Abstract
This paper considers the Holzapfel–Ogden (HO) model to examine the behavior of the left ventricle myocardium. At the tissue level, we analyze the contributions of the orientation angle of muscle fibers (MFs) and investigate their effects on the occurrence of certain cardiomyopathies and congenital diseases at the organ level. Knowing the importance of myocardial microstructure on cardiac function, we vary the angle between the direction of collagen sheets and MFs in all layers of the myocardium (from epicardium to endocardium) to model the effects of tilted MFs. Based on the HO model in which the directions of the fibers are orthogonal and using the strain energy of HO, we construct a tensile-compression test and simulate the dynamics of a cubic sample. We recover the authors’ results exhibiting the existence of residual stresses in various directions. Then, we modify the energy of HO slightly to assess the impact of the same stress states on the system with tilted MFs. A numerical tensile-compression test performed on this new cubic sample shows that, in certain directions, the heart tissue is more resistant to shear deformations in some planes than in others. Moreover, it appears that the residual stress is smaller as the angle of orientation of the MFs is small. Furthermore, we observe that the residual stress is greater in the new model compared to the normal HO model. This could affect the heart muscle at the organ level leading to hypertrophied/dilated cardiomyopathy.
Highlights
Several works have been carried out to understand the electromechanical behavior of the heart [1, 2]. is modeling requires knowledge of the morphology of the heart [3,4,5], its electrical behavior [6], and its mechanical behavior [3, 7]
Based on the modified Holzapfel–Ogden (MHO) model (Figure 2), we deeply investigate the effects of the orientation angle of muscle fibers (MFs) and the growth of the constraints on the behavior of the myocardium tissue. erefore, we discuss the occurrence of some diseases linking with the expansion of constraints in the heart muscle
It appears that, in the positive plane of the HO model (Figure 3(d)), the stress is lower than that of the corresponding modified model (Figure 4(b)) for positive angles. e same observations are made in the negative plane for negative angles. ese results show that the stresses are greater in the MHO model due to the effects of the tilt angle of the MFs. ere exist indirect experimental evidences suggesting that the characteristics and extent of the extracellular connective tissue matrix are important determinant of diastolic and systolic ventricular function [19]
Summary
Several works have been carried out to understand the electromechanical behavior of the heart [1, 2]. is modeling requires knowledge of the morphology of the heart [3,4,5], its electrical behavior [6], and its mechanical behavior [3, 7]. Several works have been carried out to understand the electromechanical behavior of the heart [1, 2]. Is modeling requires knowledge of the morphology of the heart [3,4,5], its electrical behavior [6], and its mechanical behavior [3, 7]. The mechanical behavior of the heart remains a mystery due to the difficulty of finding a stress-strain relationship. Several studies have already been performed to determine the mechanical properties and structure of heart tissue. As muscle fibers (MFs) and collagen sheets’ matrices make up heart tissue, HO exploited this structuring but assumed that MFs are perpendicular at the reference configuration (RC); hypothesis neglects the contribution of the orientation angle of MFs at the RC. There are some works which take into account the orientation of MFs
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