Postural control of a musculoskeletal model against multidirectional support surface translations

Abstract

The human body is a complex system driven by hundreds of muscles, and its control mechanisms are not sufficiently understood. To understand the mechanisms of human postural control, neural controller models have been proposed by different research groups, including our feed-forward and feedback control model. However, these models have been evaluated under forward and backward perturbations, at most. Because a human body experiences perturbations from many different directions in daily life, neural controller models should be evaluated in response to multidirectional perturbations, including in the forward/backward, lateral, and diagonal directions. The objective of this study was to investigate the validity of an NC model with FF and FB control under multidirectional perturbations. We developed a musculoskeletal model with 70 muscles and 15 degrees of freedom of joints, positioned it in a standing posture by using the neural controller model, and translated its support surface in multiple directions as perturbations. We successfully determined the parameters of the neural controller model required to maintain the stance of the musculoskeletal model for each perturbation direction. The trends in muscle response magnitudes and the magnitude of passive ankle stiffness were consistent with the results of experimental studies. We conclude that the neural controller model can adapt to multidirectional perturbations by generating suitable muscle activations. We anticipate that the neural controller model could be applied to the study of the control mechanisms of patients with torso tilt and diagnosis of the change in control mechanisms from patients' behaviors.

Fig 1. Musculoskeletal model.

A musculoskeletal model with 70 muscles and 15 DoF of joints was used. The 35 muscular-tendon actuators were as follows: gluteus medius 1, gluteus medius 2, gluteus medius 3, biceps femoris long head, biceps femoris short head, sartorius, adductor magnus, tensor fasciae latae, pectineus, gracilis, gluteus maximus 1, gluteus maximus 2, gluteus maximus 3, iliacus, psoas major, quadratus femoris, fixme gem, piriformis, rectus femoris, vastus medialis, medial gastrocnemius, lateral gastrocnemius, soleus, tibialis posterior, flexor digitorum longus, flexor hallucius longus, tibialis anterior, peroneus brevis, peroneus longus, peroneus tertius, extensor digitorum longus, extensor hallucius longus, erector spinae, internal oblique, and external oblique. The gluteus medius muscle and the gluteus maximus muscle were each composed of three muscular-tendon actuators. The musculoskeletal model had the following movements: trunk bending (q₁), trunk leaning to side (q₁₁), trunk twisting (q₈), hip flexion (q₂), hip adduction and abduction (q₁₂ and q₁₃), hip rotation (q₉ and q₁₀), knee flexion (q₃ and q₆), ankle flexion (q₄ and q₇), and ankle inversion and eversion (q₁₄ and q₁₅).

Fig 2. Diagram of a neural controller.

(A) This NC model, proposed in a previous study [36], consists of FF and FB control. u, u_fb, and u_ff are the total, FB, and FF controls, respectively. a denotes muscle activation. L^MT and ${\dot{\mathit{L}}}^{MT}$ are the length and lengthening velocity of the muscular-tendon actuators, respectively. ${\mathit{L}}_0^{MT}$ and ${\dot{\mathit{L}}}_0^{MT}$ are the initial values of the length and lengthening velocity of the muscular-tendon actuators (${\dot{\mathit{L}}}_0^{MT}={\ddot{\mathit{L}}}_0^{MT}=\mathit{0}$), respectively. L^M and ${\dot{\mathit{L}}}^M$ are the length and lengthening velocity of muscle fibers, respectively. (B) FB control is implemented as PD controllers using proprioceptive information (muscle length and lengthening velocity). k_p and k_d are PD gains.

Fig 3. Horizontal support surface translations as perturbations and index of magnitude of muscle responses against perturbations.

(A) Perturbations were applied in the form of horizontal support surface translations in 12 directions separated by 30°. A rightward translation was defined as 0°after the definition of Henry et al. [55]. When a 0°translation was applied, the surface moved in a rightward direction, and the body tilted leftward. (B) The perturbation was implemented with an s-shaped step function. The support surface was translated 3 cm in 200 ms. The velocity and acceleration at t = 0 ms and 200 ms were 0. Muscle activations from 70–270 ms were observed to evaluate simulated muscle responses (indicated in red).

Fig 4. Parameter adjustment algorithm.

u_ff candidates were calculated (indicated in orange). From results of simulations with 0-ms τ_fb and τ_trans, u_ff candidates were obtained. After selecting a u_ff, optimizations were performed for each direction of perturbations with CMA-ES (indicated in blue). Note that only one u_ff is shown in this figure. A total of 12 different optimizations were performed for a different u_ff.

Fig 5. Trends of PD gains for directions.

The values for the graph were calculated as follows. A total of 22 PD gain values for each u_ff and perturbation direction were divided by the mean of 22 values (normalization). The mean and standard deviations of the normalized values for u_ff were calculated and plotted in the graph. “p_lumbar_extensor” is the P gain for the lumbar extensor group, and “d_lumbar_extensor” is the D gain for the lumbar extensor group. Perturbation directions 120°–240°are omitted because of the symmetry of simulations.

Fig 6. Magnitudes of muscle responses against perturbations.

(A) Muscle activations in the range of 70–270 ms after the onset of perturbations were integrated and used as the index of the magnitudes of muscle activations. This time range was the same as that in a human experimental study [55]. When ∥u_ff∥² = 2.01, the ESP muscle was activated for a forward translation (90°). The value of integrated muscle activation calculated with Eq (13) was 7.30e-3 s. As 7.30e-3 s was the largest integrated value for the 12 directions, we normalized the integrated values to values of 0 to 1, such that 7.30e-3 s was defined as 1. The 12 boxes around the radar chart indicate integrated ESP muscle activations against perturbations in each direction. The number in the box denotes the value of integrated ESP muscle activation, and the number within parentheses is the normalized value. In the radar chart, the red shaded area denotes the simulation results, and the black shaded area denotes the human experimental results [55]. (B) Each row of the table contains radar charts for each ∥u_ff∥². Each column contains radar charts for each muscle (see the “Evaluation index” section for muscle names). The numbers below each radar chart are the cosine similarity values for each condition. The average of the cosine similarity for each ∥u_ff∥² and for each muscle are indicated in the right side and bottom.