ForCEPSS-A framework for cardiac electrophysiology simulations standardization

BACKGROUND AND OBJECTIVE

Simulation of cardiac electrophysiology (CEP) is an important research tool that is increasingly being adopted in industrial and clinical applications. Typical workflows for CEP simulation consist of a sequence of processing stages starting with building an anatomical model and then calibrating its electrophysiological properties to match observable data. While the calibration stages are common and generalizable, most CEP studies re-implement these steps in complex and highly variable workflows. This lack of standardization renders the execution of computational CEP studies in an efficient, robust, and reproducible manner a significant challenge. Here, we propose ForCEPSS as an efficient and robust, yet flexible, software framework for standardizing CEP simulation studies.

METHODS AND RESULTS

Key processing stages of CEP simulation studies are identified and implemented in a standardized workflow that builds on openCARP1 Plank et al. (2021) and the Python-based carputils2 framework. Stages include (i) the definition and initialization of action potential phenotypes, (ii) the tissue scale calibration of conduction properties, (iii) the functional initialization to approximate a limit cycle corresponding to the dynamic reference state according to an experimental protocol, and, (iv) the execution of the CEP study where the electrophysiological response to a perturbation of the limit cycle is probed. As an exemplar application, we employ ForCEPSS to prepare a CEP study according to the Virtual Arrhythmia Risk Prediction protocol used for investigating the arrhythmogenic risk of developing infarct-related ventricular tachycardia (VT) in ischemic cardiomyopathy patients. We demonstrate that ForCEPSS enables a fully automated execution of all stages of this complex protocol.

CONCLUSION

ForCEPSS offers a novel comprehensive, standardized, and automated CEP simulation workflow. The high degree of automation accelerates the execution of CEP simulation studies, reduces errors, improves robustness, and makes CEP studies reproducible. Verification of simulation studies within the CEP modeling community is thus possible. As such, ForCEPSS makes an important contribution towards increasing transparency, standardization, and reproducibility of in silico CEP experiments.

A smoothed boundary bidomain model for cardiac simulations in anatomically detailed geometries

This manuscript presents a novel finite difference method to solve cardiac bidomain equations in anatomical models of the heart. The proposed method employs a smoothed boundary approach that represents the boundaries between the heart and the surrounding medium as a spatially diffuse interface of finite thickness. The bidomain boundary conditions are implicitly implemented in the smoothed boundary bidomain equations presented in the manuscript without the need of a structured mesh that explicitly tracks the heart-torso boundaries. We reported some significant examples assessing the method's accuracy using nontrivial test geometries and demonstrating the applicability of the method to complex anatomically detailed human cardiac geometries. In particular, we showed that our approach could be employed to simulate cardiac defibrillation in a human left ventricle comprising fiber architecture. The main advantage of the proposed method is the possibility of implementing bidomain boundary conditions directly on voxel structures, which makes it attractive for three dimensional, patient specific simulations based on medical images. Moreover, given the ease of implementation, we believe that the proposed method could provide an interesting and feasible alternative to finite element methods, and could find application in future cardiac research guiding electrotherapy with computational models.

Confocal microscopy-based estimation of intracellular conductivities in myocardium for modeling of the normal and infarcted heart

Ventricular arrhythmias are the leading cause of mortality in patients with ischemic heart diseases, such as myocardial infarction (MI). Computational simulation of cardiac electrophysiology provides insights into these arrhythmias and their treatment. However, only sparse information is available on crucial model parameters, for instance, the anisotropic intracellular electrical conductivities. Here, we introduced an approach to estimate these conductivities in normal and MI hearts. We processed and analyzed images from confocal microscopy of left ventricular tissue of a rabbit MI model to generate 3D reconstructions. We derived tissue features including the volume fraction of myocytes (V_myo), gap junctions-containing voxels (V_gj), and fibrosis (V_fibrosis). We generated models of the intracellular space and intercellular coupling. Applying numerical methods for solving Poisson's equation for stationary electrical currents, we calculated normal (σ_myo,n), longitudinal (σ_myo,l), and transverse (σ_myo,t) intracellular conductivities. Using linear regression analysis, we assessed relationships of conductivities to tissue features. V_gj and V_myo were reduced in MI vs. control, but V_fibrosis was increased. Both σ_myo,l and σ_myo,n were lower in MI than in control. Differences of σ_myo,t between control and MI were not significant. We found strong positive relationships of σ_myo,l with V_myo and V_gj, and a strong negative relationship with V_fibrosis. The relationships of σ_myo,n with these tissue features were similar but less pronounced. Our study provides quantitative insights into the intracellular conductivities in the normal and MI heart. We suggest that our study establishes a framework for the estimation of intracellular electrical conductivities of myocardium with various pathologies.

