Bifurcation analysis of nonlinear probability model for resting potential and theoretical calculation of human ventricular myocardium elastic modulus
Abstract
This paper focuses on the cardiac pulsation model. The first purpose is to explain the generation mechanism of myocardial resting potential from two aspects of nonlinear dynamics and physiology. The second objective is to establish the basic theoretical calculation method for ventricular muscle material parameters such as elastic modulus, Poisson’s ratio and shear modulus. The physiological essence of resting potential is ion channel blocking reaction to mismatched ions, which can be described by the probability model of fully misaligned arrangement. The calculation of the elastic modulus of ventricular muscle is based on the stress distribution characteristics at the end of diastole and the modified Laplace’ law. The correctness and effectiveness of the misaligned arrangement probability model for resting potential, the modified Laplace’s law of cardiac diastole and the three-dimensional pressure equalization theory of cardiac systole are also proved in detail. A theoretical calculation method for ventricular muscle elastic modulus is established relying solely on echocardiography data instead of costly measurement methods such as magnetic resonance imaging (MRI). The reference value for longitudinal elastic modulus of human ventricular muscle was calculated and compared with experimental data of isolated porcine heart. The echocardiography measurement method based on theoretical results may provide potential assistance for the initial screening and diagnosis of cardiogenic diseases as a routine physical examination item.
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