The differential geometry of heart values

Charles S. Peskin

Research output: Contribution to journalArticlepeer-review

Abstract

Heart valves when closed consist of membranes under tension bearing a pressure load. Along the lines where the leaflets meet, special support structures under tension are needed (a fibrous ridge for the arterial valves and a network of cords for the atrioventricular valves). The equilibrium of these supports requires that the valve leaflets form cusps along each line of closure. In the aortic and pulmonary valves there is evidence that the stress in the leaflet is borne by a single family of load-bearing fibers covering the surface. Under this hypothesis, we derive a differential equation for the leaflet and show that the fibers are geodetic lines under constant tension. During the large motions of valve opening and closure certain constraints are imposed on the surface metric by the presence of (almost) inextensible fibers in the surface. The severity of the constraints depends on the number of independent families of fibers.

Original languageEnglish (US)
Pages (from-to)335-343
Number of pages9
JournalJournal of the Franklin Institute
Volume297
Issue number5
DOIs
StatePublished - May 1974

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Applied Mathematics

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