Introduction to Force-Dependent Kinematics: Theory and Application to Mandible Modeling

Abstract

Knowledge of the muscle, ligament, and joint forces is important when planning orthopedic surgeries. Since these quantities cannot be measured in vivo under normal circumstances, the best alternative is to estimate them using musculoskeletal models. These models typically assume idealized joints, which are sufficient for general investigations but insufficient if the joint in focus is far from an idealized joint. The purpose of this study was to provide the mathematical details of a novel musculoskeletal modeling approach, called force-dependent kinematics (FDK), capable of simultaneously computing muscle, ligament, and joint forces as well as internal joint displacements governed by contact surfaces and ligament structures. The method was implemented into the anybody modeling system and used to develop a subject-specific mandible model, which was compared to a point-on-plane (POP) model and validated against joint kinematics measured with a custom-built brace during unloaded emulated chewing, open and close, and protrusion movements. Generally, both joint models estimated the joint kinematics well with the POP model performing slightly better (root-mean-square-deviation (RMSD) of less than 0.75 mm for the POP model and 1.7 mm for the FDK model). However, substantial differences were observed when comparing the estimated joint forces (RMSD up to 24.7 N), demonstrating the dependency on the joint model. Although the presented mandible model still contains room for improvements, this study shows the capabilities of the FDK methodology for creating joint models that take the geometry and joint elasticity into account.

Approach for gait analysis in persons with limb loss including residuum and prosthesis socket dynamics

“…If the joint was modeled with 6 DOFs in this type of analysis, it would be unconstrained and possibly lead to non‐physiological results for residuum‐socket mechanics. An alternative approach would be to use soft tissue constraints (eg, Gasparutto et al and Skipper Andersen et al but this would depend on having good estimates of the stiffness and damping of the soft tissues in the residual limb, which are likely to be variable across subjects. Although the 4‐DOF joint model does provide a window into the residuum‐socket interaction, results of the calculated free coordinate movements are influenced by the actual anterior‐posterior and medial‐lateral translational movements which are not captured.…”

A Dynamic Jaw Model With a Finite-Element Temporomandibular Joint

“…de Zee et al (2007) used a comparable approach modeling the TMJ by using a single unilateral, planar constraint that was angled downwards and canted medially. In a more recent version, the group used an elastic contact foundation model to solve contact between the condyle and the fossa articularis using a Force Dependent Kinematics approach to track movement data and compute muscle, ligament and contact forces (Andersen et al, 2017).…”

Scapulothoracic rhythm affects glenohumeral joint force

“…The location of glenohumeral contact and the direction of the resultant force vector can be important in the biomechanical analysis of shoulder arthroplasty. Simulating contact is feasible in the AnyBody modeling by using the force-dependent kinematics feature 37 . However, implementing that feature significantly increased solution times.…”