Modelling of fibre dispersion and its effects on cardiac mechanics from diastole to systole
Modelling of fibre dispersion and its effects on cardiac mechanics from diastole to systole
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DOI：
10.1007/s10665-021-10102-w
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发表时间：
2021-06-01
影响因子：
1.3
通讯作者：
Gao, Hao
中科院分区：
文献类型：
--
作者：
Guan, Debao;Zhuan, Xin;Gao, Hao
无论是被动的还是主动的，详细的纤维构筑在心肌力学中都起着至关重要的作用。几十年来，纤维组织(动脉壁、心肌等)的数学模型一直吸引着人们的浓厚兴趣。通过考虑真实的纤维结构，即从完全排列的一族纤维，到两族纤维，以及由概率分布函数描述的分散纤维。人们普遍认为，纤维，即胶原蛋白，在压缩时不能承受载荷，因此在计算纤维组织中的应力时，有必要排除压缩的纤维。在这项研究中，我们重点研究了心肌力学中纤维分散的数学模型，并研究了不同的纤维分散对心泵功能的影响。基于最近的实验研究，心肌中的纤维分散具有非旋转对称分布的特点，该分布采用pi周期的Von Mise分布。为了排除压缩纤维对被动响应的影响，我们采用离散纤维弥散模型来近似具有有限纤维束的连续纤维分布，然后用一般结构张量来描述分散的主动张力。我们首先使用离散纤维弥散方法研究了纤维成分积分的数值精度，然后比较了具有不同纤维弥散的单轴拉伸心肌样本中的不同力学响应。最后，我们研究了两种心脏模型，兔双心室模型和人左心室模型从舒张期到收缩期的心泵功能。结果表明，离散纤维模型由于具有较高的计算效率，是排除压缩纤维的首选模型。舒张期充盈和收缩收缩都会受到分散纤维的影响，这取决于平面内和平面外的弥散程度，尤其是在收缩时。面内离散度似乎比离面离散度对心肌力学的影响更大。尽管纤维分散对兔和人模型的影响不同，但当纤维高度分散在面内和面外时，泵浦功能存在很大差异。我们的结果强调了在模拟心肌力学时使用分散纤维模型的必要性，特别是当纤维在病理条件下大部分分散时，例如纤维化。
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.