Fibroblasts are abundant in cardiac tissue. Experimental studies suggested that fibroblasts are electrically coupled to myocytes and this coupling can impact cardiac electrophysiology. In this work, we present a novel approach for mathematical modeling of electrical conduction in cardiac tissue composed of myocytes, fibroblasts, and the extracellular space. The model is an extension of established cardiac bidomain models, which include a description of intra-myocyte and extracellular conductivities, currents and potentials in addition to transmembrane voltages of myocytes. Our extension added a description of fibroblasts, which are electrically coupled with each other and with myocytes. We applied the extended model in exemplary computational simulations of plane waves and conduction in a thin tissue slice assuming an isotropic conductivity of the intra-fibroblast domain. In simulations of plane waves, increased myocyte-fibroblast coupling and fibroblast-myocyte ratio reduced peak voltage and maximal upstroke velocity of myocytes as well as amplitudes and maximal downstroke velocity of extracellular potentials. Simulations with the thin tissue slice showed that inter-fibroblast coupling affected rather transversal than longitudinal conduction velocity. Our results suggest that fibroblast coupling becomes relevant for small intra-myocyte and/or large intra-fibroblast conductivity. In summary, the study demonstrated the feasibility of the extended bidomain model and supports the hypothesis that fibroblasts contribute to cardiac electrophysiology in various manners.
F. B. Sachse, K. Glänzel, and G. Seemann. Modeling of protein interactions involved in cardiac tension development. In Int. J. Bifurcation and Chaos, vol. 13(12) , pp. 3561-3578, 2003
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
Mathematical models of cardiac anatomy and physics provide information, which help to understand structure and behavior of the heart. Miscellaneous cardiac phenomena can only be adequately described by combination of models representing different aspects or levels of detail. Coupling of these models necessitates the definition of appropriate interfaces. Adequateness and efficiency of interfaces is crucial for efficient application of the combined models.In this work an integrated model is presented consisting of several models interconnected by interfaces. The integrated model allows the reconstruction of macroscopic electro-mechanical processes in the heart. The model comprises a three-dimensional are of left ventricular anatomy represented as truncated ellipsoid. The integrated model includes electrophysiological, tension development and elastomechanical models of myocardium at levels of single cell, proteins, and tissue patches, respectively.The model is exemplified by simulations of extracorporated left ventricle of small mammals. These simulations yield temporal distributions of electrophysiological parameters as well as descriptions of electrical propagation and mechanical deformation. The simulations show characteristic macroscopic ventricular function resulting from the interplay between cellular electrophysiology, electrical excitation propagation, tension development, and mechanical deformation.
Computer aided simulations of the heart provide knowledge for cardiologic diagnosis and therapy. A model of the myocardium is presented which allows the reconstruction of electrical and mechanical processes with inclusion of feedback mechanisms. The model combines detailed models of cellular electrophysiology and force development with models of the electrical current flow and the mechanical behavior of the myocardium. Results of simulations show the connection between the electrical excitation process and the following mechanical deformation in a three dimensional, anisotropic area of the myocardium. Keywords: Mechano-Electrical Feedback, Electro-Mechanical Feedback, Cellular Models, Electrophysiology, Excitation-Propagation
A model of the electromechanical behavior of a myocardial region is presented. The model combines an electrophysiological, a force development and an excitation propagation model. All of these models incorporate the effects of deformation of the myocardium. An extension of the traditional bidomain model for excitation propagation is proposed. The extension describes the stretch dependency of the conductivity tensor of the intra- and extracellular space and is constructed outgoing from physically motivated assumptions, which simplify the behavior of the conductivity tensor. The extension makes usage of the deformation gradient tensor, which is a foundation in the theory of continuums mechanics. The performed simulations illustrate some effects of myocardial electromechanical behavior.
Knowledge of the distribution of electrical fields in the human body is of importance for scientists, engineers and physicians. This paper shows one way to achieve this knowledge by numerical calculation based on macroscopic models of the human body. An anatomical model is created by preprocessing, segmentation and classification of the digital images within the Visible Man data set. Conductivity models are derived, which describe the distribution of electrical conductivity in the human body. A conductivity model is applied to solve an exemplary forward problem in electrophysiology, which consist of the calculation of the electrical field distribution arising from cardiac sources. The cardiac sources are obtained by a model of the excitation process within the heart. The calculation of electrical fields is carried out numerically by employing the finite difference method.
F. B. Sachse, M. Wolf, C. D. Werner, and K. Meyer-Waarden. Extension of anatomical models of the human body: three dimensional interpolation of muscle fiber orientation based on restrictions. In Journal of Computing and Information Technology, vol. 6(1) , pp. 95-101, 1998
This paper is the extension of a detailed anatomical model (Sachse et al., 1996a) (Sachse et al., 1996b) with the three-dimensional orientation of skeletal muscle fibres (Figure 1). The orientation is interpolated basing on two sets with restrictions of different types. The first set consists of points for which the orientation is known. The second set consists of points with an assigned normal of orientation. These sets are created by detection with manual or automatic methods using techniques of digital image processing. The interpolation works iteratively employing the averaging orientations in the 6-neighbourhood. The average of neighbouring orientations is calculated by determination of their principal axis.
The cardiac muscarinic receptor (M2R) regulates heart rate, in part, by modulating the acetylcholine (ACh) activated K+ current IK,ACh through dissociation of G-proteins, that in turn activate KACh channels. Recently, M2Rs were noted to exhibit intrinsic voltage sensitivity, i.e. their affinity for ligands varies in a voltage dependent manner. The voltage sensitivity of M2R implies that the affinity for ACh (and thus the ACh effect) varies throughout the time course of a cardiac electrical cycle. The aim of this study was to investigate the contribution of M2R voltage sensitivity to the rate and shape of the human sinus node action potentials in physiological and pathophysiological conditions. We developed a Markovian model of the IK,ACh modulation by voltage and integrated it into a computational model of human sinus node. We performed simulations with the integrated model varying ACh concentration and voltage sensitivity. Low ACh exerted a larger effect on IK,ACh at hyperpolarized versus depolarized membrane voltages. This led to a slowing of the pacemaker rate due to an attenuated slope of phase 4 depolarization with only marginal effect on action potential duration and amplitude. We also simulated the theoretical effects of genetic variants that alter the voltage sensitivity of M2R. Modest negative shifts in voltage sensitivity, predicted to increase the affinity of the receptor for ACh, slowed the rate of phase 4 depolarization and slowed heart rate, while modest positive shifts increased heart rate. These simulations support our hypothesis that altered M2R voltage sensitivity contributes to disease and provide a novel mechanistic foundation to study clinical disorders such as atrial fibrillation and inappropriate sinus tachycardia.
