated. Wave directions and conduction velocities were quantitatively analyzed in both clinical measurements and simulated data and were compared. On average, the overall difference of wave directions was 15° (8%), and the difference of conduction velocities was 16 cm/s (17%). The method is based on routine clinical measurements and is thus easy to integrate into clinical practice. In the long run, such personalized simulations could therefore assist treatment planning and increase success rates for atrial arrhythmias.
Abstract: Thin-walled cardiac tissue samples superfused with oxygenated solutions are widely used in experimental studies. However, due to decreased oxygen supply and insufficient wash out of waste products in the inner layers of such preparations, electrophysiological functions could be compromised. Although the cascade of events triggered by cutting off perfusion is well known, it remains unclear as to which degree electrophysiological function in viable surface layers is affected by pathological processes occurring in adjacent tissue. Using a 3D numerical bidomain model, we aim to quantify the impact of superfusion-induced heterogeneities occurring in the depth of the tissue on impulse propagation in superficial layers. Simulations demonstrated that both the pattern of activation as well as the distribution of extracellular potentials close to the surface remain essentially unchanged. This was true also for the electrophysiological properties of cells in the surface layer, where most relevant depolarization parameters varied by less than 5.5 %. The main observed effect on the surface was related to action potential duration that shortened noticeably by 53 % as hypoxia deteriorated. Despite the known limitations of such experimental methods, we conclude that superfusion is adequate for studying impulse propagation and depolarization whereas repolarization studies should consider the influence of pathological processes taking place at the core of tissue sample.
Abstract: Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.
Abstract: Computer models of the electrophysiological processes in the human heart become increasingly precise and detailed. The dream of supporting diagnosis of arrhythmias and planning of therapeutic interventions comes into reach. Recent progress in the field of cellular models (including e.g. pathological cases), in the field of coupled cell patches (including e.g. heterogeneity) and in the field of validation (including e.g. intracardial multi-channel recordings) are reported.
Abstract: Computer models of the heart can improve the understanding of the electrophysiological processes in healthy and diseased heart. They become more and more important for detailled diagnosis of arrhythmias and for optimization of therapy. Models of myocardium cells known today are described - they are based on the properties of all relevant ion channels in the cell membrane. Then it is demonstrated, how many cells can be joined to form a cell patch and how finally the complete heart can be modelled. A simpler approach is using a so called cellular automaton that allows for a significant reduction of calculation time while sacrifying some accordance to reality. Adaptive cellular automatons allow for a fast simulation with acceptable accuracy. Using them some results were gained for the simulation of typical arrhythmias, in the field of validation using an animal model and for therapy planning with RF-ablation.
Abstract: Cardiac arrhythmia is currently investigated from two different points of view. One considers ECG bio-signal analysis and investigates heart rate variability, baroreflex control, heart rate turbulence, alternans phenomena, etc. The other involves building computer models of the heart based on ion channels, bio-domain models and forward calculations to finally reach ECG and body surface potential maps. Both approaches aim to support the cardiologist in better understanding of arrhythmia, improving diagnosis and reliable risk stratification, and optimizing therapy. This article summarizes recent results and aims to trigger new research to bridge the different views.
Abstract: This review article gives a comprehensive survey of the progress made in computa- tional modeling of the human atria during the last 10 years. Modeling the anatomy has emerged from simple ”peanut”-like structures to very detailed models including atrial wall and fiber di- rection. Electrophysiological models started with just two cellular models in 1998. Today, five models exist considering e.g. details of intracellular compartments and atrial heterogeneity. On the pathological side, modeling atrial remodeling and fibrotic tissue are other important aspects. The bridge to data that are measured in the catheter laboratory and on the body surface (ECG) is under construction. Every measurement can be used either for model personalization or for validation. Potential clinical applications are briefly outlined and future research perspectives are suggested.
Abstract: Cardiologists measure electric signals inside the human heart aiming at a better diagnosis and optimized therapy of atrial arrhythmias like atrial flutter and atrial fibrillation. The catheters that are used for this purpose are improving: now they are able to pick up the electric signals at up to 64 positions inside the heart simultaneously. The patterns of electric depolarization are sometimes very simple, comparable to plane waves. But in case of patients with severe atrial arrhythmias they can be quite complex: U-turns around a line of block, ectopic centres, break throughs, reentry circuits, rotors, fractionated signals and chaotic patterns are often observed. Methods of biosignal analysis can support the cardiologists in classifying the signals and extract information of high diagnostic relevance. Computer models of the electrophysiology of the human heart can serve to design better algorithms for data analysis and to test algorithms, because the “ground truth” is known.
Abstract: In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field.
Abstract: During the contraction of the ventricles, the ventricles interact with the atria as well as with the pericardium and the surrounding tissue in which the heart is embedded. The atria are stretched, and the atrioventricular plane moves toward the apex. The atrioventricular plane displacement (AVPD) is considered to be a major contributor to the ventricular function, and a reduced AVPD is strongly related to heart failure. At the same time, the epicardium slides almost frictionlessly on the pericardium with permanent contact. Although the interaction between the ventricles, the atria and the pericardium plays an important role for the deformation of the heart, this aspect is usually not considered in computational models. In this work, we present an electromechanical model of the heart, which takes into account the interaction between ventricles, pericardium and atria and allows to reproduce the AVPD. To solve the contact problem of epicardium and pericardium, a contact handling algorithm based on penalty formulation was developed, which ensures frictionless and permanent contact. Two simulations of the ventricular contraction were conducted, one with contact handling of pericardium and heart and one without. In the simulation with contact handling, the atria were stretched during the contraction of the ventricles, while, due to the permanent contact with the pericardium, their volume increased. In contrast to that, in the simulations without pericardium, the atria were also stretched, but the change in the atrial volume was much smaller. Furthermore, the pericardium reduced the radial contraction of the ventricles and at the same time increased the AVPD.
Abstract: The application of strong electrical stimuli is a common method used for terminating irregular cardiac behaviour. The study presents the influence of electrophysiological heterogeneity on the response of human hearts to electrical stimulation. The human electrophysiology was simulated using the ten Tusscher-Noble-Noble-Panfilov cell model. The anisotropic propagation of depolarisation in three-dimensional virtual myocardial preparations was calculated using bidomain equations. The research was carried out on different types of virtual cardiac wedge. The selection of the modelling parameters emphasises the influence of cellular electrophysiology on the response of the human myocardium to electrical stimulation. The simulations were initially performed on a virtual cardiac control model characterised by electrophysiological homogeneity. The second preparation incorporated the transmural electrophysiological heterogeneity characteristic of the healthy human heart. In the third model type, the normal electrophysiological heterogeneity was modified by the conditions of heart failure. The main currents responsible for repolarisation (Ito, IKs and IKI) were reduced by 25%. Successively, [Na+]i was increased by the regulation of the Na+-Ca2+ exchange function, and fibrosis was represented by decreasing electrical conductivity. Various electrical stimulation configurations were used to investigate the differences in the responses of the three different models. Monophasic and biphasic electrical stimuli were applied through rectangular paddles and needle electrodes. A whole systolic period was simulated. The distribution of the transmembrane voltage indicated that the modification of electrophysiological heterogeneity induced drastic changes during the repolarisation phase. The results illustrated that each of the heart failure conditions amplifies the modification of the response of the myocardium to electrical stimulation. Therefore a theoretical model of the failing human heart must incorporate all the characteristic features.
Abstract: BACKGROUND: Genetic predisposition is believed to be responsible for most clinically significant arrhythmias; however, suitable genetic animal models to study disease mechanisms and evaluate new treatment strategies are largely lacking. METHODS AND RESULTS: In search of suitable arrhythmia models, we isolated the zebrafish mutation reggae (reg), which displays clinical features of the malignant human short-QT syndrome such as accelerated cardiac repolarization accompanied by cardiac fibrillation. By positional cloning, we identified the reg mutation that resides within the voltage sensor of the zebrafish ether-à-go-go-related gene (zERG) potassium channel. The mutation causes premature zERG channel activation and defective inactivation, which results in shortened action potential duration and accelerated cardiac repolarization. Genetic and pharmacological inhibition of zERG rescues recessive reg mutant embryos, which confirms the gain-of-function effect of the reg mutation on zERG channel function in vivo. Accordingly, QT intervals in ECGs from heterozygous and homozygous reg mutant adult zebrafish are considerably shorter than in wild-type zebrafish. CONCLUSIONS: With its molecular and pathophysiological concordance to the human arrhythmia syndrome, zebrafish reg represents the first animal model for human short-QT syndrome.
Abstract: Ventricular wall deformation is widely assumed to have an impact on the morphology of the T-wave that can be measured on the body surface. This study aims at quantifying these effects based on an in silico approach. To this end, we used a hybrid, static-dynamic approach: action potential propagation and repolarization were simulated on an electrophysiologically detailed but static 3-D heart model while the forward calculation accounted for ventricular deformation and the associated movement of the electrical sources (thus, it was dynamic). The displacement vectors that describe the ventricular motion were extracted from cinematographic and tagged MRI data using an elastic registration procedure. To probe to what extent the T-wave changes depend on the synchrony/asynchrony of mechanical relaxation and electrical repolarization, we created three electrophysiological configurations, each with a unique QT time: a setup with physiological QT time, a setup with pathologically short QT time (SQT), and pathologically long QT time (LQT), respectively. For all three electrophysiological configurations, a reduction of the T-wave amplitude was observed when the dynamic model was used for the forward calculations. The largest amplitude changes and the lowest correlation coefficients between the static and dynamic model were observed for the SQT setup, followed by the physiological QT and LQT setups.
Abstract: This paper examined the effects that different tissue conductivities had on forward-calculated ECGs. To this end, we ranked the influence of tissues by performing repetitive forward calculations while varying the respective tissue conductivity. The torso model included all major anatomical structures like blood, lungs, fat, anisotropic skeletal muscle, intestine, liver, kidneys, bone, cartilage, and spleen. Cardiac electrical sources were derived from realistic atrial and ventricular simulations. The conductivity rankings were based on one of two methods: First, we considered fixed percental conductivity changes to probe the sensitivity of the ECG regarding conductivity alterations. Second, we set conductivities to the reported minimum and maximum values to evaluate the effects of the existing conductivity uncertainties. The amplitudes of both atrial and ventricular ECGs were most sensitive for blood, skeletal muscle conductivity and anisotropy as well as for heart, fat, and lungs. If signal morphology was considered, fat was more important whereas skeletal muscle was less important. When comparing atria and ventricles, the lungs had a larger effect on the atria yet the heart conductivity had a stronger impact on the ventricles. The effects of conductivity uncertainties were significant. Future studies dealing with electrocardiographic simulations should consider these effects.
Abstract: Despite the commonly accepted notion that action potential duration (APD) is distributed heterogeneously throughout the ventricles and that the associated dispersion of repolarization is mainly responsible for the shape of the T-wave, its concordance and exact morphology are still not completely understood. This paper evaluated the T-waves for different previously measured heterogeneous ion channel distributions. To this end, cardiac activation and repolarization was simulated on a high resolution and anisotropic biventricular model of a volunteer. From the same volunteer, multichannel ECG data were obtained. Resulting transmembrane voltage distributions for the previously measured heterogeneous ion channel expressions were used to calculate the ECG and the simulated T-wave was compared to the measured ECG for quantitative evaluation. Both exclusively transmural (TM) and exclusively apico-basal (AB) setups produced concordant T-waves, whereas interventricular (IV) heterogeneities led to notched T-wave morphologies. The best match with the measured T-wave was achieved for a purely AB setup with shorter apical APD and a mix of AB and TM heterogeneity with M-cells in midmyocardial position and shorter apical APD. Finally, we probed two configurations in which the APD was negatively correlated with the activation time. In one case, this meant that the repolarization directly followed the sequence of activation. Still, the associated T-waves were concordant albeit of low amplitude.
Abstract: Radiofrequency ablation (RFA) therapy is the gold standard in interventional treatment of many cardiac arrhythmias. A major obstacle are non transmural lesions, leading to recurrence of arrhythmias. Recent clinical studies have suggested intracardiac electrogram (EGM) criteria as a promising marker to evaluate lesion development. Seeking for a deeper understanding of underlying mechanisms, we established a simulation approach for acute RFA lesions. Ablation lesions were modeled by a passive necrotic core surrounded by a borderzone with properties of heated myocardium. Herein, conduction velocity and electrophysiological properties were altered. We simulated EGMs during RFA to study the relation between lesion formation and EGM changes using the bidomain model. Simulations were performed on a three dimensional setup including a geometrically detailed representation of the catheter with highly conductive electrodes. For validation, EGMs recorded during RFA procedures in five patients were analyzed and compared to simulation results. Clinical data showed major changes in the distal unipolar EGM. During RFA, the negative peak amplitude decreased up to 104% and maximum negative deflection was up to 88% smaller at the end of the ablation sequence. These changes mainly occurred in the first 10 s after ablation onset. Simulated unipolar EGM reproduced the clinical changes, reaching up to 83% negative peak amplitude reduction and 80% decrease in maximum negative deflection for transmural lesions. In future work, the established model may enable the development of further EGM criteria for transmural lesions even for complex geometries in order to support clinical therapy.
Abstract: Atrial fibrillation (AF) is a common cardiac disease of genuine clinical concern with high rates of morbidity, leading to major personal and National Health Service costs. Computer modelling of AF using biophysically detailed cellular models with realistic 3D anatomical geometry allows investigation of the underlying ionic mechanisms in far more detail than with experimental physiology. We have developed a 3D virtual human atrium that combines detailed cellular electrophysiology including ion channel kinetics and homeostasis of ionic concentrations with anatomical details. The segmented anatomical structure and the multi- variable nature of the system make the 3D simulations of AF computationally large and intensive.
Abstract: The interaction of spiral waves of excitation with atrial anatomy remains unclear. This simulation study isolates the role of atrial anatomical structures on spiral wave spontaneous drift in the human atrium. We implemented realistic and idealised 3D human atria models to investigate the functional impact of anatomical structures on the long-term ( approximately 40 s) behaviour of spiral waves. The drift of a spiral wave was quantified by tracing its tip trajectory, which was correlated to atrial anatomical features. The interaction of spiral waves with the following idealised geometries was investigated: (a) a wedge-like structure with a continuously varying atrial wall thickness; (b) a ridge-like structure with a sudden change in atrial wall thickness; (c) multiple bridge-like structures consisting of a bridge connected to the atrial wall. Spiral waves drifted from thicker to thinner regions and along ridge-like structures. Breakthrough patterns caused by pectinate muscles (PM) bridges were also observed, albeit infrequently. Apparent anchoring close to PM-atrial wall junctions was observed. These observations were similar in both the realistic and the idealised models. We conclude that spatially altering atrial wall thickness is a significant cause of drift of spiral waves. PM bridges cause breakthrough patterns and induce transient anchoring of spiral waves.
Abstract: Chronic atrial fibrillation (AF) is a complex disease with underlying changes in electrophysiology, calcium signaling and the structure of atrial myocytes. How these individual remodeling targets and their emergent interactions contribute to cell physiology in chronic AF is not well understood. To approach this problem, we performed in silico experiments in a computational model of the human atrial myocyte. The remodeled function of cellular components was based on a broad literature review of in vitro findings in chronic AF, and these were integrated into the model to define a cohort of virtual cells. Simulation results indicate that while the altered function of calcium and potassium ion channels alone causes a pronounced decrease in action potential duration, remodeling of intracellular calcium handling also has a substantial impact on the chronic AF phenotype. We additionally found that the reduction in amplitude of the calcium transient in chronic AF as compared to normal sinus rhythm is primarily due to the remodeling of calcium channel function, calcium handling and cellular geometry. Finally, we found that decreased electrical resistance of the membrane together with remodeled calcium handling synergistically decreased cellular excitability and the subsequent inducibility of repolarization abnormalities in the human atrial myocyte in chronic AF. We conclude that the presented results highlight the complexity of both intrinsic cellular interactions and emergent properties of human atrial myocytes in chronic AF. Therefore, reversing remodeling for a single remodeled component does little to restore the normal sinus rhythm phenotype. These findings may have important implications for developing novel therapeutic approaches for chronic AF.
Abstract: BACKGROUND: The prevalence of atrial fibrillation is increased in patients with end-stage renal disease. Previous studies suggested that extracellular electrolyte alterations caused by hemodialysis (HD) therapy could be proarrhythmic. METHODS: Multiscale models were used for a consequent analysis of the effects of extracellular ion concentration changes on atrial electrophysiology. Simulations were based on measured electrolyte concentrations from patients with end-stage renal disease. RESULTS: Simulated conduction velocity and effective refractory period are decreased at the end of an HD session, with potassium having the strongest influence. P-wave is prolonged in patients undergoing HD therapy in the simulation as in measurements. CONCLUSIONS: Electrolyte concentration alterations impact atrial electrophysiology from the action potential level to the P-wave and can be proarrhythmic, especially because of induced hypokalemia. Analysis of blood electrolytes enables patient-specific electrophysiology modeling. We are providing a tool to investigate atrial arrhythmias associated with HD therapy, which, in the future, can be used to prevent such complications.
Abstract: Computational atrial models aid the understanding of pathological mechanisms and therapeutic measures in basic research. The use of biophysical models in a clinical environment requires methods to personalize the anatomy and electrophysiology (EP). Strategies for the automation of model generation and for evaluation are needed. In this manuscript, the current efforts of clinical atrial modeling in the euHeart project are summarized within the context of recent publications in this field. Model-based segmentation methods allow for the automatic generation of ready-to-simulate patient-specific anatomical models. EP models can be adapted to patient groups based on a-priori knowledge, and to the individual without significant further data acquisition. ECG and intracardiac data build the basis for excitation personalization. Information from late enhancement (LE) MRI can be used to evaluate the success of radio-frequency ablation (RFA) procedures and interactive virtual atria pave the way for RFA planning. Atrial modeling is currently in a transition from the sole use in basic research to future clinical applications. The proposed methods build the framework for model-based diagnosis and therapy evaluation and planning. Complex models allow to understand biophysical mechanisms and enable the development of simplified models for clinical applications.
