How knee muscles and ground reaction forces shape knee buckling and ankle push-off in neuromuscular simulations of human walking

Abstract

Ankle push-off is important for efficient, human-like walking, and many prosthetic devices mimic push-off using motors or elastic elements. The knee is extended throughout the stance phase and begins to buckle just before push-off, with timing being crucial. However, the exact mechanisms behind this buckling are still unclear. We use a predictive neuromuscular simulation to investigate whether active muscles are required for knee buckling and to what extent ground reaction forces (GRFs) drive it. In a systematic parameter search, we tested how long the knee muscles vastus (VAS), gastrocnemius (GAS), and hamstrings could be deactivated while maintaining a stable gait with impulsive push-off. VAS deactivation up to 35% of the gait cycle resulted in a dynamic gait with increased ankle peak power. GAS deactivation up to 20% of the gait cycle was detrimental to gait efficiency and showed reduced ankle peak power. At the start of knee buckling, the GRF vector is positioned near the knee joint's neutral axis, assisting in knee flexion. However, this mechanism is likely not enough to drive knee flexion independently. Our findings contribute to the biomechanical understanding of ankle push-off, with applications in prosthetic and bipedal robotic design, and fundamental research on human gait mechanics.

Keywords: Ankle push-off; Gastrocnemius; Hamstrings; Knee; Predictive neuromuscular simulation; Vastus.

Fig. 1

Setup and signal flow in the pNMS. The multi-body simulation has nine degrees of freedom. Revolute joints in the hips, knees, and ankles connect the trunk, femur, tibia, and foot. Based on joint angles and angular velocities , the muscle model calculates the current length and force for each of the seven muscles per leg. A neural feedback controller computes the individual muscle stimulations based on the current muscle length , the MTU force , the head-arm-trunk segment (HAT) angle and angular velocity and , the ground contact of heel and ball , and the body load on the left and right leg . The muscle-tendon forces resulting from the given muscle stimulation and the passive, elastic tendon properties are multiplied by their respective lever arms and summed for all muscles. The total joint torques T are fed back into the multi-body simulation. We focus on the VAS, GAS, and HAM and deactivate them for defined periods.

Fig. 2

Scatter plot for stability score in (a) and selected gait characteristics when turning off GAS. In (a), only simulations that produced valid stride-normalized results are shown. Due to the normalization of to % stride time, most failed simulations fall outside the displayed y-axis limits. The failed samples often appear higher up on the y-axis due to post-processing errors in step detection when the model falls. White areas indicate regions without data points. (b) shows the average forward walking velocity (top) and the x-momentum change (bottom) of the trailing leg. In (b), the colors represent the relative change to the reference solution. The absolute value for the reference quantity is given in the title of each scatterplot. The color scale includes the 1st to 99th percentile of all results, with outliers shown in gray. Note that the y-axis limits in (b) are different from those in (a), to focus on the range of viable solutions. The cross marks the selected sample, which will be evaluated in detail. The vertical lines indicate the average timing of HO, TDc, and TO in human gait from for orientation. See Fig. S2 for scatter plots of all other metrics.

Fig. 3

Scatter plot for stability score in (a) and selected gait characteristics when turning off VAS. In (a), only simulations that produced valid stride-normalized results are shown. Due to the normalization of to % stride time, most failed simulations fall outside the displayed y-axis limits. The failed samples often appear higher up on the y-axis due to post-processing errors in step detection when the model falls. White areas indicate regions without data points. (b) shows the average forward walking velocity (top) and the x-momentum change (bottom) of the trailing leg. In (b), the color represents the relative change to the reference solution. The absolute value for the reference quantity is given in the title of each scatterplot. The color scale includes the 1st to 99th percentile of all results, with outliers shown in gray. Note that the y-axis limits in (b) are different from those in (a), to focus on the range of viable solutions. The cross marks the selected sample, which will be evaluated in detail. The vertical lines indicate the average timing of HO, TDc, and TO in human gait from Ref. for orientation. See Fig. S4 for scatter plots of all other metrics.

Fig. 4

Scatter plot for stability score (a) and selected gait characteristics when turning off HAM (b). In (a), only simulations that produced valid stride-normalized results are shown. Due to the normalization of to % stride time, most failed simulations fall outside the displayed y-axis limits. The failed samples often appear higher up on the y-axis due to post-processing errors in step detection when the model falls. White areas indicate regions without data points. (b) shows the average forward walking velocity (top) and the x-momentum change (bottom) of the trailing leg. In (b), the color represents the relative change to the reference solution. The absolute value for the reference quantity is given in the title of each scatterplot. The color scale includes the 1st to 99th percentile of all results, with outliers shown in gray. Note that the y-axis limits in (b) are different from those in (a), to focus on the range of viable solutions. The cross marks the selected sample, which will be evaluated in detail. The vertical lines indicate the average timing of HO, TDc, and TO in human gait from Ref. for orientation. During the relevant time window for ankle push-off, from 45% to 60% of the gait cycle, HAM deactivation shows almost no viable gaits. Changes in the evaluated gait characteristics mainly occur for deactivations at the end of swing. See Fig. S3 for scatter plots of all other metrics.

Fig. 5

Timing of gait events around ankle push-off. Blue curves show ankle-related measurements, orange knee-related measurements, yellow hip-related measurements, and gray the vertical GRFs of the ipsi- and contralateral leg. The gray vertical lines show HO, TDc, and TO, respectively, as indicated in the ankle power plot at the top. The shaded areas indicate double support. HO marks the beginning of terminal stance. TDc marks the end of terminal stance and the beginning of preswing. TO marks the end of preswing and the beginning of the swing phase. The blue vertical line marks the zero crossing (blue asterisk) of the ankle joint angular velocity, i.e., the point of maximum ankle dorsiflexion. The yellow vertical line marks the zero crossing (yellow asterisk) of the angular velocity of the hip joint in preswing, i.e., the start of hip flexion. The orange vertical line shows the zero crossing (orange asterisk) of the knee torque. The red vertical lines in the ankle power at the top and GRF plot at the bottom show the point of the last GRF snapshot given in Fig. 6 (e) and (j) for the reference simulation and deactivated VAS. The snapshots for GAS are provided in the appendix Fig. S7.

Fig. 6

Visualization of the GRF vector around TDc. Red shows the global GRF vector, the blue and green vectors show the individual GRFs for each leg. For some snapshots with large GRFs due to the initial loading peak, the vectors’ length is truncated as only the orientation of the vectors is important for our analysis. Snapshots above in (a)-(e) show the reference simulation, below in (f)-(j) the trial with VAS turned off. The snapshots are taken at 1% of the gait cycle before TDc, at TDc, and in uniform steps at 11%, 22%, and 33% of the second DS phase after TDc. The GRF vectors originate from the global and foot-internal centers of pressure, respectively. For the reference simulation, the GRF vectors pass in front of the knee and behind the hip joint prior to TDc in (a). With TDc and afterward, in (b) and (c), the vectors pass through the neutral axis of the knee joint. As soon as the body weight is transferred to the contralateral leg in (d) and (e), the global GRF vector moves in front of the already buckled knee joint of the trailing leg. With the deactivated VAS, the GRF vectors pass in front of the neutral axis of the knee joint in (f) and (h). Snapshots for the GAS and HAM trials are available in Figs. S7 and S8.