A low-order model for left ventricle dynamics throughout the cardiac cycle

Michael J. Moulton, Timothy W. Secomb

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


A theoretical model is used to simulate the dynamics of the left ventricle (LV) through all phases of the cardiac cycle, including interactions between myocardial contractility and ventricular pressure generation and effects of preload and afterload. The ventricle is represented as a cylinder containing helical muscle fibres with non-linear passive and active material properties, embedded in a uniform viscoelastic matrix. The dynamics of the ventricle are represented by a system of differential algebraic equations, whose numerical solution yields pressure-volume loops over successive cardiac cycles. Predicted timedependent torsional, circumferential and longitudinal strains in the LV are consistent with experimental observations. The model is used to examine the effects of changes in underlying properties of the heart, including myocardial contractility, fibre orientation, passive stiffness, atrial pressure and peripheral resistance, on observable parameters such as stroke work, ejection fraction and end-systolic pressure-volume relationship. Stroke work is shown to be linearly dependent on end-diastolic volume but also to depend on afterload. Diastolic suction and its effect on filling are demonstrated. In this modelling approach, the dynamics of the heart are represented using a low-order dynamical system, and simulations can be carried out much faster than real time. Such a model could potentially be used to deduce patient-specific parameters of ventricular performance on-line from clinically available measurements.

Original languageEnglish (US)
Pages (from-to)45-63
Number of pages19
JournalMathematical Medicine and Biology
Issue number1
StatePublished - Mar 2013


  • Cardiac mechanics
  • Diastolic heart failure
  • Mathematical model
  • Myocardial strain
  • Pressure-volume curve
  • Ventricular wall stress

ASJC Scopus subject areas

  • General Neuroscience
  • Modeling and Simulation
  • General Immunology and Microbiology
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • Applied Mathematics


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