In this work an optimization-based method of modeling the cardiac activity is presented. The method employs a personalized anatomical 3D model of the patients thorax provided by the segmentation of MRI data as well as an electrophysiological model of the heart.Cellular automaton is used to model the propagation of depolarization and repolarization fronts through the myocardium. The form of action potential (AP) curves was previously derived from the coupled myocardium cell models developed by Noble, Priebe-Beuckelmann and ten Tusscher. The results provided by these three cell models are compared.A series of body surface potential maps (BSPMs) is calculated, the signals on the nodes representing the electrodes are recorded, providing thus a simulated multichannel ECG. A root-mean-square of the difference between simulated and measured ECGs is taken as a criterion for optimization of heart model parameters.The method provides a time-dependent distribution of transmembrane voltages within the heart muscle of a patient.
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.
In this study the performance of a planar array for magnetic induction tomography (MIT) was investigated and the results of measurements to determine the precision and sensitivity of the sensor were undertaken. A planar-array MIT system utilizing flux-linkage minimization for the primary field has been constructed and evaluated. The system comprises 4 printed excitation coils of 4 turns which were shielded, 8 surface-mount inductors of inductance 10 microH as sensor, mounted such that in principle no primary-field flux threads them, and a calibration coil to produce a strong primary field. The excitation current was multiplexed via relays to drive the excitation and reference coils. The noise values were similar in real and imaginary components in the lower frequencies and the factor to which the primary field could be reduced was greatest in the nearest coil. Methods for determining the true real and imaginary components and for flux-linkage minimization for the primary field for variations in channel sensitivities are described and the results of measurements of the system's noise and drift are given. A SNR of 47 dB was observed at 4 MHz when a 0.3 Sm-1 saline filled tank of dimensions 20 cmx20 cmx10 cm was placed centrally over the array. Finally, images were reconstructed from measurements of saline samples in a free space background, with the samples moved past the array in 21 1 cm steps to emulate mechanical scanning of the array. The image reconstruction characteristics of the planar array in conjunction with the reconstruction technique employed are discussed.
C. Stehning, P. Bornert, K. Nehrke, and O. Dössel. Free breathing 3D balanced FFE coronary magnetic resonance angiography with prolonged cardiac acquisition windows and intra-RR motion correction. In Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, vol. 53(3) , pp. 719-723, 2005
A shortcoming of today's coronary magnetic resonance angiography (MRA) is its low total scan efficiency (<5%), as only small well-defined fractions of the respiratory (50%) and cardiac (10%) cycle are used for data acquisition. These precautions are necessary to prevent blurring and artifacts related to respiratory and cardiac motion. Hence, scan times range from 4 to 9 min, which may not be tolerated by patients. To overcome this drawback, an ECG-triggered, navigator-gated free breathing radial 3D balanced FFE sequence with intra-RR motion correction is investigated in this study. Scan efficiency is increased by using a long cardiac acquisition window during the RR interval. This allows the acquisition of a number of independent k-space segments during each cardiac cycle. The intersegment motion is corrected using a self-guided epicardial fat tracking procedure in a postprocessing step. Finally, combining the motion-corrected segments forms a high-resolution image. Experiments on healthy volunteers are presented to show the basic feasibility of this approach.
