Research Article: A mathematical model for active contraction in healthy and failing myocytes and left ventricles

Date Published: April 13, 2017

Publisher: Public Library of Science

Author(s): Li Cai, Yongheng Wang, Hao Gao, Yiqiang Li, Xiaoyu Luo, Vladimir E. Bondarenko.


Cardiovascular disease is one of the leading causes of death worldwide, in particular myocardial dysfunction, which may lead to heart failure eventually. Understanding the electro-mechanics of the heart will help in developing more effective clinical treatments. In this paper, we present a multi-scale electro-mechanics model of the left ventricle (LV). The Holzapfel-Ogden constitutive law was used to describe the passive myocardial response in tissue level, a modified Grandi-Pasqualini-Bers model was adopted to model calcium dynamics in individual myocytes, and the active tension was described using the Niederer-Hunter-Smith myofilament model. We first studied the electro-mechanics coupling in a single myocyte in the healthy and diseased left ventricle, and then the single cell model was embedded in a dynamic LV model to investigate the compensation mechanism of LV pump function due to myocardial dysfunction caused by abnormality in cellular calcium dynamics. The multi-scale LV model was solved using an in-house developed hybrid immersed boundary method with finite element extension. The predictions of the healthy LV model agreed well with the clinical measurements and other studies, and likewise, the results in the failing states were also consistent with clinical observations. In particular, we found that a low level of intracellular Ca2+ transient in myocytes can result in LV pump function failure even with increased myocardial contractility, decreased systolic blood pressure, and increased diastolic filling pressure, even though they will increase LV stroke volume. Our work suggested that treatments targeted at increased contractility and lowering the systolic blood pressure alone are not sufficient in preventing LV pump dysfunction, restoring a balanced physiological Ca2+ handling mechanism is necessary.

Partial Text

Myocardial dysfunction is a considerable social and economic burden because it can lead to heart failure due to repeated stresses and injuries [1]. However, our understanding of cardiac dysfunction remains incomplete. Mann and Bristow [2] suggested that heart failure could be viewed as a biomechanical model orchestrated by different subsystems, and the downstream biological remodelling is one of the drivers leading to myocardial dysfunction progression. Multi-scale and multi-physics biomechanical modelling of heart dynamics provides a unique way to gain insights of myocardial function and holds the potential for patient risk stratification and clinical decision making [3, 4].

From biomechanical perspective, myocaridal dysfunction could be considered as biomechanical model with interrelated and intricate changes and remodelling in cardiac structure and function as the result of downstream biological abnormalities [2]. Advanced biomechanical modelling of heart mechanics with multi-scale and multi-physics may hold the potential to improve our understanding of failing hearts and shed lights on effective treatments [3]. This computational work, based on an advance human myocyte electrophysiological model, a myofilament model for excitation-contraction coupling, and a multi-physics organ-level LV mechanics model, demonstrates that a multi-scale biomechanical model can be used to investigate the effects of downstream biological abnormalities on ventricular pump function. Once validated, it will provide a platform to understand the functional and structural remodelling in failing hearts.

In this study, we have modelled myocardial excitation-contraction coupling both at cellular and organ levels by incorporating a modified GPB model and the NHS model at healthy and failing states. The LV model was implemented in an in-house developed IB/FE framework. Results show that the active tension decreases with the decrease of intracellular CaT both at cellular and organ levels. In a failing heart, decreased systolic blood pressure, enhanced contractility and elevated diastolic filling pressure can improve heart pump function in the short term (i.e. increased stroke volume), however, they may lead to terminal heart failure in a longer term if a balanced physiological calcium ion handling mechanism is not restored. This study forms part of the continuous effort in multi-scale electro-mechanics modelling for clinical problems, and provides a platform to study remodelling in a failing heart from a biomechanical perspective.




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