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Modelling of fibre dispersion and its effects on cardiac mechanics from diastole to systole
Journal of Engineering Mathematics ( IF 1.3 ) Pub Date : 2021-04-20 , DOI: 10.1007/s10665-021-10102-w
Debao Guan , Xin Zhuan , William Holmes , Xiaoyu Luo , Hao Gao

Detailed fibre architecture plays a crucial role in myocardial mechanics both passively and actively. Strong interest has been attracted over decades in mathematical modelling of fibrous tissue (arterial wall, myocardium, etc.) by taking into account realistic fibre structures, i.e. from perfectly aligned one family of fibres, to two families of fibres, and to dispersed fibres described by probability distribution functions. It is widely accepted that the fibres, i.e. collage, cannot bear the load when compressed, thus it is necessary to exclude compressed fibres when computing the stress in fibrous tissue. In this study, we have focused on mathematical modelling of fibre dispersion in myocardial mechanics, and studied how different fibre dispersions affect cardiac pump function. The fibre dispersion in myocardium is characterized by a non-rotationally symmetric distribution using a \(\pi \)-periodic Von Mises distribution based on recent experimental studies. In order to exclude compressed fibres for passive response, we adopted the discrete fibre dispersion model for approximating a continuous fibre distribution with finite fibre bundles, and then the general structural tensor was employed for describing dispersed active tension. We first studied the numerical accuracy of the integration of fibre contributions using the discrete fibre dispersion approach, then compared different mechanical responses in a uniaxially stretched myocardial sample with varied fibre dispersions. We finally studied the cardiac pump functions from diastole to systole in two heart models, a rabbit bi-ventricle model and a human left ventricle model. Our results show that the discrete fibre model is preferred for excluding compressed fibres because of its high computational efficiency. Both the diastolic filling and the systolic contraction will be affected by dispersed fibres depending on the in-plane and out-of-plane dispersion degrees, especially in systolic contraction. The in-plane dispersion seems affecting myocardial mechanics more than the out-of-plane dispersion. Despite different effects in the rabbit and human models caused by the fibre dispersion, large differences in pump function exist when fibres are highly dispersed at in-plane and out-of-plane. Our results highlight the necessity of using dispersed fibre models when modelling myocardial mechanics, especially when fibres are largely dispersed under pathological conditions, such as fibrosis.



中文翻译:

从舒张期到收缩期的纤维色散建模及其对心脏力学的影响

详细的纤维结构在被动和主动的心肌力学中都起着至关重要的作用。数十年来,人们对纤维组织(动脉壁,心肌等)的数学建模引起了浓厚的兴趣,其中考虑到了现实的纤维结构,即从一个纤维家族完全对齐到两个纤维家族,再到所描述的分散纤维通过概率分布函数。人们普遍接受的是,纤维(即拼贴)在压缩时无法承受负荷,因此在计算纤维组织中的应力时有必要排除压缩纤维。在这项研究中,我们专注于心肌力学中纤维弥散的数学建模,并研究了不同的纤维弥散如何影响心脏泵功能。\(\ pi \)最近的实验研究得出的周期性Von Mises分布。为了排除压缩纤维的被动响应,我们采用离散纤维分散模型来近似有限纤维束的连续纤维分布,然后使用通用结构张量描述分散的主动张力。我们首先使用离散的纤维分散方法研究了纤维贡献积分的数值准确性,然后在具有不同纤维分散的单轴拉伸心肌样本中比较了不同的机械响应。最后,我们在两个心脏模型(兔子双心室模型和人左心室模型)中研究了从舒张期到收缩期的心脏泵功能。我们的结果表明,由于离散纤维模型具有较高的计算效率,因此它是排除压缩纤维的首选模型。舒张期充盈和收缩期收缩都将受到分散纤维的影响,这取决于面内和面外分散度,尤其是收缩期收缩。平面内分散似乎比平面外分散对心肌力学的影响更大。尽管由于纤维分散而在兔子和人体模型中产生了不同的影响,但是当纤维在面内和面外高度分散时,泵功能仍然存在很大差异。我们的结果强调了在对心肌力学建模时必须使用分散的纤维模型,尤其是当纤维在诸如纤维化之类的病理条件下大量分散时。舒张期充盈和收缩期收缩都将受到分散纤维的影响,这取决于面内和面外分散度,尤其是收缩期收缩。平面内分散似乎比平面外分散对心肌力学的影响更大。尽管由于纤维分散而在兔子和人体模型中产生了不同的影响,但是当纤维在面内和面外高度分散时,泵浦功能仍存在很大差异。我们的结果强调了在对心肌力学建模时必须使用分散的纤维模型,尤其是当纤维在诸如纤维化之类的病理条件下大量分散时。舒张期充盈和收缩期收缩都将受到分散纤维的影响,这取决于面内和面外分散度,尤其是收缩期收缩。平面内分散似乎比平面外分散对心肌力学的影响更大。尽管由于纤维分散而在兔子和人体模型中产生了不同的影响,但是当纤维在面内和面外高度分散时,泵功能仍然存在很大差异。我们的结果强调了在对心肌力学建模时必须使用分散的纤维模型,尤其是当纤维在诸如纤维化之类的病理条件下大量分散时。特别是在收缩期。平面内分散似乎比平面外分散对心肌力学的影响更大。尽管由于纤维分散而在兔子和人体模型中产生了不同的影响,但是当纤维在面内和面外高度分散时,泵功能仍然存在很大差异。我们的结果强调了在对心肌力学建模时必须使用分散的纤维模型,尤其是当纤维在诸如纤维化之类的病理条件下大量分散时。特别是在收缩期。平面内分散似乎比平面外分散对心肌力学的影响更大。尽管由于纤维分散而在兔子和人体模型中产生了不同的影响,但是当纤维在面内和面外高度分散时,泵功能仍然存在很大差异。我们的结果强调了在对心肌力学建模时必须使用分散的纤维模型,尤其是当纤维在诸如纤维化之类的病理条件下大量分散时。

更新日期:2021-04-20
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