BACKGROUND: There are no published data showing the three-dimensional sequence of repolarization and the associated potential fields in the ventricles. Knowledge of the sequence of repolarization has medical relevance because high spatial dispersion of recovery times and action potential durations favors cardiac arrhythmias. In this study we describe measured and simulated 3-D excitation and recovery sequences and activation-recovery intervals (ARIs) (measured) or action potential durations (APDs) (simulated) in the ventricular walls.METHODS: We recorded from 600 to 1400 unipolar electrograms from canine ventricular walls during atrial and ventricular pacing at 350-450 ms cycle length. Measured excitation and recovery times and ARIs were displayed as 2-D maps in transmural planes or 3-D maps in the volume explored, using specially developed software. Excitation and recovery sequences and APD distributions were also simulated in parallelepipedal slabs using anisotropic monodomain or bidomain models based on the Lou-Rudy version 1 model with homogeneous membrane properties.RESULTS: Simulations showed that in the presence of homogeneous membrane properties, the sequence of repolarization was similar but not identical to the excitation sequence. In a transmural plane perpendicular to epicardial fiber direction, both activation and recovery pathways starting from an epicardial pacing site returned toward the epicardium at a few cm distance from the pacing site. However, APDs were not constant, but had a dispersion of approximately 14 ms in the simulated domain. The maximum APD value was near the pacing site and two minima appeared along a line perpendicular to fiber directions, passing through the pacing site. Electrical measurements in dog ventricles showed that, for short cycle lengths, both excitation and recovery pathways, starting from an epicardial pacing site, returned toward the epicardium. For slower pacing rates, pathways of recovery departed from the pathway of excitation. Highest ARI values were observed near the pacing site in part of the experiments. In addition, maps of activation-recovery intervals showed mid-myocardial clusters with activation-recovery intervals that were slightly longer than ARIs closer to the epi- or endocardium, suggesting the presence of M cells in those areas. Transmural dispersion of measured ARIs was on the order of 20-25 ms. Potential distributions during recovery were less affected by myocardial anisotropy than were excitation potentials
In magnetic induction tomography reducing the influence of the primary excitation field on the sensors can provide a significant improvement in SNR and/or allow the operating frequency to be reduced. For the purposes of imaging, it would be valuable if all, or a useful subset, of the detection coils could be rendered insensitive to the primary field for any excitation coil activated. Suitable schemes which have been previously suggested include the use of axial gradiometers and coil-orientation methods (Bx sensors). This paper examines the relative performance of each method through computer simulation of the sensitivity profiles produced by a single sensor, and comparison of reconstructed images produced by sensor arrays. A finite-difference model was used to determine the sensitivity profiles obtained with each type of sensor arrangement. The modelled volume was a cuboid of dimensions 50 cmx50 cmx12 cm with a uniform conductivity of 1 S m-1. The excitation coils were of 5 cm diameter and the detection coils of 5 mm diameter. The Bx sensors provided greater sensitivity than the axial gradiometers at all depths, other than on the surface layer of the volume. Images produced using a single-planar array were found to contain distortion which was reduced by the addition of a second array.
R. Winkelmann, P. Bornert, and O. Dössel. Ghost artifact removal using a parallel imaging approach. In Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, vol. 54(4) , pp. 1002-1009, 2005
Parallel imaging techniques, which use several receive coils simultaneously, have been shown to enable a significant scan time reduction by subsampling k-space. Nevertheless, the data acquired with multiple coils in parallel exhibit some redundancy if the number of receive coils exceeds the subsampling factor. This redundancy leads to an overdetermination of the reconstruction problem, which is generally used to optimize the signal-to-noise ratio (SNR). However, it can yield further information about the quality of the reconstructed image, and can thus be used to identify and correct image artifacts. While some known approaches try to solve this problem in k-space, this study addresses it in the spatial domain and uses a modified SENSE reconstruction to reduce or completely remove ghost-type artifacts arising from processes such as motion or flow during data acquisition. Phantom and in vivo studies show significant improvements in image quality after correction, and serve as a basis for the discussion of the performance and limitations of this new approach.
Parallel imaging techniques, which in principle represent procedures of unfolding a reduced dataset, are well known and well established in MR imaging. This paper presents a further application of one particular reconstruction method, the SENSE algorithm, considered from a different point of view to remove potential foldover in conventional images acquired with multiple receive coils. Based on the coil sensitivity information, a body coverage map in the excited plane is calculated. This is used together with the measured raw data in a SENSE-type reconstruction to optimize the signal-to-noise ratio (SNR) as well as to remove foldover reliably by unfolding the image to a larger field of view. The reconstruction is performed automatically, without any user interaction, and does not affect data acquisition. Based on phantom and in vivo studies, which retain high image quality after the removal, the potential and limits of this approach are discussed, also taking into account future scanner hardware that will support a large number of parallel receiver channels.
