A mathematical model of human heart including the effects of heart contractility varying with heart rate changes |
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| Affiliation: | 1. School of Biological Science and Medical Engineering, Beihang University, Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, Beijing 100083, China;2. Beijing Advanced Innovation Centre for Biomedical Engineering, Beihang University, Beijing 102402, China;3. Beijing Key Laboratory of Rehabilitation Technical Aids for Old-Age Disability, National Research Center for Rehabilitation Technical Aids, Beijing 100176, China;1. Mathematical Institute, Oxford University, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK;2. Institute for Molecular Bioscience, The University of Queensland, Brisbane QLD 4072, Australia;3. Department of Biochemistry and Molecular Biology, Monash University, Clayton VIC 3800, Australia;4. Department of Anatomy and Developmental Biology, Monash University, Clayton VIC 3800, Australia;5. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK;1. Movement Analysis Laboratory, IRCCS Istituto Ortopedico Rizzoli, Bologna, Italy;2. Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA, USA;3. 1st Orthopedic-Traumatologic Clinic, IRCCS Istituto Ortopedico Rizzoli, Bologna, Italy;4. Nursing, Technical and Rehabilitation Assistance Service, IRCCS Istituto Ortopedico Rizzoli, Bologna, Italy;1. Facultad de Ciencias Astronómicas y Geofísicas, UNLP, 1900-La Plata, Argentina;2. IFLP, CONICET, 1900-La Plata, Argentina;3. IIS G. Peano, I-10147 Torino, Italy |
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| Abstract: | Incorporating the intrinsic variability of heart contractility varying with heart rate into the mathematical model of human heart would be useful for addressing the dynamical behaviors of human cardiovascular system, but models with such features were rarely reported. This study focused on the development and evaluation of a mathematical model of the whole heart, including the effects of heart contractility varying with heart rate changes. This model was developed based on a paradigm and model presented by Ottesen and Densielsen, which was used to model ventricular contraction. A piece-wise function together with expressions for time-related parameters were constructed for modeling atrial contraction. Atrial and ventricular parts of the whole heart model were evaluated by comparing with models from literature, and then the whole heart model were assessed through coupling with a simple model of the systemic circulation system and the pulmonary circulation system. The results indicated that both atrial and ventricular parts of the whole heart model could reasonably reflect their contractility varying with heart rate changes, and the whole heart model could exhibit major features of human heart. Results of the parameters variation studies revealed the correlations between the parameters in the whole heart model and performances (including the maximum pressure and the stroke volume) of every chamber. These results would be useful for helping users to adjust parameters in special applications. |
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| Keywords: | Mathematical modeling Ventricular contraction Atrial contraction Variable heart rate |
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