Modeling Excitable Cells with the EMI Equations: Spectral Analysis and Iterative Solution Strategy

Journal of Scientific Computing, Journal Year: 2024, Volume and Issue: 98(3)

Published: Feb. 4, 2024

Abstract In this work, we are interested in solving large linear systems stemming from the extra–membrane–intra model, which is employed for simulating excitable tissues at a cellular scale. After setting related of partial differential equations equipped with proper boundary conditions, provide its finite element discretization and focus on resulting systems. We first give relatively complete spectral analysis using tools theory Generalized Locally Toeplitz matrix sequences. The obtained information used designing appropriate preconditioned Krylov solvers. Through numerical experiments, show that presented solution strategy robust w.r.t. problem parameters, efficient scalable.

Language: Английский

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Evaluating computational efforts and physiological resolution of mathematical models of cardiac tissue

Scientific Reports, Journal Year: 2024, Volume and Issue: 14(1)

Published: July 23, 2024

Computational techniques have significantly advanced our understanding of cardiac electrophysiology, yet they predominantly concentrated on averaged models that do not represent the intricate dynamics near individual cardiomyocytes. Recently, accurate representing cells gained popularity, enabling analysis electrophysiology at micrometer level. Here, we evaluate five mathematical to determine their computational efficiency and physiological fidelity. Our findings reveal cell-based introduced in recent literature offer both precision for simulating small tissue samples (comprising thousands cardiomyocytes). Conversely, traditional bidomain model its simplified counterpart, monodomain model, are more appropriate larger masses (encompassing millions billions For simulations requiring detailed parameter variations along cell membranes, EMI emerges as only viable choice. This distinctively accounts extracellular (E), membrane (M), intracellular (I) spaces, providing a comprehensive framework studies. Nonetheless, model's applicability large-scale tissues is limited by substantial demands subcellular resolution.

Language: Английский

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Deriving the Bidomain Model of Cardiac Electrophysiology From a Cell-Based Model; Properties and Comparisons

Frontiers in Physiology, Journal Year: 2022, Volume and Issue: 12

Published: Jan. 7, 2022

The bidomain model is considered to be the gold standard for numerical simulation of electrophysiology cardiac tissue. provides important insights into conduction properties electrochemical wave traversing muscle in every heartbeat. However, normal resolution, represents average over a large number cardiomyocytes, and more accurate models based on representations all individual cells have therefore been introduced order gain insight close myocytes. here referred as EMI since both extracellular space (E), cell membrane (M) intracellular (I) are explicitly represented model. Here, we show that can derived from cell-based thus reveal relation between two models, obtain an indication error approximation. Also, present simulations comparing results thereby highlight similarities differences models. We observe deviations solutions become larger sizes. Furthermore, very similar when conductive tissue range, but resistance cardiomyocytes increased.

Language: Английский

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Efficient, cell-based simulations of cardiac electrophysiology; The Kirchhoff Network Model (KNM)

npj Systems Biology and Applications, Journal Year: 2023, Volume and Issue: 9(1)

Published: June 14, 2023

Mathematical models based on homogenized representation of cardiac tissue have greatly improved our understanding electrophysiology. However, these are too coarse to investigate the dynamics at level myocytes since cells not present in models. Recently, fine scale been proposed allow for cell-level resolution dynamics, but computationally expensive be used applications like whole heart simulations large animals. To address this issue, we propose a model that balances computational demands and physiological accuracy. The is founded Kirchhoff's current law, represents every myocyte tissue. This allows specific properties assigned individual cardiomyocytes, other cell types fibroblasts can added an accurate manner while keeping computing efforts reasonable.

Language: Английский

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A possible path to persistent re-entry waves at the outlet of the left pulmonary vein

npj Systems Biology and Applications, Journal Year: 2024, Volume and Issue: 10(1)

Published: July 23, 2024

Abstract Atrial fibrillation (AF) is the most common form of cardiac arrhythmia, often evolving from paroxysmal episodes to persistent stages over an extended timeframe. While various factors contribute this progression, precise biophysical mechanisms driving it remain unclear. Here we explore how rapid firing cardiomyocytes at outlet pulmonary vein left atria can create a substrate for re-entry wave. This grounded in recently formulated mathematical model regulation calcium ion channel density by intracellular concentration. According model, number channels controlled In particular, if concentration increases above certain target level, current weakened restore level calcium. During pacing, leading substantial reduction across membrane myocytes, which again reduces action potential duration. spatially resolved cell-based atria, show that reduced duration lead re-entry. Initiated stemming AF lasting several days, critical factor. Our findings illustrate such foster conducive environment through electrical remodeling, characterized diminished currents. underscores importance promptly addressing early prevent their progression chronic stages.

