A neuromuscular model of human locomotion combines spinal reflex circuits with voluntary movements

Abstract

Existing models of human walking use low-level reflexes or neural oscillators to generate movement. While appropriate to generate the stable, rhythmic movement patterns of steady-state walking, these models lack the ability to change their movement patterns or spontaneously generate new movements in the specific, goal-directed way characteristic of voluntary movements. Here we present a neuromuscular model of human locomotion that bridges this gap and combines the ability to execute goal directed movements with the generation of stable, rhythmic movement patterns that are required for robust locomotion. The model represents goals for voluntary movements of the swing leg on the task level of swing leg joint kinematics. Smooth movements plans towards the goal configuration are generated on the task level and transformed into descending motor commands that execute the planned movements, using internal models. The movement goals and plans are updated in real time based on sensory feedback and task constraints. On the spinal level, the descending commands during the swing phase are integrated with a generic stretch reflex for each muscle. Stance leg control solely relies on dedicated spinal reflex pathways. Spinal reflexes stimulate Hill-type muscles that actuate a biomechanical model with eight internal joints and six free-body degrees of freedom. The model is able to generate voluntary, goal-directed reaching movements with the swing leg and combine multiple movements in a rhythmic sequence. During walking, the swing leg is moved in a goal-directed manner to a target that is updated in real-time based on sensory feedback to maintain upright balance, while the stance leg is stabilized by low-level reflexes and a behavioral organization switching between swing and stance control for each leg. With this combination of reflex-based stance leg and voluntary, goal-directed control of the swing leg, the model controller generates rhythmic, stable walking patterns in which the swing leg movement can be flexibly updated in real-time to step over or around obstacles.

Figure 1

Overview of the model architecture. In the supraspinal layer, a balance control equation defines target joint angles for the swing leg at mid-swing and heel-strike. The target joint angles can be modified to perform volitional, goal-directed movements. A movement plan towards these target joint configurations is generated by minimal jerk trajectories that can be updated during execution. An internal inverse model comprising biomechanics, muscle moment arms, muscle activation properties and the spinal stretch reflex produces descending commands that realize the planned movement. The descending commands are integrated with the stretch reflex in the spinal layer. Stance leg control is realized with five dedicated reflex modules. Reflex outputs are the applied to the biomechanical model that provides feedback to the controller. A finite state machine organizes switches between early swing phase, late swing phase and stance phase.

Figure 2

Comparison with human data. Averaged hip pitch, hip roll, knee and ankle joint angle trajectories for human data (orange) and model data (blue). The model data are averaged over 100 seconds of steady state walking. Human data are taken from. Solid lines are means and shaded areas show standard deviation, across participants for the human data and across gait cycles for the model.

Figure 3

Swing leg ankle paths for a sequence of twelve center-out-return movements with passively stabilized trunk. The same movements are shown in three different views. (A) 3D perspective view, (B) side view of the sagittal plane and (C) top-down view of the horizontal plane. The dashed lines show the planned paths and the blue lines show the realized ankle paths.

Figure 4

Example movement trajectories of the swing leg with a passively stabilized trunk. The dashed black lines show the planned movement trajectory and the blue lines show the realized joint angle trajectories.

Figure 5

Joint-space error for single movements with different movement times. Each curve shows the root-mean-squared error the respective joint.

Figure 6

Avoiding obstacle during steady-state walking. Panel (A) shows the change from the normal trajectory without obstacle in the vertical direction when stepping over obstacles of varying height. Panel (B) shows the change from the normal trajectory without obstacle in the medial-lateral direction when stepping around obstacles of varying width, in either direction. Both panels show the movement from left heel-strike to push-off of the stance foot.

Figure 7

Velocity and cadence control. Panel (A) shows the relationship between the reference parameter for trunk lean and the resulting movement speed for 13 movements (blue dots) and the linear fit (red line). Panel (B) shows the effect of the trunk lean change on the walking cadence.

Figure 8

Direction control. Movement direction was adjusted by temporarily adding a constant offset value to the hip roll target angle until the target movement direction was reached, with seven different target directions. Panel (A) shows the horizontal path of the trunk center. Panel (B) shows the trunk orientation over time.