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.
Ventricular wall deformation is widely assumed to have an impact on the morphology of the T-wave that can be measured on the body surface. This study aims at quantifying these effects based on an in silico approach. To this end, we used a hybrid, static-dynamic approach: action potential propagation and repolarization were simulated on an electrophysiologically detailed but static 3-D heart model while the forward calculation accounted for ventricular deformation and the associated movement of the electrical sources (thus, it was dynamic). The displacement vectors that describe the ventricular motion were extracted from cinematographic and tagged MRI data using an elastic registration procedure. To probe to what extent the T-wave changes depend on the synchrony/asynchrony of mechanical relaxation and electrical repolarization, we created three electrophysiological configurations, each with a unique QT time: a setup with physiological QT time, a setup with pathologically short QT time (SQT), and pathologically long QT time (LQT), respectively. For all three electrophysiological configurations, a reduction of the T-wave amplitude was observed when the dynamic model was used for the forward calculations. The largest amplitude changes and the lowest correlation coefficients between the static and dynamic model were observed for the SQT setup, followed by the physiological QT and LQT setups.
BACKGROUND: The prevalence of atrial fibrillation is increased in patients with end-stage renal disease. Previous studies suggested that extracellular electrolyte alterations caused by hemodialysis (HD) therapy could be proarrhythmic. METHODS: Multiscale models were used for a consequent analysis of the effects of extracellular ion concentration changes on atrial electrophysiology. Simulations were based on measured electrolyte concentrations from patients with end-stage renal disease. RESULTS: Simulated conduction velocity and effective refractory period are decreased at the end of an HD session, with potassium having the strongest influence. P-wave is prolonged in patients undergoing HD therapy in the simulation as in measurements. CONCLUSIONS: Electrolyte concentration alterations impact atrial electrophysiology from the action potential level to the P-wave and can be proarrhythmic, especially because of induced hypokalemia. Analysis of blood electrolytes enables patient-specific electrophysiology modeling. We are providing a tool to investigate atrial arrhythmias associated with HD therapy, which, in the future, can be used to prevent such complications.
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 paper, we present an efficient method to estimate changes in forward-calculated body surface potential maps (BSPMs) caused by variations in tissue conductivities. For blood, skeletal muscle, lungs, and fat, the influence of conductivity variations was analyzed using the principal component analysis (PCA). For each single tissue, we obtained the first PCA eigenvector from seven sample simulations with conductivities between ±75% of the default value. We showed that this eigenvector was sufficient to estimate the signal over the whole conductivity range of ±75%. By aligning the origins of the different PCA coordinate systems and superimposing the single tissue effects, it was possible to estimate the BSPM for combined conductivity variations in all four tissues. Furthermore, the method can be used to easily calculate confidence intervals for the signal, i.e., the minimal and maximal possible amplitudes for given conductivity uncertainties. In addition to that, it was possible to determine the most probable conductivity values for a given BSPM signal. This was achieved by probing hundreds of different conductivity combinations with a numerical optimization scheme. In conclusion, our method allows to efficiently predict forward-calculated BSPMs over a wide range of conductivity values from few sample simulations.
Conduction velocity (CV) and CV restitution are important substrate parameters for understanding atrial arrhythmias. The aim of this work is to (i) present a simple but feasible method to measure CV restitution in-vivo using standard circular catheters, and (ii) validate its feasibility with data measured during incremental pacing. From five patients undergoing catheter ablation, we analyzed 8 datasets from sinus rhythm and incremental pacing sequences. Every wavefront was measured with a circular catheter and the electrograms were analyzed with a cosine-fit method that calculated the local CV. For each pacing cycle length, the mean local CV was determined. Furthermore, changes in global CV were estimated from the time delay between pacing stimulus and wavefront arrival. Comparing local and global CV between pacing at 500 and 300 ms, we found significant changes in 7 of 8 pacing sequences. On average, local CV decreased by 2015% and global CV by 1713%. The method allows for in-vivo measurements of absolute CV and CV restitution during standard clinical procedures. Such data may provide valuable insights into mechanisms of atrial arrhythmias. This is important both for improving cardiac models and also for clinical applications, such as characterizing arrhythmogenic substrates during sinus rhythm.