Abstract: Atrial fibrillation (AF) is the most common cardiac arrhythmia, and the total number of AF patients is constantly increasing. The mechanisms leading to and sustaining AF are not completely understood yet. Heterogeneities in atrial electrophysiology seem to play an important role in this context. Although some heterogeneities have been used in in-silico human atrial modeling studies, they have not been thoroughly investigated. In this study, the original electrophysiological (EP) models of Courtemanche et al., Nygren et al. and Maleckar et al. were adjusted to reproduce action potentials in 13 atrial regions. The parameter sets were validated against experimental action potential duration data and ECG data from patients with AV block. The use of the heterogeneous EP model led to a more synchronized repolarization sequence in a variety of 3D atrial anatomical models. Combination of the heterogeneous EP model with a model of persistent AF-remodeled electrophysiology led to a drastic change in cell electrophysiology. Simulated Ta-waves were significantly shorter under the remodeling. The heterogeneities in cell electrophysiology explain the previously observed Ta-wave effects. The results mark an important step toward the reliable simulation of the atrial repolarization sequence, give a deeper understanding of the mechanism of atrial repolarization and enable further clinical investigations.
Abstract: Multiscale cardiac modeling has made great advances over the last decade. Highly detailed atrial models were created and used for the investigation of initiation and perpetuation of atrial fibrillation. The next challenge is the use of personalized atrial models in clinical practice. In this study, a framework of simple and robust tools is presented, which enables the generation and validation of patient-specific anatomical and electrophysiological atrial models. Introduction of rule-based atrial fiber orientation produced a realistic excitation sequence and a better correlation to the measured electrocardiograms. Personalization of the global conduction velocity lead to a precise match of the measured P-wave duration. The use of a virtual cohort of nine patient and volunteer models averaged out possible model-specific errors. Intra-atrial excitation conduction was personalized manually from left atrial local activation time maps. Inclusion of LE-MRI data into the simulations revealed possible gaps in ablation lesions. A fast marching level set approach to compute atrial depolarization was extended to incorporate anisotropy and conduction velocity heterogeneities and reproduced the monodomain solution. The presented chain of tools is an important step towards the use of atrial models for the patient-specific AF diagnosis and ablation therapy planing.
Abstract: Left atrial fibrosis is thought to contribute to the manifestation of atrial fibrillation (AF). Late Gadolinium enhancement (LGE) MRI has the potential to image regions of low perfusion, which can be related to fibrosis. We show that a simulation with a patient-specific model including left atrial regional fibrosis derived from LGE-MRI reproduces local activation in the left atrium more precisely than the regular simulation without fibrosis. AF simulations showed a spontaneous termination of the arrhythmia in the absence of fibrosis and a stable rotor center in the presence of fibrosis. The methodology may provide a tool for a deeper understanding of the mechanisms maintaining AF and eventually also for the planning of substrate-guided ablation procedures in the future.
Abstract: Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.
Abstract: Atrial fibrillation (AF) is the most common arrhythmia of the heart in industrialized countries. Its generation and the transitory behavior of paroxysmal AF are still not well understood. In this work we examine the interaction of two activation sources via an isthmus as possible cause for the initiation of fibrillation episodes. For this study, the electrophysiological model of Bueno-Orovio, Cherry and Fenton is adapted to atrial electrophysiology, both for physiological and electrophysiologically remodeled conditions due to AF. We show that the interaction of the pacemakers, combined with the geometrical constraints of the isthmus, can produce fibrillatory-type irregularities, which we quantify by the loss of spatial phase coherence in the transmembrane voltage. Transitions to irregular behavior occur when the frequencies of the pacemakers exceed certain thresholds, suggesting that AF episodes are initiated by frequency changes of the activating sources (sinus node, ectopic focus).
In Europace : European Pacing, Arrhythmias, and Cardiac Electrophysiology : Journal of the Working Groups on Cardiac Pacing, Arrhythmias, and Cardiac Cellular Electrophysiology of the European Society of Cardiology, vol. 16(3) , pp. 435-443, 2014
Abstract: AIMS: Human ether-a-go-go-related gene (hERG) missense mutations N588K and L532P are both associated with atrial fibrillation (AF). However, the underlying gain-of-function mechanism is different. The aim of this computational study is to assess and understand the arrhythmogenic mechanisms of these genetic disorders on the cellular and tissue level as a basis for the improvement of therapeutic strategies. METHODS AND RESULTS: The IKr formulation of an established model of human atrial myocytes was adapted by using the measurement data of wild-type and mutant hERG channels. Restitution curves of the action potential duration and its slope, effective refractory period (ERP), conduction velocity, reentry wavelength (WL), and the vulnerable window (VW) were determined in a one-dimensional (1D) tissue strand. Moreover, spiral wave inducibility and rotor lifetime in a 2D tissue patch were evaluated. The two mutations caused an increase in IKr regarding both peak amplitude and current integral, whereas the duration during which IKr is active was decreased. The WL was reduced due to a shorter ERP. Spiral waves could be initiated by using mutation models as opposed to the control case. The frequency dependency of the VW was reversed. CONCLUSION: Both mutations showed an increased arrhythmogenicity due to decreased refractory time in combination with a more linear repolarization phase. The effects were more pronounced for mutation L532P than for N588K. Furthermore, spiral waves presented higher stability and a more regular pattern for L532P. These in silico investigations unveiling differences of mutations affecting the same ion channel may help to advance genotype-guided AF prevention and therapy strategies.
In Europace : European Pacing, Arrhythmias, and Cardiac Electrophysiology : Journal of the Working Groups on Cardiac Pacing, Arrhythmias, and Cardiac Cellular Electrophysiology of the European Society of Cardiology, vol. 16(suppl 4) , pp. iv30-iv38, 2014
Abstract: AIMS: The clinical efficacy in preventing the recurrence of atrial fibrillation (AF) is higher for amiodarone than for dronedarone. Moreover, pharmacotherapy with these drugs is less successful in patients with remodelled substrate induced by chronic AF (cAF) and patients suffering from familial AF. To date, the reasons for these phenomena are only incompletely understood. We analyse the effects of the drugs in a computational model of atrial electrophysiology. METHODS AND RESULTS: The Courtemanche-Ramirez-Nattel model was adapted to represent cAF remodelled tissue and hERG mutations N588K and L532P. The pharmacodynamics of amiodarone and dronedarone were investigated with respect to their dose and heart rate dependence by evaluating 10 descriptors of action potential morphology and conduction properties. An arrhythmia score was computed based on a subset of these biomarkers and analysed regarding circadian variation of drug concentration and heart rate. Action potential alternans at high frequencies was observed over the whole dronedarone concentration range at high frequencies, while amiodarone caused alternans only in a narrow range. The total score of dronedarone reached critical values in most of the investigated dynamic scenarios, while amiodarone caused only minor score oscillations. Compared with the other substrates, cAF showed significantly different characteristics resulting in a lower amiodarone but higher dronedarone concentration yielding the lowest score. CONCLUSION: Significant differences exist in the frequency and concentration-dependent effects between amiodarone and dronedarone and between different atrial substrates. Our results provide possible explanations for the superior efficacy of amiodarone and may aid in the design of substrate-specific pharmacotherapy for AF.
Abstract: In case of chest pain, immediate diagnosis of myocardial ischemia is required to respond with an appropriate treatment. The diagnostic capability of the electrocardiogram (ECG), however, is strongly limited for ischemic events that do not lead to ST elevation. This computational study investigates the potential of different electrode setups in detecting early ischemia at 10 minutes after onset: standard 3-channel and 12-lead ECG as well as body surface potential maps (BSPMs). Further, it was assessed if an additional ECG electrode with optimized position or the right-sided Wilson leads can improve sensitivity of the standard 12-lead ECG. To this end, a simulation study was performed for 765 different locations and sizes of ischemia in the left ventricle. Improvements by adding a single, subject specifically optimized electrode were similar to those of the BSPM: 2–11% increased detection rate depending on the desired specificity. Adding right-sided Wilson leads had negligible effect. Absence of ST deviation could not be related to specific locations of the ischemic region or its transmurality. As alternative to the ST time integral as a feature of ST deviation, the K point deviation was introduced: the baseline deviation at the minimum of the ST-segment envelope signal, which increased 12-lead detection rate by 7% for a reasonable threshold.
Abstract: Computational models of cardiac electrophysiology provided insights into arrhythmogenesis and paved the way toward tailored therapies in the last years. To fully leverage in silico models in future research, these models need to be adapted to reflect pathologies, genetic alterations, or pharmacological effects, however. A common approach is to leave the structure of established models unaltered and estimate the values of a set of parameters. Today's high-throughput patch clamp data acquisition methods require robust, unsupervised algorithms that estimate parameters both accurately and reliably. In this work, two classes of optimization approaches are evaluated: gradient-based trust-region-reflective and derivative-free particle swarm algorithms. Using synthetic input data and different ion current formulations from the Courtemanche et al. electrophysiological model of human atrial myocytes, we show that neither of the two schemes alone succeeds to meet all requirements. Sequential combination of the two algorithms did improve the performance to some extent but not satisfactorily. Thus, we propose a novel hybrid approach coupling the two algorithms in each iteration. This hybrid approach yielded very accurate estimates with minimal dependency on the initial guess using synthetic input data for which a ground truth parameter set exists. When applied to measured data, the hybrid approach yielded the best fit, again with minimal variation. Using the proposed algorithm, a single run is sufficient to estimate the parameters. The degree of superiority over the other investigated algorithms in terms of accuracy and robustness depended on the type of current. In contrast to the non-hybrid approaches, the proposed method proved to be optimal for data of arbitrary signal to noise ratio. The hybrid algorithm proposed in this work provides an important tool to integrate experimental data into computational models both accurately and robustly allowing to assess the often non-intuitive consequences of ion channel-level changes on higher levels of integration.
In Europace : European Pacing, Arrhythmias, and Cardiac Electrophysiology : Journal of the Working Groups on Cardiac Pacing, Arrhythmias, and Cardiac Cellular Electrophysiology of the European Society of Cardiology, vol. 18(suppl 4) , pp. iv35-iv43, 2016
Abstract: AIMS: P-wave morphology correlates with the risk for atrial fibrillation (AF). Left atrial (LA) enlargement could explain both the higher risk for AF and higher P-wave terminal force (PTF) in lead V1. However, PTF-V1 has been shown to correlate poorly with LA size. We hypothesize that PTF-V1 is also affected by the earliest activated site (EAS) in the right atrium and its proximity to inter-atrial connections (IAC), which both show tremendous variability. METHODS AND RESULTS: Atrial excitation was triggered from seven different EAS in a cohort of eight anatomically personalized computational models. The posterior IACs were non-conductive in a second set of simulations. Body surface ECGs were computed and separated by left and right atrial contributions. Mid-septal EAS yielded the highest PTF-V1. More anterior/superior and more inferior EAS yielded lower absolute PTF-V1 values deviating by a factor of up to 2.0 for adjacent EAS. Earliest right-to-left activation was conducted via Bachmann's Bundle (BB) for anterior/superior EAS and shifted towards posterior IACs for more inferior EAS. Non-conducting posterior IACs increased PTF-V1 by up to 150% compared to intact posterior IACs for inferior EAS. LA contribution to the P-wave integral was 24% on average. CONCLUSION: The electrical contributor's site of earliest activation and intactness of posterior IACs affect PTF-V1 significantly by changing LA breakthrough sites independent from LA size. This should be considered for interpretation of electrocardiographical signs of LA abnormality and LA enlargement.
Abstract: Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.
Abstract: Whole-chamber mapping using a 64-pole basket catheter (BC) has become a featured approach for the analysis of excitation patterns during atrial fibrillation. A flexible catheter design avoids perforation but may lead to spline bunching and influence coverage. We aim to quantify the catheter deformation and endocardial coverage in clinical situations and study the effect of catheter size and electrode arrangement using an in silico basket model. Atrial coverage and spline separation were evaluated quantitatively in an ensemble of clinical measurements. A computational model of the BC was implemented including an algorithm to adapt its shape to the atrial anatomy. Two clinically relevant mapping positions in each atrium were assessed in both clinical and simulated data. The simulation environment allowed varying both BC size and electrode arrangement. Results showed that interspline distances of more than 20 mm are common, leading to a coverage of less than 50% of the left atrial (LA) surface. In an ideal in silico scenario with variable catheter designs, a maximum coverage of 65% could be reached. As spline bunching and insufficient coverage can hardly be avoided, this has to be taken into account for interpretation of excitation patterns and development of new panoramic mapping techniques.
Abstract: BACKGROUND: Investigations on adverse biological effects of nanoparticles (NPs) in the lung by in vitro studies are usually performed under submerged conditions where NPs are suspended in cell culture media. However, the behaviour of nanoparticles such as agglomeration and sedimentation in such complex suspensions is difficult to control and hence the deposited cellular dose often remains unknown. Moreover, the cellular responses to NPs under submerged culture conditions might differ from those observed at physiological settings at the air-liquid interface. RESULTS: In order to avoid problems because of an altered behaviour of the nanoparticles in cell culture medium and to mimic a more realistic situation relevant for inhalation, human A549 lung epithelial cells were exposed to aerosols at the air-liquid interphase (ALI) by using the ALI deposition apparatus (ALIDA). The application of an electrostatic field allowed for particle deposition efficiencies that were higher by a factor of more than 20 compared to the unmodified VITROCELL deposition system. We studied two different amorphous silica nanoparticles (particles produced by flame synthesis and particles produced in suspension by the Stober method). Aerosols with well-defined particle sizes and concentrations were generated by using a commercial electrospray generator or an atomizer. Only the electrospray method allowed for the generation of an aerosol containing monodisperse NPs. However, the deposited mass and surface dose of the particles was too low to induce cellular responses. Therefore, we generated the aerosol with an atomizer which supplied agglomerates and thus allowed a particle deposition with a three orders of magnitude higher mass and of surface doses on lung cells that induced significant biological effects. The deposited dose was estimated and independently validated by measurements using either transmission electron microscopy or, in case of labelled NPs, by fluorescence analyses. Surprisingly, cells exposed at the ALI were less sensitive to silica NPs as evidenced by reduced cytotoxicity and inflammatory responses. CONCLUSION: Amorphous silica NPs induced qualitatively similar cellular responses under submerged conditions and at the ALI. However, submerged exposure to NPs triggers stronger effects at much lower cellular doses. Hence, more studies are warranted to decipher whether cells at the ALI are in general less vulnerable to NPs or specific NPs show different activities dependent on the exposure method.
Abstract: BACKGROUND: This article presents a study, which examines the effects of biphasic electrical shocks on human ventricular tissue. The effects of this type of shock are not yet fully understood. Animal experiments showed the superiority of biphasic shocks over monophasic ones in defibrillation. A mathematical computer simulation can increase the knowledge of human heart behavior. METHODS: The research presented in this article was done with different models representing a three-dimensional wedge of ventricular myocardium. The electrophysiology was described with Priebe-Beuckelmann model. The realistic fiber twist, which is specific to human myocardium was included. Planar electrodes were placed at the ends of the longest side of the virtual cardiac wedge, in a bath medium. They were sources of electrical shocks, which varied in magnitude from 0.1 to 5 V. In a second arrangement ring electrodes were placed directly on myocardium for getting a better view on secondary electrical sources. The electrical reaction of the tissue was generated with a bidomain model. RESULTS: The reaction of the tissue to the electrical shock was specific to the initial imposed characteristics. Depolarization appeared in the first 5 ms in different locations. A further study of the cardiac tissue behavior revealed, which features influence the response of the considered muscle. It was shown that the time needed by the tissue to be totally depolarized is much shorter when a biphasic shock is applied. Each simulation ended only after complete repolarization was achieved. This created the possibility of gathering information from all states corresponding to one cycle of the cardiac rhythm. CONCLUSIONS: The differences between the reaction of the homogeneous tissue and a tissue, which contains cleavage planes, reveals important aspects of superiority of biphasic pulses.
Abstract: Ablation strategies to prevent episodes of paroxysmal atrial fibrillation (AF) have been subject to many clinical studies. The issues mainly concern pattern and transmurality of the lesions. This paper investigates ten different ablation strategies on a multilayered 3-D anatomical model of the atria with respect to 23 different setups of AF initiation in a biophysical computer model. There were 495 simulations carried out showing that circumferential lesions around the pulmonary veins (PVs) yield the highest success rate if at least two additional linear lesions are carried out. The findings compare with clinical studies as well as with other computer simulations. The anatomy and the setup of ectopic beats play an important role in the initiation and maintenance of AF as well as the resulting therapy. The computer model presented in this paper is a suitable tool to investigate different ablation strategies. By including individual patient anatomy and electrophysiological measurement, the model could be parameterized to yield an effective tool for future investigation of tailored ablation strategies and their effects on atrial fibrillation.
Abstract: Computer aided simulations of the heart provide knowledge for cardiologic diagnosis and therapy. A model of the myocardium is presented which allows the reconstruction of electrical and mechanical processes with inclusion of feedback mechanisms. The model combines detailed models of cellular electrophysiology and force development with models of the electrical current flow and the mechanical behavior of the myocardium. Results of simulations show the connection between the electrical excitation process and the following mechanical deformation in a three dimensional, anisotropic area of the myocardium.
Keywords: Mechano-Electrical Feedback, Electro-Mechanical Feedback, Cellular Models, Electrophysiology, Excitation-Propagation
Abstract: Mathematical models of cardiac anatomy and physics provide information, which help to understand structure and behavior of the heart. Miscellaneous cardiac phenomena can only be adequately described by combination of models representing different aspects or levels of detail. Coupling of these models necessitates the definition of appropriate interfaces. Adequateness and efficiency of interfaces is crucial for efficient application of the combined models.
