Resistance to radial expansion limits muscle strain and work

Abstract

The collagenous extracellular matrix (ECM) of skeletal muscle functions to transmit force, protect sensitive structures, and generate passive tension to resist stretch. The mechanical properties of the ECM change with age, atrophy, and neuromuscular pathologies, resulting in an increase in the relative amount of collagen and an increase in stiffness. Although numerous studies have focused on the effect of muscle fibrosis on passive muscle stiffness, few have examined how these structural changes may compromise contractile performance. Here we combine a mathematical model and experimental manipulations to examine how changes in the mechanical properties of the ECM constrain the ability of muscle fibers and fascicles to radially expand and how such a constraint may limit active muscle shortening. We model the mechanical interaction between a contracting muscle and the ECM using a constant volume, pressurized, fiber-wound cylinder. Our model shows that as the proportion of a muscle cross section made up of ECM increases, the muscle's ability to expand radially is compromised, which in turn restricts muscle shortening. In our experiments, we use a physical constraint placed around the muscle to restrict radial expansion during a contraction. Our experimental results are consistent with model predictions and show that muscles restricted from radial expansion undergo less shortening and generate less mechanical work under identical loads and stimulation conditions. This work highlights the intimate mechanical interaction between contractile and connective tissue structures within skeletal muscle and shows how a deviation from a healthy, well-tuned relationship can compromise performance.

Keywords: Collagen; ECM; Intramuscular pressure; Muscle; Muscle fibrosis.

Fig. 1

Spatial relationship between the contractile tissues and the collagenous extracellular matrix of skeletal muscle. The spatial hierarchy of skeletal muscle is delineated by connective tissue structures surrounding muscle cells or fibers (endomysium), muscle fascicles (perimysium), and the whole muscle (epimysium). The relative proportion of a muscle’s cross section made up of these connective tissue layers increases as muscles become fibrotic

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°)

Fig. 3

Representative contractions of active muscle shortening with and without the presence of a physical constraint that limits radial expansion. The same muscle is used for both contractions, and the muscle is contracting against a load that corresponds to 50% of its maximum isometric force. The muscle shortens less during the 400-ms period of stimulation when the constraint is in place. The reduced shortening also reduces the mechanical work output of the muscle as indicated by the shaded area under the power–time plot

Fig. 4

Summary data of muscle shortening and muscle work. Data are shown at 25 and 50% of F_max and in the presence (black) and absence (white) of a physical constraint that limits radial expansion in the muscle. a During 400 ms of stimulation, the muscle undergoes less shortening when radial expansion is physically constrained. While the difference is statistically significant at 25% of F_max (p = 0.030), the trend is not statistically significant at 50% of F_max (p = 0.066). b The work output of the muscle is significantly lower when radial expansion is constrained. n = 4 and data are shown as mean ± S.E.M