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

C. S. Peskin, D. M. McQueen

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)H319-H328
JournalAmerican Journal of Physiology - Heart and Circulatory Physiology
Volume266
Issue number1 35-1
StatePublished - Jan 1 1994

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Keywords

  • differential geometry of heart valves
  • heart valve form and function
  • myocardial fiber orientation

ASJC Scopus subject areas

  • Physiology
  • Cardiology and Cardiovascular Medicine
  • Physiology (medical)

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