Mechanical equilibrium determines the fractal fiber architecture of aortic heart valve leaflets

• Published in: The American journal of physiology Vol. 266; no. 1 Pt 2; p. H319
• Main Authors: Peskin, C S, McQueen, D M
• Format: Journal Article
• Language: English
• Published: United States 01.01.1994
• Subjects: Aortic Valve - anatomy & histology; Aortic Valve - physiology; Fractals; Humans; Models, Anatomic; Models, Cardiovascular
• ISSN: 0002-9513
• 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.