Mathematical modelling of atrial and ventricular pressure–volume dynamics and their change with heart rate

This paper presents mathematical models that can simulate the cardiovascular system of a healthy sheep under normal resting conditions in which the heart rate changes significantly. The models include several new modelling features that are introduced progressively. The contraction of the cardiac ch...

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Published in:Mathematical biosciences 2022-02, Vol.344, p.108766-108766, Article 108766
Main Authors: Noreen, Shumaila, Ben-Tal, Alona, Elstad, Maja, Sweatman, Winston L., Ramchandra, Rohit, Paton, Julian
Format: Article
Language:English
Subjects:
Animals
Aorta
Aortic valve
Atria
Atrial PV loops
Blood Pressure - physiology
Cardiac output
Cardiovascular model
Cardiovascular system
Elasticity
Heart Rate
Heart rate variability
Heart valves
Heart Ventricles
Mathematical models
Models, Theoretical
Muscle contraction
Muscles
Myocardial Contraction
Sheep
Stroke volume
Time dependence
Ventricle
Ventricular inter-dependence
Ventricular Pressure
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Summary:This paper presents mathematical models that can simulate the cardiovascular system of a healthy sheep under normal resting conditions in which the heart rate changes significantly. The models include several new modelling features that are introduced progressively. The contraction of the cardiac chambers is modelled using a time-dependent muscle force with constant elasticity instead of time dependent elasticity. A new hypothesis about the mechanical contraction of the atria generates realistic pressure volume (PV) loops. The inter-ventricular interaction is modelled as well. Additionally, hysteresis is incorporated in the aortic valve to produce an end-systolic reverse (negative) flow. Most of the model parameter values are based on previous literature data while time periods of delay, atrial and ventricular contraction are derived using experimental data from 14 sheep. We provide new relationships between contraction time and delay as a function of heart period. The effects of different aspects of our modelling on the mean cardiac output, stroke volume, ejection time, ejection fraction and PV loops are studied. Model outputs are compared with published experimental results where possible, and are within a wide range of physiological observations. •New mathematical models of the cardiovascular system are presented.•The models can be used over a wide range of heart rates.•New formulas of contraction time and delay as a function of heart period are given.•Parameters of the model have been fitted to sheep data.•The model outputs are within a wide range of physiological observations.•The PV loops of all four chambers look realistic.
ISSN:0025-5564
1879-3134
DOI:10.1016/j.mbs.2021.108766