In this work an integrated model is presented consisting of several models interconnected by interfaces. The integrated model allows the reconstruction of macroscopic electro-mechanical processes in the heart. The model comprises a three-dimensional are of left ventricular anatomy represented as truncated ellipsoid. The integrated model includes electrophysiological, tension development and elastomechanical models of myocardium at levels of single cell, proteins, and tissue patches, respectively.
The model is exemplified by simulations of extracorporated left ventricle of small mammals. These simulations yield temporal distributions of electrophysiological parameters as well as descriptions of electrical propagation and mechanical deformation. The simulations show characteristic macroscopic ventricular function resulting from the interplay between cellular electrophysiology, electrical excitation propagation, tension development, and mechanical deformation.
Abstract: A model of the electromechanical behavior of a myocardial region is presented. The model combines an electrophysiological, a force development and an excitation propagation model. All of these models incorporate the effects of deformation of the myocardium. An extension of the traditional bidomain model for excitation propagation is proposed. The extension describes the stretch dependency of the conductivity tensor of the intra- and extracellular space and is constructed outgoing from physically motivated assumptions, which simplify the behavior of the conductivity tensor. The extension makes usage of the deformation gradient tensor, which is a foundation in the theory of continuums mechanics. The performed simulations illustrate some effects of myocardial electromechanical behavior.
Abstract: Fibroblasts are abundant in cardiac tissue. Experimental studies suggested that fibroblasts are electrically coupled to myocytes and this coupling can impact cardiac electrophysiology. In this work, we present a novel approach for mathematical modeling of electrical conduction in cardiac tissue composed of myocytes, fibroblasts, and the extracellular space. The model is an extension of established cardiac bidomain models, which include a description of intra-myocyte and extracellular conductivities, currents and potentials in addition to transmembrane voltages of myocytes. Our extension added a description of fibroblasts, which are electrically coupled with each other and with myocytes. We applied the extended model in exemplary computational simulations of plane waves and conduction in a thin tissue slice assuming an isotropic conductivity of the intra-fibroblast domain. In simulations of plane waves, increased myocyte-fibroblast coupling and fibroblast-myocyte ratio reduced peak voltage and maximal upstroke velocity of myocytes as well as amplitudes and maximal downstroke velocity of extracellular potentials. Simulations with the thin tissue slice showed that inter-fibroblast coupling affected rather transversal than longitudinal conduction velocity. Our results suggest that fibroblast coupling becomes relevant for small intra-myocyte and/or large intra-fibroblast conductivity. In summary, the study demonstrated the feasibility of the extended bidomain model and supports the hypothesis that fibroblasts contribute to cardiac electrophysiology in various manners.
Abstract: BACKGROUND AND PURPOSE: Atomoxetine is a selective noradrenaline reuptake inhibitor, recently approved for the treatment of attention-deficit/hyperactivity disorder. So far, atomoxetine has been shown to be well tolerated, and cardiovascular effects were found to be negligible. However, two independent cases of QT interval prolongation, associated with atomoxetine overdose, have been reported recently. We therefore analysed acute and subacute effects of atomoxetine on cloned human Ether-a-Go-Go-Related Gene (hERG) channels. EXPERIMENTAL APPROACH: hERG channels were heterologously expressed in Xenopus oocytes and in a human embryonic kidney cell line and hERG currents were measured using voltage clamp and patch clamp techniques. Action potential recordings were made in isolated guinea-pig cardiomyocytes. Gene expression and channel surface expression were analysed using quantitative reverse transcriptase polymerase chain reaction, Western blot and the patch clamp techniques. KEY RESULTS: In human embryonic kidney cells, atomoxetine inhibited hERG current with an IC(50) of 6.3 micromol.L(-1). Development of block and washout were fast. Channel activation and inactivation were not affected. Inhibition was state-dependent, suggesting an open channel block. No use-dependence was observed. Inhibitory effects of atomoxetine were attenuated in the pore mutants Y652A and F656A. In guinea-pig cardiomyocytes, atomoxetine lengthened action potential duration without inducing action potential triangulation. Overnight incubation with high atomoxetine concentrations resulted in a decrease of channel surface expression. CONCLUSIONS AND IMPLICATIONS: Whereas subacute effects of atomoxetine seem negligible under therapeutically relevant concentrations, hERG channel block should be considered in cases of atomoxetine overdose and when administering atomoxetine to patients at increased risk for the development of acquired long-QT syndrome.
Abstract: The anticholinergic antiparkinson drug orphenadrine is an antagonist at central and peripheral muscarinic receptors. Orphenadrine intake has recently been linked to QT prolongation and Torsade-de-Pointes tachycardia. So far, inhibitory effects on I Kr or cloned HERG channels have not been examined. HERG channels were heterologously expressed in a HEK 293 cell line and in Xenopus oocytes and HERG current was measured using the whole cell patch clamp and the double electrode voltage clamp technique. Orphenadrine inhibits cloned HERG channels in a concentration dependent manner, yielding an IC50 of 0.85 μM in HEK cells. Onset of block is fast and reversible upon washout. Orphenadrine does not alter the half-maximal activation voltage of HERG channels. There is no shift of the half-maximal steady-state-inactivation voltage. Time constants of direct channel inactivation are not altered significantly and there is no use-dependence of block. HERG blockade is attenuated significantly in mutant channels lacking either of the aromatic pore residues Y652 and F656. In conclusion, we show that the anticholinergic agent orphenadrine is an antagonist at HERG channels. These results provide a novel molecular basis for the reported proarrhythmic side effects of orphenadrine
Abstract: Inhibition of the atrial ultra-rapid delayed rectifier potassium current (I Kur) represents a promising therapeutic strategy in the therapy of atrial fibrillation. However, experimental and clinical data on the antiarrhythmic efficacy remain controversial. We tested the hypothesis that antiarrhythmic effects of I Kur inhibitors are dependent on kinetic properties of channel blockade. A mathematical description of I Kur blockade was introduced into Courtemanche-Ramirez-Nattel models of normal and remodeled atrial electrophysiology. Effects of five model compounds with different kinetic properties were analyzed. Although a reduction of dominant frequencies could be observed in two dimensional tissue simulations for all compounds, a reduction of spiral wave activity could be only be detected in two cases. We found that an increase of the percent area of refractory tissue due to a prolongation of the wavelength seems to be particularly important. By automatic tracking of spiral tip movement we find that increased refractoriness resulted in rotor extinction caused by an increased spiral-tip meandering. We show that antiarrhythmic effects of I Kur inhibitors are dependent on kinetic properties of blockade. We find that an increase of the percent area of refractory tissue is the underlying mechanism for an increased spiral-tip meandering, resulting in the extinction of re-entrant circuits.
Abstract: Electrophysiological modeling of cardiac tissue is commonly based on functional and structural properties measured in experiments. Our knowledge of these properties is incomplete, in particular their remodeling in disease. Here, we introduce a methodology for quantitative tissue characterization based on fluorescent labeling, three-dimensional scanning confocal microscopy, image processing and reconstruction of tissue micro-structure at sub-micrometer resolution. We applied this methodology to normal rabbit ventricular tissue and tissue from hearts with myocardial infarction. Our analysis revealed that the volume fraction of fibroblasts increased from 4.830.42% (meanstandard deviation) in normal tissue up to 6.510.38% in myocardium from infarcted hearts. The myocyte volume fraction decreased from 76.209.89% in normal to 73.488.02% adjacent to the infarct. Numerical field calculations on three-dimensional reconstructions of the extracellular space yielded an extracellular longitudinal conductivity of 0.2640.082 S/m with an anisotropy ratio of 2.0951.11 in normal tissue. Adjacent to the infarct, the longitudinal conductivity increased up to 0.4000.051 S/m, but the anisotropy ratio decreased to 1.2950.09. Our study indicates an increased density of gap junctions proximal to both fibroblasts and myocytes in infarcted versus normal tissue, supporting previous hypotheses of electrical coupling of fibroblasts and myocytes in infarcted hearts. We suggest that the presented methodology provides an important contribution to modeling normal and diseased tissue. Applications of the methodology include the clinical characterization of disease-associated remodeling. 1.
Abstract: Conduction velocity (CV) and CV restitution are important substrate parameters for understanding atrial arrhythmias. The aim of this work is to (i) present a simple but feasible method to measure CV restitution in-vivo using standard circular catheters, and (ii) validate its feasibility with data measured during incremental pacing. From five patients undergoing catheter ablation, we analyzed 8 datasets from sinus rhythm and incremental pacing sequences. Every wavefront was measured with a circular catheter and the electrograms were analyzed with a cosine-fit method that calculated the local CV. For each pacing cycle length, the mean local CV was determined. Furthermore, changes in global CV were estimated from the time delay between pacing stimulus and wavefront arrival. Comparing local and global CV between pacing at 500 and 300 ms, we found significant changes in 7 of 8 pacing sequences. On average, local CV decreased by 2015% and global CV by 1713%. The method allows for in-vivo measurements of absolute CV and CV restitution during standard clinical procedures. Such data may provide valuable insights into mechanisms of atrial arrhythmias. This is important both for improving cardiac models and also for clinical applications, such as characterizing arrhythmogenic substrates during sinus rhythm.
Abstract: In this paper, we present an efficient method to estimate changes in forward-calculated body surface potential maps (BSPMs) caused by variations in tissue conductivities. For blood, skeletal muscle, lungs, and fat, the influence of conductivity variations was analyzed using the principal component analysis (PCA). For each single tissue, we obtained the first PCA eigenvector from seven sample simulations with conductivities between ±75% of the default value. We showed that this eigenvector was sufficient to estimate the signal over the whole conductivity range of ±75%. By aligning the origins of the different PCA coordinate systems and superimposing the single tissue effects, it was possible to estimate the BSPM for combined conductivity variations in all four tissues. Furthermore, the method can be used to easily calculate confidence intervals for the signal, i.e., the minimal and maximal possible amplitudes for given conductivity uncertainties. In addition to that, it was possible to determine the most probable conductivity values for a given BSPM signal. This was achieved by probing hundreds of different conductivity combinations with a numerical optimization scheme. In conclusion, our method allows to efficiently predict forward-calculated BSPMs over a wide range of conductivity values from few sample simulations.
Abstract: Atrial arrhythmias, such as atrial flutter or fibrillation, are frequent indications for catheter ablation. Recorded intracardiac electrograms (EGMs) are, however, mostly evaluated subjectively by the physicians. In this paper, we present a method to quantitatively extract the wave direction and the local conduction velocity from one single beat in a circular mapping catheter signal. We simulated typical clinical EGMs to validate the method. We then showed that even with noise, the average directional error was below 10(°) and the average velocity error was below 5.4 cm/s. In a realistic atrial simulation, the method could clearly distinguish between stimuli from different pulmonary veins. We further analyzed eight clinical data segments from three patients in normal sinus rhythm and with stimulation. We obtained stable wave directions for each segment and conduction velocities between 70 and 115 cm/s. We conclude that the method allows for easy quantitative analysis of single macroscopic wavefronts in intracardiac EGMs, such as during atrial flutter or in typical clinical stimulation procedures after termination of atrial fibrillation. With corresponding simulated data, it can provide an interface to personalize electrophysiological (EP) models. Furthermore, it could be integrated into EP navigation systems to provide quantitative data of high diagnostic value to the physician
Abstract: Aims This computational study examined the influence of fibre orientation on the electrical processes in the heart. In contrast to similar previous studies, human diffusion tensor magnetic resonance imaging measurements were used.
Methods The fibre orientation was extracted from distinctive regions of the left ventricle. It was incorporated in a single tissue segment having a fixed geometry. The electrophysiological model applied in the computational units considered transmural heterogeneities. Excitation was computed by means of the monodomain model; the accompanying pseudo-electrocardiograms (ECGs) were calculated.
Results The distribution of fibre orientation extracted from the same transversal section showed only small variations. The fibre information extracted from the equal circumferential but different longitudinal positions showed larger differences, mainly in the imbrication angle. Differences of the endocardial myocyte orientation mainly affected the beginning of the activation sequence. The transmural propagation was faster in areas with larger imbrication angles leading to a narrower QRS complex in pseudo-ECGs.
Conclusion The model can be expanded to simulate electrophysiology and contraction in the whole heart geometry. Embedded in a torso model, the impact of fibre orientation on body surface ECGs and their relation to local pseudo-ECGs can be identified.
Abstract: Cardiac tissue exhibits spatially heterogeneous electrophysiological properties. In cardiac diseases, these properties also change in time. This study introduces a framework to investigate their role in cardiac ischemia using mathematical modeling and computational simulations at cellular and tissue level. Ischemia was incorporated by reproducing effects of hyperkalemia, acidosis, and hypoxia with a human electrophysiological model. In tissue, spatial heterogeneous ischemia was described by central ischemic (CIZ) and border zone. Anisotropic conduction was simulated with a bidomain approach in an anatomical ventricle model including realistic fiber orientation and transmural, apico-basal, and interventricular electrophysiological heterogeneities. A model of electrical conductivity in a human torso served for ECG calculations. Ischemia increased resting but reduced peak voltage, action potential duration, and upstroke velocity. These effects were strongest in subepicardial cells. In tissue, conduction velocity decreased towards CIZ but effective refractory period increased. At 10 min of ischemia 19% of subepi- and 100% of subendocardial CIZ cells activated with a delay of 34.6+/-7.8 ms and 55.9+/-18.8 ms, respectively, compared to normal. Significant ST elevation and premature T wave end appeared only with the subepicardial CIZ. The model reproduced effects of ischemia at cellular and tissue level. The results suggest that the presented in silico approach can complement experimental studies, e.g., in understanding the role of ischemia or the onset of arrhythmia.
Abstract: Bioelectric source measurements are influenced by the measurement location as well as the conductive properties of the tissues. Volume conductor effects such as the poorly conducting bones or the moderately conducting skin are known to affect the measurement precision and accuracy of the surface electroencephalography (EEG) measurements. This paper investigates the influence of age via skull conductivity upon surface and subdermal bipolar EEG measurement sensitivity conducted on two realistic head models from the Visible Human Project. Subdermal electrodes (a.k.a. subcutaneous electrodes) are implanted on the skull beneath the skin, fat, and muscles. We studied the effect of age upon these two electrode types according to the scalp-to-skull conductivity ratios of 5, 8, 15, and 30 : 1. The effects on the measurement sensitivity were studied by means of the half-sensitivity volume (HSV) and the region of interest sensitivity ratio (ROISR). The results indicate that the subdermal implantation notably enhances the precision and accuracy of EEG measurements by a factor of eight compared to the scalp surface measurements. In summary, the evidence indicates that both surface and subdermal EEG measurements benefit better recordings in terms of precision and accuracy on younger patients.
Abstract: Acute cardiac ischemia, which is caused by the occlusion of a coronary artery, often leads to lethal ventricular arrhythmias or heart failure. The early diagnosis of this pathology is based on changes of the electrocardiogram (ECG), i.e. mainly shifts of the ST segment. However, the underlying mechanisms responsible for these shifts are not completely understood. Furthermore, clinical observations indicate that some acute ischemia cases can hardly be detected using standard 12-lead ECG only. Therefore, multi-scale computer simulations of cardiac ischemia using realistic models of human ventricles were carried out in this work. For this purpose, the transmembrane voltage distributions in the heart and the corresponding body surface potentials were computed with varying transmural extent of the ischemic region at different ischemia stages. Some of the simulated ischemia cases were electrically silent, i.e. they could hardly be identified in the 12-lead ECG.
Abstract: Aims Amiodarone and cisapride are both known to prolong the QT interval, yet the two drugs have different effects on arrhythmia. Cisapride can cause torsades de pointes while amiodarone is found to be anti-arrhythmic. A computational model was used to investigate the action of these two drugs.
Methods and results In a biophysically detailed model, the ion current conductivities affected by both drugs were reduced in order to simulate the pharmacological effects in healthy and ischaemic cells. Furthermore, restitution curves of the action potential duration (APD), effective refractory period, conduction velocity, wavelength, and the vulnerable window were determined in a one-dimensional (1D) tissue strand. Moreover, cardiac excitation propagation was computed in a 3D model of healthy ventricles. The corresponding body surface potentials were calculated and standard 12-lead electrocardiograms were derived. Both cisapride and amiodarone caused a prolongation of the QT interval and the refractory period. However, cisapride did not significantly alter the conduction-related properties, such as e.g. the wavelength or vulnerable window, whereas amiodarone had a larger impact on them. It slightly flattened the APD restitution slope and furthermore reduced the conduction velocity and wavelength.
Conclusion Both drugs show similar prolongation of the QT interval, although they present different electrophysiological properties in the single-cell as well as in tissue simulations of cardiac excitation propagation. These computer simulations help to better understand the underlying mechanisms responsible for the initiation or termination of arrhythmias caused by amiodarone and cisapride.
Abstract: Mathematical modeling of cardiac electrophysiology is an insightful method to investigate the underlying mechanisms responsible for arrhythmias such as atrial fibrillation. In past years, five models of human atrial electrophysiology with different formulations of ionic currents, and consequently diverging properties, have been published. The aim of this work is to give an overview of strengths and weaknesses of these models depending on the purpose and the general requirements of simulations. Therefore, these models were systematically benchmarked with respect to general mathematical properties and their ability to reproduce certain electrophysiological phenomena, such as action potential alternans. To assess the models ability to replicate modified properties of human myocytes and tissue in cardiac disease, electrical remodeling in chronic atrial fibrillation was chosen as test case. The healthy and remodeled model variants were compared with experimental results in single-cell, 1D and 2D tissue simulations to investigate action potential and restitution properties, as well as the initiation of reentrant circuits.
