Geodesics as a mechanically optimal fiber geometry for the left ventricle

Anatomical findings as well as theoretical considerations indicate that the myocardial fibers lie along minimal length geodesics of the left ventricular wall. Based upon this knowledge it is shown that the energy spent by the actively contracting fibers during systole, as well as the passive fiber stresses developed through diastole, are minimal in comparison with any other possible fiber configuration. Subsequently, it is concluded that for a given succession of left ventricular states, fiber shortening course and hence the amount of mechanical work are uniquely determined. Comparison with experimental findings concerning global left ventricular systolic work indicates that a given course of afterload produces a unique course of ventricular volume and of mechanical work.