Computational modeling is an important tool to advance our knowledge on cardiac diseases and their underlying mechanisms. Computational models of conduction in cardiac tissues require identification of parameters. Our knowledge on these parameters is limited, especially for diseased tissues. Here, we assessed and quantified parameters for computational modeling of conduction in cardiac tissues. We used a rabbit model of myocardial infarction (MI) and an imaging-based approach to derive the parameters. Left ventricular tissue samples were obtained from fixed control hearts (animals: 5) and infarcted hearts (animals: 6) within 200 μm (region 1), 250-750 μm (region 2) and 1,000-1,250 μm (region 3) of the MI border. We assessed extracellular space, fibroblasts, smooth muscle cells, nuclei and gap junctions by a multi-label staining protocol. With confocal microscopy we acquired three-dimensional (3D) image stacks with a voxel size of 200 × 200 × 200 nm. Image segmentation yielded 3D reconstructions of tissue microstructure, which were used to numerically derive extracellular conductivity tensors. Volume fractions of myocyte, extracellular, interlaminar cleft, vessel and fibroblast domains in control were (in %) 65.03 ± 3.60, 24.68 ± 3.05, 3.95 ± 4.84, 7.71 ± 2.15, and 2.48 ± 1.11, respectively. Volume fractions in regions 1 and 2 were different for myocyte, myofibroblast, vessel, and extracellular domains. Fibrosis, defined as increase in fibrotic tissue constituents, was (in %) 21.21 ± 1.73, 16.90 ± 9.86, and 3.58 ± 8.64 in MI regions 1, 2, and 3, respectively. For control tissues, image-based computation of longitudinal, transverse and normal extracellular conductivity yielded (in S/m) 0.36 ± 0.11, 0.17 ± 0.07, and 0.1 ± 0.06, respectively. Conductivities were markedly increased in regions 1 (+75, +171, and +100%), 2 (+53, +165, and +80%), and 3 (+42, +141, and +60%). Volume fractions of the extracellular space including interlaminar clefts strongly correlated with conductivities in control and MI hearts. Our study provides novel quantitative data for computational modeling of conduction in normal and MI hearts. Notably, our study introduces comprehensive statistical information on tissue composition and extracellular conductivities on a microscopic scale in the MI border zone. We suggest that the presented data fill a significant gap in modeling parameters and extend our foundation for computational modeling of cardiac conduction.
T. Seidel, J.-C. Edelmann, and F. B. Sachse. Analyzing Remodeling of Cardiac Tissue: A Comprehensive Approach Based on Confocal Microscopy and 3D Reconstructions. In Annals of Biomedical Engineering, vol. 44(5) , pp. 1436-1448, 2016
Microstructural characterization of cardiac tissue and its remodeling in disease is a crucial step in many basic research projects. We present a comprehensive approach for three-dimensional characterization of cardiac tissue at the submicrometer scale. We developed a compression-free mounting method as well as labeling and imaging protocols that facilitate acquisition of three-dimensional image stacks with scanning confocal microscopy. We evaluated the approach with normal and infarcted ventricular tissue. We used the acquired image stacks for segmentation, quantitative analysis and visualization of important tissue components. In contrast to conventional mounting, compression-free mounting preserved cell shapes, capillary lumens and extracellular laminas. Furthermore, the new approach and imaging protocols resulted in high signal-to-noise ratios at depths up to 60 microm. This allowed extensive analyzes revealing major differences in volume fractions and distribution of cardiomyocytes, blood vessels, fibroblasts, myofibroblasts and extracellular space in control vs. infarct border zone. Our results show that the developed approach yields comprehensive data on microstructure of cardiac tissue and its remodeling in disease. In contrast to other approaches, it allows quantitative assessment of all major tissue components. Furthermore, we suggest that the approach will provide important data for physiological models of cardiac tissue at the submicrometer scale.
Electrophysiological modeling of cardiac tissue is commonly based on functional and structural properties measured in experiments. Our knowledge of these properties is incomplete, in particular their remodeling in disease. Here, we introduce a methodology for quantitative tissue characterization based on fluorescent labeling, three-dimensional scanning confocal microscopy, image processing and reconstruction of tissue micro-structure at sub-micrometer resolution. We applied this methodology to normal rabbit ventricular tissue and tissue from hearts with myocardial infarction. Our analysis revealed that the volume fraction of fibroblasts increased from 4.830.42% (meanstandard deviation) in normal tissue up to 6.510.38% in myocardium from infarcted hearts. The myocyte volume fraction decreased from 76.209.89% in normal to 73.488.02% adjacent to the infarct. Numerical field calculations on three-dimensional reconstructions of the extracellular space yielded an extracellular longitudinal conductivity of 0.2640.082 S/m with an anisotropy ratio of 2.0951.11 in normal tissue. Adjacent to the infarct, the longitudinal conductivity increased up to 0.4000.051 S/m, but the anisotropy ratio decreased to 1.2950.09. Our study indicates an increased density of gap junctions proximal to both fibroblasts and myocytes in infarcted versus normal tissue, supporting previous hypotheses of electrical coupling of fibroblasts and myocytes in infarcted hearts. We suggest that the presented methodology provides an important contribution to modeling normal and diseased tissue. Applications of the methodology include the clinical characterization of disease-associated remodeling. 1.
Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.
In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field.
Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.
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).
D. L. Weiss, M. Ifland, F. B. Sachse, G. Seemann, and O. Dössel. Modeling of cardiac ischemia in human myocytes and tissue including spatiotemporal electrophysiological variations / Modellierung kardialer Ischämie in menschlichen Myozyten und Gewebe. In Biomedizinische Technik/Biomedical Engineering, vol. 54(3) , pp. 107-125, 2009
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.
Niflumic acid [2-((3-(trifluoromethyl)phenyl)amino)-3-pyridinecarboxylic acid, NFA] is a nonsteroidal anti-inflammatory drug that also blocks or modulates the gating of a wide spectrum of ion channels. Here we investigated the mechanism of channel activation by NFA on ether-a-go-go-related gene (ERG) K(+) channel subtypes expressed in Xenopus laevis oocytes using two-electrode voltage-clamp techniques. NFA acted from the extracellular side of the membrane to differentially enhance ERG channel currents independent of channel state. At 1 mM, NFA shifted the half-point for activation by -6, -18, and -11 mV for ERG1, ERG2, and ERG3 channels, respectively. The half-point for channel inactivation was shifted by +5 to +9 mV by NFA. The structural basis for the ERG subtype-specific response to NFA was explored with chimeric channels and site-directed mutagenesis. The molecular determinants of enhanced sensitivity of ERG2 channels to NFA were isolated to an Arg and a Thr triplet in the extracellular S3-S4 linker.
