Dynamic Behavior and Stability Analysis of Human Quiet Stance with Varying Feedback Delays in a Continuous Neural Control Framework.

Postural stability during quiet human stance relies heavily on neural feedback control. However, delays in this feedback can markedly reshape closed-loop dynamics and potentially compromise balance stability. Despite this, from a theoretical perspective, the mechanisms by which such delays affect balance stability remain poorly understood. Most existing studies rely on numerical simulations of neuromechanical models of human standing, while rigorous mathematical analysis of the system's dynamic properties is still lacking. To address this gap, this study proposed a frequency-domain analytical framework based on a widely adopted neuromechanical model of human postural control. By transforming the postural control system into the complex frequency domain, we derived analytical solutions and systematically investigated how the system's characteristic roots in the Laplace domain evolved with increasing neural feedback delay. This analysis revealed the mechanisms by which delays induce instability. Furthermore, we derived critical conditions for system destabilization and provided an exact analytical expression for the delay threshold leading to instability. Based on these results, a stability criterion was proposed, providing a theoretical basis for assessing the robustness of postural control. The proposed framework applies to the study of postural stability in populations such as older adults and patients with neurodegenerative diseases. Over all, this research provides a solid theoretical foundation, both qualitative and quantitative, for understanding instability in human postural control induced by varying neural feedback delays.