Fig. 2.

a Fiber-wound cylinder model used to probe the interactions between a contracting muscle fiber and the surrounding collagen. We treat the muscle a constant volume cylinder surrounded by collagen. The surrounding collagen of the ECM is modeled as a helix which changes orientation and stretches as the muscle shortens and expands radially. In our model, L_f0 and R_f0 are the initial length and radius of the muscle fiber, L_f and R_f are the instantaneous length and radius of the contracting muscle fiber, and ϕ₀ and ϕ are the initial and instantaneous pitch angle of the helix, respectively. b The relationship between muscle fiber shortening and the stretch applied to the collagen fibers of the ECM. When the initial orientation of collagen is longitudinal (high ϕ₀), little stretch is applied to the collagen fibers even when the muscle shortens by 50% of its initial length. However, when the initial orientation of collagen is circumferential (low ϕ₀), even modest amounts of muscle fiber shortening where strain is below 20% require significant collagen stretch. Please note that strain in the muscle fibers indicates shortening, whereas the strain of the collagen indicates lengthening. c Increased stiffness of the ECM restricts muscle shortening. As the force required to stretch the collagen surrounding a muscle fiber increases, the force produced to expand the fiber radially becomes insufficient and the muscle fiber is unable to shorten. To drive these simulations, the maximum intramuscular pressure was set at 20 mmHg and the Young’s modulus of collagen was set at 550 MPa. The stiffness of the ECM was varied by changing the proportion of the muscle cross section made up of connective tissues. We explored this variable through a broad but physiologically realistic range (2–20%). Results show that the muscle fiber is constrained when the proportion of connective tissue increases and when the orientation of collagen is more circumferential (ϕ₀ < 45°)