Velocity of electrical conduction in cardiac tissue is a function of mechanical strain. Although strain-modulated velocity is a well established finding in experimental cardiology, its underlying mechanisms are not well understood. In this work, we summarized potential factors contributing to strain-velocity relationships and reviewed related experimental and computational studies. We presented results from our experimental studies on rabbit papillary muscle, which supported a biphasic relationship of strain and velocity under uni-axial straining conditions. In the low strain range, the strain-velocity relationship was positive. Conduction velocity peaked with 0.59 m/s at 100% strain corresponding to maximal force development. In the high strain range, the relationship was negative. Conduction was reversibly blocked at 118+/-1.8% strain. Reversible block occurred also in the presence of streptomycin. Furthermore, our studies revealed a moderate hysteresis of conduction velocity, which was reduced by streptomycin. We reconstructed several features of the strain-velocity relationship in a computational study with a myocyte strand. The modeling included strain-modulation of intracellular conductivity and stretch-activated cation non-selective ion channels. The computational study supported our hypotheses, that the positive strain-velocity relationship at low strain is caused by strain-modulation of intracellular conductivity and the negative relationship at high strain results from activity of stretch-activated channels. Conduction block was not reconstructed in our computational studies. We concluded this work by sketching a hypothesis for strain-modulation of conduction and conduction block in papillary muscle. We suggest that this hypothesis can also explain uni-axially measured strain-conduction velocity relationships in other types of cardiac tissue, but apparently necessitates adjustments to reconstruct pressure or volume related changes of velocity in atria and ventricles
With scanning confocal microscopy we obtained three-dimensional (3D) reconstructions of the transverse tubular system (t-system) of rabbit ventricular cells. We accomplished this by labeling the t-system with dextran linked to fluorescein or, alternatively, wheat-germ agglutinin conjugated to an Alexa fluor dye. Image processing and visualization techniques allowed us to reconstruct the t-system in three dimensions. In a myocyte lying flat on a coverslip, t-tubules typically progressed from its upper and lower surfaces. 3D reconstructions of the t-tubules also suggested that some of them progressed from the sides of the cell. The analysis of single t-tubules revealed novel morphological features. The average diameter of single t-tubules from six cells was estimated to 448172nm (mean SD, number of t-tubules 348, number of cross sections 5323). From reconstructions we were able to identify constrictions occurring every 1.871.09m along the principal axis of the tubule. The cross-sectional area of these constrictions was reduced to an average of 57.727.5% (number of constrictions 170) of the adjacent local maximal areas. Principal component analysis revealed flattening of t-tubular cross sections, confirming findings that we obtained from electron micrographs. Dextran- and wheat-germ agglutinin-associated signals were correlated in the t-system and are therefore equally good markers. The 3D structure of the t-system in rabbit ventricular myocytes seems to be less complex than that found in rat. Moreover, we found that t-tubules in rabbit have approximately twice the diameter of those in rat. We speculate that the constrictions (or regions between them) are sites of dyadic clefts and therefore can provide geometric markers for colocalizing dyadic proteins. In consideration of the resolution of the imaging system, we suggest that our methods permit us to obtain spatially resolved 3D reconstructions of the t-system in rabbit cells. We also propose that our methods allow us to characterize pathological defects of the t-system, e.g., its remodeling as a result of heart failure.
S. E. Geneser, R. M. Kirby, D. Xiu, and F. B. Sachse. Stochastic Markovian modeling of electrophysiology of ion channels: reconstruction of standard deviations in macroscopic currents. In J Theor Biol, vol. 245(4) , pp. 627-637, 2007
Markovian models of ion channels have proven useful in the reconstruction of experimental data and prediction of cellular electrophysiology. We present the stochastic Galerkin method as an alternative to Monte Carlo and other stochastic methods for assessing the impact of uncertain rate coefficients on the predictions of Markovian ion channel models. We extend and study two different ion channel models: a simple model with only a single open and a closed state and a detailed model of the cardiac rapidly activating delayed rectifier potassium current. We demonstrate the efficacy of stochastic Galerkin methods for computing solutions to systems with random model parameters. Our studies illustrate the characteristic changes in distributions of state transitions and electrical currents through ion channels due to random rate coefficients. Furthermore, the studies indicate the applicability of the stochastic Galerkin technique for uncertainty and sensitivity analysis of bio-mathematical models.
Activation of human ether-a-go-go-related gene 1 (hERG1) K+ channels mediates cardiac action potential repolarization. Drugs that activate hERG1 channels represent a mechanism-based approach for the treatment of long QT syndrome, a disorder of cardiac repolarization associated with ventricular arrhythmia and sudden death. Here, we characterize the mechanisms of action and the molecular determinants for binding of RPR260243 [(3R,4R)-4-[3-(6-methoxy-quinolin-4-yl)-3-oxo-propyl]-1-[3-(2,3,5-trifluoro-phenyl)-prop-2-ynyl]-piperidine-3-carboxylic acid] (RPR), a recently discovered hERG1 channel activator. Channels were heterologously expressed in Xenopus laevis oocytes, and currents were measured by using the two-microelectrode voltage-clamp technique. RPR induced a concentration-dependent slowing in the rate of channel deactivation and enhanced current magnitude by shifting the voltage dependence of inactivation to more positive potentials. This mechanism was confirmed by demonstrating that RPR slowed the rate of deactivation, but did not increase current magnitude of inactivation-deficient mutant channels. The effects of RPR on hERG1 kinetics and magnitude could be simulated by reducing three rate constants in a Markov model of channel gating. Point mutations of specific residues located in the S4S5 linker or cytoplasmic ends of the S5 and S6 domains greatly attenuated or ablated the effects of 3 μM RPR on deactivation (five residues), inactivation (one residue), or both gating mechanisms (four residues). These findings define a putative binding site for RPR and confirm the importance of an interaction between the S4S5 linker and the S6 domain in electromechanical coupling of voltage-gated K+ channels.
OBJECTIVE:The outward current flowing through the two-pore domain acid-sensitive potassium channel TASK-1 (I(TASK)) and its inhibition via alpha1-adrenergic receptors was studied in rat ventricular cardiomyocytes.METHODS:Quantitative RT-PCR experiments were carried out with mRNA from rat heart. Patch-clamp recordings were performed in isolated rat cardiomyocytes. TASK-1 and other K+ channels were expressed in Xenopus oocytes to study the pharmacological properties of a new TASK-1 channel blocker, A293.RESULTS:TASK-1 channels were found to be strongly expressed in rat heart. Analysis of the sensitivity of various K+ channels to A293 in Xenopus oocytes showed that at low concentrations A293 was a selective blocker of TASK-1 channels. I(TASK) in rat cardiomyocytes was dissected by application of A293 and by extracellular acidification to pH 6.0; it had an amplitude of approximately 0.30 pA/pF at +30 mV. Application of 200 nM A293 increased action potential duration (APD(50)) by 31+/-3% at a stimulation rate of 4 Hz. The plausibility of the effects of A293 on APD50 was checked with a mathematical action potential model. Application of the alpha1-adrenergic agonist methoxamine inhibited I(TASK) in Xenopus oocytes co-injected with cRNA for TASK-1 and alpha1A-receptors. In cardiomyocytes, methoxamine inhibited an outward current with characteristics similar to I(TASK). This effect was abolished in the presence of the alpha1A-antagonist 5-methyl-urapidil.CONCLUSIONS:Our results suggest that in rat cardiomyocytes I(TASK) makes a substantial contribution to the outward current flowing in the plateau range of potentials and that this current component can be inhibited via alpha1A-adrenergic receptors.
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.
