In the process of orthodontic treatment, the remodeling of cancellous bone in alveolar bone (in this paper, cancellous bone in alveolar bone is abbreviated as CBAB) is key to promoting tooth movement. Studying the mechanical behavior of CBAB is helpful to predict the displacement of teeth and achieve the best effect of orthodontic treatment. Three CBAB samples were cut from alveolar bone around the root apex of human teeth. A uniaxial compression test was used to study the transient elastic properties of CBAB. A creep test was used to study the time-dependent viscoelastic properties of CBAB. Both tests were carried out at the loading rates of 0.02 mm/min, 0.1 mm/min and 0.5 mm/min. The results revealed that CBAB is a nonlinear viscoelastic and hyperelastic material. The stress–strain curve obtained from the uniaxial compression test could be divided into three stages: the collapse stage of the front section, the exponential stage of the middle section and the almost linear stage of the rear end. According to the strain–time curve obtained from the compression creep test, a trend of increasing strain over time was relatively obvious within the first 30 s. After 200 s, the curve gradually tended to plateau. Four hyperelastic models and three viscoelastic models were used to fit the test data. Finally, the fifth-order polynomial hyperelastic model (coefficient of determination “R² > 0.999”) was used to describe the hyperelastic properties of CBAB, and the seven-parameter model of the generalized Kelvin modified model (“R² > 0.98”) was used to describe the viscoelastic properties of CBAB.

The maxillary sinus is a common anatomic limitation for orthodontic tooth movement. The effect of orthodontic forces on a particular anatomy can be studied using finite element analysis (FEA). Our study aimed to determine the effect of different tooth penetration depths into the maxillary sinus floor (MSF) on the orthodontic force system for bodily tooth movement. Using the cone-beam computed tomography of a patient with low MSF, we modeled the geometry of canine, premolar, and molar teeth with their periodontal ligaments and the alveolar bone surrounding them. The models were manually modified to simulate different root penetration depths. Thereafter, the center of resistance and stress distributions for teeth penetrating into the MS were determined using FEA. Moreover, the force systems for teeth with a low MSF to varying degree were evaluated based on the FEA results. During orthodontic tooth movement, the individual differences in the periodontal anatomy should be considered. The CR position decreases with the penetration depth, while the average hydrostatic stress in the PDL increases rapidly. In this paper, we present the correction coefficients of the orthodontic force and moment for a tooth penetrating into the MSF, which is necessary for personalized treatment planning.