Construction of a Viscoelastic Model of Human Cancellous Bone in Alveolar Bone Based on Bone Mineral Density Distribution.

Orthodontic treatment was accompanied by the remodeling of cancellous bone in alveolar bone (CBAB), which manifested as the increase or decrease in bone mineral density (BMD). BMD is closely related to the mechanical properties of the alveolar bone. Therefore, the aim of this study was to quantify the effect of BMD on its viscoelastic behavior and to assess orthodontic forces at different BMDs. A total of nine CBAB samples were cut from the cervical, middle, and apical regions of the right mandible between canine, premolars, and molars. After scanning with micro-computed tomography (micro-CT). The BMD of samples was measured and dynamic mechanical analysis (DMA) was performed. Based on the fourth-order generalized Maxwell model, a viscoelastic constitutive model characterizing the BMD variation was constructed. The BMD exhibited variations within different regions of the CBAB. The storage modulus is positively correlated with BMD, and the loss modulus is negatively correlated with BMD.

Construction of Human Periodontal Ligament Constitutive Model Based on Collagen Fiber Content.

Periodontal ligament (PDL) is mainly composed of collagen fiber bundles, and the content of collagen fiber is an important factor affecting the mechanical properties of PDL. Based on this, the purpose of this study is to explore the effect of the PDL collagen fiber content on its viscoelastic mechanical behavior. Transverse and longitudinal samples of different regions of PDL were obtained from the human maxilla. The fiber content at different regions of human PDL was quantitatively measured using image processing software, and a new viscoelastic constitutive model was constructed based on the fiber content. The nano-indentation experiment was carried out with a loading rate of 0.5 mN·s-1, a peak load of 3 mN, and a holding time of 200 s, and the model parameters were obtained through the experiment data. The results showed that with the increase of fiber content, the deformation resistance of PDL also increased, and compared with the neck and middle region, the compressive strain in the apical region of PDL was the largest. The range of reduced elastic modulus of human PDL was calculated to be 0.39~5.08 MPa. The results of the experimental data and the viscoelastic constitutive model fit well, indicating that the model can well describe the viscoelastic behavior of human PDL.

Mechanical Behavior of Human Cancellous Bone in Alveolar Bone under Uniaxial Compression and Creep Tests.

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.

Construction of hyperelastic model of human periodontal ligament based on collagen fibers distribution.

OBJECTIVE: The human periodontal ligament (PDL) dominated by collagen fibers showed hyperelastic mechanical behavior under orthodontic force. Despite previous researches on the hyperelastic model of PDL, there were certain limitations because of the types of samples and the ignorance of distribution of collagen fibers. Therefore, the aim of this study was to quantify the effect of collagen fibers distribution of human PDL on its hyperelastic behavior. METHODS: A total of 6 human PDL samples of root neck, root middle and root apex were cut from human maxillary central incisor and lateral incisor. The spatial angles of collagen fibers were observed by optical microscope, the hyperelastic model was constructed combined with the observation results. The quasi-static uniaxial tensile tests with displacement load 0.05 mm/min were carried out, and the test data were used to identify the parameters of model. RESULTS: The mechanical behavior of human PDL conformed to the trend of hyperelastic materials, and greatly depended on the spatial angles of internal collagen fibers. The R2 value statistical fit of the constitutive model to the data is excellent (R2 > 0.98). This model could excellently describe the hyperelastic properties of human PDL. SIGNIFICANCE: In this study, we quantitatively described the effect of spatial distribution of collagen fibers on the mechanical properties of human PDL. The accuracy of this model was verified by the uniaxial test data, and the relevant model parameters were acquired, which have certain reference value in subsequent researches on hyperelasticity of human PDL and clinical treatment.

Frequency-related viscoelastic properties of the human incisor periodontal ligament under dynamic compressive loading.

Studies concerning the mechanical properties of the human periodontal ligament under dynamic compression are rare. This study aimed to determine the viscoelastic properties of the human periodontal ligament under dynamic compressive loading. Ten human incisor specimens containing 5 maxillary central incisors and 5 maxillary lateral incisors were used in a dynamic mechanical analysis. Frequency sweep tests were performed under the selected frequencies between 0.05 Hz and 5 Hz with a compression amplitude that was 2% of the PDL's initial width. The compressive strain varied over a range of 4%-8% of the PDL's initial width. The storage modulus, ranging from 28.61 MPa to 250.21 MPa, increased with the increase in frequency. The loss modulus (from 6.00 MPa to 49.28 MPa) also increased with frequency from 0.05 Hz- 0.5 Hz but remained constant when the frequency was higher than 0.5 Hz. The tanδ showed a negative logarithmic correlation with frequency. The dynamic moduli and the loss tangent of the central incisor were higher than those of the lateral incisor. This study concluded that the human PDL exhibits viscoelastic behavior under compressive loadings within the range of the used frequency, 0.05 Hz- 5 Hz. The tooth position and testing frequency may have effects on the viscoelastic properties of PDL.

A biphasic visco-hyperelastic damage model for articular cartilage: application to micromechanical modelling of the osteoarthritis-induced degradation behaviour.