E. Hughes, B. Taccardi, and F. B. Sachse. A heuristic streamline placement technique for visualization of electrical current flow. In J Flow Visualization and Image Processing, vol. 13(1) , pp. 53-66, 2006
Streamline techniques are frequently applied for scientific visualization of two- and three-dimensional electric fields. Streamline distributions are expected to reflect important features of the underlying fields such as the locations of sources and sinks as well as variations of the field density. Streamline techniques fulfilling these demands in arbitrary fields are currently not developed.In this work, we present a heuristic technique, which aims at creating a linear relationship between a streamline distribution and the density of an underlying electric current field. The technique is based on a sequential optimization algorithm for placement of seed points of streamlines. In each step, a set of random trial seed points is created. Each point of the trial set is temporarily added to the set of best seed points. Streamlines are generated from the enhanced set and the fit of their distribution and the field density is determined. The best point is selected and added to the set of best seed points. The iteration ends after generation of a pre-given number of best seed points. Several examples illustrate results of this technique applied to electric current fields of small complexity and in more extensive cardiothoracic electric fields. Additionally, we characterized, with statistical studies, the influence of parameters of the algorithm on the relationship between streamline distribution and field density.
Investigating the mechanisms underlying the genesis and conduction of electrical excitation in the atria at physiological and pathological states is of great importance. To provide knowledge concerning the mechanisms of excitation, we constructed a biophysical detailed and anatomically accurate computer model of human atria that incorporates both structural and electrophysiological heterogeneities. The three-dimensional geometry was extracted from the visible female dataset. The sinoatrial node (SAN) and atrium, including crista terminalis (CT), pectinate muscles (PM), appendages (APG) and Bachmann's bundle (BB) were segmented in this work. Fibre orientation in CT, PM and BB was set to local longitudinal direction. Descriptions for all used cell types were based on modifications of the Courtemanche et al. model of a human atrial cell. Maximum conductances of Ito, IKr and ICa,L were modified for PM, CT, APG and atrioventricular ring to reproduce measured action potentials (AP). Pacemaker activity in the human SAN was reproduced by removing IK1, but including If, ICa,T, and gradients of channel conductances as described in previous studies for heterogeneous rabbit SAN. Anisotropic conduction was computed with a monodomain model using the finite element method. The transversal to longitudinal ratio of conductivity for PM, CT and BB was 1:9. Atrial working myocardium (AWM) was set to be isotropic. Simulation of atrial electrophysiology showed initiation of APs in the SAN centre. The excitation spread afterwards to the periphery near to the region of the CT and preferentially towards the atrioventricular region. The excitation extends over the right atrium along PM. Both CT and PM activated the right AWM. Earliest activation of the left atrium was through BB and excitation spread over to the APG. The conduction velocities were 0.6ms-1 for AWM, 1.2ms-1 for CT, 1.6ms-1 for PM and 1.1ms-1 for BB at a rate of 63bpm. The simulations revealed that bundles form dominant pathways for atrial conduction. The preferential conduction towards CT and along PM is comparable with clinical mapping. Repolarization is more homogeneous than excitation due to the heterogeneous distribution of electrophysiological properties and hence the action potential duration.
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
O. Dössel, F. B. Sachse, G. Seemann, and C. D. Werner. Computermodelle der elektrophysiologischen Eigenschaften des Herzens - Computer models of the electrophysiological properties of the heart. In Biomedizinische Technik, vol. 47(9-10) , pp. 250-257, 2002
Computer models of the heart can improve the understanding of the electrophysiological processes in healthy and diseased heart. They become more and more important for detailled diagnosis of arrhythmias and for optimization of therapy. Models of myocardium cells known today are described - they are based on the properties of all relevant ion channels in the cell membrane. Then it is demonstrated, how many cells can be joined to form a cell patch and how finally the complete heart can be modelled. A simpler approach is using a so called cellular automaton that allows for a significant reduction of calculation time while sacrifying some accordance to reality. Adaptive cellular automatons allow for a fast simulation with acceptable accuracy. Using them some results were gained for the simulation of typical arrhythmias, in the field of validation using an animal model and for therapy planning with RF-ablation.
Mapping of electrical endocardial activity is an important task for cardiac diagnosis and surgical treatment planning. Different kinds of catheters measure this activity with a limited number of electrodes. In recent years an increasing number of mapping systems is used in clinical routine. Various systems have been introduced and discussed in literature. This work deals with the localization of catheter electrodes in the heart with advanced techniques of digital image processing. The catheters - developed by various enterprises - differ in shape, handling and amount of electrodes. They are specified and presented in detail. Digital image analysis techniques like filters, Fourier and Hough transformation build the background and basics for this work. The main part describes the methods for the detection of the electrodes and the catheter strings. With these methods, it is possible to setup computer models for each catheter. The computer models can be used e. g. in numerical field calculation together with medical tomographic datasets.
This work deals with the simulation of the electrical cardiac excitation propagation based on anatomical models of the human heart and body. The generation of anatomical models applying different techniques of digital image processing to medical image data is described as well as the generation of electrophysiological models based on these anatomical models. Different spatial and temporal physical field distributions, e.g. the transmembrane potential, the current sources and the extracellular potentials, are calculated and visualized in sinus rhythm case as well as in pathological cases.
F. B. Sachse. Computational cardiology : modelling of anatomy, electrophysiology, and mechanics. Springer, Heidelberg. 2004.
Book Chapters (2)
F. B. Sachse, G. Seemann, and R. Mayer. Modelling of Electro-Mechanics in the Heart: Mathematical and Numerical Aspects. In High Performance Scientific Computing, Scientific Supercomputing Center Karlsruhe, pp. 36-37, 2003
F. B. Sachse, C. D. Werner, and G. Seemann. Simulation of Cardiac Electrophysiology and Electrocardiography. In Computer Simulation and Experimental Assessment of Cardiac Electrophysiology, Futura Publishing, Armonk, New York, pp. 97-104, 2001
We describe an approach to develop anatomical models of cardiac cells. The approach is based on confocal imaging of living ventricular myocytes with submicrometer resolution, digital image processing of three-dimensional stacks with high data volume, and generation of dense triangular surface meshes representing the sarcolemma including the transverse tubular system. The image processing includes methods for deconvolution, filtering and segmentation. We introduce and visualize models of the sarcolemma of whole ventricular myocytes and single transversal tubules. These models can be applied for computational studies of cell and sub-cellular physical behavior and physiology, in particular cell signaling. Furthermore, the approach is applicable for studying effects of cardiac development, aging and diseases, which are associated with changes of cell anatomy and protein distributions.
Computational modeling and simulation can provide important insights into the electrical and electrophysiological properties of cells, tissues, and organs. Commonly, the modeling is based on Maxwell's and Poisson's equations for electromagnetic and electric fields, respectively, and numerical techniques are applied for field calculation such as the finite element and finite differences methods. Focus of this work are finite element methods, which are based on an element-wise discretization of the spatial domain. These methods can be classified on the element's geometry, e.g. triangles, tetrahedrons and hexahedrons, and the underlying interpolation functions, e.g. polynomials of various order. Aim of this work is to describe finite element-based approaches and their application to extend the problem-solving environment SCIRun/BioPSE. Finite elements of various types were integrated and methods for interpolation and integration were implemented. General methods for creation of finite element system matrices and boundary conditions were incorporated. The extension provides flexible means for geometric modeling, physical simulation, and visualization with particular application in solving bioelectric field problems.
