A mathematical model of force transmission from intrafascicularly terminating muscle fibers

Many long skeletal muscles are comprised of fibers that terminate intrafascicularly. Force from terminating fibers can be transmitted through shear within the endomysium that surrounds fibers or through tension within the endomysium that extends from fibers to the tendon; however, it is unclear which pathway dominates in force transmission from terminating fibers. The purpose of this work was to develop mathematical models to (i) compare the efficacy of lateral (through shear) and longitudinal (through tension) force transmission in intrafascicularly terminating fibers, and (ii) determine how force transmission is affected by variations in the structure and properties of fibers and the endomysium. The models demonstrated that even though the amount of force that can be transmitted from an intrafascicularly terminating fiber is dependent on fiber resting length (the unstretched length at which passive stress is zero), endomysium shear modulus, and fiber volume fraction (the fraction of the muscle cross-sectional area that is occupied by fibers), fibers that have values of resting length, shear modulus, and volume fraction within physiologic ranges can transmit nearly all of their peak isometric force laterally through shearing of the endomysium. By contrast, the models predicted only limited force transmission ability through tension within the endomysium that extends from the fiber to the tendon. Moreover, when fiber volume fraction decreases to unhealthy ranges (less than 50%), the force-transmitting potential of terminating fibers through shearing of the endomysium decreases significantly. The models presented here support the hypothesis that lateral force transmission through shearing of the endomysium is an effective mode of force transmission in terminating fibers.