Murtada Sae-Ii, Humphrey Jay D, Holzapfel Gerhard A
Institute of Biomechanics, Graz University of Technology, Graz, Austria; Department of Biomedical Engineering, Yale University, New Haven, Connecticut.
Department of Biomedical Engineering, Yale University, New Haven, Connecticut.
Biophys J. 2017 Aug 8;113(3):714-727. doi: 10.1016/j.bpj.2017.06.017.
Mathematical models can facilitate an integrative understanding of the complexity underlying biological structure and function, but they must be informed and validated by empirical data. Uniaxial contraction of an arterial ring is a well-used in vitro approach for studying characteristics of smooth muscle contractility even though this experimental arrangement does not mimic the in vivo vascular geometry or loading. In contrast, biaxial contraction of an inflated and axially extended excised vessel provides broader information, both passive and active, under more realistic conditions. Few investigations have compared these two in vitro approaches directly, namely how their results overlap, how they differ, or if each provides unique complementary information. Toward this end, we present, to our knowledge, a new multiscale mathematical model of arterial contractility accounting for structural and functional constituents at molecular, cellular, and tissue levels. The artery is assumed to be a thick-walled incompressible cylinder described by an anisotropic model of the extracellular matrix and, to our knowledge, novel model of smooth muscle contractility. The latter includes a 3D structural sensitivity to deformation, including microscale muscle filament overlap and filament lattice spacing. The overall model captures uniaxial and biaxial experimental contraction data, which was not possible when accounting for filament overlap alone. The model also enables parameter sensitivity studies, which confirmed that uniaxial contraction tests are not as efficient as biaxial tests for identifying changes in vascular smooth muscle function.
数学模型有助于综合理解生物结构和功能背后的复杂性，但必须通过实验数据来提供信息并进行验证。动脉环的单轴收缩是一种常用的体外研究平滑肌收缩特性的方法，尽管这种实验设置并不能模拟体内血管的几何形状或负荷。相比之下，对充气并轴向伸展的离体血管进行双轴收缩能在更现实的条件下提供更广泛的被动和主动信息。很少有研究直接比较这两种体外方法，即它们的结果如何重叠、如何不同，或者每种方法是否提供独特的互补信息。为此，据我们所知，我们提出了一种新的动脉收缩性多尺度数学模型，该模型考虑了分子、细胞和组织水平的结构和功能成分。动脉被假定为一个厚壁不可压缩圆柱体，由细胞外基质的各向异性模型描述，并且据我们所知，还有平滑肌收缩性的新模型。后者包括对变形的三维结构敏感性，包括微观尺度的肌丝重叠和肌丝晶格间距。整体模型捕捉了单轴和双轴实验收缩数据，仅考虑肌丝重叠时这是不可能做到的。该模型还能进行参数敏感性研究，证实了在识别血管平滑肌功能变化方面，单轴收缩试验不如双轴试验有效。