Abstract: Introduction: Atrial fibrillation (AF) is the most common cardiac arrhythmia affecting around 1% of the population. Several anti-arrhythmic drugs such as e.g. amiodarone or dronedarone influence cardiac electrophysiology reducing arrhythmias. However, the electrophysiological mechanisms underlying the initiation and persistence of AF are not completely understood yet.
Methods: A mathematical model of atrial electrophysiology was modified to simulate the effects of chronic AF (cAF). Furthermore, ion channel conductivities were reduced according to the inhibition caused by two different concentrations of amiodarone and dronedarone. The resulting drug effects were investigated in healthy and cAF single-cells as well as in tissue. In a 1D tissue strand, restitution curves of the effective refractory period (ERP), the conduction velocity (CV) and the wavelength (WL) were computed. Furthermore, persistence of rotors in a 2D tissue patch was analyzed. For this purpose, four rotors were initiated in the cAF patch and then the drug effects were incorporated.
Results: Dronedarone and amiodarone prolonged the atrial action potential duration of cAF cells, whereas high concentration of amiodarone slightly shortened it in healthy cells. Furthermore, both drugs increased the ERP and slowed the CV. Dronedarone shows the longer ERP and also a higher CV. As a result, the WL was prolonged by dronedarone and shortened by high concentration of amiodarone. Low concentration of amiodarone did not change the WL. In the 2D tissue patch, dronedarone altered significantly the trajectory of rotors, but did not terminate them.
Conclusion: Computer simulations of the effects of antiarrhythmic drugs on cardiac electrophysiology are a helpful tool to better understand the mechanisms responsible for persistence and termination of AF. However, ion current measurement data available in literature show great variability of values depending on the species or temperature. Therefore, integration of drug effects into models of cardiac electrophysiology still needs to be improved.
Abstract: This book constitutes the refereed proceedings of the 4th International Conference on Functional Imaging and Modeling of the Heart, FIMH 2007, held in Salt Lake City, UT, USA in June 2007.
The 48 revised full papers presented were carefully reviewed and selected from numerous submissions. The contributions describe both experimental and computational studies and cover topics such as imaging and image analysis, cardiac electrophysiology, electro- and magnetocardiography, cardiac mechanics and clinical application, imaging and anatomical modeling.
Abstract: Simulationen des elektrophysiologischen Verhaltens des Herzens fördern das Verständnis über die Mechanismen innerhalb des Herz-Kreislauf-Systems. Darüber hinaus werden diese mathematischen Modelle die Diagnose und Therapie von Patienten, die unter Herzerkrankungen leiden, unterstützen. In dieser Arbeit wird die Vorgehensweise für die Modellierung der elektrischen Funktion des Herzens beschrieben. Hierfür werden die Modellierung der Geometrie, der kardialen Elektrophysiologie, der elektrischen Erregungsausbreitung und der EKG-Berechnung kurz erläutert. Die seit Kurzem mehr und mehr untersuchten Fälle Ischämie und personalisierte Vorhofmodellierung werden beispielhaft beschrieben und zeigen, wie die Modellierung des Herzens dazu benutzt werden kann, um Kardiologen bei der Beantwortung von offenen Fragen zu unterstützen.
Abstract: Es wird eine Methode beschrieben, wie medizinische Bilder des Herzens modellbasiert mit EKG-Daten verknüpft werden können, um damit zu einer spezifischen Diagnostik und zu einer besseren Therapieplanung in der Kardiologie zu gelangen. Zunächst wird aus MRT- oder CT-Bildern des Patienten die Geometrie seines Herzens ermittelt. Elektrokardiographische Messungen an der Körperoberfläche (EKG oder Body Surface Potential Mapping) und aus dem Inneren des Herzens (intracardial mapping) werden aufgenommen und die Orte der Messung in den Bilddatensatz eingetragen (registration). Ein elektrophysiologisches Computermodell vom Herzen des Patienten wird mit Hilfe der elektrophysiologischen Messdaten iterativ angepasst. Schließlich entsteht im Computer ein virtuelles Herz des Patienten, welches sowohl die Geometrie als auch die Elektrophysiologie wiedergibt. Ein Modell der Vorhöfe hat beispielsweise das Potenzial, die Ursachen von Vorhofflimmern zu erkennen und die Radiofrequenz-Ablationsstrategie zu optimieren. Ein Modell der Ventrikel des Herzens kann helfen, genetisch bedingte Rhythmusstörungen besser zu verstehen oder auch die Parameter bei der kardialen Resynchronisationstherapie zu optimieren. Die Modellierung des Herzens mit einem Infarktgebiet könnte die elektrophysiologischen Auswirkungen des Infarktes beschreiben und die Risikostratifizierung für gefährliche ventrikuläre Arrhythmien unterstützen oder die Erfolgsrate bei ventrikulären Ablationen erhöhen.
In Modelling and Control in Biomedical Systems. A Proceedings Volume from the 5th IFAC Symposium Hilton on the Park, Melbourne, Australia, 21-23 August, Feng, D. D.; Carson, E. R. (eds), Oxford: Pergamon, pp. 179-184, 2003
Abstract: Numerical and patient-specific models of the human atrial anatomy and electrophysiology have a high potential to enhance our knowledge regarding pathological conditions and to increase the outcome of diagnosis and therapy. This chapter briefly describes the current state of the art in modeling of generalized human atria. Furthermore, the chapter demonstrates ways to personalize human atrial anatomy and electrophysiology based on a variety of measurement data from, e.g. late enhancement magnetic resonance imaging (MRI), patch clamp technique, intracardiac electrograms and body surface potential maps. Wherever patient data cannot be collected, patient-group specific behavior can be integrated. Some examples of the personalization process are described and the validation process is discussed together with future options for personalization, validation and application.
Abstract: Atrial fibrillation (AF) is a critical pathology due to the risk of secondary diseases like thromboemboli and ventricular arrhythmia. A recent study identified a familial type of AF based on a mutation influencing the cardiac IKs channel. The mutant channel is characterized by a gain-of-function and a nearly linear current-voltage relationship. The kinetics and density of IKs in a model of atrial myocytes was adjusted to the measured characteristic to describe the mechanisms and effects of the mutation. A schematic anatomical model of the right atrium was designed to simulate the excitation propagation. The action potential duration of the mutant cell was reduced to 105 ms and the effective refractory period to 148 ms. Both factors lead to a reduction in wavelength and thus the risk of an initiation and perpetuation of AF rises. The results support the understanding of the complex behavior of cardiac cells. The described model will be used to investigate AF and potential treatments.
Abstract: Electrophysiological modeling of the heart enable quantitative description of electrical processes during normal and abnormal excitation. Cell models describe e.g. the properties of the cell membrane and the gating process of ionic channels. New measurement data is available for these channels for physiological and some pathological states. These data should be included in the models to enhance their features. In this work we describe a framework adapting ion channel models to measurement data by using a particle swarm optimization (PSO). Models of ion channels can be described by Hogdkin-Huxley equations or by Markovian models. They consider rate constants that are complex functions depending on the transmembrane voltage. Each transition has two rate constants described by several parameters. These parameters need to be varied in order to minimize the difference between measured and simulated ion channel kinetics. Since this minimization procedure is multidimensional and the function can have several local minima, conventional optimization strategies like Powells algorithm and conjugate gradient do not ensure to find the global minimum. To overcome this, a PSO was implemented that inserts several dependent particles randomly into the search space. It is based on the social behavior of swarms. As the particles are independent during each iteration the procedure can be calculated in parallel. The measurement data used for this work were current traces of a voltage-clamp protocol of reggae mutant hERG channels. The same protocol as for the measurement was assigned to the model of Lu et al. describing hERG function with a Markovian model. The value to be minimized was the sum of mean square errors between measured and simulated currents at certain time instances. Both Powell and PSO were started several times with random starting values. In 94% of the cases PSO found the minimum compared to 16% for Powell. On the other hand PSO needed approximately 100 times more function evaluations. The parallelization decreased the overall time needed by the PSO to about the same amount Powell needed. Therefore, the parallel PSO is a fast and reliable approach for adapting ion channel models to measured data.
Abstract: The sinus node (SN) is the primary pacemaker of the heart. It is a heterogeneous structure in the right atrium composed of two types of cells with different electrophysiological properties. One type is distributed more densely in the periphery the other in the center. Different gap junction types and densities exist leading to a heterogeneity in conduction. It is supposed that this complex interplay of heterogeneities is the basic mechanism that the small SN is able to electrically drive the surrounding atrial muscle. If this interplay is disturbed, the function of the SN can be effected massively. In this simulation study we want to demonstrate the effects of the L532P mutation in hERG called reggae on SN electrophysiology.
Mutant hERG channels were expressed in xenopus oocytes and the channel properties were measured with voltage-clamp technique. The data showed mainly a shift of the steady-state inactivation to more positive potentials. This leads to an increase of the ionic current during the depolarized phase. The data was integrated in the heterogeneous rabbit SN model of Zhang et al. by adapting the parameters of the IKr channel with aid of optimization methods using the same stimulation protocol as in the measurements.
The most sensitive parameter was the shift voltage of the steady-state inactivation from -19.2 mV in the physiological case to 10.1 mV in the mutant model. When inserting this mutant IKr in the central SN model the ability of the central cells to depolarize spontaneously was eliminated. Peripheral cell still beat but are affected by the mutation. The slope of the pre-potential and the upstroke velocity were not changed. The maximum diastolic potential was increased by 2 mV and the maximum systolic potential decreased by 1.5 mV. The diastolic interval was shortened slightly by 3 ms. The main effect was a reduction of the action potential duration from 108 ms to 84 ms leading to a frequency increase from 6.37 Hz to 7.62 Hz.
These effects lead to a changing SN function. The increase of the shift voltage is in good agreement with the measured changes. Especially the loss of auto-rhythmicity in the central zone is expected to change the overall SN activity. Although peripheral SN cells beat faster we expect a bradycardial function of the complete SN because of electrotonic interactions with the silent central SN cells and the low resting membrane voltage of surrounding atrial muscle cells. In a further study this suggestion has to be investigated in an anisotropic and heterogeneous 3D model.
Abstract: Atrial fibrillation (AF) is a common pathology. AF modifies the electrophysiological properties of cells (remodeling) promoting the occurrence and maintenance of AF.
Electrical remodeling includes changes in ICa,L, Ito, IK1 and IK,ACh. These effects were integrated in a human atrial computer model. Gap junction remodeling was considered in the conductivity of the monodomain equation calculating excitation. Specific features were calculated to determine the risk of AF initiation and perpetuation.
ERP was reduced from 330ms to 103ms. CV was lowered from 755mm/s to 608mm/s. The WL reduction was even higher (from 249mm to 63mm) leading to a higher probability of occurrence and maintenance of AF. A maximum of 7 spirals waves were initiated leading to a peak in the power spectrum at 10.32Hz.
The computer model underlines the relevance of remodeling in AF chronification. The results add to the knowledge of AF maintenance. Our model might prove to be a tool for the development of novel therapeutic strategies.
G. Seemann, and O. Dössel. Simulation of the cardial electrical activity: interactive control of the simulation process and modelling in pathologies.
In Proceedings of European Medical and Biological Engineering Conference, pp. 1210-1211, 1999
Abstract: Atrial fibrillation (AF) is the most common cardiac arrhythmia in the western world. Genetic variants in the cardiac I Kr channel have been identified to influence ventricular repolarization. The aim of this work is to investigate the effect of the mutation N588K on atrial repolarization and the predisposition to AF. Experimental data of N588K mutated hERG channel were incorporated in an atrial ionic model using parameter fitting. The effects of the mutation were analyzed in cell and tissue. N588K showed a gain of function effect, causing a rapid repolarization and a shortening of the action potential duration. Computer simulations of a schematic right atrial geometry were used to investigate the excitation conduction properties. The effective refractory period of mutant cells were reduced from 317 to 233 ms at 1 Hz. The conduction velocity is not significantly influenced by the mutation. Nevertheless, the wavelength of mutant cells is for all frequencies smaller, indicating that the mutation N588K predisposes the initiation and perpetuation of AF.
Abstract: Cisapride is a drug to help gastric problems. It is limited because of reports of the side-effect long QT syndrome which predisposes to arrhythmias. In this computatinal study, the effects of Cisapride on human ventricular myocytes are investigated in-silico. From literature reported effects of the drug on ion channel level are included into a virtual human ventricular cell. Cisapride has the most dominating effect on the rapid delayed rectifier current IKr. A shift in the activation and inactivation and mainly a reduction of conductivity is seen. This leads to the prolongation of the APD comparable to the long QT syndrome. In future studies, the stability of the heart under the influence of this drug will be evaluated
G. Seemann. Modeling of cardiac Ischemia in human myocytes and tissue including spatiotemporal electrophysiological variations.
In VPH Events - 4th Cardiac Physiome Workshop, 2009
Abstract: Cardiac tissue exhibits spatially heterogeneous electrophysiological properties. In cardiac diseases, these properties change also in time. This study introduces a framework to investigate their role in cardiac ischemia using mathematical modeling and computational simulations at cellular and tissue level. Ischemia was incorporated by reproducing effects of hyperkalemia, acidosis, and hypoxia with a human electrophysiological model. In tissue, spatial heterogeneous ischemia was described by central ischemic (CIZ) and border zone. Anisotropic conduction was simulated with a bidomain approach in an anatomical ventricle model including realistic fiber orientation and transmural, apico-basal, and interventricular electrophysiological heterogeneities. A model of electrical conductivity in a human torso served for ECG calculations. Ischemia raised resting but reduced peak voltage, action potential duration and upstroke velocity. These effects were strongest in subepicardial cells. In tissue, conduction velocity decreased towards CIZ but effective refractory period increases. At 10 min of ischemia 19% of subepi- and 100% of subendocardial CIZ cells activated with a delay of 34.6±7.8 ms and 55.9±18.8 ms, respectively, compared to normal. Significant ST elevation and premature T wave end appeared only with the subepicardial CIZ. The model reproduced effects of ischemia at cellular and tissue level. The results suggest that the presented in-silico approach can complement experimental studies e.g. in understanding the role of ischemia or the onset of arrhythmia.
Abstract: The heart rate is mediated by the G protein-coupled muscarinic receptor (M2R) activating the acetylcholine (ACh)-dependent K+ current (IKACh). Here, a novel model for IKACh gating is presented based on recent findings that M2R agonist binding is voltage-sensitive. Furthermore, ACh and pilocarpine (Pilo) manifest opposite voltage-dependent IKACh modulation. In a previous work, a 4-state Markov model of M2R reconstructing the voltage-dependent change in agonist affinity was proposed. In this work, a 2-state Markov model of IKACh gating purely dependent on the Gβγ concentration is proposed. IKACh is modeled based on the description of Zhang et al. Measurement data are used to parametrize the combined M2R and IKACh model for both ACh and Pilo. The channel model has a linear Gβγ dependent forward and a constant backward rate. For ACh and Pilo, optimal values of model parameters are found reconstructing the measured opposite voltage-dependent change in agonist affinity. The combined model is able to reconstruct the measured data regarding the agonist and voltage-dependent properties of the M2R-IKACh channel complex. In future studies, this channel will be integrated in a sinus node model to investigate the effect of the channel properties on heart rate
Abstract: Heterogeeities of the ventricular electrophysiol- ogy play a major role in the generation of the T-wave mor- phology and amplitude. The exact way of the distribution of electrophysiological differences is not known. In this work, a numerical approach is presented in which the excitation propagation of different heterogeneity distributions of IKs are simulated and the multi-channel ECG is calculated. The ECG data are evaluated against measured ECGs. The most realistic configuration is a combination of transmural and apico-basal heterogeneity with 35% of Endo, 30% of M and 35% of Epi cells and an apico-basal gradient with a factor of 2. This specific setup has a correlation of around 90% and a root mean square error of around 0.0795.
G. Seemann. Simulating the effects of drugs and genetic defects on atrial electrophysiology.
In 7th TRM Forum on Computer Simulation and Experimental Assessment of Cardiac Function, 2013
Abstract: P-wave assessment is frequently used in clinical practice to recognize atrial abnormalities. However, the use of P-wave criteria to diagnose specific atrial abnormalities such as left atrial enlargement has shown to be of limited use since these abnormalities can be difficult to distinguish using P-wave criteria to date. Hence, a mechanistic understanding how specific atrial abnormalities affect the P-wave is desirable. In this study, we investigated the effect of left atrial hypertrophy on P-wave morphology using an in silico approach. In a cohort of four realistic patient models, we homogeneously increased left atrial wall thickness in up to seven degrees of left atrial hypertrophy. Excitation conduction was simulated using a monodomain finite element approach. Then, the resulting transmembrane voltage distribution was used to calculate the corresponding extracellular potential distribution on the torso by solving the forward problem of electrocardiography. In our simulation setup, left atrial wall thickening strongly correlated with an increased absolute value of the P-wave terminal force (PTF) in Wilson lead V1 due to an increased negative amplitude while P-wave duration was unaffected. Remarkably, an increased PTF-V1 has often been associated with left atrial enlargement which is defined as a rather increased left atrial volume than a solely thickened left atrium. Hence, the observed contribution of left atrial wall thickness changes to PTF-V1 might explain the poor empirical correlation of left atrial enlargement with PTF-V1.
Abstract: Orientations of myocytes impact electric excitation propagation and mechanical contraction in the human heart. Measured fiber angles in experiments are obtained from different species (e. g. rat, canine, dog, human heart) and vary by various reasons. It is unclear to what ex- tent non-exact fiber angles impact the quality of computa- tional simulations. In this paper, mechanical simulations with different ventricular angles were performed and com- pared. The simulations covered the complete heart with both ventricles, both atria and the pericardium and were performed using finite element method. Helix angles were varied between 20\0 and 70\0 on endocardium and \070\0 and \020\0 on epicardium. Results showed that fiber ori- entations had only a minor contribution to the difference between endsystolic and enddiastolic pressure of < 8.3 %. The influence on stroke volume as well as AVPD is sig- nificant (changes by 34 % for SV and 241 % for APVD) , but it could not be observed that a higher AVPD yields a higher stroke volume. Concludingly, fiber orientations are important for reliable computational simulations of human hearts and should be incorporated with great care.
