Electrical wave propagation in an anisotropic model of the left ventricle based on analytical description of cardiac architecture

Mechanistic assessment and ablation of left ventricular assist device related ventricular tachycardia in patients with severe heart failure

Aims: Left-ventricular-assist-devices (lvad) are an established treatment for patients with severe heart failure with reduced ejection fraction (HF) and reduce mortality. However, HF patients have significant substrate for ventricular tachycardia (VT) and the lvad itself might be pro-arrhythmogenic. We investigated the mechanism of VT in lvad-patients in relation to the underlying etiology and provide in silico and ex-vivo data for ablation in these HF patients. Methods and Results: We retrospectively analyzed invasive electrophysiological (EP) studies of 17 patients with VT and lvad. The mechanism of VT was determined using electroanatomical, entrainment and activation time mapping. Ischemic cardiomyopathy was present in 70% of patients. VT originated from the lvad region in >30%. 1/6 patients with VT originating from the lvad region had episodes before lvad implantation, while 7/11 patients with VT originating from other regions had episodes before implantation. Number and time of radiofrequency (RF)-ablation lesions were not different between VTs originating from the lvad or other regions. Long-term freedom from VT was 50% upon ablation in patients with VT originating from the lvad region and 64% if ablation was conducted in other regions. To potentially preemptively mitigate lvad related VT in patients undergoing lvad implantation, we obtained in silico derived data and performed ex-vivo experiments targeting ventricular myocardium. Of the tested settings, application of 25 W for 30 s was safe and associated with optimal lesion characteristics. Conclusion: A significant percentage of patients with lvad undergoing VT ablation exhibit arrhythmia originating in close vicinity to the device and recurrence rates are high. Based on in silico and ex-vivo data, we propose individualized RF-ablation in selected patients at risk for/with lvad related VT.

Meander pattern of spiral wave and the spatial distribution of its cycle length

One of the most interesting dynamics of rotating spiral waves in an excitable medium is meandering. The tip of a meandering spiral wave moves along a complex trajectory, which often takes the shape of an epitrochoid or hypotrochoid with inward or outward petals. The cycle lengths (CLs) of a meandering spiral wave are not constant; rather, they depend on the meandering dynamics. In this paper, we show that the CLs take two mean values, outside T^{out} and inside T^{in} the meandering trajectory with a ratio of T^{in}/T^{out}=(n+1)/n for the inward and (n-1)/n for the outward petals, where n is the number of petals in the tip trajectory. We illustrate this using four models of excitable media and prove this result. These formulas are shown to be suitable for a meandering spiral wave in an anatomical model of the heart. We also show that the effective periods of overdrive pacing of meandering spiral waves depend on the electrode location relative to the tip trajectory. Overall, our approach can be used to study the meandering pattern from the CL data; it should work for any type of dynamics that produces complex tip trajectories of the spiral wave, for example, for a drift due to heterogeneity.

Estimation of left ventricular parameters based on deep learning method

Estimating material properties of personalized human left ventricular (LV) modelling is a central problem in biomechanical studies. In this work we use deep learning (DL) method to evaluating the passive myocardial mechanical properties inversely. In the first part of the paper, we establish a standardized geometric model of the LV. The geometric model parameters are optimized based on 27 different healthy volunteers. In the second part, we use statistical methods and Latin hypercube sampling (LHS) to obtain the geometric parameters data. The LV myocardium is described using a structure-based orthotropic Holzapfel-Ogden constitutive law. The LV diastolic pressure-volume (PV) curves are calculated by numerical simulation. Tn the third part, we establish the multiple neural networks to pblackict PV curve parameters. Then, instead of using constrained optimization problems to solve constitutive parameters, DL was used to establish the nonlinear mapping relationship of geometric parameters, PV curve parameters and constitutive parameters. The results show that the deep learning method can greatly improve the computational efficiency of numerical simulation and increase the possibility of its application in rapid feedback of clinical data.

