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:

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:

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:

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.

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:

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:

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: 211% 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:

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.

Abstract:

Congenital Long-QT Syndrome (LQTS) is a genetic dis- order affecting the repolarization of the heart. The most prevalent subtypes of LQTS are LQT1-3. In this work, we aim to evaluate the differences in the T-waves of simu- lated LQT1-3 in order to identify markers in the ECG that might help to classify patients solely based on ECG mea- surements. For LQT1, mutation S277L was used to char- acterize IKs and mutation S818L in IKr for LQT2. Volt- age clamp data were used to parametrize the ion channel equations of the ten Tusscher and Panfilov model of hu- man ventricular electrophysiology. LQT3 was integrated using an existing mutant INa model. The monodomain model was used in a transmural and apico-basal heteroge- neous model of the ventricles to calculate ventricular exci- tation propagation. The forward calculation on a torso model was performed to determine body surface ECGs. Compared to the physiological case with a QT-time of 375 ms, this interval was prolonged in all LQTS (LQT1 423 ms; LQT2 394 ms; LQT3 405 ms). The T-wave ampli- tude was changed (Einthoven lead II: LQT1 108%; LQT2 91%; LQT3 103%). Also, the width of the T-wave was en- larged (full width at half maximum: LQT1 111%; LQT2 125%; LQT3 109%). At the current state of modeling and data analysis, the three LQTS have not been distinguish- able solely by ECG data.

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:

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:

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:

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:

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 Powells 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:

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:

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:

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. [1], 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:

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 remodeled substrate induced by chronic AF (cAF) and patients suffering from familial AF. To date, the reasons for these phenomena are only incompletely understood. We analyzed the effects of these two drugs in a computational model of atrial electrophysiology. The Courtemanche-Ramirez-Nattel model was adapted to represent cAF remodeled 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 analyzed 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. 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:

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:

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:

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:

The early detection of myocardial ischemia is an essential lever for its successful treatment. We investigated an ECG monitoring system with 3 electrodes. Optimal electrode positions are determined using a cellular automaton. The spatially heterogeneous effects of myocardial ischemia were modeled by altering 4 electrophysiological parameters: action potential amplitude and duration, conduction velocity as well as resting membrane voltage. Both, transmural heterogeneity and the influence of the border zone were considered in the simulations on three patient models. The detection of myocardial ischemia is based on ST segment deviation from the physiological case. The signals used to find the best electrode positions comprise ischemic regions with different transmural extents in all 17 AHA segments. We show which ischemic ECGs can be detected given a realistic signal-to-noise ratio, false positive rate and maximum response time of the system.

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.

Abstract:

Atrial fibrillation (AF) is the most common cardiac arrhythmia. Furthermore, acute cardiac ischemia is one of the most common causes of death. Therefore, an early diagnosis and effective therapy are essential. However, the mechanisms responsible for the initiation and maintenance of arrhythmias, as well as the effects of pharmacological treatment on cardiac electrophysiology are not completely understood yet.Therefore, multiscale modeling of cardiac electrophysiology as presented in this thesis helps to better understand the responsible mechanisms. First, methods for the integration of medical measurement data into models of cardiac electrophysiology are introduced. Different models of human atrial and ventricular myocytes were adapted to chronic and familial AF, acute cardiac ischemia and pharmacological treatment. The resulting effects were investigated in multiscale simulations ranging from the ion channel up to the body surface.The presented simulations are an important step towards the understanding and improvement of the diagnosis and pharmacological therapy of AF and acute cardiac ischemia.

Abstract:

Acute cardiac ischemia is characterized by a deficient supply of the heart muscle, caused by the occlusion of one or more coronary arteries. In the temporal course of this pathology, mainly three effects can be observed: hyperkalemia, acidosis, and hypoxia. Consequently, electrophysiological characteristics, as e.g. the APD and Vm, are modified heterogeneously depending on the distance to the occlusion site. These temporal and spatial heterogeneities cause changes of the ECG and the excitation propagation pattern, which was analyzed in this work.An existing description of ischemia effects on the cellular level was used for tissue simulations. At first, a three-dimensional ventricular model was adapted, so that the spatial heterogeneities presenting during cardiac ischemia could be simulated as realistic as possible. After initializing the effects of ischemia in a single-cell environment until the requested stage was reached, differ- ent ischemia configurations were simulated. For this purpose, the transmural extent, the relation between CIZ to BZ, the size of the ischemic region, and the location of the occluded coronary ar- teries were varied. Afterwards, the corresponding ECGs were forward calculated. Here, significant changes of the ST segment could be observed. Depending on the occlusion site, the leads placed above the ischemic region were affected most by this pathology. In case of subendocardial ischemia, a ST depression in leads above the ischemic region can be noticed, whereas transmural ischemia leads to ST elevation there and ST depression at the border to healthy tissue. Depending on the relation between CIZ and BZ, the beginning of the repolarization (onset T wave) is delayed. If the BZ is large, the repolarization starts earlier than if the BZ is small. By this way, the length of the ST segment is influenced. The size of the ischemic region also influences the voltage decrease in the ST segment. Larger ischemic regions cause a stronger decrease.The temporal and spatial heterogeneities occurring during this pathology are known to favor reentry [44]. Therefore, the next part of this diploma thesis dealt with the investigation of reentrant circuits initiated during cardiac ischemia. For this purpose, a two-dimensional tissue model with a circular ischemic region, as introduced in [69], was used. However, the initiation of stable figure-of- eight reentry was difficult due to the strongly varying effective refractory periods in the different ischemic regions. Therefore, different combinations of ischemia stages and coupling intervals were tested. Furthermore, the CV was too high and the APD of human cells too long for this geometry, so that different types of blocks (e.g. at the BZ or CIZ) occurred, as refractory tissue was reached. As a consequence, only one reentrant circuit could be initiated under these conditions. For that reason, the CV was reduced from 800mm/s to 500mm/s, as shown in [69]. By this, a stable figure-of-eight reentry was initiated in this case. Finally, a numerical method for the solution of the monodomain equation was implemented in the existing simulation environment acCELLerate. Generally, this semi-implicit solver requires the solution of an additional linear system of equations. Thus, it is slower than the explicit solver, if the same time step is used. However, the semi-implicit solver is more stable and accurate than the explicit one, especially at high spatial resolutions. Therefore, longer time steps can be used, achieving the same accuracy as the explicit solver. Consequently, the total computing time can be reduced depending on the cell model by using the semi-implicit solver. However, this effect is present only, if the additional calculations contribute to less extent to the total computing time. Thus, the cell model has to be computationally complex, so that the application of the semi-implicit solver reduces the computing time.