The steady-state free precessing (SSFP) sequences, widely used in MRI today, acquire data only during a short fraction of the repetition time (TR). Thus, they exhibit a poor scan efficiency. In this paper, a novel approach to extending the acquisition window for a given TR without considerably modifying the basic sequence is explored for radial SSFP sequences. The additional data are primarily employed to increase the signal-to-noise ratio, rather than to improve the temporal resolution of the imaging. The approach is analyzed regarding its effect on the image SNR (signal to noise ratio) and the reconstruction algorithm. Results are presented for phantom experiments and cardiac functions studies. The gain in SNR is most notable in rapid imaging, since SNR enhancement for a constant repetition time may be used to compensate for the increase in noise resulting from angular undersampling.
K. Chaisaowong, F. B. Sachse, and G. Seemann. Modeling of human cardiac force development: I. Adjustment of an electrophysiological model to approach specimen-specific properties of myocytes. In Proc. 2nd ECTI Annual Conference, pp. 811-814, 2005
O. Dössel, W. Bauer, D. Farina, C. Kaltwasser, and O. Skipa. Imaging of bioelectric sources in the heart using a cellular automaton model. In Conference Proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference, vol. 2, pp. 1067-1070, 2005
The approach to solve the inverse problem of electrocardiography presented here is using a computer model of the individual heart of a patient. It is based on a 3D-MRI dataset. Electrophysiologically important tissue classes are incorporated using rules. Source distributions inside the heart are simulated using a cellular automaton. Finite Element Method is used to calculate the corresponding body surface potential map. Characteristic parameters like duration and amplitude of transmembrane potential or velocity of propagation are optimized for selected tissue classes or regions in the heart so that simulated data fit to the measured data. This way the source distribution and its time course of an individual patient can be reconstructed.
Mathematical models of biophysical phenomena have proven useful in the reconstruction of experimental data and prediction of biological behavior. By quantifying the sensitivity of a model to certain parameters, one can place an appropriate amount of emphasis in the accuracy with which those parameters are determined. In addition, investigation of stochastic parameters can lead to a greater understanding of the behavior captured by the model. This can lead to possible model reductions, or point out shortcomings to be addressed. We present polynomial chaos as a computationally efficient alternative to Monte Carlo for assessing the impact of stochastically distributed parameters on the model predictions of several cardiac electrophysiological models.
After myocardial infarction, ischemic lesions within the myocardium can be the origin of malignant arrhythmias by the mechanism of re-entry. Surface-ECG and MR-imaging data can be used to detect and classify such re- gions in a non-invasive way. For this purpose a model of the electric conductivity of the tissues within the pa- tients chest and a model of cardiac sources must be constructed out of MR-imaging data. Employing finite- element algorithms the inverse problem of electrocardiology can then be solved, leading to the reconstructionof electrical sources within the myocardium during the process of depolarisation and repolarisation.
A. Khawaja, and O. Dössel. A PCA-Based Technique for QRS Complex Estimation. In Proc. Computers in Cardiology, vol. 32, pp. 747-750, 2005
In this paper, a new method for QRS complex prediction is presented. It is based on Principal Components Analysis (PCA) and polynomial fitting techniques. QRS complexes were extracted from multi-lead ECG signals and were aligned very perfectly. The covariance matrix was calculated from the QRS complex data matrix of many heartbeats. Afterwards, the corresponding eigenvectors and eigenvalues were computed and the reconstruction parameters vectors were derived by expansion of every beat in terms of the first eigenvectors. Performing the first order poly-fit method on the elements of the reconstruction parameter vectors yielded certain linear functions. Thereafter, the following QRS complexes were estimated by calculating the corresponding reconstruction parameter vectors derived from these functions. The similarity, absolute error and RMS error between the original and predicted QRS complexes were measured
Detecting peaks and boundaries of ECG characteristic waves supplies fundamental features for extracting clinically useful information. In this paper, an accurate threshold-independent multi-lead ECG delineation system is presented. Detection of QRS complexes, P and T waves is based on wavelet transform using Haar function as prototype wavelet and analyzing the first scale details coefficients.The delineator is performed on certain selected channels. Afterwards, a method, using a special histogram-based estimation, yields the exact positions of the significant points in all multi-channel ECG signals. The algorithm is applied on MIT-BIH Arrhythmia database signals and on multi-channel ECG signals measured at our institute.The single-channel delineation method was tested on MIT-BIH Arrythmia database signals. Sensitivity and positive predictivity were greater than 99.84% and 99.89% respetively for more than 15,990 beats. Furthermore, an overall mean error of less than two sampling intervals (1 ms) is obtained comparing the manual and the automatic method, whereas the standard deviation does not exceed three sampling intervals.