Parameter variations in personalized electrophysiological models of human heart ventricles

The objectives of this study were to evaluate the accuracy of personalized numerical simulations of the electrical activity in human ventricles by comparing simulated electrocardiograms (ECGs) with real patients’ ECGs and analyzing the sensitivity of the model output to variations in the model parameters. We used standard 12-lead ECGs and up to 224 unipolar body-surface ECGs to record three patients with cardiac resynchronization therapy devices and three patients with focal ventricular tachycardia. Patient-tailored geometrical models of the ventricles, atria, large vessels, liver, and spine were created using computed tomography data. Ten cases of focal ventricular activation were simulated using the bidomain model and the TNNP 2006 cellular model. The population-based values of electrical conductivities and other model parameters were used for accuracy analysis, and their variations were used for sensitivity analysis. The mean correlation coefficient between the simulated and real ECGs varied significantly (from r = 0.29 to r = 0.86) among the simulated cases. A strong mean correlation (r > 0.7) was found in eight of the ten model cases. The accuracy of the ECG simulation varied widely in the same patient depending on the localization of the excitation origin. The sensitivity analysis revealed that variations in the anisotropy ratio, blood conductivity, and cellular apicobasal heterogeneity had the strongest influence on transmembrane potential, while variation in lung conductivity had the greatest influence on body-surface ECGs. Futhermore, the anisotropy ratio predominantly affected the latest activation time and repolarization time dispersion, while the cellular apicobasal heterogeneity mainly affected the dispersion of action potential duration, and variation in lung conductivity mainly led to changes in the amplitudes of ECGs and cardiac electrograms. We also found that the effects of certain parameter variations had specific regional patterns on the cardiac and body surfaces. These observations are useful for further developing personalized cardiac models.

Drift of Scroll Waves in a Mathematical Model of a Heterogeneous Human Heart Left Ventricle

Rotating spiral waves of electrical excitation underlie many dangerous cardiac arrhythmias. The heterogeneity of myocardium is one of the factors that affects the dynamics of such waves. In this paper, we present results of our simulations for scroll wave dynamics in a heterogeneous model of the human left ventricle with analytical anatomically based representation of the geometry and anisotropy. We used a set of 18 coupled differential equations developed by ten Tusscher and Panfilov (TP06 model) which describes human ventricular cells based on their measured biophysical properties. We found that apicobasal heterogeneity dramatically changes the scroll wave dynamics. In the homogeneous model, the scroll wave annihilates at the base, but the moderate heterogeneity causes the wave to move to the apex and then continuously rotates around it. The rotation speed increased with the degree of the heterogeneity. However, for large heterogeneity, we observed formation of additional wavebreaks and the onset of complex spatio-temporal patterns. Transmural heterogeneity did not change the dynamics and decreased the lifetime of the scroll wave with an increase in heterogeneity. Results of our numerical experiments show that the apex may be a preferable location of the scroll wave, which may be important for development of clinical interventions.

Gaussian Process Regressions for Inverse Problems and Parameter Searches in Models of Ventricular Mechanics

Patient specific models of ventricular mechanics require the optimization of their many parameters under the uncertainties associated with imaging of cardiac function. We present a strategy to reduce the complexity of parametric searches for 3-D FE models of left ventricular contraction. The study employs automatic image segmentation and analysis of an image database to gain geometric features for several classes of patients. Statistical distributions of geometric parameters are then used to design parametric studies investigating the effects of: (1) passive material properties during ventricular filling, and (2) infarct geometry on ventricular contraction in patients after a heart attack. Gaussian Process regression is used in both cases to build statistical models trained on the results of biophysical FEM simulations. The first statistical model estimates unloaded configurations based on either the intraventricular pressure or the end-diastolic fiber strain. The technique provides an alternative to the standard fixed-point iteration algorithm, which is more computationally expensive when used to unload more than 10 ventricles. The second statistical model captures the effects of varying infarct geometries on cardiac output. For training, we designed high resolution models of non-transmural infarcts including refinements of the border zone around the lesion. This study is a first effort in developing a platform combining HPC models and machine learning to investigate cardiac function in heart failure patients with the goal of assisting clinical diagnostics.