Abstract: Bidomain simulations of the heart need validated parameters to produce realistic data. Therefore, it is nec- essary to develop methods to estimate reliable values for these parameters. We developed an approach to deliver such values by designing an in-silico model of intracellular electrical conduction based on confocal microscopic data of rabbit ventricular tissue. High resolution image data were used to determine the anisotropy of electrical conduc- tivity in the myocardium, which is highly dependent on the specific tissue geometry. Gap junction protein connexin43 and extracellular space were labeled with fluorescent dyes of different spectra. The myocytes were segmented and the gap junction density in-between myocytes was extracted. Assuming conductivities for intracellular liquid and gap junction resistance, a numerical field calculation was per- formed for three principal directions in order to extract in- tracellular conductivity tensors. We calculated 9 tensors by varying the assumed conductivities by ±50%. We esti- mated the intracellular conductivities for the three princi- pal directions σi,x = 0.0653 S/m, σi,y = 0.0042 S/m and σi,z = 0.0033 S/m, respectively. The estimated conductiv- ity values were realistic regarding the electrical anisotropy but need to be improved to fit other experimental data.
Abstract: Catheter ablation of complex atrial arrhythmias is a frequently applied procedure, but its success rates are only moderate and highly dependent on the experience of the physician. Personalized atrial simulation models could assist the physician in treatment planning and thus increase success rates. In this work we created a personalized anatomical model for a specific patient from CT image data. Left atrial conduction velocity and local wave directions were determined from intracardiac electrogram (EGM) recordings. We simulated normal sinus rhythm and the clinical pacing protocol using a Cellular Automaton. The incidence direction and conduction velocity were extracted from the simulated data and compared to the results of the clinical EGMs of the same patient. We then showed that the incidence angles differed by less than 15% and that the conduction velocity error was below 12 cm/s. This implies that the model has similar electric properties compared to the real atria. In conclusion, we have presented a workflow for model personalization and validation.
Abstract: Atrial fibrillation is the most common cardiac arrhythmia in humans. The precise cellular mechanisms underlying atrial fibrillation are still poorly understood. Recent studies have identified several genetic defects as predisposing factors for this pathology. One of the identified genetic defects is the mutation N588K, which affects the cardiac IKr channel. Genetic variants in this channel have been identified to modify ventricular repolarization. The aim of this work is to investigate the effect of this mutation on atrial repolarization and the predisposition to atrial fibrillation.
Measured data obtained with whole cell voltage clamp technique of wild-type and mutated hERG channel were implemented in the Courtemanche et al. ionic model. For this purpose, channel kinetics and density of the model were adjusted using parameter fitting to the measured data. By this way, the effects of the mutation in the hERG channel could be analyzed in the whole cell and in tissue, as well. The channel mutation N588K showed a gain of function effect, causing a rapid repolarization and consequently, a shortening of the action potential duration. Computer simulations of a schematic anatomical model of the right atrium were then carried out to investigate the excitation propagation and the repolarization.
The action potential duration of the mutant cell was reduced to 116 ms and the effective refractory period to 220 ms. Both factors are linked to a shortening of the wavelength, indicating that the mutation N588K predisposes the initiation and perpetuation of atrial fibrillation.
Abstract: Knowledge of tissue distribution allows the creation of anatomical models of the human body. Anatomically based models are of increasing interest e.g. in the field of medical education, development of therapies and research on the risks of electro smog.
The motivation for this work was the creation of a female 3D anatomical model with high accuracy and resolution. The purpose of this anatomical model is to simulate the human physical behavior through the numerical calculation of fields.
The objectives were the segmentation of the Visible Female thorax applying digital image processing techniques and the evaluation of existing tools for segmentation and classification. This evaluation should deliver solutions to achieve better accuracy, to reduce the time on manual segmentation and to allow an adaptation of existing tools.
Abstract: After mathematical modeling of the healthy heart now modeling of diseases comes into the focus of research. Modeling of arrhythmias already shows a large degree of realism. This offers the chance of more detailed diagnosis and computer assisted therapy planning. Options for genetic diseases (channelopathies like Long-QT-syndrome), infarction and infarction-induced ventricular fibrillation, atrial fibrillation (AF) and cardiac resynchronization therapy are demonstrated.
Abstract: A computer model of the human heart is presented, that starts with the electrophysiology of single myocardial cells including all relevant ion channels, spans the de- and repolarization of the heart including the generation of the Electrocardiogram (ECG) and ends with the contraction of the heart that can be measured using 4D Magnetic Resonance Imaging (MRI). The model can be used to better understand physiology and pathophysiology of the heart, to improve diagnostics of infarction and arrhythmia and to enable quantitative therapy planning. It can also be used as a regularization tool to gain better solutions of the ill-posed inverse problem of ECG. Movies of the evolution of electrophysiology of the heart can be reconstructed from Body Surface Potential Maps (BSPM) and MRI, leading to a new non-invasive medical imaging technique.
Abstract: A framework for step-by-step personalization of a computational model of human atria is presented. Beginning with anatomical modeling based on CT or MRI data, next fiber structure is superimposed using a rule-based method. If available, late-enhancement-MRI images can be considered in order to mark fibrotic tissue. A first estimate of individual electrophysiology is gained from BSPM data solving the inverse problem of ECG. A final adjustment of electrophysiology is realized using intracardiac measurements. The framework is applied using several patient data. First clinical application will be computer assisted planning of RF-ablation for treatment of atrial flutter and atrial fibrillation.
Abstract: The objective of personalised modelling of the atria is to improve comprehension of the etiology of atrial arrhythmias, to enable specific diagnosis and to optimise therapy. We start with CT or MR datasets and use adapted segmentation procedures to build a patient-specific 3D-model of the atria. Then we include fibre direction based on the rules of atrial anatomy. Work in progress is also considering late enhancement MRI in order to add areas of fibrotic tissue. Next we can use BSPM data of the P-wave and solve the inverse problem of ECG to get a hypothesis about the spread of depolarisation. Finally we use intracardiac catheter signals (e.g. using a circular catheter) to measure direction and conduction velocity of depolarisation waves (sinus rhythm, atrial flutter, or following stimulation). All this is integrated into a personalised model of the atria of an individual patient. Our next goal will be to properly add ablation lines into the model.
The research leading to these results has partly received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement n 224495 (euHeart project).
Abstract: The impact of transmural infarctions of the left ventricle on the cardiac mechanical dynamics is evaluated for all 17 AHA segments in a computer model. The simulation framework consists of two parts: an electrophysiological model and an elastomechanical model of the ventricles. The electrophysiological model is used to simulate the electrophysiological processes on cellular level, excitation propagation and the tension development. It is linked to the elastomechanical model, which is based on nonlinear finite element analysis for continuum mechanics. Altogether, 18 simulations of the contraction of the ventricles were performed, 17 with an infarction in the respective AHA segment and one simulation for the control case. For each simulation, the mechanical dynamics as well as the wall thickening of the infarct region were analyzed and compared to the corresponding region of the control case. The simulation revealed details of the impact of the myocardial infarction on wall thickening as well as on the velocity of the infarct region for most of the AHA segments
Abstract: There is a large number of published studies analyzing the inhomogeneously distributed electrophysiological properties of the ventricles in a computer model. However only few of them deal with the impact on the heart’s mechanics. In 2003 Cordeiro and colleagues  analyzed the influence of the transmural left ventricular electrophysiological heterogeneity on the myocardial mechanics. Therefore, they examined the unloaded cell shortening of sub-epicardial cells, sub-endocardial cells, and cells from the middle of the wall, isolated from canine left ventricle.
In this work a heterogenous electromechanical model was used to reconstruct these experiments of Cordeiro et al. in the computer. A simulation framework, which is consisting of an electrophysiological cell model, a tension development model and an elastomechanical model was used to simulate the cell shortening. Two experiments with different heterogeneities had been conducted. The first experiment examined, how the heterogeneity of the membrane channels influences the cell shortening. In the second experiment the additional impact of the heterogeneity of the intracellular calcium handling was analyzed. The results of the simulations were compared qualitatively to the findings of Cordeiro et al.
Abstract: Elastomechanical modeling of the heart can help to gain a deeper insight into the mechanical dynamics of the heart. Furthermore it can help to enhance diagnostic strategies and to investigate new therapeutic approaches.
Phase contrast magnetic resonance imaging allows to directly measure the velocity vector field of the myocardial motion over the cardiac cycle. Aim of this work was to analyze the impact of transmural myocardial infarction on the velocity vector field of the left ventricle in a numerical model of the heart. For this purpose a multi-scale electromechanical computer framework was used. It consisted of two parts: an electrophysiological model and an elastomechanical model. The electrophysiological model described the electrophysiological processes on cellular level, the excitation propagation as well as the tension development. It was was linked to an elastomechanical model which was based on nonlinear continuum mechanics using the finite element method. The computer framework was used to simulate the contraction of the heart with left ventricular transmural infarctions, differing in size, location and stiffness of the scar tissue. For each simulation, the velocity vector field of the infarct region was analyzed and compared to the corresponding region of the control case. The simulations revealed a direct impact of the myocardial infarction on the magnitude and orientation of the velocity vectors of the affected region.
Abstract: Radiofrequency ablation (RFA) is a widely used clinical treatment for many types of cardiac arrhythmias. However, nontransmural lesions and gaps between linear lesions often lead to recurrence of the arrhythmia. Intrac- ardiac electrograms (IEGMs) provide real-time informa- tion regarding the state of the cardiac tissue surrounding the catheter tip. Nevertheless, the formation and inter- pretation of IEGMs during the RFA procedure is complex and yet not fully understood. In this in-silico study, we propose a computational model for acute ablation lesions. Our model consists of a necrotic scar core and a border zone, describing irreversible and reversible temperature induced electrophysiological phenomena. These phenom- ena are modeled by varying the intra- and extracellular conductivity of the tissue as well as a regulating zone factor. The computational model is evaluated regarding its feasibility and validity. Therefore, this model was com- pared to an existing one and to clinical measurements of ve patients undergoing RFA. The results show that the model can indeed be used to recreate IEGMs. We computed IEGMs arising from complex ablation scars, such as scars with gaps or two overlapping ellipsoid scars. For orthogo- nal catheter orientation, the presence of a second necrotic core in the near- eld of a punctiform acute ablation lesion had minor impact on the resulting signal morphology. The presented model can serve as a base for further research on the formation and interpretation of IEGMs.
Abstract: Image registration is used to reduce movement artifacts caused by contracting heart muscle in transmembrane voltage measurements using fluorescence microscopy. The applied registration methods include Thin-Plate Splines (TPS) and Gaussian Elastic Body Splines (GEBS). Landmarks are established automatically using regional cross-correlation. Then these landmarks are filtered for meaningful correspondences by requiring a minimum correlation coefficient and clustering adjacent and identical displacements. Registration of an image sequence showing a contracting muscle is realized by spatially aligning the images at maximum contraction and at rest. For the other images the movement of the muscle is interpolated using an analytical description of the contraction of heart muscle.
TPS cause amplification of displacements at the image border, while GEBS restrict landmark’s influence to a local region. Over a set of 81 images GEBS are shown to register images better and more robust than TPS, which in some cases cannot reduce movements. Validation through visualization of transmembrane voltages on contracting muscle reveals that GEBS registration removes movement artifacts better than TPS. Image regions with prominent structures are successfully tackled by GEBS registration.
Abstract: Computer simulations can significantly improve comprehension of cardiac electrophysiology. A mathematical model for the simulation of complex cardiac electrophysiology is the bidomain model. A new tool, acCELLerate, was developed using the PETSc library  for a parallel time and memory efficient implementation of the bidomain equations enabling the computation of large scale cardiac simulations. It offers an extensible modular structure. The optimization of the cost-intensive solution of the elliptical part of the bidomain equation was achieved by analyzing several iterative Krylov subspace methods and preconditioners provided by PETSc. Best performance results were achieved by using a combination of minimal residual method (MinRes), conjugate residual method (CR) or conjugate grandient method (CG) as solver with adjusted successive over-relaxation preconditioning (SOR). A validation proved the authenticity of the new tool.
Abstract: The congenital long-QT syndrome is commonly associated with a high risk for polymorphic ventricular tachy-cardia and sudden cardiac death. This is probably due to an intensification of the intrinsic heterogeneities present in ventricular myocardium. Increasing the electrophysiological heterogeneities amplifies the dispersion of repolarization which directly affects the morphology of the T wave in the ECG. The aim of this work is to investigate the effects of LQT2, a specific subtype of the long-QT syndrome (LQTS), on the Body Surface Potential Maps (BSPM) and the ECG. In this context a three-dimensional, heterogeneous model of the human ventricles is used to simulate both physiological and pathological excitation propagation. The results are used as input for the forward calculation of the BSPM and ECG. Characteristic QT prolongation is simulated correctly. The main goal of this study is to prepare and evaluate a simulation environment that can be used prospectivley to find features in the ECG or the BSPM that are characteristic for the LQTS. Such features might be used to facilitate the identification of LQTS patients.
Abstract: Muscle anisotropy is important for the realistic solution of the forward problem of electrocardiography. Whenever computer models of patient-specific anatomies are created usually no information about the muscle fiber arrangement in the heart or skeletal muscle is available. As in-vivo imaging techniques that can determine fiber orientation like Diffusion Tensor MRI are time-consuming and susceptible to motion artifacts, cardiac fiber orientation is frequently described using simplified rules. However, for the skeletal muscle there are only few suggestions for a rule-based implementation of fiber orientation into patient-specific models. In this work we evaluated a rule-based approach from the literature together with two new methods by comparing the corresponding forward calculated body surface potential maps (BSPMs) with the BSPM resulting from a reference skeletal muscle fiber distribution extracted from the thin-section photos of the Visible Man dataset (Journal of Computing and Information Technology vol.6, pp. 95-101 1998). The skeletal muscle anisotropy ratio was set to 3:1. The following fiber orientation setups were evaluated: A) the torso is divided into twelve sectors (cross-section perspective) and fiber direction was assumed to be perpendicular to the bisector as proposed by Klepfer et al. (IEEE Trans. Biomed. Eng. vol. 44, no. 8, pp. 706-719 1997); B) A 3D Sobel filter was used on the torso geometry filled with a gradient from inside to outside which generated a vector that was normal to the thoracic surface in every voxel. Fiber orientation was assumed to be perpendicular to the plane formed by these normal vectors and the direction from head to feet (longitudinal torso orientation); C) Same procedure as in B) but additionally, the back muscles which are known to have a longitudinal orientation were integrated accordingly. Potentials were extracted at 64 electrode positions from the BSPMs. The RMS was calculated at these electrode positions between the reference fiber distribution and the respective rule-based approaches. The RMS was comparable between A) and B) (8.8e-5 vs. 8.9e-5) leading to the conclusion that the twelve discrete sectors introduced no significant error. A) and B) performed also well compared to a modified version of the reference dataset where the longitudinal component of the fiber vectors was set to zero (8.3e-5). Including the longitudinal components of the back muscles as done in C) enhances the RMS to 5.5e-5. If the skeletal muscle anisotropy was neglected and only cardiac fiber orientation was taken into account, the RMS improved (!) further to only 4.0e-5. Thus it can be concluded that neglecting the longitudinal component (A) and B)) or accounting for it with a highly simplified approach (C)) is not sufficient. In cases where no detailed information about the skeletal muscle fiber arrangement is available, it is better to entirely neglect its anisotropic influence.
Abstract: The Purkinje network plays a major role for realistically simulating the activation sequence of the ventricles. In this work, we describe a method to create an endocardial stimulation profile that describes the location and time instant of ventricular stimulation, thus mimicking the His-Purkinje conduction system. By adapting model parameters stimulation profiles can be generated for different ventricular anatomies with minimal manual interaction. The stimulation profile parameters are evaluated by analyzing the excitation propagation in a three-dimensional, heterogeneous and anisotropic model of the human ventricles which are embedded in an anatomically detailed torso geometry. The calculated QRS complexes are in good agreement with the corresponding clinical recordings on the same proband.
Abstract: Patients suffering from the congenital Long-QT syndrome have been reported to react highly sensitive to the presence of beta-adrenergic agents that are produced by the sympathetic nervous system. In this work we used an anisotropic and electrophysiologically heterogeneous in- silico model to reproduce wedge experiments in which the Long-QT syndrome was induced pharmacologically. The integration of an intracellular signaling cascade allowed the prediction of the effects of adrenergic agents on the different subtypes of the Long-QT syndrome. For LQT1 the in-silico model predicted a QT prolongation in the transmural pseudo ECG without an increase in transmural dispersion of repolarization. For LQT2 and LQT3 the QT prolongation was accompanied by an increased transmural dispersion of repolarization. beta-adrenergic tonus shortened the QT interval and increased transmural dispersion of repolarization. These findings were consistent with the experimental reports.
Abstract: The shape of a simulated excitation wavefront depends on the underlying spatial resolution. The aim of this work is twofold: On the one hand we investigated the dependency of the wavefront on spatial resolution by simulating the excitation spread in three virtual patches of ventricular tissue that have different resolutions. On the other hand we simulate a realistic excitation sequence in an anisotropic and electrophysiologically heterogeneous biventricular model. Our patch experiments with different spatial resolutions demonstrated that resolutions below 0.2 mm led to a deformation of the excitation wavefront to non-elliptical shapes. The biventricular model with 0.2 mm grid size shows realistic excitation spread and conduction velocities. Similar biventricular models in conjunction with a computational representation of the thorax will be used in future to predict the effects of changes on the ion-channel level on the ECG.
