Modelling the cardiac response to a mechanical stimulation using a low-order model of the heart

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Heart diseases are one of the leading causes of death worldwide, and a dysfunction of the cardiac electrical mechanisms is responsible for a significant portion of these deaths. One of these mechanisms, the mechano-electric feedback (MEF), is the electrical response of the heart to local mechanical changes in the environment. This electrical response, in turn, leads to macroscopic changes in heart function. In this paper, we demonstrate that the MEF plays a crucial role in mechanical generation and recovery from arrhythmia which has been observed in experimental studies. To this end, we investigate the cardiac response to a mechanical stimulation using a minimal, multiscale model of the heart which couples the organ level dynamics (left ventricular pressure and volume) and contractile dynamics. By including a mechanical stimulation into the model as a (short, sudden) impulse in the muscle microscale stress, we investigate how the timing, amplitude and duration of the impulse affect the cardiac cycle. In particular, when introduced in the diastolic period of the cardiac cycle, the pulse rate can be stabilised, and ectopic beats and bifurcation can be eliminated, either temporarily or permanently. The stimulation amplitude is a key indicator to this response. We find an optimal value of the impulse amplitude above or below which the impulse maximises the stabilisation. As a result a dysfunction of the MEF can be helped using a mechanical stimulation, by allowing the heart to recover its pumping power. On the other hand, when the mechanical stimulation is introduced towards the end of systole, arrhythmia can be generated.
Original languageEnglish
Article number2021248
Pages (from-to)4871-4893
Number of pages23
JournalMathematical Biosciences and Engineering
Issue number4
Publication statusPublished - 3 Jun 2021

Bibliographical note

This is an open access article distributed under the terms of the Creative Commons Attribution License (


Leverhulme Trust Research Fellowship (RF-2018-142-9)


  • Arrhythmias
  • Cardiac cycle
  • Lumped-parameter model
  • Mechano-electric feedback
  • Multiscale model
  • Nonlinear dynamics

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics


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