Optimization of left ventricular fibre orientation of the normal heart for homogeneous sarcomere length during ejection

During the ejection phase of the cardiac cycle, left ventricular muscle fibres shorten while generating force. It was hypothesized that fibres are oriented in the wall such that the amount of shortening is the same for all fibres. We evaluated this hypothesis for the equatorial region of the left ventricle. In a finite element model of left ventricular wall mechanics fibre orientation was quantified by a helix angle which varied linearly from the inner to the outer wall. Fibre length was characterized by sarcomere length, set at 1.95 microns everywhere in the passive state of 0 transmural pressure. For a cavity pressure of 15 kPa, considered representative for ejection, inhomogeneity in mechanical loading was expressed by the variance of the sarcomere length. The variance was minimized by adapting the transmural course of fibre angle. First, only the slope was optimized and in a second optimization this was done for both slope and intercept. Optimal helix fibre angles were 69.6 degrees endocardially, 0 degree at the middle of the wall and -69.6 degrees epicardially for the first optimization and 78.2 degrees, 20.7 degrees and, -36.7 degrees respectively for the second. Sarcomere length changed from 1.95 to 1.975 +/- 0.012 and 1.981 +/- 0.004 microns (mean +/- SD) respectively.

After optimization calculated helix fibre angles were in the physiological range. Describing the transmural course of fibre angle with slope and intercept significantly improved homogeneity in mechanical load.