Finite element analysis can help increase understanding of how the material behavior of the midpalatal suture affects maxillary expansion in adolescents with unfused sutures. Mathematical material models describing the non-linear viscoelastic behavior of the midpalatal suture were previously developed. Adapting these tissue-specific models for use in a finite element program (ANSYS Mechanical R.14.5) may allow the extent of the suture’s influence on the expansion process to be understood.

Initial work endeavored to adapt the 1-D creep and relaxation models for use in the 3D finite element environment. The materials were assumed isotropic. Both models describe a bone-suture interface region and were developed based on a 9.72mm width. Improvements to the models are highlighted by a correction factor, 𝛾, that enables them to describe a thinner, more clinically appropriate, initial region width. The variable 𝛾 was derived to modify both 1D models for a region width of 1.72mm. Adapted models underwent verification testing using a test mesh based on the geometry from which the models were developed. Time and stress derivatives of the 𝛾-modified 1D creep model were encoded into ANSYS’ USERCREEP.f subroutine and compiled with the Intel 11.1 FORTRAN compiler. Creep simulations were loaded with constant expansion forces for simulated 6-week periods and evaluated against the expected results of the 1-D model. It was found that the creep strain curve could be closely replicated;​ however, the expansion of the suture region experienced tertiary creep expansion. This indicated that the creep model was not accurately adapted for ANSYS. Additional training of the constitutive model may be required to account for ANSYS calculating expansion based on the volume dimensions at the end of the previous solution iteration. The 𝛾-modified relaxation model was approximated using a Prony expansion series to define the time dependent behavior of a generalized Maxwell model. A 7-term Prony series was curve fit to a time shifted dataset generated from the 𝛾-modified relaxation equation. The model as assigned to the suture region of the test mesh. The test mesh was expanded by stepwise applications of clinically relevant (0.25mm) displacements, mimicking expansion appliance activations. 1st principal stresses within the simulated suture at the midsagittal plane peaked at 2.23 MPa for the initial appliance activation and relaxed to negligible levels in the two minutes following, thereby verifying the time-dependent behavior of the Prony approximation. Subsequent (n>1) stress peaks diminished in magnitude as equal applied displacements caused reduced strains per activation.

The Prony relaxation model needed to be simulated as part of a skull geometry to investigate what effect, if any, the suture has on the expansion process. Cranial geometry was created from patient CT images using a semi-manual masking procedure. After smoothing and rotating the masked geometry to align the midsagittal plane with the yz-plane, the model was halved and segmented to define craniofacial suture volumes. After meshing the geometry for FEA, the partial skull was constrained at boundaries where it would connect to the remainder of the skull. Material models for the craniofacial sutures were varied between linear elastic properties of bone and soft tissue and the material model of the midpalatal/intermaxillary suture was varied between being neglected, a linear soft tissue, and the non-linear relaxation model. Multiple simulation cases were loaded identically with 29 consecutive appliance activations. Activations displacements were each 0.125mm, spaced 12 hours apart. The stress relaxation properties of the midpalatal/intermaxillary suture volume had a noticeable effect on the reaction force at the appliance in the two minutes following the activation, but negligible effect on the final displacement of the dentition. Results also indicated craniofacial suture properties could significantly change final dentition position and reaction force.

Based upon the suture and partial skull simulations, it was concluded that the Prony approximation accurately replicates the expected relaxation behavior and has a noticeable effect on the system immediately post-activation. The adapted creep model is not suitable for further tests without modification to utilize the state of the previous iteration instead of initial conditions. Future work in developing a predictive finite element model of maxillary expansion may involve characterizing and incorporating into ANSYS the viscoelastic behavior of cranial bone and the craniofacial sutures. This may result in displacements and appliance reaction forces that are more reflective of clinical results.