Linear System Analyses of the Role of Reflex Gain and Delay in a Dynamic Human Spine Model

Measurement studies have linked paraspinal muscle reflexes to low back pain. However, the role of reflexes in stabilizing the spine is not clear. Previous studies enlisted biomechanical models to aid in understanding of how intrinsic stiffness stabilizes the spine. This work expands these previous studies by modeling the neuromuscular dynamic control of the spine.

The presence of delay in the reflexive system limits the availability of traditional stability analyses. However it is possible to investigate how reflex delay affects stability of the spine model using methods in linear time delayed stability. Such analyses find the maximum reflex delay, i.e., the delay margin for which stability is possible. Therefore a biomechanical model of the spine was developed that used these methods for stability. The model was able to demonstrate how reflex gains and delays affect stability.

It was shown that increased proportional reflex gain reduced the amount of co-contraction required for stability. However, increased reflex gain required a reduced delay margin of the system. Differential reflex gain had no effect on the amount of co-contraction required for stability. However, it was shown to increase the delay margin for small gains. As the differential reflex gain approached the magnitude of intrinsic muscle damping the trend was reversed, and increased gain caused the delay margin to approach zero. Increased intrinsic muscle damping did not affect the minimum co-contraction required for stability, but was shown to increase the delay margin in all cases.

This study provided a theoretical explanation for the role of reflexes in stabilizing the spine. Results agree with the trends in the published literature regarding patients with low-back pain. Specifically, these patients demonstrate abnormally larger reflex delay. To maintain stability, atypically small reflex gain is necessary. Compensatory co-contraction is required to offset the small reflex gain. Co-contraction and instability is observed in low back pain patients. The results presented here agree with measurement studies, and should aid in the development of hypotheses for future measurement studies.