# The Development of a Dynamic Finite Element Model of the Temporomandibular Joint (TMJ) and Study of Joint Mechanics, 18-R8386

**Principal Investigators**
Daniel P. Nicolella

Travis D. Eliason

Todd L. Bredbenner

Inclusive Dates: 04/01/13 – Current

**Background** — Disorders of the temporomandibular joint (TMJ)
result in an annual cost of $4 billion and affect more than half of the
population. TMJ disorder (TMD) causes pain in the jaw when speaking or chewing
that is often associated with clicking and popping of the jaw and can limit a
person's ability to open their mouth. Women ages 20 to 40 are the most prevalent
sufferers of TMD. Various studies indicate that women with TMD outnumber men
anywhere from 3:1 to 8:1. While the causes of TMJ disorder (TMD) are not
completely understood, it is thought that alterations in joint mechanics due to
osteoarthritis (OA) or trauma results in degradation and inflammation of the
joint soft tissues (cartilage and disc), which then results in pain and limited
motion. In addition, displacement of the TMJ disc is also associated with TMD.
The dynamic mechanical environment within the TMJ during chewing or clenching is
not well characterized because of the complexity of the anatomy and materials.
Within the TMJ research community, the question of how soft tissue properties
and geometry of the joint affect the mechanical environment has gone unanswered
and is the focus of this project.

**Approach** — The primary objectives of this project are:

- Develop a detailed dynamic finite element model of the TMJ and mandible from head CT scans.
- Determine muscle activation timings and magnitude to achieve dynamic mouth opening and closing using a new a proportional–integral–derivative (PID) controller method.
- Perform sensitivity analyzes of TMJ disc properties to determine the importance of those properties in the resulting forces and stresses of the TMJ during normal mandible movements.
- Implement an element erosion or damage material model for the TMJ disc to investigate the effects of disc degeneration on the muscle forces required for normal mandible movements.
- Develop a statistical shape model of the TMJ coupled with the dynamic finite element model.
- Investigate the effect of gender differences on TMJ stress using the FE-coupled statistical shape model.

**Accomplishments ** — A dynamic finite element model of the
skull, mandible, TMJ and musculature has been developed using a generic anatomy
database and implemented in an open-source finite element analysis program
(FEBio v. 1.5, University of Utah). The model consists of the skull, mandible,
upper and lower dentition, and bilateral temporalis, masseter, lateral
pterygoid, digastric muscles (see illustration). The skull, mandible and teeth
are modeled as rigid bodies while the muscles are modeled using
three-dimensional active contraction continuum elements. The material model used
for the muscle elements is a transversely isotropic Moony-Rivlin with
viscoelasticity. Force is generated along a locally defined fiber axis direction
using a modified active contraction model. The muscle material model parameters
are taken from the literature. Motion of the mandible relative to the maxilla
(skull) is produced by coordinated active, time-varying contraction of opposing
muscle groups and is constrained by contact between the mandibular condyle and
the temporal bone in the mandibular fossa, contact between the upper and lower
dentition, and the constraint supplied by the deformation of the attached
musculature.

The initial muscle activations have been determined using a traditional
parameter optimization method. The control parameters in this case consist of
activation levels for each muscle as a function of time throughout the targeted
motion. The muscle activation parameters are determined using a non-linear
least-squares (NLS) optimization approach that aims to minimize the difference
between an *a priori* determined mandibular motion and the muscle-controlled
mandibular motion. Initially, the muscle activation parameters were determined
using a simplified model consisting of only two muscles, idealized versions of
the masseter and the digastric muscles with a targeted motion of opening and
closing the jaw within a three-second time frame. The targeted motion was
produced by uniformly rotating the mandible with respect to the maxilla from the
initial closed position through approximately 0.3 radians (17 degrees) and back
to the closed position. For the NLS optimization, the muscle activation
parameters consisted of 7 activation time points for each muscle evenly spaced
over three seconds resulting in a total of 14 muscle activation parameters. The
left and right muscles were activated equally for both the masseter and the
digastric muscles.

A new method for determining muscle activation forces and timings will be developed for this project. This method uses a PID controller interfaced with the finite element model to adjust muscle forces and timings during the simulation in a feedback loop to minimize the error between the model displacement and a predefined displacement curve. The PID controller method can determine muscle activation timings in a single forward dynamics simulation rather than the hundreds or thousands of FE model simulations required using the traditional NLS optimization.