Cardiac re-entry dynamics & self-termination in DT-MRI based model of Human Foetal Heart

The effect of heart geometry and anisotropy on cardiac re-entry dynamics and self-termination is studied here in anatomically realistic computer simulations of human foetal heart. 20 weeks of gestational age human foetal heart isotropic and anisotropic anatomy models from diffusion tensor MRI data sets are used in the computer simulations. The fibre orientation angles of the heart were obtained from the DT-MRI primary eigenvalues. In a spatially homogeneous electrophysiological mono domain model with the DT-MRI based heart geometries, we initiate simplified Fitz-Hugh-Nagumo kinetics cardiac re-entry at a prescribed location in a 2D slice, and in the full 3D anatomy model. In a slice of the heart, the MRI based fibre anisotropy changes the re-entry dynamics from pinned to anatomical re-entry. In the full 3D MRI based model, the foetal heart fibre anisotropy changes the re-entry dynamics from a persistent re-entry to the re-entry self-termination

BeatBox - HPC simulation environment for biophysically and anatomically realistic cardiac electrophysiology

The BeatBox simulation environment combines flexible script language user interface with the robust computational tools, in order to setup cardiac electrophysiology in-silico experiments without re-coding at low-level, so that cell excitation, tissue/anatomy models, stimulation protocols may be included into a BeatBox script, and simulation run either sequentially or in parallel (MPI) without re-compilation. BeatBox is a free software written in C language to be run on a Unix-based platform. It provides the whole spectrum of multi scale tissue modelling from 0-dimensional individual cell simulation, 1-dimensional fibre, 2-dimensional sheet and 3-dimensional slab of tissue, up to anatomically realistic whole heart simulations, with run time measurements including cardiac re-entry tip/filament tracing, ECG, local/global samples of any variables, etc. BeatBox solvers, cell, and tissue/anatomy models repositories are extended via robust and flexible interfaces, thus providing an open framework for new developments in the field. In this paper we give an overview of the BeatBox current state, together with a description of the main computational methods and MPI parallelisation approaches.Comment: 37 pages, 10 figures, last version submitted to PLOS ON

Cardiac re-entry dynamics and self-termination in DT-MRI based model of Human Foetal Heart

The effect of human fetal heart geometry and anisotropy on anatomy induced drift and self-termination of cardiac re-entry is studied here in MRI based 2D slice and 3D whole heart computer simulations. Isotropic and anisotropic models of 20 weeks of gestational age human fetal heart obtained from 100 μm voxel diffusion tensor MRI data sets were used in the computer simulations. The fiber orientation angles of the heart were obtained from the orientation of the DT-MRI primary eigenvectors. In a spatially homogeneous electrophysiological monodomain model with the DT-MRI based heart geometries, cardiac re-entry was initiated at a prescribed location in a 2D slice, and in the 3D whole heart anatomy models. Excitation was described by simplified FitzHugh-Nagumo kinetics. In a slice of the heart, with propagation velocity twice as fast along the fibers than across the fibers, DT-MRI based fiber anisotropy changes the re-entry dynamics from pinned to an anatomical re-entry. In the 3D whole heart models, the fiber anisotropy changes cardiac re-entry dynamics from a persistent re-entry to the re-entry self-termination. The self-termination time depends on the re-entry's initial position. In all the simulations with the DT-MRI based cardiac geometry, the anisotropy of the myocardial tissue shortens the time to re-entry self-termination several folds. The numerical simulations depend on the validity of the DT-MRI data set used. The ventricular wall showed the characteristic transmural rotation of the helix angle of the developed mammalian heart, while the fiber orientation in the atria was irregula

Dynamics of cardiac re-entry in micro-CT and serial histological sections based models of mammalian hearts

Cardiac re-entry regime of self-organised abnormal synchronisation underlie dangerous arrhythmias and fatal fibrillation. Recent advances in the theory of dissipative vortices, experimental studies, and anatomically realistic computer simulations, elucidated the role of cardiac re-entry interaction with fine anatomical features in the heart, and anatomy induced drift. The fact that anatomy and structural anisotropy of the heart is consistent within a species suggested its possible functional effect on spontaneous drift of cardiac re-entry. A comparative study of the anatomy induced drift could be used in order to predict evolution of atrial arrhythmia, and improve low-voltage defibrillation protocols and ablation strategies. Here, in micro-CT based model of rat pulmonary vein wall, and in sheep atria models based on high resolution serial histological sections, we demonstrate effects of heart geometry and anisotropy on cardiac re-entry anatomy induced drift, its pinning to fluctuations of thickness in the layer. The data sets of sheep atria and rat pulmonary vein wall are incorporated into the BeatBox High Performance Computing simulation environment. Re-entry is initiated at prescribed locations in the spatially homogeneous mono-domain models of cardiac tissue. Excitation is described by FitzHugh-Nagumo kinetics. In the in-silico models, isotropic and anisotropic conduction show specific anatomy effects and the interplay between anatomy and anisotropy of the heart. The main objectives are to demonstrate the functional role of the species hearts geometry and anisotropy on cardiac re-entry anatomy induced drift. In case of the rat pulmonary vein wall with ~90 degree transmural fibre rotation, it is shown that the joint effect of the PV wall geometry and anisotropy turns a plane excitation wave into a re-entry pinned to a small fluctuation of thickness in the wall