A. Khawaja, S. Sanyal, and O. Dössel. A wavelet-based technique for baseline wander correction in ECG and multi-channel ECG. In IFMBE Proceedings, vol. 9, pp. 291-292, 2005
In this paper, a new offline method for automatic baseline drift correction in Electrocardiogram is presented. It is based on Discrete Wavelet Transform (DWT) and analyzing high scale Approximation Coefficients (AC). A set of 650 noisy ECG signals was created by mixing different artificially generated noise-free ECGs and baseline wanders. By applying different mother Wavelets on each noisy signal, twelve stage DWT decomposition was carried out and twelve filtered ECGs were reconstructed by canceling the highest level AC at each stage. The similarities between initially generated baseline and canceled AC, as well as between the corresponding noise-free and reconstructed ECGs were examined every time by means of Correlation technique. The results from all 650 signals were considered in order to find the suitable Wavelet and AC level. The highest correlations, better than 99.9% for baseline and 99.99% for filtered ECG, were found with the ninth scale approximation coefficients when using Daubechies11 or Symlet12 as prototype wavelet. The algorithm was applied on various MIT-BIH and Multi-channel ECG signals. Furthermore, the baseline elimination results were considered to be very promising.
J. Qin, M. Reumann, S. H. Osswald, and O. Dössel. Developing Algorithms for The Optimization of Overpacing Strategies in Patients with Atrial Fibrillation. In Biomedizinische Technik, vol. 50(S1) , pp. 1426-1427, 2005
Atrial Fibrillation (AF) is the most common cardiac arrhythmia with overall prevalence of almost 1%. Treatment options range from pharmacological to surgical options. While ablation strategies are the most common thera- pies, it has been testified that overdrive stimulation can prevent AF successfully. The presented work suggests an approach to simulate the excitation propagation with various overdrive pacing frequencies based on a detailed cell model in a simplified anatomical structure. Through simulations, a relationship between the overdrive pac- ing position and its frequency with respect to the onset of AF was shown. The method applied in this work can be used to further develop optimization strategies for overdrive pacing. In the long run, the application trans- ferred to individual patient data might be used to increase the success rate of overdrive pacing in terminating atrial fibrillation.
