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Am J Physiol Heart Circ Physiol 266: H319-H328, 1994;
0363-6135/94 $5.00
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AJP - Heart and Circulatory Physiology, Vol 266, Issue 1 319-H328, Copyright © 1994 by American Physiological Society

ARTICLES

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

C. S. Peskin and D. M. McQueen
Courant Institute of Mathematical Sciences, New York University, New York 10012.

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.


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A. L. Goldberger, L. A. N. Amaral, J. M. Hausdorff, P. Ch. Ivanov, C.-K. Peng, and H. E. Stanley
Fractal dynamics in physiology: Alterations with disease and aging
PNAS, February 19, 2002; 99(suppl_1): 2466 - 2472.
[Abstract] [Full Text] [PDF]


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