Mechanical equilibrium determines the fractal fiber architecture of aortic heart valve leaflets.
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.
Peskin
C S
CS
Courant Institute of Mathematical Sciences, New York University, New York 10012.
McQueen
D M
DM
D001021:Aortic Valve / Q000033:anatomy & histology* / Q000502:physiology*; D017709:Fractals; D006801:Humans; D008953:Models, Anatomic; D008955:Models, Cardiovascular