1. Does Function Follow Form in the TMJ Disc?
A Metabolic and Structural Investigation
William McCarty and Andrea Pallante
Department of Bioengineering & Whitaker Institute of Biomedical Engineering, University of California-San Diego
INTRODUCTION
The temporomandibular joint (TMJ) is a diarthrodial hinge that connects the mandible to the temporal bone, which are separated by a biconcave disc. The TMJ disc is approximately elliptical (10 by 19 mm) and ranges from 1 to 4 mm in thickness. The TMJ disc functions to distribute and sustain TMJ loads and deformation during joint movement. The central portion of the disc contains mainly chondrocyte-like cells, which primarily secrete glycosaminoglycans (GAG) and the peripheral edges contain mainly fibroblastic cells, which primarily secrete collagen type I. The extracellular matrix (ECM) proteins secreted by the cell populations dictate the mechanical properties of the disc. Anterior displacement of the TMJ disc results in abnormal wear and deformations to the disc.
OBJECTIVE
· To use a two-compartment model for cell type to calculate a mechanical property distribution in the disc based on ECM protein production.
· Investigate the effects of anterior displacement on disc deformations.
METHODS
ECM Spatial Distributions
· Virtual Cell was used to solve the PDEs (Eqs. 1 and 2) shown below. The generation term, ε, was a function of space as shown in the sketch to the right. The inner cylinder generation of GAG was higher than the outer cylinder, and those trends were reversed for collagen production (see Table 1 for values). The steady state values of both GAG and collagen concentration are shown in Figs. 1 and 2.
Conversion of ECM Concentration to Mechanical Moduli
· The concentration of GAG was assumed to account for the entire bulk modulus of the tissue, and converted to a spatially varying modulus by virial expansion of the concentration, following the procedure of Chahine et al(1), (Eq. 3). The collagen concentration was used to predict a tensile modulus using the phenomenological results of Roeder et al(2). These modulus values were imported into two field variables in Continuity for use in the mechanical modeling of tissue deformation. Renderings of those field variables are shown in Figs. 3 and 4.
TMJ Disc Mesh
· A 3D mesh was developed using Continuity, a finite element modeling and
problem solving software, with a tri-cubic Hermite basis function in rectangular coordinates (8 nodes and 1 element). Node labels and boundary conditions were applied to the initial mesh.
Boundary Conditions:
Nodes 1-4 value was fixed in x3-direction.
Nodes 1 and 4 value was fixed in the x1- and x2-directions.
Nodes 1-4 cross derivatives (wrt s(1)s(2)) do not change in x1-, x2-, or x3.
Nodes 1-4 derivatives wrt s(1) and wrt s(2) do not change in the x3-direction.
The mesh was further refined four times in the x3-direction, and three times in
both the x1- and x2-directions allowing boundary conditions and node labels
to be propagated throughout the mesh.
Table 1: Parameter values and descriptions
Figure 1: Steady state distribution of GAG (mg/mL)
Figure 3: Field variable 1: bulk modulus
Figure 2: Steady state distribution of collagen (mg/mL)
Figure 4: Field variable 2: tensile modulus
Joint Loading Model for Normal and Anterior Displacement
The 3D mesh was loaded into the Biomechanics module of
Continuity and modeled as a transversely isotropic
exponential function of Lagrangian strains. Average values
for bulk and tensile modulus were used based on the Virtual
Cell data, as the simulation could not be completed when
using the field variables. The mesh was subjected to a
pressure of 600 kPa on an element of interest for normal loading conditions
(CENTER) and loading when the disc is anteriorly displaced (AD). These elements are on the
superior (top) surface of the mesh. The simulation was run to 6 seconds, in 0.1 s increments. AD
CENTER x2 AD
CENTER
(Eq. 1) N1 N4 x1
(Eq. 2) x3
Figure 5: Free body diagram of the loading conditions for a normal and anteriorly displaced TMJ disc.
RESULTS
The results for ECM concentrations solved by Virtual Cell are shown in Figs 1 and 2. This data was imported into Continuity and shown as rendered field variables in Figs 3 and 4.
The mechanical loading scheme, shown in Fig 5 and applied to the construct in two cases: Center and AD, resulted in mesh deformations as shown in Figs 6 and 7, with corresponding deformation fields shown in Figs 8 and 9. The AD case clearly shows more significant mesh deformation and non-uniform strain fields in the posterior band of the disc.
(Eq. 3)
DISCUSSION
During jaw motion, the TMJ disc normally repeatedly deforms to support joint loads. Anterior disc displacement results in abnormal strain patterns in the posterior disc, resulting in friction and wear. These simulations show that the spatial distribution of the tensile and bulk moduli, a direct consequence of the distribution of cell types with different metabolic rates in the disc, allows for minimal deformation in the normal case, but may be responsible for the abnormal strains and degradative wear seen in anterior disc displacement.
Figure 6: Line element mesh for center stress: deformed (red) and undeformed (blue), with nodes.
Figure 7: Line element mesh for AD stress: deformed (red) and undeformed (blue), with nodes.
REFERENCES
(1) Chahine+, Biophys. J. (2005) (2) Roeder+, J. Biomech.E.. (2002)
ACKNOWLEDGMENTS
Stuart Campbell; Virtual Cell- NRCAM, NCRR; Continuity NBCR
Figure 8: E33 strain rendering for center stress application. Strain is concentrated in this center region.
Figure 9: E33 strain rendering for AD stress application. Large strains are seen in the posterior disc.
Printed 6/27/2018