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
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
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
I. M. Graf. Electrical stimulation of the human left ventricle. Universität Karlsruhe (TH). Dissertation. 2005
D. U. J. Keller. Investigating Options for a Low Cost and High Performance Doppler OCT. University of Western Australia. Dissertation. 2005
R. Schnell. Druck-Volumen Beziehung im menschlichen Herzen. Implementierung in ein mechanisches Herzmodell. Universität Karlsruhe (TH), Institut für Biomedizinische Technik. Dissertation. 2005
G. Seemann. Modeling of electrophysiology and tension development in the human heart. Institut für Biomedizinische Technik. Dissertation. 2005
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 Theses (5)
K. Albrecht. Computerunterstützte Evaluation und Optimierung der biventrikulären Schrittmacher-Therapie bei Patienten mit Herzinsuffizienz. Universität Karlsruhe (TH), Institut für Biomedizinische Technik. Diplomarbeit. 2005
J. Buchta. Elektrophysiologische Auswirkungen von genetischen Mutationen im menschlichen Herzen. Institute of Biomedical Engineering, Universität Karlsruhe (TH). Diplomarbeit. 2005
Das Ziel dieser Arbeit war es, die elektrophysiologischen Auswirkungen genetischer Mu- tationen (siehe Abschnitt 2.2.4) zu untersuchen. Anstatt auf der klassischen Hodgkin- Huxley-Formulierung basierende Modelle (siehe Kapitel 3) wurden dazu aktuelle Markov- Modelle verwendet (siehe Kapitel 4), deren Aufbau sich an die Konformationszusta ̈nde der Kanalproteine anpasst.Im Konkreten wurden dazu zwei Mutationen (E544A und E544K) in einem fu ̈r die Aktivie- rung und Deaktivierung verantwortlichen Bereich des Kanalproteins HERG kodierenden Gens betrachtet (siehe Abschnitt 5.1). HERG ist fu ̈r das Gating der schnellen Komponente des verzo ̈gert gleichrichtenden Kaliumstroms IKr verantwortlich, der einen entscheidenden Einfluss auf die Repolarisierungsphase wa ̈hrend des Verlaufs eines Aktionspotenzials hat (siehe Abschnitt 2.4.2). Die Mutation E544A, eine Substitution der Glutaminsa ̈ure durch Alanin, beschleunigt sowohl die Aktivierung als auch die Deaktivierung des Kanals. Die Mutation E544K, bei welcher Lysin anstatt Glutaminsa ̈ure eingebaut wird, verlangsamt dagegen die Aktivierung, wa ̈hrend die Deaktivierung schneller als im physiologischen Fall verla ̈uft.Um diese vera ̈nderte Kinetik zu simulieren, wurden zehn Parameter der von Mazhari et al. vorgestellten Markov-Kette des IKr-Kanals (siehe Abschnitt 4.5.2) angepasst. Die Ergebnisse, die mit den urspru ̈nglichen Parametern des Modells erzielt wurden (siehe Ka- pitel 6), zeigten starke Abweichungen zu den Messergebnissen an gesunden Zellen. Somit war es notwendig, auch die Parameter fu ̈r den Wildtyp neu zu bestimmen. Dabei muss auch noch einmal hervorgehoben werden, dass in allen Fa ̈llen lediglich Gating-Parameter vari- iert, aber die Dichte der Kana ̈le und damit die maximale Leitfa ̈higkeit konstant gehalten wurden. U ̈ber die Messung einzelner Kana ̈le hinausgehend ist es mithilfe des Zellmodells nun mo ̈glich, die Auswirkungen der gea ̈nderten Parameter auf das Aktionspotenzial und IKr wa ̈hrend des Aktionspotenzials darzustellen. Wa ̈hrend die gea ̈nderte Kinetik im Strom- verlauf ersichtlich wurde, wirkten sich die Mutationen allerdings auf das Aktionspotenzial nur marginal aus. Es ist daher nicht davon auszugehen, dass diese Mutationen symptomatische Auswirkungen beim Menschen hervorrufen.Um einen Parametersatz zu erlangen, der Simulationsergebnisse so nahe wie mo ̈glich an den Messergebnissen liefert, wurde die Abha ̈ngigkeit der Abweichung dieser beiden Gro ̈ßen funktionell dargestellt. Dabei wurde beachtet, dass die Topographie des Parameterraums stark von der Gewichtung der unterschiedlichen Beitra ̈ge des zu minimierenden Gesamt- fehlers abha ̈ngt. Das gewa ̈hlte Simplex-Verfahren (siehe Abschnitt 5.2) eignet sich fu ̈r die Minimierung dieses Gesamtfehlers v. a. deshalb, da es keine Gradienten beno ̈tigt, deren Be- rechnung sehr zeitintensiv gewesen wa ̈re. Das Verfahren stellte sich als erfolgreich heraus, um in einer sehr großen aber dennoch durch Wahl der Startwerte begrenzten Umge- bung ein (relatives) Minimum zu finden. Eine Verbesserung zur Auffindung des globalen Minimums ko ̈nnte sich ein vorheriges Abtasten des Parameterraums mit einem so ge- nannten Simulated-Annealing-Algorithmus (Simulierte Abku ̈hlung) als hilfreich heraus stellen. Dieses