On the implications of interpreting the stability index: a spine example

Quantifying the stability of the spinal column offers a perspective on the effectiveness of the motor control strategy to ensure a stable spine—and minimize the risk of injury from experiencing an unstable event. There are essentially three energy based methods of calculating a stability index for the lumbar spine. All three methods involve mathematical manipulation of an 18×18 Hessian matrix. The purpose of this paper was to consider the mathematical implications for the three methods of determining a single stability index, and examine the effects of biological factors such as muscle activation in each of these methods. The first approach computes the Hessianʹs determinant and is thought to represent a more global or “average” perspective on stability. A second approach computes the smallest eigenvalue of the Hessian matrix to determine the weakest link of the spine. The final method determines an average critical stiffness difference for the spine and is intended to effectively determines how far a human spine is from instability, and allows comparison between tasks. This study shows that the same interpretation of stability is achieved via all three computational approaches—they agree as to whether the spine is stable or not. However they appear to differ in their sensitivity to the effect of muscle activation patterns.