Relating reflex gain modulation in posture control to underlying neural network properties using a neuromusculoskeletal model

Abstract

During posture control, reflexive feedback allows humans to efficiently compensate for unpredictable mechanical disturbances. Although reflexes are involuntary, humans can adapt their reflexive settings to the characteristics of the disturbances. Reflex modulation is commonly studied by determining reflex gains: a set of parameters that quantify the contributions of Ia, Ib and II afferents to mechanical joint behavior. Many mechanisms, like presynaptic inhibition and fusimotor drive, can account for reflex gain modulations. The goal of this study was to investigate the effects of underlying neural and sensory mechanisms on mechanical joint behavior. A neuromusculoskeletal model was built, in which a pair of muscles actuated a limb, while being controlled by a model of 2,298 spiking neurons in six pairs of spinal populations. Identical to experiments, the endpoint of the limb was disturbed with force perturbations. System identification was used to quantify the control behavior with reflex gains. A sensitivity analysis was then performed on the neuromusculoskeletal model, determining the influence of the neural, sensory and synaptic parameters on the joint dynamics. The results showed that the lumped reflex gains positively correlate to their most direct neural substrates: the velocity gain with Ia afferent velocity feedback, the positional gain with muscle stretch over II afferents and the force feedback gain with Ib afferent feedback. However, position feedback and force feedback gains show strong interactions with other neural and sensory properties. These results give important insights in the effects of neural properties on joint dynamics and in the identifiability of reflex gains in experiments.

Fig. 1

Neuromusculoskeletal model. A muscle pair actuated a one degree of freedom joint while being controlled by a spinal network with populations of motoneurons (MN), group Ia interneurons (IA), Renshaw cells (RC), inhibitory interneurons (IN), excitatory interneurons (EX) and group Ib interneurons (IB). Feedback is provided by Ia, Ib and II afferents

Fig. 2

Lumped reflex gain model used to fit reflex gains onto the output of the perturbation experiments of the neuromusculoskeletal model. In this lumped model, the force disturbance d is applied to a single inertia m. Muscle viscoelasticity is represented by a stiffness k and viscosity b. Reflexive feedback is represented by a positional feedback gain k _p, a velocity feedback gain k _v and a force feedback gain k _f. A single reflexive feedback neural time delay τ _del is represented by H _del. The first order muscle activation dynamics are H _act. Output of this lumped model is joint position

Fig. 3

Four-second segment of a perturbation experiment on the NMS model and the output of the lumped reflex gain fit for a single condition. Disturbance torque (top) and resulting arm motion (bottom). Simulation experiment with the NMS model (solid) and the fit of the lumped reflex gain model (dashed). In this case VAF of the fit was 0.95

Fig. 4

Sensitivity of reflex gain parameters k _p, k _v, k _f and RMS of joint deviation to the velocity component d _Ia of the muscle spindle. Lines indicate the linear regression fit; the normalized slope determined the sensitivity measure S _ij

Fig. 5

Sensitivity measure S _ij for the eight lumped reflex gain model parameters (m, b, k, k _p, k _v, k _f, τ _del, τ _act) and RMS of the joint position. Low RMS indicates high task performance: the force disturbances result in small deviations. For each graph, only the eight parameters with the highest sensitivity values are shown

Fig. 6

Sensitivity measure S _ij of the lumped reflex gains k _p, k _v, k _f to the sensory parameters of the muscle spindle and Golgi tendon organs. The most closely related neural substrates of each reflex gain parameter are indicated with an asterisk (*), e.g: velocity feedback gain k _v is expected to be closest related to the velocity components d _Ia and e _Ia. (See Eqs. 1–3 and Table 1 for a list of these parameters)