A new synergistic model for simulating exercise incorporating control mechanisms at cellular and organ scales

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The physiological response of the cardio-vascular system (CVS) to physical activity is of great importance to those working in sporting research and has profound consequences for the health and well-being of people. Coronary vasodilation and the physiological mechanisms involved in exercise have frequently been the focus of numerical models for simulating exercise. This is partly achieved using the time-varying-elastance (TVE) theory, which prescribes the pressure-volume relationship of the ventricle as a periodic function of time, tuned using empirical data. The empirical foundations of the TVE method however, and its suitability for CVS modelling are frequently questioned. To overcome this challenge, we adopt a different synergistic approach in which a model for the microscale heart muscle (myofibers) activity is embedded within a macro organ-scale CVS model. We developed such a synergistic model by including the coronary flow and various control mechanisms at the circulation level through feedback and feedforward means, and at the microscale (contractile) through the regulation of ATP availability and myofiber force depending on exercise intensity or heart rate. The coronary flow produced by the model displays the well-known 2-phase character of the flow, which is preserved under exercise. The model is tested by simulating reactive hyperemia, which is a transient occlusion of the coronary flow, successfully reproducing the additional coronary flow following the block removal. On-transient exercise results reveal a rise in both cardiac output and mean ventricle pressure as expected. The stroke volume increases initially, but then declines during the latter period of HR rise, corresponding with one of the main physiological responses to exercise. The pressure-volume loop expands during exercise, as systolic pressure rises. The Myocardial oxygen demand increases during exercise and the coronary blood supply increases in response, causing an excess of oxygen supply to the heart. Off-transient exercise recovery is largely a reverse of this response, although the behaviour is slightly more varied, with sudden spikes in coronary resistance. Different levels of fitness and exercise intensity are tested and reveal that the stroke volume rises until a level of myocardial oxygen demand is reached at which point it declines. This level of demand is independent of fitness or exercise intensity. An advantage of our model is demonstrated in the correspondence between the micro and organ scale mechanics so that cellular pathologies can be traced from exercise performance with relatively little computational or experimental expense.
Original languageEnglish
Article number107141
Number of pages18
JournalComputers in Biology and Medicine
Early online date8 Jun 2023
Publication statusPublished - Sept 2023

Bibliographical note

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).


  • Nonlinear dynamics
  • Multi-scale model
  • Exercise
  • Cardiac cycle
  • Lumped-parameter model


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