A mathematical model treating the left ventricular wall as nested ellipsoidal shells with helical fibers accurately predicts changes in muscle fiber direction and length during the cardiac cycle.
The relations between end-diastolic ( D ) and end-systolic ( S ) fiber angles (α) and sarcomere lengths ( s ) have been previously studied at different sites in canine left ventricular myocardium. However, no postulates have been advanced for predicting a and s in successive states of the ejection cycle ( D or S) or at different sites in one state when the semimajor ( Z ) and semiminor (R) axes of the wall surfaces for successive states and the fiber orientations and sarcomere lengths at one site in one state are known. In this study, the myocardial fibers were regarded as the matrix of a myocardial continuum: they are prisoners of the heart wall and must comply with the movements of the wall. Using the same values as in the preceding article, the wall was treated as a nested set of truncated ellipsoidal shells of revolution with shell volumes preserved from D to S. Both confocal and nonconfocal configurations were analyzed. In each shell, the fibers were assumed to follow a "helical" path with a constant advance in each turn about the Z axis (the simplest possible path). The results of this assumption were compatible with previously reported values of a and s measured at various sites in the left ventricular free wall in states D and S . These results suggest a postulate for the heart wall: in the beating heart, each muscle fiber changes direction and length uniquely as the wall changes shape.
Streeter et al. (1973) studied this question.