Osteoarthritis-induced microstructural and compositional changes of articular cartilage affect its load-bearing capacity and the damage resistance. The aim of the present study is to analyse effects of the osteoarthritis-induced microstructural degradation on the damage behaviour of articular cartilages. A poro-visco-hyperelastic damage model is proposed within the theoretical framework of continuum mechanics to describe the deformation and damage behaviour of collagen fibrils and highly hydrated proteoglycan matrix in articular cartilages. An integral-type nonlocal algorithm is employed to overcome the mesh dependence of simulation results involving strain localization. 3D computational models for a normal cartilage and two osteoarthritic cartilages with different degeneration levels are developed to study the degradation of the damage resistance of articular cartilages. In addition, the present simulations take into account the alterations of collagen fibril networks as well as compositional changes of cartilage constituents at different osteoarthritic stages. The material parameters of the constitutive model are identified by comparing the computational results to unconfined compression tests. The simulation results of spherical indentation tests show that damage in the articular cartilage with high-stage osteoarthritis is much more significant than that in the normal cartilage under identical loadings. The proposed computational methods can be used for studying the relationship between the damage behaviour and the complex morphology of the collagen fibril networks in biomaterials.

Viscoelastic properties of human periodontal ligament: Effects of the loading frequency and location.

OBJECTIVES: To determine the viscoelastic properties of the human periodontal ligament (PDL) using dynamic mechanical analysis (DMA). MATERIALS AND METHODS: This study was carried out on three human maxillary jaw segments containing six upper central incisors and four lateral incisors. DMA was used to investigate the mechanical response of the human PDL. Dynamic sinusoidal loading was carried out with an amplitude of 3 N and frequencies between 0.5 Hz and 10 Hz. All samples were grouped by tooth positions and longitudinal locations. RESULTS: An increase of oscillation frequency resulted in marked changes in the storage and loss moduli of the PDL. The storage modulus ranged from 0.808 MPa to 7.274 MPa, and the loss modulus varied from 0.087 MPa to 0.891 MPa. The tanδ, representing the ratio between viscosity and elasticity, remained constant with frequency. The trends for storage and loss moduli were described by exponential fits. The dynamic moduli of the central incisor were higher than those of the lateral incisor. The PDL samples from the gingival third of the root showed lower storage and loss moduli than those from the middle third of the root. CONCLUSIONS: Human PDL is viscoelastic through the range of frequencies tested: 0.5-10 Hz. The viscoelastic relationship changed with respect to frequency, tooth position, and root level.

Tensile testing of the mechanical behavior of the human periodontal ligament.

BACKGROUND: The periodontal ligament (PDL) plays a key role in alveolar bone remodeling and resorption during tooth movements. The prediction of tooth mobility under functional dental loads requires a deep understanding of the mechanical behavior of the PDL, which is a critical issue in dental biomechanics. This study was aimed to examine the mechanical behavior of the PDL of the maxillary central and lateral incisors from human. The experimental results can contribute to developing an accurate constitutive model of the human PDL in orthodontics. METHODS: The samples of human incisors were cut into three slices. Uniaxial tensile tests were conducted under different loading rates. The transverse sections (cervical, middle and apex) normal to the longitudinal axis of the root of the tooth were used in the uniaxial tensile tests. Based on a bilinear simplification of the stress-strain relations, the elastic modulus of the PDL was calculated. The values of the elastic modulus in different regions were compared to explore the factors that influence the mechanical behavior of the periodontal ligament. RESULTS: The obtained stress-strain curves of the human PDL were characterized by a bilinear model with two moduli (E1 and E2) for quantifying the elastic behavior of the PDL from the central and lateral incisors. Statistically significant differences of the elastic modulus were observed in the cases of 1, 3, and 5 N loading levels for the different teeth (central and lateral incisors). The results showed that the mechanical property of the human incisors' PDLs is dependent on the location of PDL (ANOVA, P = 0.022, P < 0.05). The elastic moduli at the middle planes were greater than at the cervical and apical planes. However, at the cervical, middle, and apical planes, the elastic moduli of the mesial and distal site were not significantly different (ANOVA, P = 0.804, P > 0.05). CONCLUSIONS: The values of elastic modulus were determined in the range between 0.607 and 4.274 MPa under loads ranging from 1 to 5 N. The elastic behavior of the PDL is influenced by the loading rate, tooth type, root level, and individual variation.

Anisotropic constitutive model incorporating multiple damage mechanisms for multiscale simulation of dental enamel.

An anisotropic constitutive model is proposed in the framework of finite deformation to capture several damage mechanisms occurring in the microstructure of dental enamel, a hierarchical bio-composite. It provides the basis for a homogenization approach for an efficient multiscale (in this case: multiple hierarchy levels) investigation of the deformation and damage behavior. The influence of tension-compression asymmetry and fiber-matrix interaction on the nonlinear deformation behavior of dental enamel is studied by 3D micromechanical simulations under different loading conditions and fiber lengths. The complex deformation behavior and the characteristics and interaction of three damage mechanisms in the damage process of enamel are well captured. The proposed constitutive model incorporating anisotropic damage is applied to the first hierarchical level of dental enamel and validated by experimental results. The effect of the fiber orientation on the damage behavior and compressive strength is studied by comparing micro-pillar experiments of dental enamel at the first hierarchical level in multiple directions of fiber orientation. A very good agreement between computational and experimental results is found for the damage evolution process of dental enamel.