Microstructural model of perimysial collagen fibers for resting myocardial mechanics during ventricular filling

To study the structural contribution of perimysial collagen fibers to the passive mechanics of ventricular myocardium, we modeled the coiled fibers as helical springs using elastica theory to represent the fibers as initially curved, inextensible rods that could bend and twist. The extensional behavior in the physiological range of left, ventricular (LV) pressures was dependent on structural parameters that were estimated histologically for rat and dog: collagen fiber diameter, coil period, collagen fiber tortuosity (fiber length in 2 dimensions/midline length), and number density (N-d) Of collagen fibers per cross-sectional area of tissue. The difference in each geometric parameter was not great (27% maximal difference for N-d) However, the combined effect of all parameters accounted for a 102% difference in tissue stiffness. The only other model parameter was the Young's modulus (E) for bending of collagen, which was calculated from a linear regression of stress and strain scaled according to the geometric parameters. Despite an approximately fivefold difference in tissue stiffness, the resulting E was only 18.5% different (135 vs. 160 MPa for rat and dog, respectively). With the mean values from each species, the model was able to predict the stress-strain behavior of both rat and dog myocardium in the physiological range of LV pressures, suggesting that the perimysial collagen fibers may be the most important contributors to passive stiffness of the myocardium in the direction of the muscle fibers. It also appears that these large collagen fibers are not stretching to generate stress in the normal range of ventricular pressures, but rather stress gradually increases as collagen fibers straighten through bending and twisting. Finally, to understand the importance of differences in collagen architecture, one should measure the detailed collagen structure, not simply collagen density.