F. B. Sachse, G. Seemann, and B. Taccardi. Relationship of Strain and Conduction Velocity in Cardiac Muscle in the High Strain Range. In Biophys. J (Annual Meeting Abstracts), pp. 2644, 2006
F. B. Sachse, G. Seemann, and B. Taccardi. Insights into Electrophysiological Studies with Papillary Muscle by Computational Models. In Lecture Notes in Computer Science, vol. 3504, pp. 216-225, 2005
Cardiac electro-mechanical models are valuable tools to gain insights in physiology and pathophysiology of the heart. Progressive models can be created by fusion of various basic models. In this work biventricular models of cardiac electro-mechanics were developed by fusion of anatomical, electrical, and mechanical models. The importance of anatomical modeling was researched by inclusion of two different anatomical models, i.e. an analytical and a magnetic resonance diffusion tensor imaging based model. The fused models were applied in simulations of physiological behavior and results of these were analyzed. Significant difference of deformation were found, which can be attributed to the anatomical models. The analysis emphasized the importance of appropriate anatomical modeling for simulations of cardiac mechanics.
F. B. Sachse, and B. Taccardi. Visualization of Electrical Current Flow with a New Streamline Technique: Application in Mono- and Bidomain Simulations of Cardiac Tissue. In Proc. IEEE EMBS, pp. 1846-1849, 2004
F. B. Sachse, K. Glänzel, and G. Seemann. Modeling of electro-mechanical coupling in cardiac myocytes: feedback mechanisms and cooperativity. In Lecture Notes in Computer Science, vol. 2674, pp. 62-71, 2003
Modeling of mechanisms involved in electrophysiology and tension development of cardiac myocytes can enhance the understanding of physiological and pathophysiological cardiac phenomena. Interactions of divers components are necessary for cellular electro-mechanics. Particularly, the interactions between proteins in the cell membrane, sarcoplasmic reticulum and sarcomere are of importance. In this work hybrid electro-mechanical models of cardiac myocytes were derived on basis of recently developed models as well as of measurements ranging from protein to multi-cell level. The models quantify dynamically the electrophysiology and tension development by states, partly associated to configurations of the involved proteins, and the transition between these states. The models allow the reconstruction of electro-mechanical phenomena. Results of simulations with the hybrid models were performed illustrating their properties. The models may help to clarify feedback and cooperativity mechanisms, pathophysiological changes and metabolism of myocytes.
F. B. Sachse, and G. Seemann. Modeling of cardiac electro-mechanics in a truncated ellipsoid model of left ventricle. In Lecture Notes in Computer Science, vol. 2673, pp. 253-260, 2003
Modeling of cardiac electro-mechanics enables and simplifies understanding of physiology and pathophysiology of the heart. In this work a model is presented, which allows the reconstruction of macroscopic electro-mechanical processes in the left ventricle of small mammals. The model combines a three-dimensional model of left ventricular anatomy represented as truncated ellipsoid with an integrated electromechanical model. The integrated model includes electrophysiological, force development and elastomechanical models of myocardium. The model is illustrated by simulations, which reflect the behavior of an extracorporated heart. These simulations yield temporal distributions of electrophysiological parameters as well as descriptions of electrical propagation and mechanical deformation. The simulations show the connection between cellular electrophysiology, electrical excitation propagation, force development, and mechanical deformation.
F. B. Sachse, G. Seemann, and C. D. Werner. Modeling of Force Development in the Human Heart with a Cellular Automaton Parameterized by Numerical Experiments. In Proc. IEEE EMBS and BMES, pp. 1226-1227, 2002
F. B. Sachse, C. D. Werner, and O. Dössel. A Software System for the Anatomically Contrained Reconstruction of Conductivity Distributions in Human Body. In Proc. 21th Conf. IEEE Eng. in Med. and Biol., pp. 886, 1999
A model based method is presented to assign the fibre orientation in the human heart. The approach uses anatomical models, which are derivable from medical tomographic images. These models describe the geometry of the atria and ventricles. The approach extends the models by applying information from morphological measurements, which examine the fibre orientation for the different anatomical structures in the dissected normal hearts. The orientation of myocardial fibres is interpolated based on restrictions, which are determined with automatic methods inside and on the surface of myocardial structures. For each structure a different rulebased method is chosen. The method is illustrated with an exemplary anatomical model, which was constructed with techniques of digital image processing based on the Visible Female data set
F. B. Sachse, C. D. Werner, K. Meyer-Waarden, and O. Dössel. Applications of the Visible Man Dataset in Electrocardiology: Calculation and Visualization of Body Surface Potential Maps of a Complete Heart Cycle. In Proc. Second Users Conference of the National Library of Medicines Visible Human Project, pp. 47-48, 1998
This study deals with the forward problem in electrocardiography, which consists of computing the electrical potential distribution in the human body due to cardiac sources. Thereby, an important task is the selection of appropriate models, because their properties determine the quality and costs of the solution of the forward problem. Subject of this study is an examination, which regions of the body should be included in impedance models. Therefore, different impedance models, varying in position and size, are examined. They were derived from a realistically shaped, highly detailed anatomical model. The model originates from tomographies of the Visible Man dataset, National Library of Medicine, Bethesda, Maryland (USA), using techniques of digital image processing. The examination is carried out by analysis and comparison of computed body surface potential maps, which are numerically calculated based on a set of different models using the finite difference method
F. B. Sachse, M. Glas, M. Müller, and K. Meyer-Waarden. Segmentation and Tissue-Classification of the Visible Man Dataset Using the Computertomographic Scans and the Thin-Section Photos. In Proc. First Users Conference of the National Library of Medicines Visible Human Project, 1996
F. B. Sachse, M. Müller, and K. Meyer-Waarden. Vergleichende Betrachtung von Modellen zur Berechnung von elektromagnetischen Feldern im menschlichen Körper. In Biomedizinische Technik, vol. 41-1, pp. 558-559, 1996
F. B. Sachse, M. Müller, and K. Meyer-Waarden. Erstellung von gewebeklassifizierten Modellen des menschlichen Körpers zur numerischen Feldberechnung basierend auf bildgebenden Verfahren der Medizin. In Biomedizinische Technik, vol. 40(s1) , pp. 163-164, 1995
F. B. Sachse, M. Müller, and K. Meyer-Waarden. Macroscopic Models of the Electric Tissue Impedance in Human - Requirements, Creation and Application. In IX. International Conference On Electrical Bio-Impedance, 1995
F. B. Sachse, M. Müller, and K. Meyer-Waarden. Erstellung von gewebeklassifizierten Modellen des menschlichen Körpers und deren Verwaltung durch eine attributierte Geometriedatenbank. In Biomedizinische Technik/Biomedical Engineering, vol. 39(s1) , pp. 358361, 1994
Bidomain simulations of the heart need validated parameters to produce realistic data. Therefore, it is nec- essary to develop methods to estimate reliable values for these parameters. We developed an approach to deliver such values by designing an in-silico model of intracellular electrical conduction based on confocal microscopic data of rabbit ventricular tissue. High resolution image data were used to determine the anisotropy of electrical conduc- tivity in the myocardium, which is highly dependent on the specific tissue geometry. Gap junction protein connexin43 and extracellular space were labeled with fluorescent dyes of different spectra. The myocytes were segmented and the gap junction density in-between myocytes was extracted. Assuming conductivities for intracellular liquid and gap junction resistance, a numerical field calculation was per- formed for three principal directions in order to extract in- tracellular conductivity tensors. We calculated 9 tensors by varying the assumed conductivities by ±50%. We esti- mated the intracellular conductivities for the three princi- pal directions σi,x = 0.0653 S/m, σi,y = 0.0042 S/m and σi,z = 0.0033 S/m, respectively. The estimated conductiv- ity values were realistic regarding the electrical anisotropy but need to be improved to fit other experimental data.
