Associations between condylar height relative to occlusal plane and condylar osseous condition and TMJ loading based on 3D measurements and finite element analysis

Selection of participants

All data collection and procedures for this study were approved by the ethics committee of the West China Hospital of Stomatology Institutional Review Board (approval number: WCHSIRB-D-2022–364). The study followed the recommendations of the Declaration of Helsinki. All participants provided informed consent to participate in the study and for the publication of their anonymized case details and images.

The anonymous CT data (120 kV, 300 mA, 1 mm slice thickness, and 0.49 mm³ voxel size) were acquired from patients who underwent TMJ assessment in the Department of TMJs between October 2018 and August 2022.

The inclusion criteria of participants were: (1) patients diagnosed with TMD according to the Diagnostic Criteria for Temporomandibular Disorders (DC/TMD)^19,20; (2) patients with permanent dentition; (3) patients aged 18 years and above and under 40 years; (4) patients with established first permanent molar occlusion. The exclusion criteria were: (1) patients with a history of orthodontic treatment, plastic or craniofacial surgery; (2) patients with a history of severe dental or periodontal tissue disease, loss or restorative treatment of multiple teeth (≥ 3); (3) patients with a history of cleft lip and palate, or other systemic diseases affecting craniofacial growth and development; (4) patients with incomplete lateral cephalograms or CT images.

3D data measurements

Localization of the anatomical landmarks

The CT image data in DICOM format was processed using Mimics Research software (Version 20.0; Materialize, Leuven, Belgium), and a 3D stomatognathic model was reconstructed for each patient (Fig. 1a). The midsagittal plane was constructed using three cranial anatomical points: the Sella (S) point, the Basion (Ba) point, and the Anterior nasal spine (ANS) point²¹; and the horizontal plane, defined for the left and right sides, was the plane perpendicular to the midsagittal plane and passing through the Orbitale (Or) point and Porion (Po) point (Fig. 1c). Anatomical landmark points were defined as in Table 1 and located using the multiple planar reformat tool. The coordinates (x, y, z) of each point were exported for subsequent calculation. The x-direction was defined as parallel to the midsagittal plane and the horizontal plane on each side, with the positive value of the x-coordinate toward the front. The y-direction was defined as perpendicular to the midsagittal plane, with the positive value of the y-coordinate toward the right. The z-direction was defined as parallel to the midsagittal plane and perpendicular to the horizontal plane on each side, with the positive value of the z-coordinate upward.

Measurement of the anatomical parameters

Ten anatomical parameters were selected, including the CHO, L, ALR, Angle α, FH-MP angle, FH-OP angle, FH-MOP angle, AJS, PJS, and SJS, and the ultimate angle was measured by projecting onto the midsagittal plane. The abbreviations and definitions of the above parameters are given in Table 1, and the projection methods and measurements are shown schematically in Fig. 1d. To exclude the effect of absolute mandibular size, a relative index—Angle α—was constructed to represent the change in the relative proportion of CHO.

All measurements and calculations were performed separately on the left and right sides, to avoid bias caused by facial asymmetry or deformity. The coordinates (x, y, z) of each marked points were obtained in Mimics software. Vector operations were used to obtain the angular measurement projected into the midsagittal plane by substituting the marked point coordinates into the formula. Let (overrightarrow{n}) represent the normal vector of the midsagittal plane, and the two vectors expressed the measured angle (β) be (overrightarrow{a}) and (overrightarrow{b}), calculated as follows:

where ({n}_{x}), ({n}_{y}), and ({n}_{z}) are the x, y, and z components of (overrightarrow{n}) respectively; and ({n}^{S}), ({n}^{Ba}), and ({n}^{ANS}) are the coordinates of S, Ba, and ANS point composing the midsagittal plane. As shown in Fig. 2h–k, the angular measurements were visualized.

Modifications of Angle α for the three-dimensional stomatognathic (3DS) finite element model. (a) Schematic of modifications of the condylar position, the FH-MP angle, and the FH-OP angle. Simulations of modifying the condylar position from four directions: I, II, III, and IV. Simulations of modifying the FH-MP angle from two directions: clockwise (highlighted in blue) and counterclockwise (highlighted in green) around the mandibular angle as the rotation center. Simulations of modifying the FH-OP angle from two directions: clockwise (highlighted in yellow) and counterclockwise (highlighted in purple) around the mesial point of the mandibular central incisor as the rotation center. (b) The mandibular model after modification of the condyle positions. (c) The mandibular model after modification of the FH-MP angle and FH-OP angle.

Imaging evaluation and grouping

Evaluation of condylar osseous condition

The osseous changes of the condyle were assessed and scored in terms of bone surface flattening, bone erosion, osteophytes, bone sclerosis, and bone cysts according to the CT images²². The first three items were scored on a scale of 0–3 and the last two items were scored on a scale 0–2²³. The condylar osseous condition was diagnosed and classified into the following categories¹⁹:

1. 1.

   Normal: Normal relative size of the condylar head, and absence of the above-mentioned osseous changes.