M. Wilhelms, O. Dössel, and G. Seemann. In silico investigation of electrically silent acute cardiac ischemia in the human ventricles. In IEEE Transactions on Biomedical Engineering, vol. 58(10) , pp. 2961-2964, 2011
Acute cardiac ischemia, which is caused by the occlusion of a coronary artery, often leads to lethal ventricular arrhythmias or heart failure. The early diagnosis of this pathology is based on changes of the electrocardiogram (ECG), i.e. mainly shifts of the ST segment. However, the underlying mechanisms responsible for these shifts are not completely understood. Furthermore, clinical observations indicate that some acute ischemia cases can hardly be detected using standard 12-lead ECG only. Therefore, multi-scale computer simulations of cardiac ischemia using realistic models of human ventricles were carried out in this work. For this purpose, the transmembrane voltage distributions in the heart and the corresponding body surface potentials were computed with varying transmural extent of the ischemic region at different ischemia stages. Some of the simulated ischemia cases were electrically silent, i.e. they could hardly be identified in the 12-lead ECG.
The objective of personalised modelling of the atria is to improve comprehension of the etiology of atrial arrhythmias, to enable specific diagnosis and to optimise therapy. We start with CT or MR datasets and use adapted segmentation procedures to build a patient-specific 3D-model of the atria. Then we include fibre direction based on the rules of atrial anatomy. Work in progress is also considering late enhancement MRI in order to add areas of fibrotic tissue. Next we can use BSPM data of the P-wave and solve the inverse problem of ECG to get a hypothesis about the spread of depolarisation. Finally we use intracardiac catheter signals (e.g. using a circular catheter) to measure direction and conduction velocity of depolarisation waves (sinus rhythm, atrial flutter, or following stimulation). All this is integrated into a personalised model of the atria of an individual patient. Our next goal will be to properly add ablation lines into the model.The research leading to these results has partly received funding from the European Communitys Seventh Framework Programme (FP7/2007-2013) under grant agreement n 224495 (euHeart project).
A framework for step-by-step personalization of a computational model of human atria is presented. Beginning with anatomical modeling based on CT or MRI data, next fiber structure is superimposed using a rule-based method. If available, late-enhancement-MRI images can be considered in order to mark fibrotic tissue. A first estimate of individual electrophysiology is gained from BSPM data solving the inverse problem of ECG. A final adjustment of electrophysiology is realized using intracardiac measurements. The framework is applied using several patient data. First clinical application will be computer assisted planning of RF-ablation for treatment of atrial flutter and atrial fibrillation.
T. Fritz, O. Jarrousse, D. Keller, G. Seemann, and O. Dössel. In silico analysis of the impact of transmural myocardial infarction on cardiac mechanical dynamics for the 17 AHA segments. In Proceedings of the 6th International Conference on Functional Imaging and Modeling of the Heart, vol. LNCS, 6666, pp. 241-249, 2011
The impact of transmural infarctions of the left ventricle on the cardiac mechanical dynamics is evaluated for all 17 AHA segments in a computer model. The simulation framework consists of two parts: an electrophysiological model and an elastomechanical model of the ventricles. The electrophysiological model is used to simulate the electrophysiological processes on cellular level, excitation propagation and the tension development. It is linked to the elastomechanical model, which is based on nonlinear finite element analysis for continuum mechanics. Altogether, 18 simulations of the contraction of the ventricles were performed, 17 with an infarction in the respective AHA segment and one simulation for the control case. For each simulation, the mechanical dynamics as well as the wall thickening of the infarct region were analyzed and compared to the corresponding region of the control case. The simulation revealed details of the impact of the myocardial infarction on wall thickening as well as on the velocity of the infarct region for most of the AHA segments
T. Fritz, G. Seemann, and O. Dössel. Analyzing transmural myocardial infarction of the left ventricle using computer modeling. In 4th Cardiac Physiome Workshop, vol. Poster, 2011
Elastomechanical modeling of the heart can help to gain a deeper insight into the mechanical dynamics of the heart. Furthermore it can help to enhance diagnostic strategies and to investigate new therapeutic approaches. Phase contrast magnetic resonance imaging allows to directly measure the velocity vector field of the myocardial motion over the cardiac cycle. Aim of this work was to analyze the impact of transmural myocardial infarction on the velocity vector field of the left ventricle in a numerical model of the heart. For this purpose a multi-scale electromechanical computer framework was used. It consisted of two parts: an electrophysiological model and an elastomechanical model. The electrophysiological model described the electrophysiological processes on cellular level, the excitation propagation as well as the tension development. It was was linked to an elastomechanical model which was based on nonlinear continuum mechanics using the finite element method. The computer framework was used to simulate the contraction of the heart with left ventricular transmural infarctions, differing in size, location and stiffness of the scar tissue. For each simulation, the velocity vector field of the infarct region was analyzed and compared to the corresponding region of the control case. The simulations revealed a direct impact of the myocardial infarction on the magnitude and orientation of the velocity vectors of the affected region.
