Session: 07-02-01: Nonlinear Dynamics, Control, and Stochastic Mechanics

Paper Number: 119019

119019 - Why Do Humans Twist Their Ankle: A Nonlinear Dynamical Stability Model for Lower Limb 

Ankle injuries, which make up approximately 40% of all the lower extremity injuries, are among the most common types of sports injuries. Although ankle injuries resulting from postural instability are frequently observed during high-speed and intense physical activities, most current research has been limited to static or quasi-static models of the lower limb or has focused solely on the ankle joint itself. Several standard techniques are available to measure postural stability, which refers to an individual's ability to maintain an upright and stable posture even after experiencing unpredictable perturbations. The static standing steadiness test assesses the subject's ability to maintain stillness, but it overlooks the role of gravity and kinematic mechanisms in falling. Tests that assess dynamic postural stability, such as the Star Excursion Balance Test (SEBT), are actually quasi-static tests that provide adequate safety for the subjects but differ significantly from actual instability scenarios. In this study, in order to explain the kinetic mechanism underlying postural instability and ankle twists, we present a nonlinear dynamical model for the human lower limb that takes into account transient behavior and large rotations.

Ankle injuries are most commonly seen in activities involving jumping and landing. Here we focus on this specific motion pattern and examine the postural stability of the lower limb under different landing velocities and initial inclination angles. We assume that instability occurs in the coronal (frontal) plane. The landing of the lower limb on the ground is modeled as a mechanical system with two Degrees of Freedom (DoFs). The leg is represented as a rigid bar, and the foot is modeled as an elastic foundation that allows movement in one direction. The foot stiffness is assumed to be determined by the foot's medial longitudinal arch (MLA), which is simulated as an arch-spring mechanism. We simplify the hip joint as a kinematic pair that permits vertical displacement and rotation, but restricts horizontal movement. The ankle joint is modeled as a turning pair with a specified rotational stiffness. When the lower limb experiences external perturbations, the foot begins to rotate around its lateral edge. The configuration of the lower limb mechanism can be completely defined by two DoFs: the vertical displacement y and the inclination angle a. The upright, stable configuration occurs at (y,a) = (0,0). Clearly, the mechanism remains stable if the parameter trajectory returns to (0,0) after an impact, whereas the mechanism loses stability if the trajectory becomes unbounded. Thus, the ankle twist scenario is described as a transient stability problem for a 2 DoF mechanical system.

The transient response of the 2 DoF system after an external impact is determined by its potential energy landscape. The upright, stable configuration presents a local minimum at (0, 0) on the potential energy terrain.  Thus, under small perturbations, the transient trajectory oscillates around and eventually ends at this local minimum, indicating that the individual maintains postural stability after the impact. However, when the external perturbation energy increases, the trajectory may surpass the energy hilltop and escape from the potential energy minimum, resulting in a loss of stability and causing the individual to fall down. The index-1 saddle point (equilibrium point with only one unstable eigenvalue) on the potential energy landscape plays a critical role in determining whether this transition occurs, acting as a mountain pass that must be overcome. The minimum impact energy required to lose stability is equal to the potential energy level of the index-1 saddle point. We normalize this minimum impact energy by the potential energy at (0,0) and use the resulting normalized energy level as an indicator of lower limb postural stability. A larger stability indicator indicates that the lower limb system can withstand larger perturbation energy without losing stability. This stability indicator can be further used to evaluate lower limb stability in patients and identify individuals at high risk of ankle injury before any injury occurs.

Presenting Author: Yue Guan University of Memphis

Presenting Author Biography: Dr. Yue Guan is an assistant professor in the Department of Mechanical Engineering at the University of Memphis. Her research interests include nonlinear dynamics, biomechanics, computational mechanics, and other related fields.

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