Simulations of the electrophysiological behavior of the heart improve the comprehension of the mechanisms of the cardiovascular system. Furthermore, the mathematical modeling will support diagnosis and therapy of patients suffering from heart diseases. In this paper, the chain of modeling of the electrical function in the heart is described. The components are explained briefly, namely modeling of cardiac geometry, reconstructing the cardiac electrophysiology and excitation propagation. Additionally, the mathematical methods allowing to implement and solve these models are outlined. The three recently more investigated cases atrial fibrillation, ischemia and long-QT syndrome are described and show how cardiac modeling can support cardiologists in answering their open questions.
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).
This paper examined the effects that different tissue conductivities had on forward-calculated ECGs. To this end, we ranked the influence of tissues by performing repetitive forward calculations while varying the respective tissue conductivity. The torso model included all major anatomical structures like blood, lungs, fat, anisotropic skeletal muscle, intestine, liver, kidneys, bone, cartilage, and spleen. Cardiac electrical sources were derived from realistic atrial and ventricular simulations. The conductivity rankings were based on one of two methods: First, we considered fixed percental conductivity changes to probe the sensitivity of the ECG regarding conductivity alterations. Second, we set conductivities to the reported minimum and maximum values to evaluate the effects of the existing conductivity uncertainties. The amplitudes of both atrial and ventricular ECGs were most sensitive for blood, skeletal muscle conductivity and anisotropy as well as for heart, fat, and lungs. If signal morphology was considered, fat was more important whereas skeletal muscle was less important. When comparing atria and ventricles, the lungs had a larger effect on the atria yet the heart conductivity had a stronger impact on the ventricles. The effects of conductivity uncertainties were significant. Future studies dealing with electrocardiographic simulations should consider these effects.
Atrial arrhythmias, such as atrial flutter or fibrillation, are frequent indications for catheter ablation. Recorded intracardiac electrograms (EGMs) are, however, mostly evaluated subjectively by the physicians. In this paper, we present a method to quantitatively extract the wave direction and the local conduction velocity from one single beat in a circular mapping catheter signal. We simulated typical clinical EGMs to validate the method. We then showed that even with noise, the average directional error was below 10(°) and the average velocity error was below 5.4 cm/s. In a realistic atrial simulation, the method could clearly distinguish between stimuli from different pulmonary veins. We further analyzed eight clinical data segments from three patients in normal sinus rhythm and with stimulation. We obtained stable wave directions for each segment and conduction velocities between 70 and 115 cm/s. We conclude that the method allows for easy quantitative analysis of single macroscopic wavefronts in intracardiac EGMs, such as during atrial flutter or in typical clinical stimulation procedures after termination of atrial fibrillation. With corresponding simulated data, it can provide an interface to personalize electrophysiological (EP) models. Furthermore, it could be integrated into EP navigation systems to provide quantitative data of high diagnostic value to the physician
Bioelectric source measurements are influenced by the measurement location as well as the conductive properties of the tissues. Volume conductor effects such as the poorly conducting bones or the moderately conducting skin are known to affect the measurement precision and accuracy of the surface electroencephalography (EEG) measurements. This paper investigates the influence of age via skull conductivity upon surface and subdermal bipolar EEG measurement sensitivity conducted on two realistic head models from the Visible Human Project. Subdermal electrodes (a.k.a. subcutaneous electrodes) are implanted on the skull beneath the skin, fat, and muscles. We studied the effect of age upon these two electrode types according to the scalp-to-skull conductivity ratios of 5, 8, 15, and 30 : 1. The effects on the measurement sensitivity were studied by means of the half-sensitivity volume (HSV) and the region of interest sensitivity ratio (ROISR). The results indicate that the subdermal implantation notably enhances the precision and accuracy of EEG measurements by a factor of eight compared to the scalp surface measurements. In summary, the evidence indicates that both surface and subdermal EEG measurements benefit better recordings in terms of precision and accuracy on younger patients.