Atrial myofiber orientation is complex and has multiple discrete layers and bundles. A novel robust semi-automatic method to incorporate atrial anisotropy and heterogeneities into patient-specific models is introduced. The user needs to provide 22 distinct seed-points from which a network of auxiliary lines is constructed. These are used to define fiber orientation and myocardial bundles. The method was applied to 14 patient-specific volumetric models derived from CT, MRI and photographic data. Initial electrophysiological simulations show a significant influence of anisotropy and heterogeneity on the excitation pattern and P-wave duration (20.7% shortening). Fiber modeling results show good overall correspondence with anatomical data. Minor modeling errors are observed if more than four pulmonary veins exist in the model. The method is an important step towards creating realistic patient-specific atrial models for clinical applications.
Atrial fibre architecture has complex patterns of bundles and layers and is known to impact on atrial electrophysiology, especially in fast-conducting bundles like Crista Terminalis, Bachmanns bundle and pectinate muscles. Based on a priori knowledge of atrial fibre structure, we incorporated rule-based fibre orientation in seven volumetric models of human atria using a semi-automatic approach. We were able to introduce multiple layers of myofibres and regional heterogeneities of ion channels in the models. We evaluated the influence of complete atrial fibre architecture on multiple modelling scales. First, we simulated atrial excitation in the isotropic and anisotropic models using the model of Courtemanche et al. in combination with the monodomain approach. Second, we computed body surface potentials from the simulated transmembrane voltages and compared these to measured ECGs from the respective patients. Temporal behaviour of the atrial excitation sequences was significantly altered in the anisotropic models compared to the sequences in the isotropic models. Complete atrial activation was achieved approximately 20% faster in the anisotropic models mostly due to fast conducting myofibre bundles. Electrophysiological heterogeneities influenced right atrial transmembrane voltage distribution over time due to a less negative action potential plateau in Crista Terminalis cells. P-wave duration was significantly shorted by the introduction of atrial anisotropy and the error to measured P-wave duration was reduced. Furthermore, a pattern change in body surface potential distribution over time was observed. The anisotropic patterns showed a better match to the measurements. Thus, the modelling error by using generalised fibre architecture for patient-specific models was smaller than by using isotropic models. The results highlight the necessity to incorporate atrial anisotropy in personalised models to produce more realistic simulations. The semi-automatic approach allows the use of these models for future clinical applications.
Background: Patients with end-stage renal disease show an increased prevalence of atrial fibrillation. A combined simulation and electrocardio- gram analysis study revealed a correlation between the changes in plasma electrolytes and intra-atrial conduction velocity related to hemodialysis (HD) session. A recognized limitation of the study is that simulations were performed on single-cell level. We present a computer study to investigate the influence of HD-related electrolyte modifications on atrial electrophys- iology in a volumetric environment.Methods: Based on the Courtemanche-Ramirez-Nattel model and its parameterization for different atrial tissues, we studied action potential, effective refractory period, conduction velocity (CV) restitution, and wave length restitution for common atrial myocardium (CAM) and fast conducting Crista Terminalis (CT). We used isotropic, homogeneous tissue patches. External stimuli were applied with 184 different pacing rates (PRs) from 330 to 1250 milliseconds.Results: The effect of temporary HD- related electrolyte changes on the action potential morphology and effective refractory period showed results consistent with the previous single-cell study. Action potential morphology was not significantly altered both in CAM and CT, but resting potential decreased from ␣82.6 to ␣88.2 mV for CAM and from ␣81.7 to ␣87.3 mV for CT. Effective refractory period decreased from 32 (pre-HD) to 308 milliseconds (end-HD). At a PR of 832 milliseconds, CV dropped by ␣6.3% for both types of tissue (CAM: 741 694 mm/s; CT: 746 699 mm/s). Wave length increased slightly with higher PR, but rapidly fell off below a PR of 450 milliseconds. Wave length was ␣30 mm shorter in the end-HD condition.Conclusions: Conduction velocity decrease and consequent wave length shortening increases vulnerability for atrial fibrillation onset, especially in conjunction with structural dilation often present in atria of end-stage renaldisease patients. Temporary HD-caused electrical remodeling has equal effects on regular and fast-conducting tissue. Although there is no biophysical model for fast interatrial condition pathways (eg, Bachmann dundle) available, the HD influence on them should also be similar and therefore slow down interatrial conduction significantly. It has been suggested that constantly repeating alteration of atrial electrophysiology may lead to a longer lasting electrical atrial remodeling; future studies should therefore investigate the long-term HD effects.