The segmentation of three-dimensional microscopic images of car- diac tissues provides important parameters for characterizing cardiac diseases and modeling of tissue function. Segmenting these images is, however, chal- lenging. Currently only time-consuming manual approaches have been devel- oped for this purpose. Here, we introduce an efficient approach for the semi-automatic segmentation (SAS) of cardiomyocytes and the extracellular space in image stacks obtained from confocal microscopy. The approach is based on a morphological watershed algorithm and iterative creation of wa- tershed seed points on a distance map. Results of SAS were consistent with re- sults from manual segmentation (Dice similarity coefficient: 90.8±2.6%). Cell volume was 4.6±6.5% higher in SAS cells, which mainly resulted from cell branches and membrane protrusions neglected by manual segmentation. We suggest that the novel approach constitutes an important tool for characterizing normal and diseased cardiac tissues. Furthermore, the approach is capable of providing crucial parameters for modeling of tissue structure and function.
The heart rate is mediated by the G protein-coupled muscarinic receptor (M2R) activating the acetylcholine (ACh)-dependent K+ current (IKACh). Here, a novel model for IKACh gating is presented based on recent findings that M2R agonist binding is voltage-sensitive. Furthermore, ACh and pilocarpine (Pilo) manifest opposite voltage-dependent IKACh modulation. In a previous work, a 4-state Markov model of M2R reconstructing the voltage-dependent change in agonist affinity was proposed. In this work, a 2-state Markov model of IKACh gating purely dependent on the Gβγ concentration is proposed. IKACh is modeled based on the description of Zhang et al. Measurement data are used to parametrize the combined M2R and IKACh model for both ACh and Pilo. The channel model has a linear Gβγ dependent forward and a constant backward rate. For ACh and Pilo, optimal values of model parameters are found reconstructing the measured opposite voltage-dependent change in agonist affinity. The combined model is able to reconstruct the measured data regarding the agonist and voltage-dependent properties of the M2R-IKACh channel complex. In future studies, this channel will be integrated in a sinus node model to investigate the effect of the channel properties on heart rate
Various types of heart disease are associated with structural remodeling of cardiac cells. In this work, we present a software framework for automated analyses of structures and protein distributions involved in excitation-contraction coupling in cardiac muscle cells (myocytes). The software framework was designed for processing sets of three-dimensional image stacks, which were created by fluorescent labeling and scanning confocal microscopy of ventricular myocytes from a rabbit infarction model. Design of the software framework reflected the large data volume of image stacks and their large number by selection of efficient and automated methods of digital image processing. Specifically, we selected methods with small user interaction and automated parameter identification by analysis of image stacks. We applied the software framework to exemplary data yielding quantitative information on the arrangement of cell membrane (sarcolemma), the density of ryanodine receptor clusters and their distance to the sarcolemma. We suggest that the presented software framework can be used to automatically quantify various aspects of cellular remodeling, which will provide insights in basic mechanisms of heart diseases and their modeling using computational approaches. Further applications of the developed approaches include clinical cardiological diagnosis and therapy planning.
M. Karl, O. Dössel, G. Seemann, F. Sachse, and V. Heuveline. Time and memory efficient implementation of the cardiac bidomain equations. In 4th European Conference of the International Federation for Medical and Biological Engineering, IFMBE Proceedings, vol. 22, 2008
Computer simulations can significantly improve comprehension of cardiac electrophysiology. A mathematical model for the simulation of complex cardiac electrophysiology is the bidomain model. A new tool, acCELLerate, was developed using the PETSc library  for a parallel time and memory efficient implementation of the bidomain equations enabling the computation of large scale cardiac simulations. It offers an extensible modular structure. The optimization of the cost-intensive solution of the elliptical part of the bidomain equation was achieved by analyzing several iterative Krylov subspace methods and preconditioners provided by PETSc. Best performance results were achieved by using a combination of minimal residual method (MinRes), conjugate residual method (CR) or conjugate grandient method (CG) as solver with adjusted successive over-relaxation preconditioning (SOR). A validation proved the authenticity of the new tool.
While chloroquine remains an important therapeutic agent for treatment of malaria in many parts of the world, its safety margin is very narrow. Chloroquine inhibits the cardiac inward rectifier K+ current IK1 and can induce lethal ventricular arrhythmias. In this study, we characterized the biophysical and molecular basis of chloroquine block of Kir2.1 channels that underlie cardiac IK1. The voltage- and K+-dependence of chloroquine block implied that the binding site was located within the ion conduction pathway. Site-directed mutagenesis revealed the location of the chloroquine binding site within the cytoplasmic pore domain, rather than within the transmembrane pore. Molecular modeling suggested that chloroquine blocks Kir2.1 channels by plugging the cytoplasmic conduction pathway, stabilized by negatively charged and aromatic amino acids within a central pocket. Unlike most ion channel blockers, chloroquine does not bind within the transmembrane pore. These findings explain how a relatively low-affinity blocker like chloroquine can effectively block IK1 even in the presence of high affinity endogenous blockers. Moreover, our findings provide the structural framework for the design of safer, alternative compounds that are devoid of Kir2.1 blocking properties.
Based on the Weiner-Hermite polynomial chaos expansion, the stochastic Galerkin method efficiently computes nu- merical solutions for stochastic systems. Unlike such tech- niques as sensitivity analysis, perturbation methods, and second moment-analysis, this method is applicable to a large number of systems while requiring less computational effort than sampling based stochastic methods like Monte Carlo. We utilize the stochastic Galerkin method to assess the impact of stochastic rate coefficients on the predictions of Markovian cardiac ion channel models
Drug-induced long QT syndrome is a disorder characterized by impaired repolarization of the ventricular action potential which can lead to arrhythmia and sudden death. The most common form involves block of hERG1a channels which encode Ikr current in myocytes. Compounds which activate hERG1a channels could then provide an effective treatment for this disorder. We have studied a recently identified hERG1a activator, PD-118057, using the two microelectrode voltage clamp technique to analyze its affect on hERG1a current expressed in Xenopus oocytes. At 10 microM, PD118057 enhanced wild-type hERG1a current by slowing the rate of inactivation and shifting the voltage dependence to more positive potentials. Consistent with an inactivation perturbing mechanism, PD118057 failed to enhance the current magnitude of an inactivation removed hERG1a mutant channel, G628C/S631C. Unlike other hERG1a activators such as RPR260243, PD118057 did not alter the rate of hERG1a deactivation, suggesting a distinct binding site on the channel protein. Wild-type dEAG1 does not exhibit C-type inactivation and, as expected was unaffected by 10 microM PD118057. A single mutation in the S6 domain (Ala478Gly) of dEAG1 introduced a fast inactivation mechanism with similar time constants as for hERG1a channels. Ala478Gly dEAG current magnitude was enhanced by PD118057 in a concentration dependent manner through removal of the fast inactivation process. In contrast, other S6 mutations that introduce a marginally slower inactivation mechanism did not exhibit sensitivity to PD118057.