2. 2.

   Indeterminate: Normal relative size of the condylar head, and presence of bone surface flattening and/or bone sclerosis without other observed osseous changes.

3. 3.

   Osseous destruction (OD): The presence of at least one of bone erosion, osteophytes, and bone cysts with/without other osseous changes were observed.

3D Finite element analysis

Finite element models

A 3DS finite element model was constructed from the data of a patient with normal condylar osseous condition and morphology. In addition to CT data, the digital dental model and Magnetic Resonance Imaging (MRI) data (3D scanning mode, slice thickness of 1.0 mm, TR: 3200.0, TE: 411.0) were collected for this patient. Initial STL models of the dentition, mandible, maxilla and articular disc were reconstructed using Mimics software according to the patient’s anatomical characteristics (Fig. 1S in the Supplementary Material)^24,25. All initial models were imported into Geomagic Studio software (Raindrop, North Carolina, America) for smoothing and repair. A circle of periodontal membrane was arranged at the junction of the teeth and jawbone (Fig. 1S in the Supplementary Material), and the thickness of the periodontal membrane was set as 0.2 mm. The right side of mandible and maxilla were excised along the sagittal plane leaving only the left side. Modification of Angle α was simulated in two ways, including changing the condylar position and changing the FH-MP angle and the FH-OP angle (Fig. 2a).

1. (1)

   The condylar position was moved in the following four sagittal directions by modifying the Angle α. A total of 9 models for computation were obtained (Fig. 2b). Temporal bone and articular disc were moved according to the movement of condyle.

   1. Setting I

      Changing the CHO in a direction perpendicular to OP; the Angle α value was increased/decreased by 3°, while the L (length) value remained invariant.

   2. Setting II

      Changing the CHO in a direction parallel to OP; the Angle α was decreased/increased by 3°, with the L (length) value increased accordingly by 13.78 mm or decreased by 10.87 mm.

   3. Setting III

      Changing the CHO in a direction perpendicular to the connecting line between Co and L1; the Angle α was increased/decreased by 3°, with the L (length) value changed accordingly by 1.87 mm.

   4. Setting IV

      Changing the CHO in a direction parallel to the connecting line between Co and L1; the d (diameter) was increased/decreased by 5%, with the L (length) value changed accordingly by 4.12 mm.

2. (2)

   By modifying the FH-MP of the 3DS model, three basic models were established with the vertical growth patterns of hypodivergent, normodivergent and hyperdivergent facet types²⁶. Based on the basic models, the occlusal plane inclination of the models was modified according to the FH-OP of -7–9° (hypodivergent group), -3–13° (normodivergent group), and 1–17° (hyperdivergent group) (Fig. 2c).

Modified models were imported in to 3-Matic Research software (Version 12.0; Materialize, Leuven, Belgium) for dividing the finite element mesh (FEM). The mesh of the entire model was designed as a modified 10-node quadratic tetrahedron element (C3D10M). The mesh size of contact surfaces was refined enough for convergence requirements. The material properties of four components in FEM shown in Table 2^27,28,29. In total, the model had 3,896,926 elements and 3,400,348 nodes.

Loading and boundary conditions

FEM models were imported into ABAQUS software (2020; Dassault Systèmes Simulia Corp., USA) to complete the load and boundary conditions application and calculation. In order to simulate the actual occlusion, six sets of muscle forces were considered with the following force settings: superficial masseter—47.6 N, deep masseter—20.4 N, anterior temporalis—43.7 N, middle temporalis—39.5 N, posterior temporalis—23.9 N, and medial pterygoid—18.9 N^32,33. The contact relationships of the articular disc with the condyle and articular fossa, and of the upper teeth with the lower teeth, were set to be hard contact with a friction coefficient of 0.001³⁴. Two output variables, contact pressure (CPRESS) and contact force (CFN), were derived by ABAQUS software for characterizing the action force between two surfaces³⁵. The six degrees of freedom were fixed on the upper surface of the maxilla and temporal bone. Meanwhile, symmetric boundary conditions were set on the symmetrical faces of the mandible and maxilla.

Statistical analysis

The above anatomical landmark localization and image assessment were done by at least two experienced specialists. Inter-observer and intra-observer assessments were performed using intraclass correlation coefficient (ICC), and selected measurements were re-estimated at two-week intervals to assess the inter- and intra-examiner reliability of the studied measurements. The ICC values for inter- and re-test reliability were greater than 0.75 for all measures (P < 0.05). The measured data was conducted using the mean values.

Data were statistically analyzed using IBM SPSS Statistics (v.22; IBM Corp, Chicago, IL), and p < 0.05 was considered statistically significant. Descriptive results of quantitative data were expressed as mean ± standard deviation; normality and chi-square tests were assessed using the Shapiro–Wilk test and Levene test. For indicators of continuous variables with normal distribution, one-way analysis of variance (ANOVA) was applied for multiple group comparisons, and SNK tests were used for further post-hoc testing. For indicators of continuous variables without normal distribution or variance, a Kruskal–Wallis test was used.