Optimization of cardiac fiber orientation for homogeneous fiber strain at beginning of ejection

Mathematical models of left ventricular (LV) wall mechanics show that fiber stress depends heavily on the choice of musele fiber orientation in the wall. This finding brought us to the hypothesis that fiber orientation may be such that mechanical load in the wall is homogeneous. Aim of this study was to use the hypothesis to compute a distribution of fiber orientation within the wall. In a finite element model of LV wall mechanics, fiber stresses and strains were calculated at beginning of ejection (BE). Local fiber orientation was quantified by helix (HA) and transverse (TA) fiber angles using a coordinate system with local r-, c-, and l-directions perpendicular to the wall, along the circumference and along the meridian, respectively. The angle between the c-direction and the projection of the fiber direction on the cl-plane (HA) varied linearly with transmural position in the wall. The angle between the c-direction and the projection of the fiber direction on the cr-plane (TA) was zero at the epicardial and endocardial surfaces. Midwall TA increased with distance from the equator. Fiber orientation was optimized so that fiber strains at BE were as homogeneous as possible. By optimization with TA = 0°, HA was found to vary from 81,0° at the endocardium to − 35.8 at the epicardium. Inclusion of TA in the optimization changed these angles to respectively 90.1° and − 48.2° while maximum TA was 15.3°. Then the standard deviation of fiber strain (εf) at BE decreased from ± 12.5% of mean εf to ± 9.5%. The root mean square (RMS) difference between computed HA and experimental data reported in literature was 15.0° compared to an RMS difference of 11.6° for a linear regression line through the latter data.