Conduction in the Heart Wall: Helicoidal Fibers Minimize Diffusion Bias

The mammalian heart must function as an efficient pump while simultaneously conducting electrical signals to drive the contraction process. In the ventricles, electrical activation begins at the insertion points of the Purkinje network in the endocardium. How does the diffusion component of the subsequent excitation wave propagate from the endocardium in a healthy heart wall without creating directional biases? We show that this is a consequence of the particular geometric organization of myocytes in the heart wall. Using a generalized helicoid to model fiber orientation, we treat the myocardium as a curved space via Riemannian geometry, and then use stochastic calculus to model local signal diffusion. Our analysis shows that the helicoidal arrangement of myocytes minimizes the directional biases that could lead to aberrant propagation, thereby explaining how electrophysiological principles are consistent with local measurements of cardiac fiber geometry. We discuss our results in the context of the need to balance electrical and mechanical requirements for heart function.

Suppression of turbulence by heterogeneities in a cardiac model with fiber rotation

Electrical scroll wave turbulence in human ventricles is associated with ventricular fibrillation and sudden cardiac death. We perform three-dimensional simulations on the basis of the anisotropic Fenton-Karma model and show that macroscopic, insulating heterogeneities (e.g., blood vessels) can cause the spontaneous formation of pinned scroll waves. The wave field of these vortices is periodic, and their frequencies are sufficiently high to push the free, turbulent vortices into the system boundaries where they annihilate. Our study considers cylindrical heterogeneities with radii in the range of 0.1 to 2 cm that extend either in the transmural or a perpendicular direction. Thick cylinders cause the spontaneous formation of multi-armed rotors according to a radius-dependence that is explained in terms of two-dimensional dynamics. For long cylinders, local pinning contacts spread along the heterogeneity by fast and complex self-wrapping.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

Mechano-electric heterogeneity of the myocardium as a paradigm of its function

Myocardial heterogeneity is well appreciated and widely documented, from sub-cellular to organ levels. This paper reviews significant achievements of the group, led by Professor Vladimir S. Markhasin, Russia, who was one of the pioneers in studying and interpreting the relevance of cardiac functional heterogeneity.

A model model: a commentary on DiFrancesco and Noble (1985) 'A model of cardiac electrical activity incorporating ionic pumps and concentration changes'

This paper summarizes the advances made by the DiFrancesco and Noble (DFN) model of cardiac cellular electrophysiology, which was published in Philosophical Transactions B in 1985. This model was developed at a time when the introduction of new techniques and provision of experimental data had resulted in an explosion of knowledge about the cellular and biophysical properties of the heart. It advanced the cardiac modelling field from a period when computer models considered only the voltage-dependent channels in the surface membrane. In particular, it included a consideration of changes of both intra- and extracellular ionic concentrations. In this paper, we summarize the most important contributions of the DiFrancesco and Noble paper. We also describe how computer modelling has developed subsequently with the extension from the single cell to the whole heart as well as its use in understanding disease and predicting the effects of pharmaceutical interventions. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

Drift of Scroll Wave Filaments in an Anisotropic Model of the Left Ventricle of the Human Heart

Scroll waves are three-dimensional vortices which occur in excitable media. Their formation in the heart results in the onset of cardiac arrhythmias, and the dynamics of their filaments determine the arrhythmia type. Most studies of filament dynamics were performed in domains with simple geometries and generic description of the anisotropy of cardiac tissue. Recently, we developed an analytical model of fibre structure and anatomy of the left ventricle (LV) of the human heart. Here, we perform a systematic study of the dynamics of scroll wave filaments for the cases of positive and negative tension in this anatomical model. We study the various possible shapes of LV and different degree of anisotropy of cardiac tissue. We show that, for positive filament tension, the final position of scroll wave filament is mainly determined by the thickness of the myocardial wall but, however, anisotropy attracts the filament to the LV apex. For negative filament tension, the filament buckles, and for most cases, tends to the apex of the heart with no or slight dependency on the thickness of the LV. We discuss the mechanisms of the observed phenomena and their implications for cardiac arrhythmias.