A model of the lower limb for analysis of human movement

Abstract

Computer models that estimate the force generation capacity of lower limb muscles have become widely used to simulate the effects of musculoskeletal surgeries and create dynamic simulations of movement. Previous lower limb models are based on severely limited data describing limb muscle architecture (i.e., muscle fiber lengths, pennation angles, and physiological cross-sectional areas). Here, we describe a new model of the lower limb based on data that quantifies the muscle architecture of 21 cadavers. The model includes geometric representations of the bones, kinematic descriptions of the joints, and Hill-type models of 44 muscle-tendon compartments. The model allows calculation of muscle-tendon lengths and moment arms over a wide range of body positions. The model also allows detailed examination of the force and moment generation capacities of muscles about the ankle, knee, and hip and is freely available at www.simtk.org .

FIGURE 1

The coordinate systems of the bone segments. The systems are oriented so that when all joint angles are 0° the x-axes points anteriorly, the y-axes points superiorly, and the z-axes points to the right (laterally for the right leg). The joints in the model are defined as translations and rotations between these coordinate systems.

FIGURE 2

Three-dimensional model of the lower limb. (a) Bony geometry included models of the pelvis, femur, patella, tibia, fibula, talus, calcaneus, metatarsals, and phalanges. Muscle–tendon geometry used line segment paths constrained to origin and insertion points, wrapping surfaces (e.g., cylinder in b) and via points (e.g., highlighted points in c).

FIGURE 3

Hill-type model of muscle used to estimate tendon and muscle force. (a) The muscle–tendon length (l^MT) derived from the muscle–tendon geometry was used to compute muscle fiber length (l^M), tendon length (l^T), pennation angle (α) muscle force (F^M), and tendon force (F^T). (b) Tendon was represented as a non-linear elastic element. We assumed that the stain in tendon $((l^{\mathrm{T}}-l_{\mathrm{S}}^{\mathrm{T}})/l_{\mathrm{S}}^{\mathrm{T}})$ was 0.033 when muscle generated maximum isometric force $(F_{\mathrm{o}}^{\mathrm{M}})$. Muscle was represented as a passive elastic element in parallel with an active contractile element (CE). Normalized active and passive force length curves were scaled by maximum isometric force $(F_{\mathrm{o}}^{\mathrm{M}})$ and optimal fiber length $(l_{\mathrm{o}}^{\mathrm{M}})$ derived from experimental measurements for each muscle.

FIGURE 4

Moment arms of muscles crossing the knee in the model (solid), Buford et al. (dashed), Spoor and van Leeuwen (dot-dashed), and Grood et al. (shaded area). Muscle moment arms are shown for (a) biceps femoris long head (BFLH) and biceps femoris short head (BFSH), (b) gastrocnemius lateralis (GL) and gastrocnemius medialis (GM), (c) gracilis (Grac) and sartorius (Sart), (d) semimembranosus (SM) and semitendinosus (ST), (e) rectus femoris (RF), vastus intermedius (VI), and grouped quadriceps (Quad), and (f) vastus lateralis (VL), vastus medialis (VM), and grouped quadriceps (Quad).

FIGURE 5

Passive joint moments calculated by the model and measured experimentally. Passive joint moment was summed from all muscles crossing each joint and compared to experimental results reported by Riener et al. and Anderson et al. There are no experimental results for passive adduction/abduction moments. The joints of the model were positioned to match those used by Anderson et al. The ankle moment (a) was calculated when knee and hip flexion angles were 80° and 50°. The knee moment (b) was calculated when the hip flexion and ankle angles were 70° and 0°. The hip flexion moment (c) was calculated when the knee angle was 10°.

FIGURE 6

Maximum isometric ankle moments over a range of ankle angles. Dorsiflexion moments and angles are positive; plantarflexion moments and angles are negative. The moments estimated with the model were compared to a previous model described by Delp et al. and experimental data reported by Anderson et al., Marsh et al., and Sale et al. The gray region indicates one standard deviation of the data reported by Anderson et al.

FIGURE 7

Maximum isometric knee moments over a range of knee angles. Flexion moments and angles are positive; extension moments are negative. The moments estimated with the model were compared to a previous model described by Delp et al. and experimental data reported by Anderson et al., Murray et al., and Van Eijden et al. The gray region indicates one standard deviation of the data reported by Anderson et al.

FIGURE 8

Maximum isometric hip flexion moments over a range of hip flexion angles. Flexion moments and angles are positive; extension moments and angles are negative. The moments estimated with the model were compared to a previous model described by Delp et al. and experimental data reported by Anderson et al., Inman et al., and Waters et al. The gray region indicates one standard deviation of the data reported by Anderson et al.

FIGURE 9

Maximum isometric hip adductor moments over a range of hip adduction angles. Adduction moments and angles are positive; abduction moments and angles are negative. The moments estimated with the model were compared to a previous model described by Delp et al. and experimental data reported by Cahalan et al. and Olson et al.