Atrial fibrillation (AF) is a common pathology. AF modifies the electrophysiological properties of cells (remodeling) promoting the occurrence and maintenance of AF.Electrical remodeling includes changes in ICa,L, Ito, IK1 and IK,ACh. These effects were integrated in a human atrial computer model. Gap junction remodeling was considered in the conductivity of the monodomain equation calculating excitation. Specific features were calculated to determine the risk of AF initiation and perpetuation.ERP was reduced from 330ms to 103ms. CV was lowered from 755mm/s to 608mm/s. The WL reduction was even higher (from 249mm to 63mm) leading to a higher probability of occurrence and maintenance of AF. A maximum of 7 spirals waves were initiated leading to a peak in the power spectrum at 10.32Hz.The computer model underlines the relevance of remodeling in AF chronification. The results add to the knowledge of AF maintenance. Our model might prove to be a tool for the development of novel therapeutic strategies.
Catheter ablation of complex atrial arrhythmias is a frequently applied procedure, but its success rates are only moderate and highly dependent on the experience of the physician. Personalized atrial simulation models could assist the physician in treatment planning and thus increase success rates. In this work we created a personalized anatomical model for a specific patient from CT image data. Left atrial conduction velocity and local wave directions were determined from intracardiac electrogram (EGM) recordings. We simulated normal sinus rhythm and the clinical pacing protocol using a Cellular Automaton. The incidence direction and conduction velocity were extracted from the simulated data and compared to the results of the clinical EGMs of the same patient. We then showed that the incidence angles differed by less than 15% and that the conduction velocity error was below 12 cm/s. This implies that the model has similar electric properties compared to the real atria. In conclusion, we have presented a workflow for model personalization and validation.
T. Fritz, O. Jarrousse, G. Seemann, and O. Dössel. Analyzing the transmural electromechanical heterogeneity of the left ventricle in a computer model. In Biomedizinische Technik / Biomedical Engineering (Proceedings BMT2010), vol. 55(Suppl 1) , 2010
There is a large number of published studies analyzing the inhomogeneously distributed electrophysiological properties of the ventricles in a computer model. However only few of them deal with the impact on the hearts mechanics. In 2003 Cordeiro and colleagues  analyzed the influence of the transmural left ventricular electrophysiological heterogeneity on the myocardial mechanics. Therefore, they examined the unloaded cell shortening of sub-epicardial cells, sub-endocardial cells, and cells from the middle of the wall, isolated from canine left ventricle.In this work a heterogenous electromechanical model was used to reconstruct these experiments of Cordeiro et al. in the computer. A simulation framework, which is consisting of an electrophysiological cell model, a tension development model and an elastomechanical model was used to simulate the cell shortening. Two experiments with different heterogeneities had been conducted. The first experiment examined, how the heterogeneity of the membrane channels influences the cell shortening. In the second experiment the additional impact of the heterogeneity of the intracellular calcium handling was analyzed. The results of the simulations were compared qualitatively to the findings of Cordeiro et al.
Patients suffering from the congenital Long-QT syndrome have been reported to react highly sensitive to the presence of beta-adrenergic agents that are produced by the sympathetic nervous system. In this work we used an anisotropic and electrophysiologically heterogeneous in- silico model to reproduce wedge experiments in which the Long-QT syndrome was induced pharmacologically. The integration of an intracellular signaling cascade allowed the prediction of the effects of adrenergic agents on the different subtypes of the Long-QT syndrome. For LQT1 the in-silico model predicted a QT prolongation in the transmural pseudo ECG without an increase in transmural dispersion of repolarization. For LQT2 and LQT3 the QT prolongation was accompanied by an increased transmural dispersion of repolarization. beta-adrenergic tonus shortened the QT interval and increased transmural dispersion of repolarization. These findings were consistent with the experimental reports.
D. U. J. Keller, O. Dössel, and G. Seemann. Simulating cardiac excitation in a high resolution biventricular model. In Proceedings BMT 2010, 44. DGBMT Jahrestagung, 3-Länder-Tagung D-A-CH, Rostock, vol. 55(s1) , pp. 205-208, 2010
The shape of a simulated excitation wavefront depends on the underlying spatial resolution. The aim of this work is twofold: On the one hand we investigated the dependency of the wavefront on spatial resolution by simulating the excitation spread in three virtual patches of ventricular tissue that have different resolutions. On the other hand we simulate a realistic excitation sequence in an anisotropic and electrophysiologically heterogeneous biventricular model. Our patch experiments with different spatial resolutions demonstrated that resolutions below 0.2 mm led to a deformation of the excitation wavefront to non-elliptical shapes. The biventricular model with 0.2 mm grid size shows realistic excitation spread and conduction velocities. Similar biventricular models in conjunction with a computational representation of the thorax will be used in future to predict the effects of changes on the ion-channel level on the ECG.
