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.
D. L. Weiss, D. U. J. Keller, G. Seemann, and O. Dössel. The influence of fibre orientation, extracted from different segments of the human left ventricle, on the activation and repolarization sequence: a simulation study. In Europace, vol. 9(suppl 6) , pp. vi96-vi104, 2007
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.
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.
I. M. Graf, G. Seemann, D. L. Weiss, and O. Dössel. Influence of electrophysiological heterogeneity on electrical stimulation in healthy and failing human hearts. In Medical & Biological Engineering & Computing, vol. 43(6) , pp. 783-792, 2005
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.
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.
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.
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.
F. B. Sachse, G. Seemann, K. Chaisaowong, and D. Weiß. Quantitative reconstruction of cardiac electromechanics in human myocardium: Assembly of electrophysiological and tension generation models. In J. Cardiovasc. Electrophysiol., vol. 14(S10) , pp. S210-S218, 2003
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
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).
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.
PURPOSE: To demonstrate a rapid MR technique that combines imaging and R2* mapping based on a single radial multi-gradient-echo (rMGE) data set. The technique provides a fast method for online monitoring of the administration of (super-)paramagnetic contrast agents as well as image-guided drug delivery. MATERIALS AND METHODS: Data are acquired using an rMGE sequence, resulting in interleaved undersampled radial k-spaces representing different echo times (TEs). These data sets are reconstructed separately, yielding a series of images with different TEs used for pixelwise R2* mapping. A fast numerical algorithm implemented on a real-time reconstruction platform provides online estimation of the relaxation rate R2*. Simultaneously the images are summed for the computation of a high-resolution image. RESULTS: Convenient high-resolution R2* maps of phantoms and the liver of a healthy volunteer were obtained. In addition to stable intrinsic baseline maps, the proposed technique provides particularly accurate results for the high relaxation rates observed during the presence of (super-)paramagnetic contrast agents. Assuming that the change in R2* is proportional to the concentration of the agent, the technique offers a rough estimate for dynamic dosage. CONCLUSION: The simultaneous online display of morphological and parametric information permits convenient, quantitative surveillance of contrast-agent administration.
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.
D. L. Weiss, G. Seemann, and O. Doessel. A framework for incorporation of arbitrary 3D electrophysiological heterogeneities in simulations of the human heart. In 41. Jahrestagung der DGBMT im VDE. Proceedings BMT 2007, vol. 52, 2007
D. L. Weiss, G. Seemann, and O. Dössel. The end of T wave need not coincide with final repolarization in tissue: a simulation study. In Heart Rhythm, vol. 4(5s) , pp. 159, 2007
D. L. Weiss, G. Seemann, and O. Dössel. Efficient Solving of Mathematical Models Describing the Behavior of Cardiac Myocytes. In Biomedizinische Technik, vol. 50(1) , pp. 566-567, 2005
D. L. Weiss, G. Seemann, and O. Dössel. Epicardial stimulation of a virtual left ventricular wall comprising heterogeneity and anisotropy. In Proc. IFMBE / EMBEC, vol. 11, 2005
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.
D. L. Weiss, G. Seemann, F. B. Sachse, and O. Dössel. Epicardial Activation Increases Transmural Dispersion of Repolarization in a Heterogeneous Model of Wild-Type and Short QT Mutant Tissue. In Proc. Computers in Cardiology, vol. 32, pp. 117-120, 2005
P. Carrillo, G. Seemann, E. Scholz, D. L. Weiss, and O. Dössel. Impact of the hERG Channel Mutation N588K on the Electrical Properties of the Human Atrium. In 4th European Conference of the International Federation for Medical and Biological Engineering, IFMBE Proc., vol. 22(22) , pp. 2583-2586, 2009
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.
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.
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.
D. U. J. Keller, G. Seemann, D. L. Weiss, and O. Dössel. Detailed anatomical modeling of human ventricles based on diffusion tensor MRI. In Gemeinsame Jahrestagung der Deutschen, der Österreichischen und der Schweizerischen Gesellschaft für Biomedizinische Technik, vol. 50/1, 2006
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.