Abstract: Intracardiac electrograms are the key in under- standing, interpretation and treatment of cardiac arrhythmias. However, electrogram morphologies are strongly variable due to catheter position, orientation and contact. Simulations of intracardiac electrograms can improve comprehension and quantification of influencing parameters and therefore reduce misinterpretations. In this study simulated intracardiac electro- grams are analyzed regarding tilt angles of the catheter relative to the propagation direction, electrode tissue distances as well as clinical filter settings. Catheter signals are computed on a realistic 3D catheter geometry using bidomain simulations of cardiac electrophysiology. Thereby high conductivities of the catheter electrodes are taken into account. For validation, simulated electrograms are compared with in vivo electrograms recorded during an EP-study with direct annotation of catheter orientation and tissue contact. Good agreement was reached regarding timing and signal width of simulated and measured electrograms. Correlation was 0.92±0.07 for bipolar, 0.92±0.05 for unipolar distal and 0.80 ± 0.12 for unipolar proximal electrograms for different catheter orientations and locations.
Abstract: Complex fractionated atrial electrograms (CFAE) are a target for catheter ablation as they coincide with areas of slow conduction. In this study we simulated different vol- ume fractions of diffuse and patchy fibrosis up to 50 %. Catheter signals for different electrode spacings were cal- culated and characteristic features were compared to a clinical database of CFAE-signals. A linear slowing of global conduction velocities was found independent of the type of fibrosis. For patchy fibrosis, electrograms displayed fractionation, which was not seen for diffuse fibrosis of the same degree. In comparison to clinical data, simulated electrograms showed up to 10 zero crossings per electro- gram, which was also seen for clinical EGMs with medium fractionation (class 2 of 3). For both, clinical (84 %) and simulated (88 %) signals, a significant difference in ampli- tude is present between fractionated and non-fractionated signals.
Abstract: Atrial fibrillation (AF) is a common cardiac disease with high rates of morbidity, leading to major personal and NHS costs. Computer modeling of AF using a detailed cellular model with realistic 3D anatomical geometry allows investigation of the underlying ionic mechanisms in far more detail than in a physiology laboratory. We have developed a 3D virtual human atrium that combines detailed cellular electrophysiology, including ion channel kinetics and homeostasis of ionic concentrations, with anatomical detail. The segmented anatomical structure and multi-variable nature of the system makes the 3D simulations of AF large and computationally intensive. The computational demands are such that a full problem solving environment requires access to resources of High Performance Computing (HPC), High Performance Visualization (HPV), remote data repositories and a backend infrastructure. This is a classic example of eScience and Gridenabled computing. Initial work has been carried out using multiple processor machines with shared memory architectures. As spatial resolution of anatomical models increases, requirement of HPC resources is predicted to increase many-fold ( ~ 1 – 10 teraflops). Distributed computing is essential, both through massively parallel systems (a single supercomputer) and multiple parallel systems made accessible through the Grid.
Abstract: Atrial fibrillation (AF) induced electrical remodelling of ionic channels shortens action potential duration and reduces atrial excitability. Experimental data of AF-induced electrical remodelling (AFER) from two previous studies on human atrial myocytes were incorporated into a human atrial cell computer model to simulate their effects on atrial electrical behaviour. The dynamical behaviors of excitation scroll waves in an anatomical 3D homogenous model of human atria were studied for control and AF conditions. Under control condition, scroll waves meandered in large area and became persistent when entrapped by anatomical obstacles. In this case, a mother rotor dominated atrial excitation. Action potentials from several sites behaved as if the atrium were paced rapidly. Under AF conditions, AFER increased the stability of re-entrant scroll waves by reducing meander. Scroll wave break up leads to wavelets underpinning sustained chronic AF. Our simulation results support the hypothesis that AF-induced electrical remodelling perpetuates and sustains AF.
Abstract: Atrial fibre architecture has complex patterns of bundles and layers and is known to impact on atrial electrophysiology, especially in fast-conducting bundles like Crista Terminalis, Bachmann’s bundle and pectinate muscles. Based on a priori knowledge of atrial fibre structure, we incorporated rule-based fibre orientation in seven volumetric models of human atria using a semi-automatic approach. We were able to introduce multiple layers of myofibres and regional heterogeneities of ion channels in the models. We evaluated the influence of complete atrial fibre architecture on multiple modelling scales. First, we simulated atrial excitation in the isotropic and anisotropic models using the model of Courtemanche et al. in combination with the monodomain approach. Second, we computed body surface potentials from the simulated transmembrane voltages and compared these to measured ECGs from the respective patients. Temporal behaviour of the atrial excitation sequences was significantly altered in the anisotropic models compared to the sequences in the isotropic models. Complete atrial activation was achieved approximately 20% faster in the anisotropic models mostly due to fast conducting myofibre bundles. Electrophysiological heterogeneities influenced right atrial transmembrane voltage distribution over time due to a less negative action potential plateau in Crista Terminalis cells. P-wave duration was significantly shorted by the introduction of atrial anisotropy and the error to measured P-wave duration was reduced. Furthermore, a pattern change in body surface potential distribution over time was observed. The anisotropic patterns showed a better match to the measurements. Thus, the modelling error by using generalised fibre architecture for patient-specific models was smaller than by using isotropic models. The results highlight the necessity to incorporate atrial anisotropy in personalised models to produce more realistic simulations. The semi-automatic approach allows the use of these models for future clinical applications.
Abstract: The human atria contain fine structures, which can hardly be distinguished with common medical imaging techniques. However, some of these structures play an important role in the electrophysiologic depolarisation sequence of the atria. We present a semi-automatic algorithm to segment the sinus node, Bachmann’s Bundle and the Terminal Crest in given anatomical shape models of the atria. The algorithm bases on anatomical knowledge of the atria and only requires the user to provide few distinct landmarks in the atria as input. Incorporation of these structures into patient individual atrial geometries augments the electrophysiological correctness of the models.
Abstract: Background: Patients with end-stage renal disease show an increased prevalence of atrial fibrillation. A combined simulation and electrocardio- gram analysis study revealed a correlation between the changes in plasma electrolytes and intra-atrial conduction velocity related to hemodialysis (HD) session. A recognized limitation of the study is that simulations were performed on single-cell level. We present a computer study to investigate the influence of HD-related electrolyte modifications on atrial electrophys- iology in a volumetric environment.
Methods: Based on the Courtemanche-Ramirez-Nattel model and its parameterization for different atrial tissues, we studied action potential, effective refractory period, conduction velocity (CV) restitution, and wave length restitution for common atrial myocardium (CAM) and fast conducting Crista Terminalis (CT). We used isotropic, homogeneous tissue patches. External stimuli were applied with 184 different pacing rates (PRs) from 330 to 1250 milliseconds.
Results: The effect of temporary HD- related electrolyte changes on the action potential morphology and effective refractory period showed results consistent with the previous single-cell study. Action potential morphology was not significantly altered both in CAM and CT, but resting potential decreased from ␣82.6 to ␣88.2 mV for CAM and from ␣81.7 to ␣87.3 mV for CT. Effective refractory period decreased from 32 (pre-HD) to 308 milliseconds (end-HD). At a PR of 832 milliseconds, CV dropped by ␣6.3% for both types of tissue (CAM: 741 694 mm/s; CT: 746 699 mm/s). Wave length increased slightly with higher PR, but rapidly fell off below a PR of 450 milliseconds. Wave length was ␣30 mm shorter in the end-HD condition.
Conclusions: Conduction velocity decrease and consequent wave length shortening increases vulnerability for atrial fibrillation onset, especially in conjunction with structural dilation often present in atria of end-stage renal
disease patients. Temporary HD-caused electrical remodeling has equal effects on regular and fast-conducting tissue. Although there is no biophysical model for fast interatrial condition pathways (eg, Bachmann dundle) available, the HD influence on them should also be similar and therefore slow down interatrial conduction significantly. It has been suggested that constantly repeating alteration of atrial electrophysiology may lead to a longer lasting electrical atrial remodeling; future studies should therefore investigate the long-term HD effects.
Abstract: Current models of the human atria represent geometries of single individuals or base on statistical data. We present a work-flow for the creation of patient-specific atrial models. Furthermore we show a framework to compare simulated P- waves and body surface potential maps (BSPMs) of individual patients with measurements. Models of the atrial and thorax anatomy were segmented from MRI data. Volumetric atrial models were semi-automatically enhanced with electrophys- iologically (EP) relevant structures. Simulations were performed on an anisotropic voxel-based mesh and were forward calculated to obtain simulated BSPMs. BSPMs were acquired using a 64 electrode ECG system. Comparison of simulated and measured P-waves in Einthoven leads showed a general agreement of both, although no personalization of the atrial electrophysiology model was performed. P-wave duration was longer in the simulations, highlighting the need for elec- trophysiological model personalization. Simulated and measured BSPMs revealed similar patterns. The presented method enables realistic simulations of atrial activation on patient-specific volumetric atrial models with EP relevant myocardial structures resulting in computed ECGs (P-wave) and BSPMs with show physiological morphologies
Abstract: Motivation: Anatomical models of the heart can be used to conduct multi-physics simulations. These simulations can aid basic and clinical research and are being translated into clinical practice nowadays.
Problem statement: The human myocardium has very complex fiber structure, which has a strong impact on cardiac physiology. To understand and evaluate 3D fiber orientation in volumetric cardiac models, it is often necessary to project these onto printed pictures.
Approach: Images of myocardial fibers using color-coded cylinders, color-coded streamlines and anaglyph methods are compared.
Results: Streamlines provide a good distinction of myocardial bundles. Cylinders show the most accurate results. Color-coded representations reveal abrupt changes in fiber direction. Anaglyph visualizations give an illusion of depth in 2D prints and can display overlaying bundles.
Conclusions: Streamlines are superior in imaging global fiber orientation, whereas cylinders give better results for local structures. Color-coding increases information where fiber structure is very complex, e.g. in the atria. Anaglyph images cause a loss in color information but help the viewer to understand the 3D object. Overall, it is necessary to choose the appropriate method of picturing fibers for specific tasks.
Abstract: Atrial myofiber orientation is complex and has multiple discrete layers and bundles. A novel robust semi-automatic method to incorporate atrial anisotropy and heterogeneities into patient-specific models is introduced. The user needs to provide 22 distinct seed-points from which a network of auxiliary lines is constructed. These are used to define fiber orientation and myocardial bundles. The method was applied to 14 patient-specific volumetric models derived from CT, MRI and photographic data. Initial electrophysiological simulations show a significant influence of anisotropy and heterogeneity on the excitation pattern and P-wave duration (20.7% shortening). Fiber modeling results show good overall correspondence with anatomical data. Minor modeling errors are observed if more than four pulmonary veins exist in the model. The method is an important step towards creating realistic patient-specific atrial models for clinical applications.
Atrial fibrillation (AF) is the most common cardiac arrhythmia. Over 4.5 million people in the European Union suffer from AF. The mechanisms leading to AF are still not completely understood although various theories were proposed. Numerical models of the human atria can help to understand these mechanisms. Personalized atrial models may in fu- ture be used to set up patient-specific therapies.
Personalization of atrial models splits into different tasks. The individual atrial and thorax anatomy are derived from various imaging modalities (CT, MRI). Valuable information is hidden in these data, such as atrial wall thickness and myocardial fiber structure. The missing parts are added to the geometric model using rule-based approaches. Atrial electrophysiology is adapted to different pathologies (e.g. remodeling, genetic defects) and to ECG and intracardiac measurements of the individual patient by tuning model parameters (e.g. conductivity).
Personalization of atrial anatomy enables a realistic simulation of atrial excitation propagation during sinus rhythm. Ad- justment of the generalized electrophysiology model to the according patient group provides insights into the substrate of the known global effects. Adaption of these model parameters to the individual patient results in a better fit of simu- lated intracardiac and ECG signals to the measurements.
With the help of various personalization techniques, generalized atrial models can be adapted to patient data. These models may in future be used for personalized model-based AF-treatment planning.
Abstract: Abstract. Atrial fibrillation (AF) is the most common cardiac arrhyth- mia. Patient-specific computational modeling of the atria can provide a better understanding about mechanisms underlying the arrhythmia and will potentially be used for model-based ablation therapy evaluation and planning. Electrical excitation spreads from the left to the right atrium at discrete locations. The location of the muscular bridges cannot be determined from image data. In the present study, left atrial activation sources were manually identified in local activation time maps of 4 AF patients. This information was used to adjust rule-based placed intera- trial bridges in anatomical atrial models of the patients. Sinus rhythm simulations showed a better qualitative agreement to the measured left atrial activation patterns after the adjustment of the bridges. For one patient, the simulated body surface potential (BSP) pattern after the adjustment correlated better to measured BSP maps. The results show that the fusion of intracardiac electrical measurements of early left atrial activation can be used to refine patient atria models with information of the myocardial structure which cannot be imaged. In future, such personalized atrial models may be used to support EP interventions.
Abstract: As possible cause for atrial fibrillation (AF) we study the influence of a reduced excitability on the interaction of pacemaker waves in the Bueno-Orovio model with parameters adapted to atrial electrophysiology (aBO). One of the two pacemakers represents the sinus node and the other one a self-excitatory source in the left atrium. The pacemakers are spatially separated and their waves get in contact via a small bridge. In previous studies based on the FitzHugh-Nagumo (FHN) model it was shown that three different types of irregular activation patterns can occur in this problem. In the aBO model adapted to physiological conditions only one type is observed because, different from the FHN model, a reduction of excitability due to high-frequency pacing does not occur. If the excitability is reduced in the aBO model, all types of irregularities are recovered and, in addition, a further type is found. Because transitions from regular to irregular behavior depend on the pacing frequency, our findings provide a possible explanation for the phenomenon of paroxysmal AF.
Abstract: While human ether-à-go-go-related gene (hERG) mutations N588K and K897T are associated with atrial fib- rillation (AF), the underlying arrhythmogenic mechanisms are understood only incompletely. In this work, an ap- proach integrating IKr measurement data from transgenic Xenopus oocytes into established computational models of cardiac electrophysiology is presented. Parameters are es- timated using a minimization formulation, which is handled by a hybrid particle swarm optimization (PSO) and trust- region-reflective (TRR) algorithm. Cell models adapted to the mutation measurements show a significantly shorter ac- tion potential (AP) with less pronounced spike-and-dome morphology. Results of single cell simulations compare with myocytes in chronic AF.
Abstract: Atrial fibrillation (AF) is a common arrhythmia with progressive nature. This progression is partly caused by AF itself by modifying — amongst others — the electrophysiological properties of the myocytes. These changes are referred to as electrical remodeling and were integrated in a computational model of human atrial myocytes in this work.
In particular, the maximum conductivities of Ito, IK1, IKs, IKur, ICa,L, INa,Ca, and the Ca2+ leak current from the sarcoplasmic reticulum, as well as the cell capacitance were altered. In an additional setup, the influence of potential gap junction remodeling was investigated.
Wavelength was reduced from 225 mm to 110 mm, respectively 92 mm when considering gap junction remodeling at a basic cycle length of 400 ms. Action potential morphology was changed from spike-and-dome to a more triangular repolarization phase. However, our results show that including IKur remodeling prevents the plateau phase from disappearing completely.
Abstract: Pharmacological therapy of atrial fibrillation (AF) is still a major clinical challenge. Particularly AF of early onset has a significant familiar component and was asso- ciated with various gene mutations. In this study, we de- signed and optimized antiarrhythmic agents for atrial sub- strates affected by human ether-a`-go-go-related gene mu- tations L532P and N588K. A virtual multichannel blocker was designed aiming at a restoration of the wild-type (WT) action potential (AP) on the single cell and tissue level. Furthermore, the amiodarone and dronedarone concen- trations yielding the smallest difference between WT and mutated APs were identified. The WT AP at a basic cy- cle length (BCL) of 1000 ms could be restored by signifi- cant block of IK r and IK ur (\039%) and less pronounced block of IKs, ICa,L, Ib,Na, and Ib,Ca (17%) for both mutations. Effective dronedarone concentrations of 88 nM for L532P and 40 nM for N588K yielded matches almost as good while amiodarone could not sufficiently restore the WT AP. APD90 restitution was effectively restored by the tuned N588K agent whereas differences of up to 34 ms were observed for low BCLs using the tuned L532P agent. Our results provide insight into the pharmacodynamic re- sponse of mutated myocytes and may aid in the optimiza- tion of patient group-specific therapeutic approaches.
Abstract: Vernakalant is a new antiarrhythmic agent for the treatment of atrial fibrillation. While it has proven to be effective in a large share of patients in clinical studies, its underlying mode of action is not fully understood. In this work, we aim to link experimental data from the subcellular, tissue, and system level using an in-silico approach. A Hill’s equation-based drug model was extended to cover the frequency dependence of sodium channel block. Two model variants were investigated: M1 based on subcellular data and M2 based on tissue level data. 6 action potential (AP) markers were evaluated regarding their dose, frequency and substrate dependence. M1 comprising potassium, sodium, and calcium channel block reproduced the reported prolongation of the refractory period. M2 not including the effects on potassium channels reproduced reported AP morphology changes on the other hand. The experimentally observed increase of ERP accompanied by a shortening of APD90 was not reproduced. Thus, explanations for the drug-induced changes are provided while none of the models can explain the effects in their entirety. These results foster the understanding of vernakalant’s cellular mode of action and point out relevant gaps in our current knowledge to be addressed in future in-silico and experimental research on this aspiring antiarrhythmic agent.