Current models of the human atria represent geometries of single individuals or base on statistical data. We present a work-flow for the creation of patient-specific atrial models. Furthermore we show a framework to compare simulated P- waves and body surface potential maps (BSPMs) of individual patients with measurements. Models of the atrial and thorax anatomy were segmented from MRI data. Volumetric atrial models were semi-automatically enhanced with electrophys- iologically (EP) relevant structures. Simulations were performed on an anisotropic voxel-based mesh and were forward calculated to obtain simulated BSPMs. BSPMs were acquired using a 64 electrode ECG system. Comparison of simulated and measured P-waves in Einthoven leads showed a general agreement of both, although no personalization of the atrial electrophysiology model was performed. P-wave duration was longer in the simulations, highlighting the need for elec- trophysiological model personalization. Simulated and measured BSPMs revealed similar patterns. The presented method enables realistic simulations of atrial activation on patient-specific volumetric atrial models with EP relevant myocardial structures resulting in computed ECGs (P-wave) and BSPMs with show physiological morphologies
Motivation: Anatomical models of the heart can be used to conduct multi-physics simulations. These simulations can aid basic and clinical research and are being translated into clinical practice nowadays.Problem statement: The human myocardium has very complex fiber structure, which has a strong impact on cardiac physiology. To understand and evaluate 3D fiber orientation in volumetric cardiac models, it is often necessary to project these onto printed pictures.Approach: Images of myocardial fibers using color-coded cylinders, color-coded streamlines and anaglyph methods are compared. Results: Streamlines provide a good distinction of myocardial bundles. Cylinders show the most accurate results. Color-coded representations reveal abrupt changes in fiber direction. Anaglyph visualizations give an illusion of depth in 2D prints and can display overlaying bundles. Conclusions: Streamlines are superior in imaging global fiber orientation, whereas cylinders give better results for local structures. Color-coding increases information where fiber structure is very complex, e.g. in the atria. Anaglyph images cause a loss in color information but help the viewer to understand the 3D object. Overall, it is necessary to choose the appropriate method of picturing fibers for specific tasks.
M. Wilhelms, O. Dössel, and G. Seemann. Simulating the Impact of the Transmural Extent of Acute Ischemia on the Electrocardiogram. In Computing in Cardiology, vol. 37, pp. 13-16, 2010
During acute cardiac ischemia, electrophysiological properties of the affected tissue are altered in the subendocardium firstly. If the occlusion worsens, the effects spread transmurally. Diagnosis of cardiac ischemia, which should be improved by computer simulations, is based on shifts of the ST segment. In this work, we simulated heterogeneous ischemic regions with varying transmural extent. The excitation propagation and ECGs were calculated for the different setups. We showed that ST segment polarity can be dependent on the transmural extent of the ischemic region. In case of subendocardial ischemia, short action potentials were initiated in the ischemic zone causing a slight transmural gradient of the transmembrane voltage. Therefore, the ST segment was depressed in leads near the ischemic region in the chosen case. During transmural ischemia, this gradient showed in the opposite direction from epicardium to endocardium leading to ST segment elevation.
M. Wilhelms, G. Seemann, M. Weiser, and O. Dössel. Benchmarking Solvers of the Monodomain Equation in Cardiac Electrophysiological Modeling. In Biomedizinische Technik / Biomedical Engineering, vol. 55(s1) , pp. 99-102, 2010
The monodomain model is a mathematical description of the electrical excitation propagation in the heart. The numerical solution of this reaction-diffusion equation is a computationally demanding task. Aspects that have to be considered are the accuracy and stability of the solution on the one hand and the computing time on the other hand. Two first order methods an explicit and a semi-implicit scheme solving the monodomain equation were compared in this work. For the benchmark of the solvers, three cell models with different computational complexity were used. Thus, the contribution of the solvers to the total computing time could be analyzed. Generally, if the same time step was used, the semi-implicit was slower than the explicit one, since an additional linear system of equations had to be solved. However, the semi-implicit solver was more accurate and showed better stability behavior than the explicit one, especially at high spatial resolutions. Therefore, larger time steps could be used, achieving the same accuracy and a shorter total computing time as the explicit solver. However, this effect was present only, if the additional calculations of the semi-implicit solver contributed less to the total computing time, i.e. the cell model had to be computationally complex.