How muscle fiber lengths and velocities affect muscle force generation as humans walk and run at different speeds

Abstract

The lengths and velocities of muscle fibers have a dramatic effect on muscle force generation. It is unknown, however, whether the lengths and velocities of lower limb muscle fibers substantially affect the ability of muscles to generate force during walking and running. We examined this issue by developing simulations of muscle-tendon dynamics to calculate the lengths and velocities of muscle fibers from electromyographic recordings of 11 lower limb muscles and kinematic measurements of the hip, knee and ankle made as five subjects walked at speeds of 1.0-1.75 m s(-1) and ran at speeds of 2.0-5.0 m s(-1). We analyzed the simulated fiber lengths, fiber velocities and forces to evaluate the influence of force-length and force-velocity properties on force generation at different walking and running speeds. The simulations revealed that force generation ability (i.e. the force generated per unit of activation) of eight of the 11 muscles was significantly affected by walking or running speed. Soleus force generation ability decreased with increasing walking speed, but the transition from walking to running increased the force generation ability by reducing fiber velocities. Our results demonstrate the influence of soleus muscle architecture on the walk-to-run transition and the effects of muscle-tendon compliance on the plantarflexors' ability to generate ankle moment and power. The study presents data that permit lower limb muscles to be studied in unprecedented detail by relating muscle fiber dynamics and force generation to the mechanical demands of walking and running.

Keywords: biomechanics; human gait; muscle architecture; musculoskeletal model; plantarflexors; simulation.

Fig. 1.

Simulation of muscle fiber length and velocity from inputs of processed electromyography (EMG) and joint angles. Processed EMG was used as muscle excitation and a first-order model of activation dynamics determined activation (a) for each muscle. Joint angles from motion capture and a musculoskeletal model determined muscle–tendon length (L^MT). Activation and muscle–tendon length were used with an equilibrium model of muscle–tendon contraction dynamics to produce a forward simulation of muscle force (F^M), fiber length (L^M) and fiber velocity (v^M).

Fig. 2.

(A) A musculoskeletal model describing the geometry and force generation properties of 11 lower limb muscles used. (B) A Hill-type equilibrium model of muscle–tendon contraction dynamics. Muscle was represented as a passive elastic element in parallel with an active contractile element (CE). Tendon was represented as a non-linear elastic element in series with the muscle. The muscle–tendon length (L^MT) derived from the path geometry and joint angles was used to compute muscle fiber length (L^M), fiber shortening velocity (v^M), tendon length (L^T), pennation angle (α), muscle force (F^M) and tendon force (F^T). (C) The force–length curves modeled the effects, active/passive force–length multipliers f_AL and f_PL, of normalized fiber length, , on the active and passive force generated by muscle fibers. The active force–length curve included ascending, plateau and descending regions. (D) The force–velocity curve modeled the effect, force–velocity multiplier f_v, of normalized fiber velocity, , on the active force generated by muscle fibers. The force–velocity curve included shortening () and lengthening () regions. (E) The tendon force–strain curve modeled the proportion of maximum isometric force, tendon force–strain multiplier f_T, in the tendon as a function of the strain in the tendon []. The force in the tendon would equal maximum isometric force (i.e. f_T=1) at a tendon strain of 10% in the plantarflexors (PF) or 4% in all other muscles.

Fig. 3.

Average experimentally measured and processed EMG for 11 muscles for subjects walking at four speeds and running at four speeds (N=5). We collected surface EMG for 11 lower limb muscles: gastrocnemius lateralis, gastrocnemius medialis, soleus, tibialis anterior, biceps femoris long head (LH), semitendinosus, rectus femoris, gluteus maximus, gluteus medius, vastus lateralis and vastus medialis. The raw signal was high-pass filtered at 30 Hz, rectified, and low-pass filtered at 10 Hz. Each subject's filtered EMG measurements were normalized to the maximum value detected for each muscle across all speeds.

Fig. 4.

Average experimentally measured ground reaction forces and joint kinematics for subjects walking at four speeds (top) and running at four speeds (bottom) (N=5). Vertical and horizontal ground reaction forces per body weight (GRF/BW) were used to identify three consecutive joint cycles from heel strike to heel strike. Joint angles (in degrees) for the hip (flexion/extension), knee (flexion/extension) and ankle (dorsiflexion/plantarflexion), were calculated from marker data using an inverse kinematics algorithm and a musculoskeletal model scaled to each subject. These joint kinematics were prescribed during the forward simulations.

Fig. 5.

Average simulated ankle joint moments and powers generated by muscles crossing the ankle in walking and running trials (N=5). Ankle joint moments generated by gastrocnemius lateralis, gastrocnemius medialis, soleus and tibialis anterior during each simulation were summed. The summed moment was multiplied by the ankle angular velocity to calculate ankle joint power. Simulated ankle moment and power were compared with values calculated using inverse dynamics (ID). Shaded regions indicate ±1 s.d. of ID results for the five subjects at 1.25 and 3.0 m s⁻¹. See supplementary material Figs S4 and S5 for all speed comparisons.

Fig. 6.

Force generation ability in 11 muscles at eight speeds (mean and 1 s.d., N=5). Force generation ability of gastrocnemius lateralis (Gas lat), gastrocnemius medialis (Gas med), soleus, tibialis anterior (Tib ant), gluteus maximus (Glut max), gluteus medius (Glut med), vastus lateralis (Vas lat), vastus medialis (Vas med), biceps femoris long head (BFLH), semitendinosus (Semiten) and rectus femoris (Rec fem) in walking (darker bars, 1.0–1.75 m s⁻¹) and running (lighter bars, 2.0–5.0 m s⁻¹); a repeated measures ANOVA indicated that speed had a significant effect (*P<0.05) in five muscles during walking and three muscles during running.

Fig. 7.

Mean and 1 s.d. (N=5) of the force–velocity multiplier (f_v) at the instant of largest active force in walking at 1.75 m s⁻¹ (small dot) and running at 2.0 m s⁻¹ (big dot) plotted on the force–velocity curve. A paired Student's t-test (gastrocnemius medialis and soleus) or a Wilcoxon signed-rank test (gastrocnemius lateralis) was used identify differences in f_v in between walking and running. The change from walking to running decreased fiber shortening velocity () and increased f_v in soleus. We did not detect a significant difference between walking and running in gastrocnemius medialis and gastrocnemius lateralis.

Fig. 8.

Average normalized fiber length () and period of highest activation of 11 muscles during gait at four walking speeds and four running speeds (N=5). Colors indicate gait speed in walking (1.00–1.75 m s⁻¹) and running (2.00–5.00 m s⁻¹). Thick horizontal lines indicate portions of the gait cycle when a muscle's activation exceeded 80% of the maximum value for that speed. Vertical lines on the abscissa indicate the instant of toe off for each of the eight speeds. Thin grey lines bound the plateau of the force–length curve, where normalized fiber length is between 0.95 and 1.05.

Fig. 9.

Average normalized fiber velocity () and period of highest activation of 11 muscles during gait at four walking speeds and four running speeds (N=5). Colors indicate gait speed in walking (1.00–1.75 m s⁻¹) and running (2.00–5.00 m s⁻¹). Thick horizontal lines indicate portions of the gait cycle when a muscle's activation exceeded 80% of the maximum value for that speed. Vertical lines on the abscissa indicate the instant of toe off for each of the eight speeds. When fibers are shortening, is positive; when fibers are lengthening, is negative.