Fig 1.
Musculoskeletal model used to study human locomotion.
The model is constrained in the sagittal plane and has 9 DoFs: hip and knee flexion/extension, ankle plantar/dorsal flexion for each leg, and a 3-DoFs planar joint between the pelvis and the ground. The movements are generated by the activation of 9 muscles per leg: gluteus maximus (GMAX), biarticular hamstrings (HAMS), iliopsoas (ILPSO), rectus femoris (RF), vasti (VAS), biceps femoris short head (BFSH), gastrocnemius medialis (GAS), soleus (SOL), and tibialis anterior (TA).
Table 1.
Assigned weight for each component of the cost function for the three optimization sets.
Table 2.
Boundaries of the three gait characteristics targeted during the three optimization sets.
The first set shows the optimizations’ results where the gait target to reach is the desired speed that varied from the lower to the upper boundary. The second set shows the optimizations’ results with a fixed step duration and a varying target step length. Finally, the third set shows the optimizations’ results with a fixed value of step length, changing the target step duration.
Table 3.
Correlation coefficients of identified key reflex parameters: Three reflexes were found to have a significant effect on speed through the modulation of step length, four to have an impact on all the three gait characteristics, and two able to modulate step length and step duration accordingly with small effects on speed.
Fig 2.
Regression analysis of step length modulators.
The solutions obtained by the three sets of optimizations are represented by the blue dots, whereas the red curve represents the regression. The plot on the left shows the data distribution and regression for the speed modulation, while the plots on the center and the right show the step length and step duration modulation, respectively. The reflexes presented facilitate speed and step length increasing with minimal effect on the step period. The offset length of the hamstrings’ stretch reflex presents an influence on step duration modulation, but the global increasing tendency of speed reflects the behavior found in the modulation of step length.
Fig 3.
Regression analysis of step length and step duration modulators with effects on speed.
The stretch reflex gain of iliopsoas during pre-swing and the length offset during swing have a decreasing impact on speed due to decreasing step length and increasing step duration for the former and primarily for step duration increasing for the latter. On the other hand, the stretch reflex gain of gluteus maximus in landing preparation has an increasing linear effect on the speed with nonlinear effects on step length and step duration. The length offset of tibialis anterior’s stretch reflex can modulate fast speed with large step lengths and short step durations but has less effect in the modulation of slow gaits.
Fig 4.
Regression analysis of step length and step duration modulators with effects on speed.
Increasing the stretch reflex gain of hamstrings during landing preparation leads to a decreasing in step length and step duration resulting in a low influence in speed modulation. Similarly, the increasing length offset of hamstrings’ stretch relfex during landing preparation results in an increased step length and step duration with a small effect on speed modulation.
Fig 5.
Diagram of the reflex controller with key reflexes modulating gait highlighted.
The reflexes that were found to modulate mainly step length are highlighted in yellow. In contrast, those modulating step length and step duration together are highlighted in green and red depending on whether they showed a significant effect on speed (green) or not (red).
Table 4.
Boundaries of the three gait measures reached with the optimization of key reflexes.
The optimization of the key reflexes alone could obtain the same performances of the gaits obtained optimizing all the reflexes suggesting that the major role of modulation is delegated to the key reflexes.
Fig 6.
Representation of gait behavior with snapshots taken at different frames of for the speed modulation solution with target speed equal to 1.2 m/s.
The instant taken is represented together with the behavior of vertical and horizontal ground reaction forces.
Fig 7.
Joints angles and ground reaction forces for low, intermediate, and high values of the three gait characteristics.
The cyan curves describe the slow gaits with small step lengths and long step durations, whereas the dark blue curves describe the fast gaits with large step lengths and short step durations. The change observed in speed modulation is closer to the only step length modulation than the modulation of step duration.
Fig 8.
Hamstrings and iliopsoas activity show a significant increase with increasing speed and step duration. Gluteus maximus activation is less evident, but it increases activation at the fastest speeds, whereas the rectus femoris does not show significant changes.
Fig 9.
Higher activation is observed for both the vasti and biceps femoris short head muscles at fast speeds and large step lengths.
Fig 10.
Soleus and gastrocnemius activity increase with the increase of speed, but no significant changes are seen for the modulation of step length and step duration. Similarly, tibialis anterior activity increases with speed, whereas for step length and step duration modulation, it can be observed anticipation and delay of activation during the gait cycle for large step lengths and short durations, respectively.