Kinematic modeling of single muscle fiber during diaphragm shortening

Understanding the kinematics of the diaphragm muscle at the single fiber level is important in understanding the mechanics of its membrane. Nevertheless, the geometric parameters of single muscle fiber contraction remain poorly understood. We modeled the kinematics of a single muscle fiber of the diaphragm to determine the relationships among fiber shape, perimeter of the fiber cross-section, and apparent surface area of the fiber during muscle shortening. We used the models to identify which constraints on the geometric parameters are most consistent with physiological data on diaphragmatic muscle shortening. Our kinematic models use isovolumic fibers with elliptical cross-sections, and these models have the following properties: (1) constant cross-sectional shape, (2) inextensible cross-sectional perimeter, (3) constant cross-sectional transverse dimension, or (4) constant apparent surface area. These models were investigated during muscle shortening of the diaphragm from functional residual capacity to total lung capacity. The model that matches physiologic data best has zero transverse strain and has a relationship between fiber shape and muscle shortening consistent with published data on single muscle fiber mechanics