IntroductionAtrial fibrillation (AF) is the most common cardiac arrhythmia. Over 4.5 million people in the European Union suffer from AF. The mechanisms leading to AF are still not completely understood although various theories were proposed. Numerical models of the human atria can help to understand these mechanisms. Personalized atrial models may in fu- ture be used to set up patient-specific therapies.MethodsPersonalization of atrial models splits into different tasks. The individual atrial and thorax anatomy are derived from various imaging modalities (CT, MRI). Valuable information is hidden in these data, such as atrial wall thickness and myocardial fiber structure. The missing parts are added to the geometric model using rule-based approaches. Atrial electrophysiology is adapted to different pathologies (e.g. remodeling, genetic defects) and to ECG and intracardiac measurements of the individual patient by tuning model parameters (e.g. conductivity).ResultsPersonalization of atrial anatomy enables a realistic simulation of atrial excitation propagation during sinus rhythm. Ad- justment of the generalized electrophysiology model to the according patient group provides insights into the substrate of the known global effects. Adaption of these model parameters to the individual patient results in a better fit of simu- lated intracardiac and ECG signals to the measurements.ConclusionWith the help of various personalization techniques, generalized atrial models can be adapted to patient data. These models may in future be used for personalized model-based AF-treatment planning.
In spite of the considerable medical and technical progress during the last years, catheter ablation of atrial fibrillation is still challenging. For a successful execution of the ablation and the avoidance of intricacies the catheter must be in contact with the endocardium, which is still difficult to assure with existent techniques. It would be desirable to detect the endocardial catheter contact directly from the signal shape and its properties. In this work, significant signal property changes were detected and investigated, which allow an automatic contact detection. Furthermore, atrial electrograms were simulated and compared with a database of measured and annotated signals. During these simulations, the distance between endocardium and the catheter tip could be chosen discretionary. The simulated signals revealed themselves to be very accurate. Simulations can now be used to analyse intracardiac signals more closely. The exact position of the catheter will hereby always be assured, which is not always granted in clinical practice.
Background: Catheter ablation of complex atrial arrhythmias, such as atrial fibrillation and atypical atrial flutter, is still challenging. Clinically evaluated ablation methods are leading to moderate success rates. Assessments of intracardiac electrograms are often done subjectively by the physician. Automatic algorithms can therefore improve the analysis of complex atrial electrograms (EGMs). In this work, we demonstrate a quantitative analysis of intracardiac EGMs from circular mapping catheters in humans. Both the wave direction and the local conduction velocity (CV) were calculated from individual wave fronts passing the catheter.Methods: Intracardiac EGMs measured with circular mapping catheters in humans were retrospectively analyzed. Five data sets from 3 patients undergoing catheter ablation of atrial fibrillation or flutter were available. Using a nonlinear energy operator, activation times from 9 bipolar catheter signals were calculated for each atrial activity. The resulting activation pattern was fitted to a cosine-shaped data model that has been validated in a previous simulation study. The cosine phase represented the wave direction. From the cosine amplitude and the catheter radius, the conduction velocity was calculated.Results: The wave directions in all five measurements were stable with a standard deviation below 10°. Calculated CVs were in the range of 70 to 110 cm/s, which is in accordance with published values. In one patient, electrograms were recorded during atrial stimulation. Stimulation cycle length was decreased from 500 to 300 milliseconds. Conduction velocity decreased by approximately 10% at a cycle length of 300 milliseconds compared with the CV at 500 milliseconds.Conclusion: The results show the ability to reliably extract wave direction and conduction velocity from intracardiac EGMs recorded with circular mapping catheters. Detected directions were stable, and the CV values were in a physiological range. As individual beats are analyzed, the method will also enable the quantitative study of singular events such as ectopic beats and facilitate the localization of tachycardia origins. Further, it will help to measure substrate parameters such as the CV and even CV restitution behavior. This way, the method can help to identify patient-specific physiological parameters that can be integrated into patient-specific models. Furthermore, it can directly provide quantitative data of high diagnostic value to the examiner and thereby improve clinical success rates.
M. Wilhelms, O. Dössel, and G. Seemann. Comparing Simulated Electrocardiograms of Different Stages of Acute Cardiac Ischemia. In FIMH 2011, LNCS, vol. 6666, pp. 11-19, 2011
Diagnosis of acute cardiac ischemia depends on characteristic shifts of the ST segment. The transmural extent of the ischemic region and the temporal stage of ischemia have an impact on these changes. In this work, computer simulations of realistic ventricles with different transmural extent of the ischemic region were carried out. Furthermore, three stages within the first half hour after the occlusion of the distal left anterior descending coronary artery were regarded. The transmembrane voltage distributions and the corresponding body surface ECGs were calculated. It was observed how the electrophysiological properties worsen in the course of ischemia, so that almost no excitation was initiated in the central ischemic zone 30 minutes after the occlusion. In addition to these temporal effects, also the transmural extent of the ischemic region had an impact on the direction and intensity of the ST segment shift.