Stochastic modeling of human lumbar functional spinal units system degeneration

Abstract

The degeneration of the human lumbar functional spinal units (FSUs) system is a global health concern. The FSUs system consists of four interdependent subsystems, each with an intervertebral disc and a facet joint that are subject to degeneration over time. The FSUs system fails when the overall disc height reduction or any facet joint contact force reaches the corresponding threshold. Existing research mainly uses regression-based models to describe the relationship between age and intervertebral disc height in the general population. A specific patient’s time-related progression of the FSUs system’s degeneration indicators are yet to be quantitatively characterized by the prediction models. We develop a stochastic model for the FSUs system degeneration process. The model captures the uncertainties of subsystems’ and components’ degeneration initiation time, order and interdependencies. Two failure mechanisms are proposed based on biomechanics and the components’ spatial and mechanical interdependencies. To facilitate the model’s clinical applications, individual-specific characteristics are incorporated into the extended models. Reliability metrics such as the overall reliability functions, mean time to failure and mean residual life are proposed for practical application purposes. Actual time-series data are collected for model validation. The results show that the proposed model outperforms existing stochastic and biostatistical models.