Abstract
The aim of this study was to predict stress modification in the temporomandibular joint (TMJ) after symphyseal distraction (SD). The study was performed using three-dimensional finite element analysis using a complete mastication model. Geometric data were obtained from MRI and CT scans of a healthy male patient and each component was meshed as various regions. The distraction was performed with a 10 mm expansion after simulation of a surgical vertical osteotomy line on the model in the mandibular midline region. The geometry and mesh of the bone callus were constructed. The bone callus was modelled as a strengthened region characterized by a Young’s modulus corresponding to consolidated bone to predict the long-term biomechanical effect of SD. Boundary conditions for jaw closing simulations were represented by different jaw muscle load directions. The von Mises stress distributions in both joint discs and condyles during closing conditions were analysed and compared before and after SD. Stress distribution was similar in discs and on condylar surfaces in the pre- and post-distraction models. The outcomes of this study suggest that anatomical changes in TMJ structures should not predispose to long-term tissue fatigue and demonstrate the absence of clinical permanent TMJ symptoms after SD.
Mandibular incisor crowding often reflects a transverse bone deficiency. Classically, this orthodontic problem is treated by teeth extraction, teeth slicing or dental compensation. An alternative surgical procedure, introduced by Guerrero et al., is mandibular midline distraction osteogenesis. This technique involves a biological process of new bone formation between bone segments that are gradually separated by a tooth-borne, bone-borne or hybrid device. Distraction osteogenesis in the symphyseal area widens the mandibular bone in order to increase space on the dental arch. The surgical procedure consists of a vertical osteotomy of basal and alveolar bone subsequent to orthodontic incisor root tip expansion. Bone elongation begins after osteotomy has been performed and when distraction occurs. Orthodontic treatment quickly corrects the incisor crowding, resulting in definitive change and adequate mandibular dimension for stable occlusion. Many clinical studies have evaluated the long-term effect and clinical effects of this procedure on mandibular structures. According to these publications, no patient presented temporomandibular joint (TMJ) symptoms or dysfunction, but small changes in the position of the condyles were observed during symphyseal distraction (SD) and could lead to chronic pain. From a clinical perspective, this could be explained by the low expansion rate and the physiological adaptability of the condyles. Biomechanical assessment of the TMJ after SD requires careful study. No human experimental studies have been conducted on the TMJ during SD as its structures are difficult to reach for biomechanical evaluation. The use of experimental devices inside the mandibular joint structure could damage the tissues, thus interfering with normal function and influencing mechanical behaviour. Consequently, finite element (FE) models have been used extensively to analyse stress distribution in the TMJ as this technique allows investigation in areas that are difficult to access and which are risk-free for the patient. Few FE studies have evaluated the biomechanical effects of SD on the TMJ. All the previous studies have analysed the displacement field and the stability level during SD using different devices. To date, no study showing stress distribution in the TMJ discs during jaw closing has been reported. The present study using a high resolution, three dimensional FE (3D-FEA) model aims to predict and compare the location and intensity of the maximum stress values on the TMJ discs during jaw closing before and after a mandibular midline distraction procedure.
Material and methods
Model 1: pre-symphyseal distraction
Geometry and mesh
The geometric data for the complete model were obtained from a 30-year-old healthy volunteer (asymptomatic joints) and a fully dentate male patient. The contours of the skull, the compact and cancellous parts of the mandible and the mandibular and maxillary teeth were obtained from axial, coronal and sagittal computed tomography (CT) images. The helicoidal, multislice CT scan was performed with a GE Lightspeed VCT 64 CT device (General Electric Medical System, Milwaukee, USA) at 120 kV and 160 mA. Tomographic slices, 0.625 mm thick, were obtained using the helicoidal technique. Soft tissues such as discs and capsule joint contours were built from sagittal magnetic resonance imaging (MRI). MRI was performed using a Gyroscan Intera 1.5-T MR system (Philips Medical Systems, Best, The Netherlands). The scanning parameters for sagittal images were: echo 1 T2 weighted fast spin echo sequences and a slicing thickness 2.5 mm. MRI and CT image acquisition were performed on a patient with a custom incisor splint to obtain 10 mm jaw opening (inter-incisal distance). The soft elements were located by an experienced maxillofacial surgeon and a radiologist. Modelling of the soft elements (articular disc, connective tissue and capsule) was performed from a set of sagittal slices. Articular discs and connective tissues (capsule and temporomandibular ligament) were located from the MRI images, and manually generated as one single body. 3D surface meshes and tetrahedral element volume meshes (I-DEAS Universal File format) were obtained successively using segmentation software (AMIRA ® ). The FE model consisted of 386,092 tetrahedral elements. The volume meshes of each part were exported into the FORGE ® FE analysis program (Transvalor, GLpre 2005).
Mechanical properties
The mechanical properties of mandibular bone components, skull, teeth, articular disc and connective tissues with capsule were assumed, as a first approximation, to be homogeneous and isotropic. A non-linear hyperelastic model was assigned to the discs and connective tissues through a neo-Hookean model, as defined below.
For a hyperelastic material, the stress–strain relationship derives from a strain energy density function W that verifies:
where S is the second Piola–Kirchhoff stress tensor and C the right Cauchy–Green deformation tensor given by
F is the deformation gradient.
For incompressible isotropic hyperelastic materials, the Cauchy stress σ can be expressed in terms of the invariants I 1 and I 2 (the third invariant I 3 = 1) of the left Cauchy–Green deformation tensor B:
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