Areas of Effectiveness of Half-Sine Monophasic and Biphasic Depolarizing Defibrillation Pulses on the Diagram of Energy / Phase of Fibrillation Cycle

Благодарим АО «ПО «УОМЗ», в лице главного конструктора КБ медицинских изделий Чупова Алексея Александровича, за активное развитие прикладных исследований в области электрической дефибрилляции.Поступила: 15.12.2021. Принята в печать: 12.01.2022.We are grateful to JSC PA UOMZ, represented by the chief designer of the design bureau of medical devices, Aleksey A. Chupov, for the active development of applied research in the field of electrical defibrillation.Received: 15.12.2021. Accepted: 12.01.2022.Целью данного исследования является сравнение областей эффективности полусинусоидальных монополярного и биполярного деполяризующих дефибрилляционных импульсов на диаграмме энергия / фаза цикла фибрилляции. Результаты компьютерного моделирования показали, что области эффективности у монополярного и биполярного дефибрилляционных импульсов имеют существенное различие. У биполярного импульса доля цикла фибрилляции, на которой обеспечивается удлинение рефрактерности, при низких значениях энергии дефибрилляционного импульса существенно превышает таковую у монополярного импульса. Можно предположить, что этим обеспечивается энергетическое преимущество биполярного импульса дефибрилляции перед монополярным.The aim of this study is to compare the areas of effectiveness of half-sine monophasic and biphasic depolarizing defibrillation pulses in the diagram of energy / phase of fibrillation cycle. The study was carried out on the ten Tusscher-Panfilov 2006 model of the human ventricular myocyte under the influence of simulated fibrillation in the BeatBox simulation environment under the Fedora operating system. The simulation was carried out on a computer under the Windows 10 operating system, the Fedora operating system was implemented in the Oracle VM VirtualBox virtualization environment. The results of computer simulations have shown that the areas of effectiveness for monophasic and biphasic defibrillation pulses are significantly different. In a biphasic pulse, the fraction of a fibrillation cycle at which refractoriness is extended is significantly higher than that of a monophasic pulse at low defibrillation pulse energies. It can be assumed that this provides the energy advantage of a biphasic defibrillation pulse over a monophasic one.Настоящие исследования выполнены при реализации проекта «Создание высокотехнологичного производства медицинских изделий для восстановления функции сердца в обеспечение общедоступной дефибрилляции».This research was carried out during the implementation of the project “Creation of high-tech production of medical devices for the restoration of heart function to ensure public defibrillation”

Comparison of the Energy Efficiency of Defibrillation Pulses Based on the Hypothesis of Guaranteed Defibrillation

Благодарим АО «ПО «УОМЗ», в лице главного конструктора КБ медицинских изделий Чупова Алексея Александровича, за активное развитие прикладных исследований в области электрической дефибрилляции.Поступила: 27.09.2021. Принята в печать: 12.01.2022.We are grateful to JSC PA UOMP, represented by the chief designer of the design bureau of medical devices, Aleksey A. Chupov, for the active development of applied research in the field of electrical defibrillation.Received: 27.09.2021. Accepted: 12.01.2022.Целью данного исследования является сравнение на основе гипотезы гарантированной дефибрилляции энергетической эффективности биполярного трапецеидального импульса с фиксированной длительностью фронта и среза с основными типами дефибрилляционных импульсов: классической трапецеидальной (truncated exponential) со спадом вершины 50%, прямоугольной и полусинусоидальной. Результаты компьютерного моделирования на базе гипотезы гарантированной дефибрилляции показали, что дефибрилляционные импульсы энергетически эффективны (имеют низкие значения пороговой энергии дефибрилляции) в достаточно узком диапазоне значений длительности фаз, за пределами которого наблюдается быстрый рост пороговой энергии. По энергетической эффективности трапецеидальный импульс с пологими фронтом и срезом очень близок к полусинусоидальному, и при этом он имеет более широкий диапазон энергетически эффективных длительностей. Существенно более высокую минимальную пороговую энергию гарантированной дефибрилляции имеют прямоугольный и классический трапецеидальный со спадом вершины 0,5 импульсы, при этом классический трапецеидальный импульс имеет более равномерную характеристику в области энергетически эффективных длительностей. Из полученных результатов можно предположить, что максимальную длительность фаз дефибрилляционного импульса следует ограничивать значением не более 9 мс. При этом номинальная выделенная энергия на сопротивлении нагрузки 175 Ом должна составлять не менее 140 Дж. Возможность увеличения длительности импульса без значимого падения его энергетической эффективности позволит обеспечить выделение большей энергии у больных с высоким сопротивлением грудной клетки и, соответственно, большую вероятность проведения успешной дефибрилляции. Указанное выше увеличит также вероятность проведения успешной дефибрилляции у больных при ошибках наложения дефибрилляционных электродов или использовании сухих многоразовых дефибрилляционных электродов.The aim of this study is to compare, on the basis of the guaranteed defibrillation hypothesis, the energy efficiency of a trapezoidal defibrillation pulse with fixed rise and fall times with the main types of defibrillation pulses: truncated exponential with the tilt of 50%, rectangular and half-sine. The study was carried out using the ten Tusscher–Panfilov 2006 human ventricular myocyte model subjected to simulated fibrillation in the BeatBox simulation environment. Depolarizing excitation stimuli with a high frequency were used to simulate fibrillation. The results of computer simulation based on the hypothesis of the guaranteed defibrillation showed that defibrillation pulses are energetically efficient (have low values of threshold energy of defibrillation) in a rather narrow range of phase duration values, beyond which a rapid increase in the threshold energy is observed. In terms of energy efficiency, the trapezoidal pulse with the sloping rise and fall is very close to the half-sine one, and at the same time it has a wider range of energetically effective durations. Significantly higher minimum threshold energy of guaranteed efibrillation is a characteristic of rectangular and truncated exponential pulses, while the truncated exponential pulse has a more uniform characteristic in the area of energetically effective durations. From the results obtained, it can be assumed that the maximum duration of the phases of the defibrillation pulse should be limited to the value of no more than 9ms. In this case, the nominal delivered energy at the load impedance of 175Ω should be at least 140J. The possibility of increasing the pulse duration without a significant drop in its energy efficiency will ensure the delivery of more energy in patients with high transthoracic impedance and, accordingly, a greater probability of successful defibrillation. The above will also increase the probability of successful defibrillation in patients with defibrillation electrodes placement errors.Настоящие исследования выполнены при реализации проекта «Создание высокотехнологичного производства медицинских изделий для восстановления функции сердца в обеспечение общедоступной дефибрилляции».This research was carried out during the implementation of the project “Creation of high-tech production of medical devices for the restoration of heart function to ensure public defibrillation.

