Combined Multibody Musculoskeletal Dynamic Modeling and Finite Element Modeling of the Human Tibia in Countermovement Jumps

Abstract

Computational models have been used to examine and estimate various motions and loading conditions of the human body that are otherwise difficult to examine experimentally. To study human musculoskeletal dynamics, biomechanical multibody models can be utilized with inverse or forward dynamics. To study the stress and strain response of complicated geometries, such as bones, finite element models can be utilized under specific loads and boundary conditions. When examining an injury mechanism or studying a specific motion, tackling both areas of computational modeling can provide insightful information (e.g. reaction forces or stress distribution. This thesis presents the work of combining a musculoskeletal dynamic model and a finite element model to examine the dynamics of countermovement jumping and the resulting stress on the human tibia.

The objectives of this thesis were to study the impact dynamics and investigate the stresses and strains of the human tibia during countermovement jumping. This work utilized multibody dynamic modeling and finite element modeling to investigate the risk of injuries in a jumping-landing motion. Initially, experimental data of position and ground reaction forces were obtained from a subject during countermovement jumping. This data is utilized in an inverse kinematics analysis to obtain joint angles of the lower extremity. A multibody model was constructed with segment lengths and parameters that are specific to the subject. The human was represented as four rigid links in the sagittal plane connected with revolute joints. Inverse dynamics was applied on the model with inputs of angles and positions of countermovement jumping to provide joint torques. Following that, a static optimization was performed to obtain muscle forces, while tackling the problem of redundancy. A total of 9 muscles were defined in the model and included in the static optimization problem under the objective function of minimizing muscle stress. With obtaining muscle forces, joint contact forces were also computed. Finally, a finite element model of the tibia was used to examine the stresses and strain under calculated loads of countermovement jumping. With a countermovement jump, the flexion/extension torques about the hip, knee, and ankle were slightly higher during the jumping phase than the landing phase. However, the stresses and strains were higher in the medial shaft of the tibia during landing phase than during jumping. This suggests that an injury to the tibia (i.e. stress fracture) is possible at locations of lower cross-sectional area under repetitive impact loads and elevated stresses of countermovement jumps.

This framework provided a potential of examining motion dynamics and structural bone response of the human body under loadings specific to the motion studied. It can be utilized as a tool for training in sports, or as a tool in prevention of injury in specific motions. This work also provides the first documented investigation that compares a finite element analysis of jumping and landing.