A simple phenomenological approach for myocardial contraction: formulation, parameter sensitivity study and applications in organ level simulations

Abstract

Contraction in myocardial tissue is the result of a complex process through which chemical energy on the cellular level is converted into the mechanical energy needed to circulate blood throughout the body. Due to its vital role for the organism, myocardial contractility is one of the most intensively investigated subjects in medical research. In this contribution, we suggest a novel phenomenological approach for myocardial contraction that is capable of producing realistic intracellular calcium concentration (ICC) and myocyte shortening graphs, can be easily calibrated to capture different ICC and contraction characteristics and, at the same time, is straightforward to implement and ensures efficient computer simulations. This study is inspired by the fact that existing models for myocardial contractility either contain a number of complex equations and material parameters, which reduce their feasibility, or are very simple and cannot accurately mimic reality, which eventually influences the realm of computer simulations. The proposed model in this manuscript considers first the evolution of the ICC through a logarithmic-type ordinary differential equation (ODE) having the normalized transmembrane potential as the argument. The ICC is further put into an exponential-type ODE which determines the shortening of the myocyte (active stretch). The developed approach can be incorporated with phenomenological or biophysically based models of cardiac electrophysiology. Through examples on the material level, we demonstrate that the shape of the ICC and myocardial shortening curves can be easily modified and accurately fitted to experimental data obtained from rat and mouse hearts. Moreover, the performance of the model in organ level simulations is illustrated through several multi-field initial-boundary value problems in which we show variations in volume-time relations, heterogeneous characteristics of myocardial contraction and application of a drug in a virtual left ventricle model.

A new approach for analysing motion and deformation of left ventricle: Post‐processing 3D echocardiography data with finite element method

“…where 𝑎, 𝑏, 𝑎 f , 𝑏 f , 𝑎 s , 𝑏 s , 𝑎 fs , 𝑏 fs are non-negative material constants describing the deformation state of the isotropic and orthotropic microstructure of the myocardium along with the invariants 𝐼 1 ∶= tr 𝑪, 𝐼 4f ∶= 𝒇 0 ⋅ 𝑪𝒇 0 , 𝐼 4s ∶= 𝒔 0 ⋅ 𝑪𝒔 0 , 𝐼 8fs ∶= 𝒇 0 ⋅ 𝑪𝒔 0 and the right Cauchy-Green tensor 𝑪 = 𝑭 𝑇 𝑭, see the recent work [5] regarding the details of the model.…”

“…Apart from dealing with real data in clinics, extensive efforts have been devoted to achieve virtual modelling of the heart with the aim to understand the working mechanisms of the heart in healthy and disease state [2][3][4][5][6]. In the field of virtual modelling, the finite element method (FEM) is one of the most utilized numerical tools.…”

Fast and reliable reduced‐order models for cardiac electrophysiology

“…The human cardiovascular system is highly complex, exhibiting multi-scale behavior involving multi-physics phenomena [20,56]. While for several centuries the study of the human heart was largely a clinical or empirical science, in recent decades there has been significant progress in developing mathematical models which are consistent with clinical observations [1,10,11,14,28,59]. Such physics-based models seek to be complementary to empirical models which may be obtained via patient-specific imaging, test results or even population-wide studies.…”