Verfahren erlaubt im Gegensatz zum Simplex-Algorithmus ein Verlassen eines lokalen Minimums.Aufbauend auf diese Arbeit ko ̈nnten weitere Mutationen untersucht werden, die neben einer vera ̈nderten Kinetik fu ̈r die Aktivierung und Deaktivierung auch Auswirkungen auf die Inaktivierung und den dazu geho ̈rigen Umkehrprozess (recovery from inactivation) haben. Des Weiteren wa ̈ren Untersuchungen anderer Markov-Modelle von Interesse, wie sie in u.a. in dieser Arbeit vorgestellt wurden. Vor allem das Modell von Irvine et al. fu ̈r den Na+-Strom ko ̈nnte an Mutationen angepasst werden, die fu ̈r das LQT3- oder Brugada- Syndrom (siehe Abschnitt 2.6) relevant sind. Jedoch stellen komplexe Modelle wie dieses aufgrund einer großen Anzahl gekoppelter Differenzialgleichungen, kleiner Zeitschritte fu ̈r die Integration und dadurch bedingten langen Rechenzeiten eine Herausforderung dar.
Y. Cao. The Excitation Thresholds for Healthy and Ischemic Human Left Ventricle. Universität Karlsruhe (TH), Institut für Biomedizinische Technik. Diplomarbeit. 2005
H. Chen. Simulated Electromechanical Heterogeneity in Human Left Ventricle. Institute of Biomedical Engineering, Universität Karlsruhe (TH). Diplomarbeit. 2005
After adjusting the parameters of the conductance or properties of late sodium current, transient outward current, slow component of delayed rectifier potassium current, sodium calcium exchange current, as well as the intracellular calcium release and uptake current, the heterogeneous action potential, calcium transient and tension development were re- constructed in Endo, M and Epi cell in human left ventricle. The morphology, amplitude and time courses showed good agreement with the experimental recordings. This modified model suggested that the different APs of the three types of myocytes are based on the different ion current density or ion channel properties. The simulation of the calcium tran- sient predicted that the heterogeneous calcium activities are based both on the different shape of APs and calcium related gene expressions. The mechanical function of Epi, M and Endo cells were described by a tension development model and the time to peak in the tension development curves could explain how the inhomogeneous electrophysiology leads to a more homogenized contraction in left ventricle.Limitations in the Modified ModelTheir are some limitations in the modified model, but the principle behavior of the model is in good agreement with the physiological measurement. Some of the limitations are inherited from the Iyer et al. model, and some are from the modification for the hetero- geneity.Limitation in Experimental DataTo formulate the ion currents in cardiac myocytes, the concrete experimental data must be known, like the current density at different clamped voltages, its frequency dependence and other properties. In cell models for human left ventricular myocytes, though, all the research tried to model the electrophysiology based on more recently experimental data in human ventricle, there were still some currents based on animal experiments, because no human data was available at the moment. For example, in the Iyer et al. model, the current-voltage relations of current INaK was adopted from a formulation given for guinea pig. For the same reason, in this simulation for electromechanical heterogeneity, some currents were adapted according to the canine ventricular experiments, like the adaptation of the INaCa scaling factor in midmyocardial cell, the current density through RyR channels in both Epi and M cells and so on. More data on human left ventricle are needed to accomplish the cell model.Many of the ion currents in the Iyer et al. model were based on voltage clamp experiments in which cloned human cardiac ion channels are heterologously expressed. Therefore, till now there is still no obvious evidence to prove that the cloned ion channels had exactly the same properties as the nature ones . Some modification in this work was also based on the gene expression experiment of the ion channels. More proofs of the relation between existing channel proteins and those who really function in cellular membrane were required to support such modification.Weak Influence of IKs on APDFig. 