D. U. J. Keller, D. L. Weiss, O. Dössel, and G. Seemann. Transferring ventricular myocyte orientation to individual patient data based on diffusion tensor MRI measurements. In Tagungsband 6. Jahrestagung der Deutschen Gesellschaft für Computer- und Roboterassistierte Chirurgie e. V., pp. 255-258, 2007
M. W. Krueger, D. L. Weiss, and O. Doessel. Intraventricular outweighs transmural dispersion of repolarization after epicardial pacing in a virtual human left ventricle. In 41. Jahrestagung der DGBMT im VDE. Proceedings BMT 2007, vol. 52, 2007
M. W. Krueger, D. L. Weiss, G. Seemann, and O. Dössel. Die Begrenztheit theoretischer Modelle der menschlichen Biologie und ihr großer Nutzen für das Verständnis des Körpers. In Challenges and Limitations of Models in Science and Theology, 2007
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.
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.
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.
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.
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.
G. Seemann, D. L. Weiß, F. B. Sachse, and O. Dössel. Electrophysiology and Tension Development in a Transmural Heterogeneous Model of the Visible Female Left Ventricle. In Lecture Notes in Computer Science, vol. 3504, pp. 172-182, 2005
G. Seemann, D. L. Weiß, F. B. Sachse, and O. Dössel. Familial atrial fibrillation: simulation of the mechanisms and effects of a slow rectifier potassium channel mutation in human atrial tissue. In Proc. Computers in Cardiology, vol. 31, pp. 125-128, 2004
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.
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.
D. L. Weiss. Anatomical and electrophysiological modeling of the human ventricles -- from the ion channel to the electrocardiogram. Universitätsverlag Karlsruhe. Dissertation. 2008
D. L. Weiß. Vergleich des Verhaltens eines Elektrophysiologischen Zellmodells mit einem Zellulären Automaten bei Simulierten Atrialen Fibrillationen. Institute of Biomedical Engineering, Universität Karlsruhe (TH). Dissertation. 2002
Gegenstand dieser Studienarbeit ist der Vergleich zweier verschiedener elektrophy- siologischer Modelle der Erregungsausbreitung im Herzen. Diese Modelle werden daraufhin untersucht, inwieweit sie bei simulierten Fibrillationen in menschlichem Vorhofgewebe vergleichbare Ergebnisse liefern.Eine Einfu ̈hrung in das Thema und die Aufgabenstellung liefert das erste Kapitel. Das zweite Kapitel hat die Elektrophysiologie von Einzelzellen und das Verhalten von Herzmuskelzellen im Zellverband zum Inhalt. Die verwendeten Modelle werden im dritten Kapitel vorgestellt. Es handelt sich dabei zum einen um ein Zellmodell, bei dem sich die elektrophysiologischen Eigen- schaften der Einzelzelle aus gekoppelten Differentialgleichungen ergeben. Zusammen mit einem der anschließend vorgestellten Erregungsausbreitungsmodelle ermo ̈glicht es eine Simulation der Erregung im Zellverband. Zum anderen wird der Zellula ̈re Automat eingefu ̈hrt, der ein regelbasiertes Modell darstellt. Da mit den ausgewa ̈hl- ten elektrophysiologischen Modellen kreisende Erregungen simuliert werden, finden zusa ̈tzlich verschiedene Modellvorstellungen fu ̈r die Auslo ̈sung kreisender Erregun- gen Beru ̈cksichtigung.Im vierten Kapitel werden die Ergebnisse dieser Arbeit beschrieben. Unter verschie- denen Voraussetzungen werden die Wesensmerkmale der beiden Modelle bei Ar- rhythmien in Form von kreisenden Erregungen untersucht und verglichen. Die zu- grunde liegende Anatomie erstreckt sich dabei in ein, zwei und drei Dimensionen. Das Verhalten der Modelle wird zuna ̈chst in homogenen Gewebeausschnitten betrachtet. Daru ̈ber hinaus wird der Einfluss von anatomischen Hindernissen untersucht, wie sie beispielsweise durch nicht erregbares Gewebe vorliegen. Die Simulationen wer- den zusa ̈tzlich bei einer verringerten Leitfa ̈higkeit des Gewebes durchgefu ̈hrt, um den Einfluss leitfa ̈higkeitsa ̈ndernder Pharmaka auf die Erregungsmuster zu ermitteln. Ei- ne abschließende Beurteilung und eine Zusammenfassung der Gemeinsamkeiten und Unterschiede im Verhalten der Modelle bei kreisenden Erregungen runden dieses Kapitel ab.
