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March 21, 2006Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering SciencesOpen Access

Asymptotic properties of mathematical models of excitability

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Key result

In mathematical models of cardiac excitability, suppressing tissue excitability below a critical limit blocks active propagation and causes front dissipation, explaining re-entrant wave termination.

Population

Mathematical models of biological excitability, including Hodgkin-Huxley model of nerve axon, Noble model of…

Design

Preclinical

Authors

IBIrina V. BiktashevaRSRadostin D. SimitevRSRebecca Suckley

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Overview

Small-parameter analysis sharpens multi-scale cardiac excitability models; extends singular perturbation theory for computational research.

Structured PICO

P
Population
Mathematical models of biological excitability, including Hodgkin-Huxley model of nerve axon, Noble model of heart Purkinje fibres, and Courtemanche et al. model of human atrial cells
I
Intervention
Analysis of small parameters and suppression of tissue excitability
O
Outcome
Behavior of fronts of excitation waves, including propagation speed and dissipation

In mathematical models of cardiac excitability, suppressing excitability leads to wave dissipation that does not recover, which accounts for breakups and self-termination of re-entrant waves.

Limitations

  • The approximation overestimates the conduction velocity by almost 50% compared to the full model due to the adiabatic elimination of the m gate.
  • The peak voltage is overestimated by about 13 mV due to the replacement of m with m(E).
  • The caricature model replaces functions with constants, which is a crude approximation.

Cite This Study

Biktasheva et al. (2006) studied Cardiac excitability (mathematical models). Mathematical modeling of excitability was evaluated. In mathematical models of cardiac excitability, suppressing tissue excitability below a critical limit blocks active propagation and causes front dissipation, explaining re-entrant wave termination.

synapsesocial.com/papers/6a5e0e4570eb43e754d8a3d0https://doi.org/10.1098/rsta.2006.1770
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Also Consider

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  1. 1Non-Tikhonov Asymptotic Properties of Cardiac Excitability2004 · 20 citations
  2. 2Alteration in Sodium Channel Gate Kinetics of the Hodgkin-Huxley Equations Applied to an Electric Field Model for Interaction Between Excitable Cells1981 · 16 citations
  3. 3Asymptotic analysis and analytical solutions of a model of cardiac excitation2006
  4. 4A SIMPLIFIED MODEL OF PROPAGATION AND DISSIPATION OF EXCITATION FRONTS2003 · 17 citations
  5. 5Dissipation of the Excitation Wave Fronts2002 · 45 citations