Anisotropic conductive reduced graphene oxide/silk matrices promote post-infarction myocardial function by restoring electrical integrity

Myocardial infarction (MI) remains the leading cause of death globally, often leading to impaired cardiac function and pathological myocardial microenvironment. Electrical conduction abnormalities of the infarcted myocardium not only induce adverse myocardial remodeling but also prevent tissue repair. Restoring the myocardial electrical integrity, particularly the anisotropic electrical signal propagation within the injured area after infarction is crucial for an effective function recovery. Herein, optimized reduced graphene oxide (rGO) functionalized electrospun silk fibroin (rGO/silk) biomaterials presenting anisotropic conductivity and enhanced suturablity were developed and investigated as cardiac patches for their potential in improving the post-MI myocardial function of rat models. The results show that the anisotropic conductive rGO/silk patches exhibit remarkable therapeutic effect on repairing the infarcted myocardium compared to the nonconductive silk and isotropic conductive rGO/silk patches as determined by the enhanced pumping function, reduced susceptibility to arrhythmias, thickened left ventricular walls and improved survival of functional cardiomyocytes. Their notable effect on promoting the angiogenesis of capillaries in the infarcted myocardium has also been demonstrated. This study highlights an effective and biomimetic reconstruction of the electrical myocardial microenvironment based on the anisotropic conductive rGO/silk biomaterials as a promising option for promoting the repair of infarcted myocardium. STATEMENT OF SIGNIFICANCE: The dysfunctional electrical microenvironment in the infarcted myocardium not only aggravates the adverse myocardial remodeling but also limits the effect of cardiac regenerative medicine. Although various conductive biomaterials have been employed to restore the electrical network in the infarcted myocardium in vivo, the anisotropic nature of the myocardial electrical microenvironment which enables directional electrical signal propagation were neglected. In this study, an anisotropic conductive rGO/silk biomaterial system is developed to improve the myocardial function post infarction by restoring the anisotropic electrical microenvironment in the infarcted myocardium. The promoted effects of anisotropic conductive grafts on repairing infarcted hearts are demonstrated with improved pumping function, cardiomyocyte survival, resistance to ventricular fibrillation, and angiogenesis of capillary network.

Approaches for determining cardiac bidomain conductivity values: progress and challenges

Modelling the electrical activity of the heart is an important tool for understanding electrical function in various diseases and conduction disorders. Clearly, for model results to be useful, it is necessary to have accurate inputs for the models, in particular the commonly used bidomain model. However, there are only three sets of four experimentally determined conductivity values for cardiac ventricular tissue and these are inconsistent, were measured around 40 years ago, often produce different results in simulations and do not fully represent the three-dimensional anisotropic nature of cardiac tissue. Despite efforts in the intervening years, difficulties associated with making the measurements and also determining the conductivities from the experimental data have not yet been overcome. In this review, we summarise what is known about the conductivity values, as well as progress to date in meeting the challenges associated with both the mathematical modelling and the experimental techniques. Graphical abstract Epicardial potential distributions, arising from a subendocardial ischaemic region, modelled using conductivity data from the indicated studies.

Finite element modelling of discontinuous action potential propagation in larval zebrafish and human cardiac tissue

Recently the larval zebrafish has emerged as a model organism which is used to assist in the studies of human cardiac electrophysiology. Although they share many similar electrophysiological characteristics, it has been found that the conduction velocity (CV) of action potential (AP) propagation in larval zebrafish heart is up to two orders of magnitude smaller than in the adult mammalian heart. To address this difference, we have developed three dimensional discrete models of larval zebrafish ventricular fibres (LZVF) in order to simulate AP propagation, taking into account the cellular nature of the tissues and intercellular conduction via gap junctions. Since our ultimate goal is to simulate a whole larval zebrafish heart, we have used the phenomenological Fitzhugh Nagumo (FHN) equations to describe transmembrane currents, and manually adjusted the FHN parameters, to fit published AP shapes for larval zebrafish ventricular cells. This has the benefit of reduced computational load compared to approaches based on biophysical ion current models. We have created models for 48 and 72 h post fertilisation LZVF tissue using published AP and cell size data for zebrafish embryos and used mammalian values for passive electrical parameters. Using the gap junction resistivity per myocyte as an adjustable parameter, we were able to obtain CVs in both of our LZVF models which agree with experimental observations. In order to validate our approach, we have applied it to a human ventricular fibre (HVF) model similar in structure and parameters to other models of the mammalian heart, but adjusting the FHN parameters to fit published AP shapes for human ventricular cells. We find good agreement with the human models. The gap junction resistivities used in the LZVF models are significantly higher than in the HVF case and are consistent with a lower density of gap junctions connecting cells.