High-performance computing for computational biology of the heart

This thesis describes the development of Beatbox — a simulation environment for computational biology of the heart. Beatbox aims to provide an adaptable, approachable simulation tool and an extensible framework with which High Performance Computing may be harnessed by researchers. Beatbox is built upon the QUI software package, which is studied in Chapter 2. The chapter discusses QUI’s functionality and common patterns of use, and describes its underlying software architecture, in particular its extensibility through the addition of new software modules called ‘devices’. The chapter summarises good practice for device developers in the Laws of Devices. Chapter 3 discusses the parallel architecture of Beatbox and its implementation for distributed memory clusters. The chapter discusses strategies for domain decomposition, halo swapping and introduces an efficient method for exchange of data with diagonal neighbours called Magic Corners. The development of Beatbox’s parallel Input/Output facilities is detailed, and its impact on scaling performance discussed. The chapter discusses the way in which parallelism can be hidden from the user, even while permitting the runtime execution user-defined functions. The chapter goes on to show how QUI’s extensibility can be continued in a parallel environment by providing implicit parallelism for devices and defining Laws of Parallel Devices to guide third-party developers. Beatbox’s parallel performance is evaluated and discussed. Chapter 4 describes the extension of Beatbox to simulate anatomically realistic tissue geometry. Representation of irregular geometries is described, along with associated user controls. A technique to compute no-flux boundary conditions on irregular boundaries is introduced. The Laws of Devices are further developed to include irregular geometries. Finally, parallel performance of anatomically realistic meshes is evaluated

Mathematical and Computational Study of Markovian Models of Ion Channels in Cardiac Excitation

This thesis studies numerical methods for integrating the master equations describing Markov chain models of cardiac ion channels. Such models describe the time evolution of the probability that ion channels are in a particular state. Numerical simulations of such models are often computationally demanding because many solvers require relatively small time steps to ensure numerical stability. The aim of this project is to analyse selected Markov chains and develop more efficient and accurate solvers. We separate a Markov chain model into fast and slow time-scales based on the speed of transitions between states. Eliminating the fast transitions, we find an asymptotic reduction of zeroth-order and first-order in a small parameter describing the time-scales separation. We apply the theory to a Markov chain model of the fast sodium channel INa. We consider several variants for classifying some transitions as fast in order to find reduced systems that yield a good accuracy. However, the time step size is still restricted by numerical instabilities. We adapt the Rush-Larsen technique originally developed for gate models. Assuming that a transition matrix can be considered constant during each time step, we solve the Markov chain model analytically. The solution provides a recipe for a stable exponential solver, which we call "Matrix Rush-Larsen" (MRL). Using operator splitting we design an even more flexible "hybrid" method that combines the MRL with other solvers. The resulting improvement in stability allows a large increase in the time step size. In some models, we obtain reasonably accurate results 27 times faster using a hybrid method than with the forward Euler method, even with the maximal time step allowed by the stability constraint. Finally, we extend the cardiac simulation package BeatBox by the developed exponential solvers. We upgrade a format of "ionic" modules which describe a cardiac cell, in order to allow for a specific definition of Markov chain models. We also modify a particular integrator for ionic modules to include the MRL and the hybrid method. To test the functionality of the code, we have converted a number of cellular models into the ionic format. The documented code is available in the official BeatBox package distribution