We introduce a framework to characterize and visualize the transverse tubular system of cardiac myocytes imaged with confocal microscopy. We imaged rabbit ventricular cells and cell segments with fluorescein linked to dextran. The image datasets were deconvolved with the Richardson-Lucy algorithm using the point spread function extracted from images of fluorescent beads. The transverse tubular system (t-system) was segmented with the methods of digital image processing. We reconstructed single transverse tubules and quantitatively described these in terms of length, cross-sectional area, ellipticity and orientation. These results should yield geometric markers for studies of protein distribution and provide insights into the function of the t-system.
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.
T. G. McNary, K. Sohn, B. Taccardi, and F. B. Sachse. Mechano-Electrical feedback mechanisms in cardiac tissue: Experimental setup and preliminary measurement results. In Proc. 2nd Annual Mountain West Biomedical Engineering Conference, 2006
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
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.
O. Dössel, G. Seemann, D. L. Weiß, and F. B. Sachse. 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, O. Dössel, G. Seemann, and F. B. Sachse. 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
Electrical activity in biological media can be described in a mathematical way, which is applicable to computer-based simulation. Biophysically mathematical descriptions provide important insights into the electrical and electrophysiological properties of cells, tissues, and organs. Examples of these descriptions are Maxwell's and Poisson's equations for electromagnetic and electric fields. Commonly, numerical techniques are applied to calculate electrical fields, e.g. the finite element method. Finite elements can be classified on the order of the underlying Interpolation. High-order finite elements provide enhanced geometric flexibility and can increase the accuracy of a solution. The aim of this work is the design of a framework for describing and solving high-order finite elements in the SCIRun/BioPSE software system, which allows geometric modeling, simulation, and visualization for solving bioelectric field problems. Currently, only low-order elements are supported. Our design for high-order elements concerns interpolation of geometry and physical fields. The design is illustrated by an implementation of one-dimensional elements with cubic interpolation of geometry and field variables.
O. Dössel, G. Seemann, D. L. Weiß, and F. B. Sachse. 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.
R. Liu, Y. Shang, F. B. Sachse, and O. Dössel. 3D active surface method for segmentation of medical image data: Assessment of different image forces. In Biomedizinische Technik, vol. 48-1, pp. 28-29, 2003
M. Nalbach, O. Skipa, F. B. Sachse, and O. Dössel. Investigation of the source space of electrocardiography and magnetocardiography using isotropic and anisotropic thorax models. In Proc. Computers in Cardiology, pp. 501-504, 2002
Noninvasive Imaging of the bioelectric processes on the heart using Electrocardiography (ECG) and Magnetocardiography (MCG) data is a widely discussed research topic of the recent years. The source space of ECG is compared with the source space of MCG and vice versa to investigate the difference of information content of these mapping techniques for source imaging purposes. The approach allows the calculation of the intersection and non-intersection part (the calculation of silent sources) of MCG (ECG) in comparison to ECG (MCG). The investigation was carried out on a Finite Element model which was constructed from a magnetic resonance imaging (MRI) dataset of a volunteer. Anisotropic fibre orientation was applied to myocardium to investigate its effect on the differences of the source spaces.
O. Dössel, G. Seemann, and F. B. Sachse. Excitation Propagation and Force Development in the Left Ventricle of the Visible Female Data Set. In Biomedizinische Technik, vol. 47-1/1, pp. 221-224, 2002
A new approach to the reconstruction of transmembrane potentials (TMP) in anisotropic finite element heart model is presented. The solution is sought in the form of 3D patches constructed by the interpolation of TMP distributions. The method is evaluated using TMP distributions generated with a cellular automaton.
Knowledge of tissue distribution allows the creation of anatomical models of the human body. Anatomically based models are of increasing interest e.g. in the field of medical education, development of therapies and research on the risks of electro smog.The motivation for this work was the creation of a female 3D anatomical model with high accuracy and resolution. The purpose of this anatomical model is to simulate the human physical behavior through the numerical calculation of fields.The objectives were the segmentation of the Visible Female thorax applying digital image processing techniques and the evaluation of existing tools for segmentation and classification. This evaluation should deliver solutions to achieve better accuracy, to reduce the time on manual segmentation and to allow an adaptation of existing tools.
The inverse problem of electrocardiology might provide a powerful clinical investigation method for visualising the electrical activity of the heart. To use this method one requires accurate models of the human torso and heart. The objective of this work was to create an accurate model of the human ventricles including the valves from images recorded using Magnetic Resonance Imaging (MRI). This model is used as a "generic" model, and is adapted to a given individual with a host mesh fit to spatially registered Ultrasound (US) images.
O. Skipa, F. B. Sachse, C. D. Werner, and O. Dössel. Simulation study of the effect of Modelling errors on the solution of the inverse cardiac source imaging problem using realistic source patterns. In Proc. Computers in Cardiology, vol. 28, pp. 41-44, 2001
The effect of the modelling errors on the solution of the inverseproblem of electrocardiographyis investigated. The electrocardiographicsignal is simulated using ajnite element model of human torso and realistic source patterns gained with a cellular automaton. Noise is added to simulated measurementsand the inverseproblem is solved. Modelling errors consist offalse conductivity assumptions, changed anisotropy ratio of skeletal muscles and geometric errors. The effect of modeling errors on optimal regulariza- tion parameter determination is investigated. The changes in muscle anisotropy and heart position are shown to have the highest effect on reconstructed epicardial potentials. CRESO and L-curve criteria for optimal regularization parameter estimation are compared.
O. Doessel, C. Werner, and F. Sachse. Modelling of normal and arrhythmogenic electrical excitation of the human heart. In World Congress on Medical Physics, vol. 27, pp. 205, 2000
M. Hoefele, F. B. Sachse, C. D. Werner, and O. Dössel. Elastische Registrierung multimodaler dreidimensionaler medizinischer Datensätze am Beispiel des Visible Female Datensatzes. In Biomedizinische Technik, vol. 45-1, pp. 503-504, 2000
O. Dössel, G. Seemann, F. B. Sachse, and C. D. Werner. Parametrisierung Zellulärer Automaten der Erregungsausbreitung im Herzen ausgehend von elektrophysiologischen Zellmodellen. In Biomedizinische Technik, vol. 45-1, pp. 481-482, 2000
O. Skipa, F. B. Sachse, and O. Dössel. Linearization approach for impedance reconstruction in human body from surface potentials measurements. In Biomedizinische Technik, vol. 45-1, pp. 410-411, 2000
In this paper, a new method for QRS complex analysis and estimation based on principal component analysis (PCA) and polynomial fitting techniques is presented. Multi-channel ECG signals were recorded and QRS complexes were obtained from every channel and aligned perfectly in matrices. For every channel, the covariance matrix was calculated from the QRS complex data matrix of many heartbeats. Then the corresponding eigenvectors and eigenvalues were calculated and reconstruction parameter vectors were computed by expansion of every beat in terms of the principal eigenvectors. These parameter vectors show short-term fluctuations that have to be discriminated from abrupt changes or long-term trends that might indicate diseases. For this purpose, first-order poly-fit methods were applied to the elements of the reconstruction parameter vectors. In healthy volunteers, subsequent 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. Based on this work, thresholds can be defined for changes in the parameter vectors that indicate diseases.
