Peskin C S, McQueen D M
Courant Institute of Mathematical Sciences, New York University, New York 10012.
Am J Physiol. 1994 Jan;266(1 Pt 2):H319-28. doi: 10.1152/ajpheart.1994.266.1.H319.
In this work, the structure of the aortic valve is derived from its function, which (in the closed-valve configuration) is to support a uniform pressure load. It is assumed that this load is transferred to the aortic wall by a one-parameter family of fibers under tension. The equation of equilibrium for this fiber structure turns out to be equivalent to the equation of motion of vortex lines in the self-induction approximation. The method of Buttke (J. Comput. Phys. 76:301-326, 1988) is used to solve these equations and, hence, to determine the fiber architecture of the aortic leaflets. Because of a singularity at the center of the aortic valve, the computed fiber architecture has a fractal character with increasing complexity at progressively smaller scales. The computed fiber architecture resembles the branching braided structure of the collagen fibers that support the real aortic valve.
在这项研究中，主动脉瓣的结构源自其功能，（在瓣膜关闭状态下）该功能是承受均匀的压力负荷。假定此负荷通过一族处于张力状态的单参数纤维传递至主动脉壁。结果表明，这种纤维结构的平衡方程等同于自感近似下涡线的运动方程。采用布特克的方法（《计算物理杂志》76:301 - 326, 1988）求解这些方程，进而确定主动脉瓣小叶的纤维结构。由于主动脉瓣中心存在奇点，计算得到的纤维结构具有分形特征，且在越来越小的尺度上复杂度不断增加。计算得到的纤维结构类似于支撑真实主动脉瓣的胶原纤维的分支编织结构。
