心肌细胞是心脏的功能构建块,但大多数为模拟心脏力学而开发的模型并不代表单个细胞及其周围的基质。相反,它们在均质化组织水平上工作,假设细胞和亚细胞结构和过程均匀缩放。在这里,我们提出了一个数学和数值框架,用于在微观尺度上探索组织水平的心脏力学,并给出了嵌入矩阵中的细胞的明确三维几何表示。我们在这样的几何形状上定义了数学模型,并使用来自组织拉伸和剪切实验的公开数据对我们的模型进行了参数化。然后,我们使用该模型来探索细胞外空间和细胞内空间之间的机械差异。通过敏感性分析,我们发现细胞外基质的刚度对于收缩下的细胞内应力值最重要。观察到应变和应力值遵循沿膜集中的正切模式,在收缩和拉伸下都有很大的空间变化。我们还研究了它如何扩展到更大尺寸的模拟,考虑多细胞结构域。我们的工作扩展了现有的连续模型,为探索复杂的细胞-细胞和细胞-基质相互作用提供了一个新的基于几何的框架。
Cardiomyocytes are the functional building blocks of the heart-yet most models developed to simulate cardiac mechanics do not represent the individual cells and their surrounding matrix. Instead, they work on a homogenized tissue level, assuming that cellular and subcellular structures and processes scale uniformly. Here we present a mathematical and numerical framework for exploring tissue-level cardiac mechanics on a microscale given an explicit three-dimensional geometrical representation of cells embedded in a matrix. We defined a mathematical model over such a geometry and parametrized our model using publicly available data from tissue stretching and shearing experiments. We then used the model to explore mechanical differences between the extracellular and the intracellular space. Through sensitivity analysis, we found the stiffness in the extracellular matrix to be most important for the intracellular stress values under contraction. Strain and stress values were observed to follow a normal-tangential pattern concentrated along the membrane, with substantial spatial variations both under contraction and stretching. We also examined how it scales to larger size simulations, considering multicellular domains. Our work extends existing continuum models, providing a new geometrical-based framework for exploring complex cell-cell and cell-matrix interactions.