A global optimization method for prediction of muscle forces of human musculoskeletal system.

Inverse dynamic optimization is a popular method for predicting muscle and joint reaction forces within human musculoskeletal joints. However, the traditional formulation of the optimization method does not include the joint reaction moment in the moment equilibrium equation, potentially violating the equilibrium conditions of the joint. Consequently, the predicted muscle and joint reaction forces are coordinate system-dependent. This paper presents an improved optimization method for the prediction of muscle forces and joint reaction forces. In this method, the location of the rotation center of the joint is used as an optimization variable, and the moment equilibrium equation is formulated with respect to the joint rotation center to represent an accurate moment constraint condition. The predicted muscle and joint reaction forces are independent of the joint coordinate system. The new optimization method was used to predict muscle forces of an elbow joint. The results demonstrated that the joint rotation center location varied with applied loading conditions. The predicted muscle and joint reaction forces were different from those predicted by using the traditional optimization method. The results further demonstrated that the improved optimization method converged to a minimum for the objective function that is smaller than that reached by using the traditional optimization method. Therefore, the joint rotation center location should be involved as a variable in an inverse dynamic optimization method for predicting muscle and joint reaction forces within human musculoskeletal joints.

Incidence of thoracic and lumbar spine injuries for restrained occupants in frontal collisions.

The increased utilization of three-point restraint systems has greatly reduced the incidence of spinal injuries in motor vehicle accidents. Nevertheless, several studies which rely upon the National Automotive Sampling System (NASS) have documented lower thoracic and upper lumbar fractures in restrained occupants involved in frontal collisions of moderate severities. Although it has been postulated that the injury mechanism may be related to the occupant being out-of-position or sitting in an unusual posture, conclusions with regard to the precise mechanism of injury are difficult due to the lack of information contained in the NASS database. In addition, previous studies have not reported statistical significance of these injuries. In this study, we combined statistical analysis of frontal collisions in the NASS database with the analysis of data acquired from sled and crash tests, which utilized anthropomorphic test devices (ATDs), in order to evaluate the incidence and potential injury mechanisms underlying thoracic and lumbar spine fractures in moderate frontal impacts. In the first portion of the study, we performed a statistical analysis of the NASS database to estimate the incidence rate of spinal fracture. This was complemented with measurements and analysis of lumbar spine load data derived from frontal sled and crash tests. Analysis of the NASS database demonstrated that thoracolumbar spinal injuries are rare when an occupant is restrained by a lap and shoulder belt, and are often accompanied by abdominal injury. The spinal loads measured during frontal impacts with restrained and nominally positioned ATDs were found to be well below injury thresholds. Our results also suggest that the potential for isolated fracture is increased when the geometry of occupant-to-restraint interaction is compromised, as occurs when an occupant submarines the lap belt.

Muscle forces predicted using optimization methods are coordinate system dependent.

Optimization methods are widely used to predict in vivo muscle forces in musculoskeletal joints. Moment equilibrium at the joint center (usually chosen as the origin of the joint coordinate system) has been used as a constraint condition for optimization procedures and the joint reaction moments were assumed zero. This study, through the use of a three-dimensional elbow model, investigated the effect of coordinate system origin (joint center) location on muscle forces predicted using a nonlinear static optimization method. The results demonstrated that moving the origin of the coordinate system medially and laterally along the flexion-extension axis caused dramatic variations in the predicted muscle forces. For example, moving the origin of the coordinate system from a position 5mm medial to 5mm lateral of the geometric elbow center caused the predicted biceps force to vary from 12% to 46% and the brachialis force to vary from 80% to 34% of the total muscle loading. The joint reaction force reduced by 24% with this medial to lateral variation of the coordinate system origin location. This data revealed that the muscle forces predicted using the optimization method are sensitive to the coordinate system origin location due to the zero joint reaction moment assumption in the moment constraint condition. For accurate prediction of muscle load distributions using optimization methods, it is necessary to determine the accurate coordinate system origin location where the condition of a zero joint reaction moment is satisfied.