Abstract: Atrial fibrillation (AF) is still a major health problem in the western society. Especially for familial AF, the pharmacological therapy is still not sufficiently successful. In this work, channel blocker properties were in-silico adapted to optimize drug therapy for patients suffering from familial AF. The Courtemanche-Ramirez-Nattel (CRN) cell model was the basis for the simulations. Adaptations in the model due to familial AF were implemented using an existing description of the L532P mutation. A fitting algorithm was designed which adapted all conductivities of the ion channels described in the CRN model to restore the healthy action potential (AP). To find the minimal deviation of the healthy AP and the AP of the L532P mutation, the trust-region-reflective algorithm was used. The best matched APs were achieved by a significant blockade of the IKr and the IKur current. 1D tissue strand simulations were performed using different basic cycle lengths (BCL) to evaluate the results of the optimization. It was shown that for the found adaptation of the conductivities, the AP duration, and the progressions of the conduction velocity, effective refractory period, and wavelength (WL) could be restored. The WL was increased by 53.37% compared to the mutation and had a value of 233.48 mm (BCL = 1 s).
Abstract: Fibrosis is strongly linked with the mechanisms of atrial fibrillation (AF), the most common arrhythmia. Direct electrotonic coupling between atrial myocytes and fibroblast has been suggested to contribute to these mechanisms. We use a 3D biophysical model of the atria to study the effects of fibrosis on atrial electrophysiology. Realistic tissue geometry, regional heterogeneity and myofiber anisotropy are integrated in the model. The model also accounts for the effects AF induced ionic remodeling, which has been shown to promote AF. The model simulations demonstrated that fibrosis significantly reduced both the atrial conduction velocity and action potential duration. Both these factors contributed to a large (45%) reduction of the atrial activation wavelength. This is comparable with the wavelength reduction (65%) due to ionic remodeling. As a result, the sustenance of re- entrant waves in the 3D atria was substantially increased with both fibrosis and remodeling. Hence, the elecrotonic changes induced by fibrosis can be comparable to those due to ionic remodeling, and both factors can provide substrate for re-entry in the 3D atria model.
Abstract: Local activation time (LAT) maps help to understand the path of electrical excitation in cardiac arrhythmias. They can be generated automatically from intracardiac electrograms using various criteria provided by commercial electroanatomical mapping systems. This study compares existing criteria and a novel method based on the non-linear energy operator (NLEO) with respect to their precision and robustness.
Abstract: In spite of the considerable medical and technical progress during the last years, catheter ablation of atrial fibrillation is still challenging. For a successful execution of the ablation and the avoidance of intricacies the catheter must be in contact with the endocardium, which is still difficult to assure with existent techniques. It would be desirable to detect the endocardial catheter contact directly from the signal shape and its properties. In this work, significant signal property changes were detected and investigated, which allow an automatic contact detection. Furthermore, atrial electrograms were simulated and compared with a database of measured and annotated signals. During these simulations, the distance between endocardium and the catheter tip could be chosen discretionary. The simulated signals revealed themselves to be very accurate. Simulations can now be used to analyse intracardiac signals more closely. The exact position of the catheter will hereby always be assured, which is not always granted in clinical practice.
I. M. Popp, G. Seemann, and O. Dössel. Investigation of the influence of electric fields on human ventricular myocardium including realistic fiber orientation: a simulation study.
Abstract: The aim of this work is to enlarge the knowledge about the electrophysiological phenomena that describes the defibrillation procedure. We simulated this using a three-dimensional computer model in which the human cardiac tissue is incorporated in blood bath medium. Two initial situations were imposed: the tissue being in a resting state and the tissue being half resting, half depolarized, before the electrical shock was applied. For obtaining a more detailed look over these situations we varied the fiber orientation and the magnitude of the electrical impulse. The effects of intracellular electrical discontinuities represented an important target in our study. The temporal evolution of the transmembrane voltage was always followed until the tissue went back into the resting phase.
Abstract: Defibrillation of the heart is used widely to resuscitate pa tients with fibrillating heart, being the most effective ther apy for this otherwise lethal disturbance of cardiac rhythm. The basic electrophysilogical mechanisms of this proce dure are not well understood. The aim of this work is to in vestigate the conditions that influence the so called virtual electrodes that appear in human ventricular myocardium and also their effects. A two-dimensional and a three dimensional computer model of cardiac tissue is used. For this the temporal evolution of the transmembrane voltage is studied until the entire tissue is repolarized, the needed time interval being around 400 ms.
Abstract: Defibrillation is the most important measure of resuscitation aiming at restoration of the physiological heart rhythm. A complete understanding of the defibrillation mechanism has not been achieved yet. The research presented in this article gives a mathematical computer simulation of the defibrillation of chaotically fibrillating human ventricular myocardium. The study was done with a model representing a three-dimensional wedge of human ventricular myocardial tissue. The cellular electrophysiology was described with the Priebe-Beuckelmann model. The electrical activity of the cardiac tissue was calculated with a bidomain model. A spiral wave was induced in the myocardium with standard S1-S2 protocols. The myocardium was brought into a chaotically fibrillating state by breaking the spiral wave. Few hundred milliseconds after the chaotically fibrillation started, monophasic electrical defibrillating shocks were applied through planar electrodes. The defibrillation shocks were applied at different moments. At each chosen moment we studied both cases of electrical polarity. The reaction of myocardium was studied during the following 400 ms. The results are indicating important information related to the factors, which are influencing the defibrillation success.
Abstract: Over the last decades, the information content derived from cardiac electric and magnetic field measurements has been debated. Our co-workers Wilhelms et al. inves- tigated electrically silent acute ischemia in human ven- tricles caused by occlusion of a coronary artery. In the present work, we extend the previous study by calculating associated magnetic fields produced by early stage acute ischemia with varying transmural extent. Multiscale com- putational simulations were performed for calculations of body surface potential maps (BSPM) and magnetocardio- grams (MCG) on a magnetometer sensor matrix situated above the anterior chest wall. Depending on the ischemia size, the ST-segments of the simulated electrocardiograms (ECG) experienced depression for subendocardial cases and elevation for transmural ischemia. One intermedi- ate extent resulted in a zero ST-segment which makes it diagnostically indistinguishable from the healthy case. Magnetic field calculations for this electrically silent is- chemia also revealed no difference compared to the control case. Otherwise, both ECG and MCG signals during ST- segments showed either depression or elevation from zero line. In this simulation study, MCG did not deliver addi- tional information to uncover electrically silent ischemia. For a general conclusion, further in-silico investigations with different ischemia shapes, sizes and positions should be performed and clinical studies with recordings of both ECG and MCG signals have to be conducted.
Abstract: The goal of this research was to classify cardiac excitation patterns during atrial fibrillation (AFib). For this purpose, virtual models of intracardiac mapping catheters were moved across in-silico cardiac tissue to extract local activation times (LATs) of each catheter electrode from simulated cardiac action potential (AP) signals. The resulting LAT patterns consisting of the LATs of all electrodes resemble patterns measured in clinical cases. The LATs represent the input information for features that were used to separate four different excitation patterns during AFib. Those four excitation patterns were plane wave, ectopic focus (spherical wave), rotor (spiral wave) and block. A feature selection algorithm was used to investigate the features concerning their power to classify the different simulated excitation patterns. The scores of the selected features were used to train and optimize a support vector machine (SVM). The optimized and cross-validated SVM was then used to classify the simulated cardiac excitation patterns. The achieved overall classification accuracy of this SVM model was 98.4 %.
Abstract: The purpose of this study is to develop a computer model-based planning environment for therapeutically cardiac interventions, i.e. surgical or catheter ablation procedures in atrial cases and placing pacemaker electrodes in biventricular pacing. Existing mathematical models are used to simulate the electrophysiology on an anatomical pig model during a heart cycle. The results of these models were validated in multiple domestic pig animal experiments. We found that the models created enable us to simulate the electrical behaviour of the heart nearly in real time and that it reproduces the properties of the heart in atrial flutter and in ventricular pacing with different pacing locations. The results of computer-based simulations may lead to a better understanding of cardiac rhythm disorders and the development of new, less invasive operative techniques.
Abstract: The output data generated in whole heart simula- tions are usually single or multiple parameters at each point in the simulation space. Visualizing data sets of gigabyte size puts great stress on the hardware and can be slow and tedious. Creating animated movies to analyze the excitation propaga- tion can take hours on standard systems. We present two par- allel visualization techniques to improve rendering of large datasets from cardiac simulations.
The Scalable Parallel Visualization Networking (SPVN) toolkit provides the ability to assist in optimizing the utility and functionality of the aggregate resources in visualization clusters. Run time visualization offers the opportunity to visu- alize the results of cardiac simulations on the fly on High Per- formance Computers. Parallel visualization techniques enable fast manipulation of high resolution whole heart data sets and simulation results. The SPVN system has the potential to be linked with the simulation environment similar to the run time visualization described.
Future efforts will focus on creating a simulation and visu- alization environment with appropriate characteristics for clinical setting. Specifically, speed, intuitive control and the ability to render diverse signals will likely be critical to drive adoption in the clinical setting.
Abstract: Orthogonal recursive bisection (ORB) algorithm can be used as data decomposition strategy to distribute a large data set of a cardiac model to a distributed memory supercomputer. It has been shown previously that good scaling results can be achieved using the ORB algorithm for data decomposition. However, the ORB algorithm depends on the distribution of computational load of each element in the data set. In this work we investigated the dependence of data decomposition and load balancing on different rotations of the anatomical data set to achieve optimization in load balancing. The anatomical data set was given by both ventricles of the Visible Female data set in a 0.2 mm resolution. Fiber orientation was included. The data set was rotated by 90 degrees around x, y and z axis, respectively. By either translating or by simply taking the magnitude of the resulting negative coordinates we were able to create 14 data sets of the same anatomy with different orientation and position in the overall volume. Computation load ratios for non – tissue vs. tissue elements used in the data decomposition were 1:1, 1:2, 1:5, 1:10, 1:25, 1:38.85, 1:50 and 1:100 to investigate the effect of different load ratios on the data decomposition. The ten Tusscher et al. (2004) electrophysiological cell model was used in monodomain simulations of 1 ms simulation time to compare performance using the different data sets and orientations. The simulations were carried out for load ratio 1:10, 1:25 and 1:38.85 on a 512 processor partition of the IBM Blue Gene/L supercomputer. The results show that the data decomposition does depend on the orientation and position of the anatomy in the global volume. The difference in total run time between the data sets is 10 s for a simulation time of 1 ms. This yields a difference of about 28 h for a simulation of 10 s simulation time. However, given larger processor partitions, the difference in run time decreases and becomes less significant. Depending on the processor partition size, future work will have to consider the orientation of the anatomy in the global volume for longer simulation runs.
Abstract: Multi-scale, multi-physical heart models have not yet been able to include a high degree of accuracy and resolution with respect to model detail and spatial resolution due to computational limitations of current systems. We propose a framework to compute large scale cardiac models. Decomposition of anatomical data in segments to be distributed on a parallel computer is carried out by optimal recursive bisection (ORB). The algorithm takes into account a computational load parameter which has to be adjusted according to the cell models used. The diffusion term is realized by the monodomain equations. The anatomical data-set was given by both ventricles of the Visible Female data-set in a 0.2 mm resolution. Heterogeneous anisotropy was included in the computation. Model weights as input for the decomposition and load balancing were set to (a) 1 for tissue and 0 for non-tissue elements; (b) 10 for tissue and 1 for non-tissue elements. Scaling results for 512, 1024, 2048, 4096 and 8192 computational nodes were obtained for 10 ms simulation time. The simulations were carried out on an IBM Blue Gene/L parallel computer. A 1 s simulation was then carried out on 2048 nodes for the optimal model load. Load balances did not differ significantly across computational nodes even if the number of data elements distributed to each node differed greatly. Since the ORB algorithm did not take into account computational load due to communication cycles, the speedup is close to optimal for the computation time but not optimal overall due to the communication overhead. However, the simulation times were reduced form 87 minutes on 512 to 11 minutes on 8192 nodes. This work demonstrates that it is possible to run simulations of the presented detailed cardiac model within hours for the simulation of a heart beat.
Abstract: Increasing biophysical detail in multi physical, multiscale cardiac model will demand higher levels of parallelism in multi-core approaches to obtain fast simulation times. As an example of such a highly parallel multi-core approaches, we develop a completely distributed bidomain cardiac model implemented on the IBM Blue Gene/L architecture. A tissue block of size 50 times 50 times 100 cubic elements based on ten Tusscher et al. (2004) cell model is distributed on 512 computational nodes. The extracellular potential is calculated by the Gauss-Seidel (GS) iterative method that typically requires high levels of inter-processor communication. Specifically, the GS method requires knowledge of all cellular potentials at each of it iterative step. In the absence of shared memory, the values are communicated with substantial overhead. We attempted to reduce communication overhead by computing the extracellular potential only every 5th time step for the integration of the cell models. We also investigated the effects of reducing inter-processor communication to every 5th, 10th, 50th iteration or no communication within the GS iteration. While technically incorrect, these approximation had little impact on numerical convergence or accuracy for the simulations tested. The results suggest some heuristic approaches may further reduce the inter-processor communication to improve the execution time of large-scale simulations.
Abstract: Cardiac electrophysiology procedures are routinely used to treat patients with rhythm disorders. The success rates of ablation procedures and cardiac resynchronization therapy are still sub-optimal. Recent advances in medical imaging, image processing and cardiac biophysical modeling have the potential to improve patient outcome. This manuscript provides an overview of how these advances have been translated into the clinical environment.
Abstract: There is still a need for research to understand the co- herences of the origin of arrhythmias such like rotors and possible ablation strategies. The aim of this work was the analysis of typical signal characteristics near a rotor cen- ter. Rotors were simulated on 2D patch geometry (100 mm x 100 mm) with spatial resolution of 0.1mm. Based on extracellular potentials, different features were evalu- ated: Local activation time, peak to peak amplitude, steep- est negative slope and approximate entropy were com- pared regarding their ability to indicate the rotor tip lo- cation. Furthermore, typical signal patterns of different mapping catheters centered at the rotor tip position were analyzed. The determined maximum distances between the focal point of phase singularities and determined centers by the peak to peak amplitudes were maximal 1.7 mm.
Abstract: Atrial fibrillation is a common irregular heart rhythm. Until today there is still a need for research to quantify typical signal characteristics of rotors, which can induce atrial fibrillation. In this work, signal characteristics of a stable and a more unstable rotor in a realistic heart model including fiber orientation were analyzed with the following methods: peak-to-peak amplitude, Hilbert phase, approximate entropy and RS-difference. In this simulation model the stable rotor rotated with a cycle length of 145 ms and stayed in an area of 1.5 mm x 3 mm. Another more unstable rotor with a cycle length of 190msmovedinanareaof10mmx4mm. Inadistance of 2 mm to the rotor tip, the peak-to-peak amplitude decreased significantly, whereas the RS-difference and the approximate entropy were maximal. The rotor center trajectories were detected by phase singularity points determined by the Hilbert transform. We showed that more unstable rotors resulted in more amplitude changes over time and also the cycle length differed more. Furthermore, we presented typical activation time patterns of the Lasso catheter centered at the rotor tip and in different distances to the rotor tip. We suggest that cardiologists use a combination of the described methods to determine a rotor tip position in a more robust manner.
M. Rottmann, G. Seemann, and O. Dössel. Analysis of characteristic signal morphologies of double potentials near block lines in an atrial simulation model.
In Biomedical Technology/ Biomedical Engineering, 2015
Abstract: Modeling of cardiac electro-mechanics enables and simplifies understanding of physiology and pathophysiology of the heart. In this work a model is presented, which allows the reconstruction of macroscopic electro-mechanical processes in the left ventricle of small mammals. The model combines a three-dimensional model of left ventricular anatomy represented as truncated ellipsoid with an integrated electromechanical model. The integrated model includes electrophysiological, force development and elastomechanical models of myocardium. The model is illustrated by simulations, which reflect the behavior of an extracorporated heart. These simulations yield temporal distributions of electrophysiological parameters as well as descriptions of electrical propagation and mechanical deformation. The simulations show the connection between cellular electrophysiology, electrical excitation propagation, force development, and mechanical deformation.
Abstract: Cardiac electro-mechanical models are valuable tools to gain insights in physiology and pathophysiology of the heart. Progressive models can be created by fusion of various basic models. In this work biventricular models of cardiac electro-mechanics were developed by fusion of anatomical, electrical, and mechanical models. The importance of anatomical modeling was researched by inclusion of two different anatomical models, i.e. an analytical and a magnetic resonance diffusion tensor imaging based model. The fused models were applied in simulations of physiological behavior and results of these were analyzed. Significant difference of deformation were found, which can be attributed to the anatomical models. The analysis emphasized the importance of appropriate anatomical modeling for simulations of cardiac mechanics.
Abstract: Modeling of mechanisms involved in electrophysiology and tension development of cardiac myocytes can enhance the understanding of physiological and pathophysiological cardiac phenomena. Interactions of divers components are necessary for cellular electro-mechanics. Particularly, the interactions between proteins in the cell membrane, sarcoplasmic reticulum and sarcomere are of importance. In this work hybrid electro-mechanical models of cardiac myocytes were derived on basis of recently developed models as well as of measurements ranging from protein to multi-cell level. The models quantify dynamically the electrophysiology and tension development by states, partly associated to configurations of the involved proteins, and the transition between these states. The models allow the reconstruction of electro-mechanical phenomena. Results of simulations with the hybrid models were performed illustrating their properties. The models may help to clarify feedback and cooperativity mechanisms, pathophysiological changes and metabolism of myocytes.
Abstract: Atrial fibrillation (AF) is the most common cardiac arrhythmia, and is mainly sustained by reentrant circuits and rapid ectopic activity. In the present study, we performed computer simulations using a 3D human atrial model including fibre orientation, electrophysiological heterogeneities and tissue anisotropy. Membrane kinetics were described as in the human atrial action potential model by Maleckar et al., including AF-induced ionic remodeling. The impact of ionic changes on reentrant activity was investigated by characterizing arrhythmia stability, rotor dynamics and dominant frequency (DF). Our simulations show that reentrant circuits tend to organize around the pulmonary veins and the right atrial appendage. Simulated IK1 and INa blocks lead to slower DF in the whole atria, expanded wave meandering and reduction of secondary wavelets. INaK block slightly reduces DF and does not notably change the propagation pattern. Regularity and coupling indices of electrograms are usually higher in the right atrium than in the left atrium, entailing a higher likelihood of arrhythmia generation in the latter, as occurs in AF patients.