C. D. Werner, F. B. Sachse, C. Baltes, and O. Dössel. The Visible Man Dataset in Medical Education: Electrophysiology of the Human Heart. In Proc. Third Users Conference of the National Library of Medicines Visible Human Project, 2000
C. D. Werner, F. B. Sachse, and O. Dössel. Simulation der elektrischen Erregung im menschlichen Herzen auf vierdimensionalen tomographischen Patientendatensätzen. In Biomedizinische Technik, vol. 45(s1) , pp. 367-368, 2000
Die Simulation der elektrischen Erregungsausbreitung im menschlichen Herzen gewinnt bei der kardiologischen Ausbildung, Diagnostik und Therapieplanung zunehmend an Bedeutung. Eine Möglichkeit die elektrische Erregungsausbreitung zu simulieren, basiert auf der Erstellung anatomischer Modelle, die die Basis für physiologische Modelle bilden. Auf statischen anatomischen Modellen basierende physiologische Modelle vernachlässigen bei der Simulation der Erregungsausbreitung den Einfluß der Bewegung auf die Berechnung der elektrischen Quellen im Herzen. Ziel dieser Arbeit ist es, ein dynamisches digitales Herzmodell zur Berechnung der elektrischen Quellen im menschlichen Herzen zu erstellen, das die Bewegung des Herzens berücksichtigt.
I. H. d. Boer, F. B. Sachse, and O. Dössel. Entwicklung eines 4-Kamera-Systems zur Lokalisation einer Elektrodenanordnung auf dem Thorax. In Biomedizinische Technik, vol. 43-1, pp. 56-57, 1998
N. H. Busch, F. B. Sachse, C. D. Werner, and O. Dössel. Segmentation klinischer vierdimensionaler magnetresonanztomographischer Aufnahmen mittels Aktiver Kontur Modelle und haptischer Interaktion. In Biomedizinische Technik, vol. 43-1, pp. 526-529, 1998
C. D. Werner, F. B. Sachse, and O. Dössel. Vergleichende Betrachtung von isotropen und anisotropen Modellen der Erregungsausbreitung im Herzen. In Biomedizinische Technik, vol. 43, pp. 69-70, 1998
C. D. Werner, F. B. Sachse, and O. Dössel. Electrical excitation of the human heart: A comparison of electrical source distribution in models of different spatial resolution. In Proc. Computers in Cardiology, vol. 25, pp. 309-312, 1998
Subject of this study is the simulation of the electrical excitation propagation based on anatomical and physiological models of the human heart. An anatomical model of high spatial resolution was created applying advanced strategies of 3D digital image processing to the Visible Human data set provided by the National Library of Medicine, Bethesda, Maryland (USA). It comprises 42 classes of tissue including the cardiac conduction system. In addition, the fibre orientation of the cardiac and skeletal muscle was determined end assigned to each voxel of the model. Source distributions were calculated based on a 3D bidomain model applying a cellular automaton to these models to simulate the excitation process. The anisotropic behaviour of the cardiac muscle with regard to electrical conductivity and propagation velocity was taken into account as well as physiological properties of the cardiac tissue. Source distributions of differently scaled models were compared
Die in dieser Arbeit vorgestellte Strategie der Segmentation und Klassifikation drei- und Vierdimensionaler MR-Datensätze ermöglicht die Erstellung anatomischer Modelle des menschlichen Körpers. Zur Segmentation dieser Datensätze kommen unterschiedliche Verfahren zum Einsatz. Schwerpunkte bilden dabei das Region Growing und die Aktiven Konturen. Bei beiden Segmentationsverfahren werden zur Filterung der Datensätze unterschiedliche Filter (u. a. Gauß-, Sobelfilter, nichtlineare adaptive Diffusionsfilter, morphologische Filter) angewendet. Das aktive Konturen-Verfahren wird weiterhin durch die Wahl geeigneter Potentialfunktionen unterstützt.
C. Werner, F. Sachse, and O. Dössel. Applications of the visible human male dataset in electrocardiology: simulation of the electrical excitation propagation. In Proceedings of 2nd User Conference of the National Liberary of Medicines Visible Human Project, pp. 69-70, 1998
Due to its high spatial resolution the Visible Man dataset provides a good possibility to simulate certain aspects of human physiology based on detailed, macroscopic models of the human anatomy. This study deals with the simulation of the electrical excitation propagation in the human heart. Along with applications in education, diagnosis and therapy, this simulation is used in manifold fields of research, such as solving the forward problem of electrocardiography with a realistic boundary condition or validating solutions of the inverse problem of electrocardiography. The simulation is based on an anatomical and physiologocal model of the heart of the Visible Man. The anatomical model was created exploring the data provided with the thin-section photos of the Visible Man dataset. The simulation of the electrical excitation propagation was performed by a cellular automaton which combines the anatomical model with physiological parameters of the electrical excitation propagation. It allowed to calculated the electrical source distribution in the heart numerically which was used to solve the forward problem of electrocardiology which is the calculation of body surface potential maps from a given source distribution.
C. D. Werner, F. B. Sachse, and O. Dössel. Modellierung der Erregungsausbreitung im Herzen am Beispiel des Visible Man Datensatzes. In Biomedizinische Technik, vol. 42(Ergänzungsband) , pp. 195-196, 1997
M. Müller, F. B. Sachse, and K. Meyer-Waarden. Creation of finite element models of human body based upon tissue-classified voxel representations. In Proc. First Users Conference of the National Library of Medicine, 1996
Numerical methods like finite difference methods (FD), finite integration techniques (FIT), the boundary element method (BEM) or the finite element method (FE) have been proven to be powerful tools for the calculation of electric, magnetic, electromagnetic and thermal fields.
H. Jausel, F. B. Sachse, and K. Meyer-Waarden. Optimierung von Spulenkonfigurationen für die Magnetostimulation mit der numerischen Feldberechnung. In Biomedizinische Technik, vol. 40(s1) , pp. 345-348, 1995
F. B. Sachse. Modelle des menschlichen Körpers zur Berechnung von physikalischen Feldern. Universität Karlsruhe (TH), Institut für Biomedizinische Technik. . 1998
K. Chaisaowong, F. B. Sachse, and G. Seemann. Hybride Visualisierung der Menschlichen Anatomie und Physikalischer Felder: Interaktive Benutzeroberfläche mit Inter-Prozess Kommunikation. Universität Karlsruhe (TH), Institut für Biomedizinische Technik. . 1999