Language: Английский

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Convergence Analysis of BDDC Preconditioners for Composite DG Discretizations of the Cardiac Cell-By-Cell Model

SIAM Journal on Scientific Computing, Journal Year: 2023, Volume and Issue: 45(6), P. A2836 - A2857

Published: Nov. 15, 2023

.A balancing domain decomposition by constraints (BDDC) preconditioner is constructed and analyzed for the solution of composite discontinuous Galerkin discretizations reaction-diffusion systems ordinary partial differential equations arising in cardiac cell-by-cell models. The latter are different from classical bidomain monodomain models based on homogenized descriptions tissue at macroscopic level, therefore they allow representation individual cells, cell aggregates, damaged tissues, nonuniform distributions ion channels membrane. resulting discrete have global solutions across boundaries, hence proposed BDDC appropriate dual primal spaces with additional which transfer information between cells (subdomains) without influencing overall discontinuity solution. A scalable convergence rate bound proved preconditioned operator, while numerical tests validate this investigate its dependence discretization parameters.Keywordscardiac modelscomposite methodsscalable methodsBDDC preconditionersMSC codes65N5565M5565F1092C30

Language: Английский

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Biophysical Modeling of Cardiac Cells: From Ion Channels to Tissue

Biophysica, Journal Year: 2025, Volume and Issue: 5(1), P. 5 - 5

Published: Feb. 14, 2025

Cardiovascular diseases have become the leading cause of death in developed countries. Among these, some are related to disruptions electrical synchronization cardiac tissue arrhythmias such as atrial flutter, ventricular tachycardia, or fibrillation. Their origin is diverse and involves several spatial temporal scales, ranging from nanoscale ion channel dysfunctions tissue-level fibrosis ischemia. Mathematical models play a crucial role elucidating mechanisms underlying by simulating physiological properties across different scales. These investigate effects genetic mutations, pathological conditions, anti-arrhythmic interventions on heart dynamics. Despite their varying levels complexity, they proven be important understanding triggers arrhythmia, optimizing defibrillation protocols, exploring nonlinear dynamics electrophysiology. In this work, we present modeling approaches electrophysiology cells share examples our own research where these significantly contributed arrhythmias. Although computational faces challenges integrating data multiple it remains an indispensable tool for advancing knowledge biophysics improving therapeutic strategies.

Language: Английский

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Determining properties of human‐induced pluripotent stem cell‐derived cardiomyocytes using spatially resolved electromechanical metrics

The Journal of Physiology, Journal Year: 2025, Volume and Issue: unknown

Published: Feb. 17, 2025

Abstract Human‐induced pluripotent stem cell‐derived cardiomyocytes (hiPSC‐CMs) are increasingly important in preclinical drug assessments, particularly for identifying potential cardiotoxicity. In this study, we utilize data from microphysiological systems of hiPSC‐CMs to evaluate cellular characteristics, such as action duration, beat rate, conduction velocity and mechanical displacement. Based on these data, high‐fidelity mathematical models facilitate precise assessments critical biophysical parameters the cells, including membrane ion channel conductances, cross‐bridge cycle transition rates cell‐to‐cell conductance. We emphasize distinction between synchronized transients travelling waves, highlighting their implications deducing properties hiPSC‐CMs. analyse effects compounds flecainide, quinidine, nifedipine, verapamil, blebbistatin omecamtiv. Our findings show that drug‐induced changes describing currents contractile machinery close ranges reported literature, computed biomarkers align well with measured biomarkers. This study is first apply spatially resolved, cell‐based identify through measurements transmembrane displacement, marking a significant step forward using computational evaluating safety offering new approach early identification adverse reactions. image Key points Optical human‐induced present opportunities advance understanding how human heart cells function interact. Although direct optical yield valuable biomarkers, they fall short revealing underlying properties, example, novel perturb channels. Drug best understood capture cell dynamics based physical laws. Traditionally, have been averaged over all collections, thus overlooking spatiotemporal waves. Here, use recently developed models, representing spatial electrical coupling, determine collections

Language: Английский

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Arrhythmogenic influence of mutations in a myocyte-based computational model of the pulmonary vein sleeve

Scientific Reports, Journal Year: 2022, Volume and Issue: 12(1)

Published: April 29, 2022

Abstract In the heart, electrophysiological dysregulation arises from defects at many biological levels (from point mutations in ion channel proteins to gross structural abnormalities). These disrupt normal pattern of electrical activation, producing ectopic activity and reentrant arrhythmia. To interrogate mechanisms that link these primary macroscopic electrophysiologic most prior computational studies have utilized either (i) detailed models myocyte dynamics limited spatial scales, or (ii) homogenized action potential conduction reproduce arrhythmic tissue organ levels. Here we apply our recent model (EMI), which integrates activation propagation across study human atrial arrhythmias originating pulmonary vein (PV) sleeves. small structures initiate supraventricular include pronounced myocyte-to-myocyte heterogeneities expression intercellular coupling. test EMI’s cell-based architecture this physiological context asked whether known underlie fibrillation are capable initiating arrhythmogenic behavior via increased excitability reentry a schematic PV sleeve geometry. Our results illustrate improved resolution can directly how changes individual level manifest as arrhythmia sleeve.

Language: Английский

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The simplified Kirchhoff network model (SKNM): a cell-based reaction–diffusion model of excitable tissue

Scientific Reports, Journal Year: 2023, Volume and Issue: 13(1)

Published: Sept. 30, 2023

Abstract Cell-based models of excitable tissues offer the advantage cell-level precision, which cannot be achieved using traditional homogenized electrophysiological models. However, this enhanced accuracy comes at cost increased computational demands, necessitating development efficient cell-based The widely-accepted bidomain model serves as standard in cardiac electrophysiology, and under certain anisotropy ratio conditions, it is well known that can reduced to simpler monodomain model. Recently, Kirchhoff Network Model (KNM) was developed a counterpart In paper, we aim demonstrate KNM simplified same steps employed derive from We present Simplified (SKNM), produces results closely aligned with those while requiring significantly less resources.

Language: Английский

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