Dynamical properties of Beeler–Reuter cardiac cell model with respect to stimulation parameters

Halfar, Radek

doi:10.1080/00207160.2019.1649662

Cited by 8 publications

(2 citation statements)

References 13 publications

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“…Once solved numerically, the model outputs a time series of transmembrane potential (voltage) v i , which we refer to as the AP. The ODEs that make up the Beeler-Reuter model are described mathematically in [40]. However, instead of working directly with the ODE equations of the Beeler-Reuter model, it is sufficient for our purposes to consider the model as a mapping from the parameter space P to the space of AP traces V T , we defined this mapping in Definition 2.1.…”

Section: The Action Potential Modelmentioning

confidence: 99%

Improving inversion of model parameters from action potential recordings with kernel methods

Oslandsbotn

Forsch

Cloninger

2023

Preprint

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Computational models of cardiac electrophysiology hold great potential in the drug discovery process to bridge the gap between in vitro and in vivo preclinical trials. Current methods for solving inverse problems in cardiac electrophysiology are limited by their accuracy, scalability, practicality, or a combination of these. We investigate the feasibility of using kernel methods to solve the inverse problem of estimating the parameters of ionic membrane currents from observations of corresponding action potential (AP) traces. In particular, we consider AP traces generated by a cardiac cell action potential model, which mimics those obtained experimentally in measurable in vitro cardiac systems. This proof-of-concept study aims to improve existing pipelines for identifying drug effects in "heart-on-a-chip" systems by introducing a new approach to solving the inverse problem. Using synthetic training data from the 1977 Beeler-Reuter AP model of mammalian ventricular cardiomyocytes, we demonstrate our recently proposed boosted KRR solver StreaMRAK, which is particularly robust and well-adapted for high-complexity functions. We show that this method is less memory demanding, estimates the model parameters with higher accuracy, and is less sensitive to parameter identifiability problems than existing methods, such as standard KRR solvers and loss-minimization schemes based on nearest neighbor heuristics.

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Section: The Action Potential Modelmentioning

confidence: 99%

Improving inversion of model parameters from action potential recordings with kernel methods

Oslandsbotn

Forsch

Cloninger

2023

Preprint

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“…The parameter γ varies from 0.35 to 0.525 to show the original system's HCOM dynamics. Bifurcations with outputs of the 0-1 test for chaos K (see Reference [21][22][23][24][25]) and maximal Lyapunov exponent L, are given in Figure 1. Hereafter, for the sake of simplicity, we analyze only the first variable q 1 since variables q 1 and q 2 are joined together by the way they are defined.…”

Section: The Impulsive Control Systemmentioning

confidence: 99%

Chaos Control and Anti-Control of the Heterogeneous Cournot Oligopoly Model

Lampart

Lampartová

2020

Mathematics

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The main aim of this paper focuses on chaos suppression (control) and stimulation (anti-control) of a heterogeneous Cournot oligopoly model. This goal is reached by applying the theory of dynamical systems, namely impulsive control. The main aim was to demonstrate, through massive numerical simulations and estimation of the maximal Lyapunov exponent, the 0-1test for chaos, and bifurcation analysis, that it is possible to control the dynamical behavior of the investigated model by finding injection values under which the desired phenomena are attained. Moreover, it was shown that there are injection values for which the injected system admits a self-excited cycle or chaotic trajectory.

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On extensive dynamics of a Cournot heterogeneous model with optimal response

Lampart

Lampartová

Orlando

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The objective of this paper is the study of the dynamical properties analysis of an original specification of the classical Cournot heterogeneous model with optimal response; specifically, a new approach that considers ordinal utility instead of cardinal monetary amounts is proposed where the classical decision of quantity is disentangled from the decision on imitation. The analysis is performed by means of bifurcation diagrams, the 0–1 test for chaos, power spectral density, histograms, and trajectory analysis. For this purpose, a new perturbation parameter ε of the initial condition is introduced, and together with the intensity of choice parameter β determining the share of responders vs imitators, the system is researched. Depending on ε and β, extreme reach dynamics, and coexisting attractors, periodic and chaotic trajectories are investigated through massive simulations. Those dynamics represent alternation between stability, cycles and chaos in the market. As the dynamics are completely endogenous, it means that swings in economy are intrinsic to the system and that they may persist unless controlled.

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Dynamical properties of Beeler–Reuter cardiac cell model with respect to stimulation parameters

Cited by 8 publications

References 13 publications

Improving inversion of model parameters from action potential recordings with kernel methods

Improving inversion of model parameters from action potential recordings with kernel methods

Chaos Control and Anti-Control of the Heterogeneous Cournot Oligopoly Model

On extensive dynamics of a Cournot heterogeneous model with optimal response

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