Leg stiffness of sprinters using running-specific prostheses

Abstract

Running-specific prostheses (RSF) are designed to replicate the spring-like nature of biological legs (bioL) during running. However, it is not clear how these devices affect whole leg stiffness characteristics or running dynamics over a range of speeds. We used a simple spring-mass model to examine running mechanics across a range of speeds, in unilateral and bilateral transtibial amputees and performance-matched controls. We found significant differences between the affected leg (AL) of unilateral amputees and both ALs of bilateral amputees compared with the bioL of non-amputees for nearly every variable measured. Leg stiffness remained constant or increased with speed in bioL, but decreased with speed in legs with RSPs. The decrease in leg stiffness in legs with RSPs was mainly owing to a combination of lower peak ground reaction forces and increased leg compression with increasing speeds. Leg stiffness is an important parameter affecting contact time and the force exerted on the ground. It is likely that the fixed stiffness of the prosthesis coupled with differences in the limb posture required to run with the prosthesis limits the ability to modulate whole leg stiffness and the ability to apply high vertical ground reaction forces during sprinting.

Figure 1.

A schematic of a simple spring–mass model used to characterize the overall biomechanics of bouncing gaits such as running and sprinting. This model represents the body's mass as a point mass and the leg as a massless linear spring. At the initial point of ground contact, the leg spring is uncompressed and equals a length denoted by L₀. During the stance phase, the leg spring is compressed, and reaches maximal leg compression (ΔL) at approximately mid-stance. The CoM is displaced vertically (Δy), and horizontally, where one-half the angle swept by the leg spring during ground contact is denoted as θ.

Figure 2.

Representative vertical ground reaction forces from a non-amputee (bioL), the unaffected leg (UL) and affected leg (AL) of a unilateral amputee and a bilateral amputee (BL) running at four different speeds ((a) 3 m s⁻¹; (b) 5 m s⁻¹; (c) 7 m s⁻¹; (d) 9 m s⁻¹). Peak forces were higher in bioL and tended to be higher in UL, compared with AL and BL subjects. Thick black line, bioL; thin line, UL; red solid line, AL; blue dashed line, BL. (Online version in colour.)

Figure 3.

Average dimensionless leg stiffness (K_leg) and vertical stiffness (K_vert) across speed. (a) Non-amputees (bioL) increased K_leg with increasing speed; whereas subjects with a unilateral amputation did not change leg stiffness in their UL. (b) K_leg decreased with increasing speed in the AL of unilateral amputees and bilateral amputees (BL). (c,d) All subjects increased K_vert with increasing speed; however, non-amputees increased vertical stiffness to a greater extent than subjects with an amputation. The linear fit equations for K_leg were bioL: K_leg = 0.93x + 16.64, R² = 0.192, p < 0.001; UL: K_leg = 0.24x + 18.36, R² = 0.016, p = 0.385; AL: K_leg = −0.53x + 22.26, R² = 0.092, p = 0.034; BL: K_leg = −0.60x + 22.28, R² = 0.182, p = 0.017. The linear fit equations for K_vert were bioL: K_vert = 23.72x − 44.49, R² = 0.889, p < 0.001; UL: K_vert = 16.00x − 17.00, R² = 0.740, p < 0.001; AL: K_vert = 19.63x − 22.12, R² = 0.810, p < 0.001; BL: K_vert = 19.15x − 14.06, R² = 0.583, p < 0.001. Plus symbols with dashed line, bioL; open circles with solid line, AL; filled circles with solid line, UL; crosses with dashed line, BL. (Online version in colour.)

Figure 4.

Average peak vertical ground reaction force (vGRF_peak) and (c,d) leg compression (ΔL) across speed. (a,b) Non-amputees (bioL) increased vGRF_peak at faster speeds. Subjects with a unilateral amputation increased vGRF_peak to a greater extent in their UL than in their AL. Subjects with bilateral amputations (BL) increased vGRF_peak with speed by a similar magnitude as unilateral AL, which was less than non-amputees and unilateral UL. (c,d) Non-amputees (bioL) did not change leg compression across velocity. Subjects with a unilateral amputation did not change leg compression in their UL, but increased leg compression with their AL at faster speeds. Subjects with bilateral amputations (BL) also increased leg compression at faster speeds. The linear fit equations for vGRF_peak were bioL: vGRF_peak = 0.144x + 2.40, R² = 0.615, p < 0.001; UL: vGRF_peak = 0.135x + 2.66, R² = 0.528, p < 0.001; AL: vGRF_peak = 0.094x + 2.42, R² = 0.341, p < 0.001; BL: vGRF_peak = 0.067x + 2.57, R² = 0.745, p < 0.001. The linear fit equations for ΔL were bioL: ΔL = 0 x + 0.196, R² = 0, p = 0.934; UL: ΔL = 0.003x + 0.226, R² = 0.014, p = 0.421; AL: ΔL = 0.009x + 0.172, R² = 0.206, p = 0.001; BL: ΔL = 0.012 x + 0.150, R² = 0.660, p < 0.001. (a,c) Crosses with dashed line, bioL; (a,c) circles with filled line, UL; (b,d) open circles with solid line, AL; crosses with solid line, BL. (Online version in colour.)

Figure 5.

Half angle swept (θ) and landing velocity (v_land) across speed. (a,b) All subjects increased θ at faster speeds. The increase in θ was not as substantial in non-amputees (bioL) compared with all other conditions across speed. (c,d) v_land decreased across velocity for all conditions. The linear fit equations for θ were bioL: θ = 1.21x + 18.53, R² = 0.639, p < 0.001; UL: θ = 1.75x + 17.75, R² = 0.642, p < 0.001; AL: θ = 1.93x + 15.51, R² = 0.777, p < 0.001; BL: θ = 1.98x + 15.92, R² = 0.752, p < 0.001. The linear fit equations for v_land were bioL: v_land = −0.021x + 0.779, R² = 0.359, p < 0.001; UL: v_land = −0.025x + 0.759, R² = 0.333, p = 0.154; AL: v_land = −0.007x + 0.680, R² = 0.043, p < 0.001; BL: v_land = −0.024x + 0.649, R² = 0.651, p < 0.001. (a,c) Crosses with dashed line, bioL; filled circles with continuous line, UL. (b,d) open circles with solid line, AL; crosses with solid line, BL. (Online version in colour.)

Figure 6.

The dimensionless Groucho number across speed. The Groucho number increased with speed for in all subjects; however, the slopes were significantly greater for biological legs (bioL and UL) compared with legs with running-specific prostheses (AL and BL). Lower Groucho numbers indicate running with a ‘softer’ gait. The linear fit equations for Grouch number were bioL: Gr = 0.180x + 0.954, R² = 0.771, p < 0.001; UL: Gr = 0.170x + 0.920, R² = 0.593, p < 0.001; AL: Gr = 0.084x + 1.224, p = 0.001, R² = 0.227; BL: Gr = 0.064x + 1.124, R² = 0.339, p < 0.001. (a) Crosses with dashed line, bioL; filled circles with dashed line, UL. (b) Open circles with solid line, AL; crosses with dashed line, BL. (Online version in colour.)

Figure 7.

Representative force–length plots from a (a) non-amputee (bioL), (b) the UL and (c) AL of a unilateral amputee and a bilateral amputee (BL) running at four different speeds (d). Loading stiffness (upward arrow) tended to increase with speed in bioL (bioL and UL), but was independent of speed in legs with running-specific prostheses (AL and BL).