Abstract: ntracardiac electrograms are essential for the diagnosis and treatment of various cardiac arrhythmias. To gain reliable information about structural alterations of un- derlying tissue, it is necessary to interpret these electro- grams correctly. Therefore it has to be understood how other parameters influence the signal. Realistic 3D geome- tries were created and simulated using the bidomain model. Based on these simulations, the influences of catheter orien- tation, tissue thickness and conduction velocity on the amplitudes of intracardiac electrograms were evaluated.
Abstract: The segmentation of three-dimensional microscopic images of car- diac tissues provides important parameters for characterizing cardiac diseases and modeling of tissue function. Segmenting these images is, however, chal- lenging. Currently only time-consuming manual approaches have been devel- oped for this purpose. Here, we introduce an efficient approach for the semi-automatic segmentation (SAS) of cardiomyocytes and the extracellular space in image stacks obtained from confocal microscopy. The approach is based on a morphological watershed algorithm and iterative creation of wa- tershed seed points on a distance map. Results of SAS were consistent with re- sults from manual segmentation (Dice similarity coefficient: 90.8±2.6%). Cell volume was 4.6±6.5% higher in SAS cells, which mainly resulted from cell branches and membrane protrusions neglected by manual segmentation. We suggest that the novel approach constitutes an important tool for characterizing normal and diseased cardiac tissues. Furthermore, the approach is capable of providing crucial parameters for modeling of tissue structure and function.
Abstract: The development of new devices used for defibrillation and cardioversion is often supported by numerical simulations of the induced electric potentials and current distributions. The commonly used tools incorporate isotropic models of the tissue properties present in the human torso. A comparative study was conducted to characterize the influence of anisotropic compared to isotropic tissue modeling. Defibrillation shocks with amplitudes of 1000 V and 2000 V were simulated and a set of varying conductivity values and anisotropy ratios was examined. The inclusion of tissue anisotropy produced significantly smaller values for current density compared to isotropic calculations especially in the myocardial tissue.
Abstract: This work aimed at the detection of rotor centers within the atrial cavity during atrial fibrillation on the basis of phase singularities. A voxel based method was established which employs the Hilbert transform and the phase of unipolar electrograms. The method provides a 3D overview of phase singularities at the endocardial surface and within the blood volume. Mapping those phase singularities from the inside of the atria at the endocardium yielded rotor center trajectories.We discuss the results for an unstable and a more stable rotor. The side length of the areas covered by the trajectories varied from 1.5mm to 10 mm. These results are important for cardiologists who target rotors with RF ablation in order to cure atrial fibrillation.
Abstract: The fiber orientation in the atria has a significant contribution to the electrophysiologic behavior of the heart and to the genesis of arrhythmia. Atrial fiber orientation has a direct effect on excitation propagation, activation patterns and the P-wave. We present a rule-based algorithm that works robustly on different volumetric meshes composed of either isotropic hexahedra or arbitrary tetrahedra as well as on 3-dimensional triangular surface meshes in patient-specific geometric models. This method fosters the understanding of general pro-arrhythmic mechanisms and enhances patient-specific modeling approaches.
Abstract: Simulation of cardiac excitation is often a trade-off between accuracy and speed. A promising minimal, time-efficient cell model with four state variables has recently been presented together with parametrizations for ventricular cell behaviour. In this work, we adapt the model parameters to reproduce atrial excitation properties as given by the Courtemanche model. The action potential shape is considered as well as the restitution of action potential duration and conduction velocity. Simulation times in a single cell and a tissue patch are compared between the two models. We further present the simulation of a sinus beat on the atria in a realistic 3D geometry using the fitted minimal model in a monodomain simulation.
Abstract: Patient-specific model adaptation and validation requires a comparison of simulations with measured patient data. For patients suffering from atrial fibrillation, such data is mainly available as intracardiac catheter signals. In this work, we demonstrate the simulation of clinically relevant catheter data as measured using circular mapping catheters (such as Lasso or Orbiter) and coronary sinus catheters using atrial simulations on a realistic geometry. Four circular catheters are modeled using a projection technique for two distinct types of application. We show that in sinus rhythm, the choice of a distinct electrophysiological model does not impair the signal quality. Finally, we compare simulated potentials to a real clinical measurement. In the future, with patient- specific models available, such comparisons can constitute an important interface for personalizing cardiac models.
Abstract: Intracardiac catheter recordings are available in common clinical practice. They can therefore be employed to adapt and validate atrial computer models of individual patients. Hence, their information content needs to be analyzed quantitatively. During treatment of atrial arrhythmia such as atrial flutter or fibrillation, the location of ectopic foci in the pulmonary veins is of special interest. In this study, virtual catheter signals are extracted from an atrial simulation on a realistic geometry with normal sinus rhythm as well as ectopic stimuli in all four pulmonary veins. Using a simplified Pan-Tompkins algorithm, the activation times are determined. Based on the analysis of the activation sequence in a circular mapping catheter simulated on the posterior left atrial wall, all four ectopic foci can clearly be associated with the pulmonary vein they came from. For a catheter on the anterior wall, this is possible for three of the four ectopic beats. Despite the knowledge gathered for the personalization of patient models, such simulations may help cardiologists to better classify measured signals.
Abstract: Background: Catheter ablation of complex atrial arrhythmias, such as atrial fibrillation and atypical atrial flutter, is still challenging. Clinically evaluated ablation methods are leading to moderate success rates. Assessments of intracardiac electrograms are often done subjectively by the physician. Automatic algorithms can therefore improve the analysis of complex atrial electrograms (EGMs). In this work, we demonstrate a quantitative analysis of intracardiac EGMs from circular mapping catheters in humans. Both the wave direction and the local conduction velocity (CV) were calculated from individual wave fronts passing the catheter.
Methods: Intracardiac EGMs measured with circular mapping catheters in humans were retrospectively analyzed. Five data sets from 3 patients undergoing catheter ablation of atrial fibrillation or flutter were available. Using a nonlinear energy operator, activation times from 9 bipolar catheter signals were calculated for each atrial activity. The resulting activation pattern was fitted to a cosine-shaped data model that has been validated in a previous simulation study. The cosine phase represented the wave direction. From the cosine amplitude and the catheter radius, the conduction velocity was calculated.
Results: The wave directions in all five measurements were stable with a standard deviation below 10°. Calculated CVs were in the range of 70 to 110 cm/s, which is in accordance with published values. In one patient, electrograms were recorded during atrial stimulation. Stimulation cycle length was decreased from 500 to 300 milliseconds. Conduction velocity decreased by approximately 10% at a cycle length of 300 milliseconds compared with the CV at 500 milliseconds.
Conclusion: The results show the ability to reliably extract wave direction and conduction velocity from intracardiac EGMs recorded with circular mapping catheters. Detected directions were stable, and the CV values were in a physiological range. As individual beats are analyzed, the method will also enable the quantitative study of singular events such as ectopic beats and facilitate the localization of tachycardia origins. Further, it will help to measure substrate parameters such as the CV and even CV restitution behavior. This way, the method can help to identify patient-specific physiological parameters that can be integrated into patient-specific models. Furthermore, it can directly provide quantitative data of high diagnostic value to the examiner and thereby improve clinical success rates.
Abstract: Patient-specific cardiac simulations are approaching clinical applications. They could for example improve the treatment of atrial fibrillation (AF). Currently, many patients suffering from AF are treated with minimally-invasive catheter ablation. Using this technique, trigger sources for AF (mainly the pulmonary veins), are electrically isolated from the rest of the atrium. However, a large set of different ablation strategies is currently used in clinical practice. Therefore, the choice of a certain ablation strategy as well as the probability for successful and sustained AF termination are strongly dependent on the experience of the cardiologist. Atrial simulations could assist the cardiologist in the choice of a suitable method for an individual patient. For this, the atrial models have to be adapted to the patient. Besides anatomical modeling, several challenges must be faced in this process. First, an appropriate model of cellular electrophysiology and excitation conduction must be chosen. The model must provide the necessary accuracy and at the same time be fast enough for clinical applications. As a trade-off between accuracy and speed, we propose a minimal model adapted to atrial electrophysiology. Second, a main problem is the adaptation of physiological parameters in the patient-specific model as well as its validation. Therefore, an interface between clinical data and the model is needed. Data collected in standard clinical workflow are mainly intracardiac catheter ECGs. We therefore present techniques to model such catheter measurements. Signals from both circular mapping catheters (such as Lasso or Orbiter) as well as Coronary Sinus catheters can be simulated and compared to clinical signals. These are important steps towards clinical applications of atrial models. The long-term goal then is to assist the cardiologist in the choice of the best treatment for an individual patient.
Abstract: Heterogeneity of ion channel properties within human ventricular tissue determines the sequence of repolarization under healthy conditions. In this computational study, the impact of different extend of electrophysiological heterogeneity in both human ventricles on the ECG was investigated by a forward calculation of the cardiac electrical signals on the body surface. The gradients ranged from solely transmural, interventricular and apico-basal up to full combination of these variations. As long interventricular heterogeneities were neglected, the transmural gradient generated a positive T wave that was increased when apico-basal variations were considered. Inclusion of interventricular changes necessitated the incorporation of both transmural and apico-basal heterogeneities to reproduce the positive T wave.
Abstract: Diagnosis of acute cardiac ischemia depends on characteristic shifts of the ST segment. The transmural extent of the ischemic region and the temporal stage of ischemia have an impact on these changes. In this work, computer simulations of realistic ventricles with different transmural extent of the ischemic region were carried out. Furthermore, three stages within the first half hour after the occlusion of the distal left anterior descending coronary artery were regarded. The transmembrane voltage distributions and the corresponding body surface ECGs were calculated. It was observed how the electrophysiological properties worsen in the course of ischemia, so that almost no excitation was initiated in the central ischemic zone 30 minutes after the occlusion. In addition to these temporal effects, also the transmural extent of the ischemic region had an impact on the direction and intensity of the ST segment shift.
Abstract: The sinus node (SN), which is the primary pacemaker of the heart, is a heterogeneous structure, i.e. there is a difference between center and periphery regarding morphology, electrophysiology and electrical coupling. The behavior of the whole SN in detail is difficult to investigate experimentally. Therefore, realistic computer models are helpful to understand the electrophysiological mechanisms quantitatively. In this work, different models of the SN including heterogeneity are benchmarked.
Several approaches considering SN heterogeneity exist. One possible description of the electrical conduction is the mosaic model, in which the density of two discrete cell types, central and peripheral cells, is varied from the center to the periphery of the SN. The gradient model is another approach for this task. As the name implies, there is a gradual transition in cell morphology and electrophysiology between the center and periphery.
The behavior of single nodal cells were described best by the rabbit SN model of Zhang et al. , offering explicit formulations for central and peripheral cells. A one-dimensional model of the SN and surrounding atrial tissue and a two-dimensional slice of the SN and adjoining crista terminalis (CT) were applied. Both approaches describing electrical conduction were compared using these different geometric models, in order to find the most exact model in relation to measured data describing activation patterns and action potential durations.
Abstract: During acute cardiac ischemia, electrophysiological properties of the affected tissue are altered in the subendocardium firstly. If the occlusion worsens, the effects spread transmurally. Diagnosis of cardiac ischemia, which should be improved by computer simulations, is based on shifts of the ST segment. In this work, we simulated heterogeneous ischemic regions with varying transmural extent. The excitation propagation and ECGs were calculated for the different setups. We showed that ST segment polarity can be dependent on the transmural extent of the ischemic region. In case of subendocardial ischemia, short action potentials were initiated in the ischemic zone causing a slight transmural gradient of the transmembrane voltage. Therefore, the ST segment was depressed in leads near the ischemic region in the chosen case. During transmural ischemia, this gradient showed in the opposite direction from epicardium to endocardium leading to ST segment elevation.
Abstract: The monodomain model is a mathematical description of the electrical excitation propagation in the heart. The numerical solution of this reaction-diffusion equation is a computationally demanding task. Aspects that have to be considered are the accuracy and stability of the solution on the one hand and the computing time on the other hand. Two first order methods – an explicit and a semi-implicit scheme – solving the monodomain equation were compared in this work. For the benchmark of the solvers, three cell models with different computational complexity were used. Thus, the contribution of the solvers to the total computing time could be analyzed. Generally, if the same time step was used, the semi-implicit was slower than the explicit one, since an additional linear system of equations had to be solved. However, the semi-implicit solver was more accurate and showed better stability behavior than the explicit one, especially at high spatial resolutions. Therefore, larger time steps could be used, achieving the same accuracy and a shorter total computing time as the explicit solver. However, this effect was present only, if the additional calculations of the semi-implicit solver contributed less to the total computing time, i.e. the cell model had to be computationally complex.
Abstract: Generally, models of cardiac electrophysiology describe physiologic conditions in detail. However, other conditions, such as drug interactions or mutations of ion channels are of interest for research. Therefore, the simulated ion currents have to be fitted to measured voltage or patch clamp data. In this work, three different methods for the model parametrization were compared: one based on Powell’s algorithm implemented in a modular C++ framework and two optimization techniques realized in Matlab. The latter two approaches differed in solving the ordinary differential equations describing the channel gating. They can either be approximated numerically or solved analytically, since the transmembrane voltage is a piecewise constant function during the applied clamp protocol. All three methods were compared regarding computing time and quality of the fit using least squares. The modular C++ framework was slower than the numerical Matlab method, which took longer than the analytical one. The quality of the fit was similar for almost all analyzed methods. Therefore, the analytical method grants a fast and reliable solution for the calibration of ion current models for applications with constant membrane voltage, as e.g. in case of voltage or patch clamp data.
Abstract: Various types of heart disease are associated with structural remodeling of cardiac cells. In this work, we present a software framework for automated analyses of structures and protein distributions involved in excitation-contraction coupling in cardiac muscle cells (myocytes). The software framework was designed for processing sets of three-dimensional image stacks, which were created by fluorescent labeling and scanning confocal microscopy of ventricular myocytes from a rabbit infarction model. Design of the software framework reflected the large data volume of image stacks and their large number by selection of efficient and automated methods of digital image processing. Specifically, we selected methods with small user interaction and automated parameter identification by analysis of image stacks. We applied the software framework to exemplary data yielding quantitative information on the arrangement of cell membrane (sarcolemma), the density of ryanodine receptor clusters and their distance to the sarcolemma. We suggest that the presented software framework can be used to automatically quantify various aspects of cellular remodeling, which will provide insights in basic mechanisms of heart diseases and their modeling using computational approaches. Further applications of the developed approaches include clinical cardiological diagnosis and therapy planning.
Abstract: Using OpenCL, we developed a cross-platform software to compute electrical excitation conduction in cardiac tissue. OpenCL allowed the software to run parallelized and on different computing devices (e.g., CPUs and GPUs).We used the macroscopic mono-domain model for excitation conduction and an atrial myocyte model by Courtemanche et al. for ionic currents. On a CPU with 12 HyperThreading-enabled Intel Xeon 2.7 GHz cores, we achieved a speed-up of simulations by a factor of 1.6 against existing software that uses OpenMPI. On two high-end AMD FirePro D700 GPUs the OpenCL software ran 2.4 times faster than the OpenMPI implementation. The more nodes the discretized simulation domain contained, the higher speed-ups were achieved.
Abstract: Anatomically realistic computational models provide a powerful platform for investigating mechanisms that underlie atrial rhythm disturbances. In recent years, novel techniques have been developed to construct structurally-detailed, image-based models of 3D atrial anatomy. However, computational models still do not contain full descriptions of the atrial intramural myofiber architecture throughout the entire atria. To address this, a semi-automatic rule-based method was developed for generating multi-layer myofiber orientations in the human atria. The rules for fiber generation are based on the careful anatomic studies of Ho, Anderson and co-workers using dissection, macrophotography and visual tracing of fiber tracts. Separately, a series of high color contrast images were obtained from sheep atria with a novel confocal surface microscopy method. Myofiber orientations in the normal sheep atria were estimated by eigen-analyis of the 3D image structure tensor. These data have been incorporated into an anatomical model that provides the quantitative representation of myofiber architecture in the atrial chambers. In this study, we attempted to compare the two myofiber generation approaches. We observed similar myo-bundle structure in the human and sheep atria, for example in Bachmann's bundle, atrial septum, pectinate muscles, superior vena cava and septo-pulmonary bundle. Our computational simulations also confirmed that the preferential propagation pathways of the activation sequence in both atrial models is qualitatively similar, largely due to the domination of the major muscle bundles.
G. Seemann. Modeling of electrophysiology and tension development in the human heart.
Institut für Biomedizinische Technik. Dissertation. 2005
Abstract: Comprehension of the beating of the human heart is important for cardiac research and will improve many clinical applications.
Simulations based on models describing cardiac electro-mechanics can acquire insights into this behavior. This work focuses on the mathematical reconstruction of electrophysiology, excitation conduction, and tension development in the human heart on the cellular and the tissue level. The tissue models represent accurate anatomical shapes of the atria and the ventricles and incorporate electrophysiological heterogeneity and anisotropic conduction. The simulations comprehend the physiological behavior of the ventricles and of the atrium including the sinoatrial node as well as pathological cases like ventricular and atrial fibrillation and genetic defects in ionic channels.
Student Thesis (2)
G. Seemann. Interaktive Bedienoberfläche für die Simulation und Visualisierung der elektrischen Erregung im Herz.
Universität Karlsruhe (TH), Institut für Biomedizinische Technik. Studienarbeit. 2000