5.10 showed that IKs had a little influence on action potential duration, that the APD changed only about 24 ms when the total current was blocked. Bosch et al. reported a prolongation of about 140 ms in human ventricular cells when total IKs was blocked , which is much longer than the simulation. In the studies of the heterogeneity in ventricle, many experiments have proved that IKs was a very important component of ion currents, which prolonged APD in M cells.The low IKs current density or the influences of other ion currents occurred in repolari- zation might cause smaller effects of IKs on APD. Since the current density of IKr was set to match the experiment of Magyar et al., the conductance of IKs was doubled in the simulation to fit the ratio of IKs : IKr in the same experiment . Even though, the difference of APD in different position of the ventricle was still not as noticeable as in experiments.After the modification of late INa, IK1 and Iup in calcium handling, the APD changed more significantly. So APD in the Iyer et al. model might depend more on such currents and intracellular calcium concentration than IKs.Controversial Influence of INaCa on APDThe heterogeneous distribution of INaCa was firstly proposed by Zygmunt et al. in 2000, who have measured the whole cell current of INaCa in Endo, M and Epi cells in canine left ventricle . INaCa can be triggered both by release of calcium from SR or by rapid removal of external sodium. In their experiments, INaCa was largest in M cell and smallest in Endo cell under both conditions. As conclusion, they have drawn that larger INaCa might contribute to the prolongation of APD in M cell, though weaker IKs and larger late INa may play a more important role in this prolongation. The modification of INaCa in the Priebe-Beuckelmann model confirmed this determination and presented that larger INaCa prolonged the APD . In our simulation, largest INaCa in M cell and smallest INaCa in Endo cell were obtained by adjusting the conductance of INaCa, but the influence of the current to action potential duration was controversial compared to the report of Zygmunt et al.. Fig. 5.13 shows the INaCa current and the action potential of three types of cells after modifying the conductance of INaCa. M cell presents a larger INaCa but shorter APD. In further, more experimental data is needed to determine the influences of INaCa on APD accurately.Insignificant Difference of Time to Peak in Calcium TransientCompared with the experiments of Cordeiro et al., there are still some disagreements in the calcium activities and tension development in the simulation. The time to peak of calcium transients is shortest in Endo cell after the modification, but the experimental data shows that it is shortest in subepicardium. The relation of time to peak, as well as the duration of tension development in Endo and M cells is reversed as in the experiment.Lower Computational EfficiencyMost ion currents in the Iyer et al. model were described with Markov chain models, which sustain more variables and smaller calculation steps, compared with other models. In the Iyer et al. model there are 67 variables, whereas the Priebe-Beuckelmann model and the ten Tusscher et al. model consist of only 15 and 16 variables, respectively. This leads to a higher model complexity, namely lower computational efficiency, especially when tissue simulations were accomplished.PerspectivesAll the simulations till now were based on the single cell model. The simulation of the whole ventricular wall can be applied to reconstruct the cellular physiology in a tissue, the excitation propagation and contraction in the ventricular wall. With the simulation in the intact ventricular wall, a more realistic electrophysiology of the myocytes in different layers can be also obtained, because for the single cell model, the cells are always stimu- lated by a preset depolarizing current, while in nature heart they are mostly stimulated by the neighboring cells.The modified Iyer et al. model has directed the focus on the electromechanical hetero- geneity of human left ventricle and succeeded to reconstructed the APs, calcium transients and tension development of Endo, M and Epi cells. It can help to reconstruct the virtual heart with precise properties in different cell types of left ventricle. More research in hetero- geneity should be carried out on the basis of the results. Further more, it helps to study the basis and mechanisms of cardiac diseases like ventricular tachycardia.
Y. Jiang. Implementation of a stochastic regularization method to solve the inverse problem of electrocardiography. Institut für Biomedizinische Technik, Universität Karlsruhe (TH). Masterarbeit. 2005