Student Theses (1)
D. L. Weiß. Charakterisierung der Ventrikelwand durch anatomische und elektrophysiologische Modellierung. Institute of Biomedical Engineering, Universität Karlsruhe (TH). Diplomarbeit. 2003
Die computergestu ̈tzte Simulation des Verhaltens von Herzmuskelzellen und der Ausbreitung der elektrischen Erregung im Herzgewebe hilft Technikern und Medizinern, Vorga ̈nge im Herzen zu analysieren und zu verstehen. Exakte Modelle ko ̈nnen die Realita ̈t sehr gut nachbilden. Daher ist die Entwicklung eines Modelles der menschlichen linksventrikula ̈ren Herzwand unter Beru ̈ck- sichtigung transmural heterogener Ionenstro ̈me und der anisotropen Faserorientierung Gegenstand dieser Diplomarbeit.Kapitel 1 liefert eine Einfu ̈hrung in das Thema und erla ̈utert die Aufgabenstellung. Das zweite Kapitel hat die Elektrophysiologie von einzelnen Zellen zum Inhalt. Im darauf folgenden Kapitel wird eine U ̈bersicht u ̈ber die Anatomie und Elektrophysiologie des menschlichen Herzens sowie u ̈ber das Verhalten kardialer Myozyten im Zellverband gegeben.Kapitel 4 stellt die bisher untersuchten elektrophysiologischen Unterschiede innerhalb der ventriku- la ̈ren Herzwand vor. Hauptaugenmerk liegt auf transmuralen Ionenstromgradienten, die in mensch- lichen Ventrikeln festgestellt werden konnten. Weiterhin wird auf Messungen der Faserorientierung im menschlichen Herzen eingegangen.Das Zellmodell, welches im Laufe der Arbeit an die Anforderungen angepasst wurde, wird im fu ̈nften Kapitel vorgestellt. Es handelt sich um ein Modell, bei dem sich die elektrophysiologischen Eigenschaften der Einzelzelle aus gekoppelten Differentialgleichungen ergeben. Eine Simulation der Erregung im Zellverband wird mit einem der anschließend dargestellten Modelle der elektrischen Erregungsausbreitung ermo ̈glicht.In Kapitel 6 wird auf die Entwicklung des heterogenen Ventrikelwandmodelles eingegangen. Die elektrophysiologischen Modellanpassungen finden zuna ̈chst auf einzelzellula ̈rer Ebene statt. Die Definitionen verschiedener Ionenstro ̈me werden so modifiziert, dass das Verhalten dieser Stro ̈me vom Modell realita ̈tsnah abgebildet wird. Als Qualita ̈tskriterium der Anpassung wird anschließend der Verlauf des Aktionspotentials mit den gefundenen Parametrisierungen herangezogen. Durch Untersuchung des Verhaltens im elektrotonisch gekoppelten Zellverband werden weitere Parameter des Ventrikelwandmodelles bestimmt. Die Einbringung der anisotropen Faserorientierung in das zugrunde liegende anatomische Modell bildet den Abschluss dieses Kapitels.Kapitel 7 gibt einen U ̈berblick, wie sich ein Modell der menschlichen ventrikula ̈ren Wand unter Be- ru ̈cksichtigung transmuraler Inhomogenita ̈ten der Ionenstro ̈me und einer anisotropen Orientierung der Herzmuskelzellen im Computer generieren la ̈sst. Die Ergebnisse, die sich mit dem entwickelten Herzwandmodell erzielen lassen, werden im achten Kapitel beschrieben. Mit dem Modell wird sowohl das Verhalten von Einzelzellen als auch das von Zellen in einem eindimensionalen und einem dreidimensionalen gekoppelten Verband untersucht. Weiterhin wird das Verhalten im physiologischen und in pathologischen Fa ̈llen betrachtet. Dabei zeigt sich, dass die erzielten Simulationsresultate zum gro ̈ßten Teil mit denen von Experimenten vergleichbar sind. Lediglich die Ursachen des LQT1-Syndroms mu ̈ssen neu u ̈berdacht werden, da sich die Messergebnisse mit den bisherigen Annahmen nicht erkla ̈ren lassen.