Impedance and conductivity of bovine myocardium during freezing and thawing at slow rates - implications for cardiac cryo-ablation

Increasing impedance during freezing might be a valuable marker for guiding cardiac cryo-ablation. We provide model based insights on how decreasing temperature below the freezing point of tissue relates to the percentage of frozen water. Furthermore, we provide experimental data for comparing this percentage with the increase in impedance. Measurements were performed on a bovine tissue sample at frequencies between 5 and 80 kHz. Slow cooling and heating rates were applied to minimize temperature gradients in the myocardial sample and to allow accurate assessment of the freezing point. Computer simulation was applied to link impedance with temperature dependent conductivities. The osmotic virial equation was used to estimate the percentage of frozen water. Measurements identified the freezing point at -0.6 ^∘C. At -5 ^∘C, impedance rose by more than a factor of ten compared to that at the freezing point and the percentage of frozen water was estimated as being 89%. At -49 ^∘C impedance had increased by up to three orders of magnitude and ice formation was most pronounced in the extracellular space. Progressive ice formation in tissue is reflected by a large increase in impedance, and impedance increases monotonically with the percentage of frozen water. Its analysis allows for experimental assessment of factors relevant to cell death. Solid ice contributes to the rupture of the micro-vasculature, while phase shifts reflect concentration differences between extra- and intracellular space driving osmotic water transfer across cell membranes.

Generation of a cohort of whole-torso cardiac models for assessing the utility of a novel computed shock vector efficiency metric for ICD optimisation

Implanted cardiac defibrillators (ICDs) seek to automatically detect and terminate potentially lethal ventricular arrhythmias by applying strong internal electric shocks across the heart. However, the optimisation of the specific electrode design and configurations represents an intensive area of research in the pursuit of reduced shock strengths and fewer device complications and risks. Computational whole-torso simulations play an important role in this endeavour, although knowing which specific metric should be used to assess configuration efficacy and assessing the impact of different patient anatomies and pathologies, and the corresponding effect this may have on different metrics has not been investigated. We constructed a cohort of CT-derived high-resolution whole torso-cardiac computational models, including variants of cardiomyopathies and patients with differing torso dimensions. Simulations of electric shock application between electrode configurations corresponding to transveneous (TV-ICD) and subcutaneous (S-ICD) ICDs were modelled and conventional metrics such as defibrillation threshold (DFT) and impedance computed. In addition, we computed a novel metric termed the shock vector efficiency (η), which quantifies the fraction of electrical energy dissipated in the heart relative to the rest of the torso. Across the cohort, S-ICD configurations showed higher DFTs and impedances than TV-ICDs, as expected, although little consistent difference was seen between healthy and cardiomyopathy variants. η was consistently <2% for S-ICD configurations, becoming as high as 13% for TV-ICD setups. Simulations also suggested that a total torso height of approximately 20 cm is required for convergence in η. Overall, η was seen to be approximately negatively correlated with both DFT and impedance. However, important scenarios were identified in which certain values of DFT (or impedance) were associated with a range of η values, and vice-versa, highlighting the heterogeneity introduced by the different torsos and pathologies modelled. In conclusion, the shock vector efficiency represents a useful additional metric to be considered alongside DFT and impedance in the optimisation of ICD electrode configurations, particularly in the context of differing torso anatomies and cardiac pathologies, which can induce significant heterogeneity in conventional metrics of ICD efficacy.

Confocal Microscopy-Based Estimation of Parameters for Computational Modeling of Electrical Conduction in the Normal and Infarcted Heart

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.

Quantifying the effect of uncertainty in input parameters in a simplified bidomain model of partial thickness ischaemia

Reduced blood flow in the coronary arteries can lead to damaged heart tissue (myocardial ischaemia). Although one method for detecting myocardial ischaemia involves changes in the ST segment of the electrocardiogram, the relationship between these changes and subendocardial ischaemia is not fully understood. In this study, we modelled ST-segment epicardial potentials in a slab model of cardiac ventricular tissue, with a central ischaemic region, using the bidomain model, which considers conduction longitudinal, transverse and normal to the cardiac fibres. We systematically quantified the effect of uncertainty on the input parameters, fibre rotation angle, ischaemic depth, blood conductivity and six bidomain conductivities, on outputs that characterise the epicardial potential distribution. We found that three typical types of epicardial potential distributions (one minimum over the central ischaemic region, a tripole of minima, and two minima flanking a central maximum) could all occur for a wide range of ischaemic depths. In addition, the positions of the minima were affected by both the fibre rotation angle and the ischaemic depth, but not by changes in the conductivity values. We also showed that the magnitude of ST depression is affected only by changes in the longitudinal and normal conductivities, but not by the transverse conductivities.