Biomechanical stress regulates mammalian tooth replacement via the integrin β1‐RUNX2‐Wnt pathway
2019; Springer Nature; Volume: 39; Issue: 3 Linguagem: Inglês
10.15252/embj.2019102374
ISSN1460-2075
AutoresXiaoshan Wu, Jinrong Hu, Guoqing Li, Yan Li, Li Yang, Jing Zhang, Fu Wang, Ang Li, Lei Hu, Zhipeng Fan, Shouqin Lü, Gang Ding, Chunmei Zhang, Jinsong Wang, Mian Long, Songlin Wang,
Tópico(s)Dental Trauma and Treatments
ResumoArticle12 December 2019Open Access Source DataTransparent process Biomechanical stress regulates mammalian tooth replacement via the integrin β1-RUNX2-Wnt pathway Xiaoshan Wu Xiaoshan Wu Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Department of Oral and Maxillofacial Surgery, Xiangya Hospital, Central South University, Changsha, China Search for more papers by this author Jinrong Hu Jinrong Hu Center of Biomechanics and Bioengineering, Key Laboratory of Microgravity (National Microgravity Laboratory) and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China Search for more papers by this author Guoqing Li Guoqing Li Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Search for more papers by this author Yan Li Yan Li Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Fortune Link Triones Scitech Co., Ltd., Beijing, China Search for more papers by this author Yang Li Yang Li Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Search for more papers by this author Jing Zhang Jing Zhang Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Search for more papers by this author Fu Wang Fu Wang Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Department of Oral Basic Science, School of Stomatology, Dalian Medical University, Dalian, China Search for more papers by this author Ang Li Ang Li Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Key Laboratory of Shaanxi Province for Craniofacial Precision Medicine Research, College of Stomatology, Xi'an Jiaotong University, Xi'an, China Search for more papers by this author Lei Hu Lei Hu Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Search for more papers by this author Zhipeng Fan Zhipeng Fan Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Search for more papers by this author Shouqin Lü Shouqin Lü Center of Biomechanics and Bioengineering, Key Laboratory of Microgravity (National Microgravity Laboratory) and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China Search for more papers by this author Gang Ding Gang Ding Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Department of Stomatology, Yidu Central Hospital, Weifang Medical University, Weifang, China Search for more papers by this author Chunmei Zhang Chunmei Zhang Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Search for more papers by this author Jinsong Wang Jinsong Wang Department of Biochemistry and Molecular Biology, Capital Medical University School of Basic Medical Sciences, Beijing, China Search for more papers by this author Mian Long Mian Long Center of Biomechanics and Bioengineering, Key Laboratory of Microgravity (National Microgravity Laboratory) and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China Search for more papers by this author Songlin Wang Corresponding Author Songlin Wang [email protected] orcid.org/0000-0002-7066-2654 Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Department of Biochemistry and Molecular Biology, Capital Medical University School of Basic Medical Sciences, Beijing, China Search for more papers by this author Xiaoshan Wu Xiaoshan Wu Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Department of Oral and Maxillofacial Surgery, Xiangya Hospital, Central South University, Changsha, China Search for more papers by this author Jinrong Hu Jinrong Hu Center of Biomechanics and Bioengineering, Key Laboratory of Microgravity (National Microgravity Laboratory) and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China Search for more papers by this author Guoqing Li Guoqing Li Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Search for more papers by this author Yan Li Yan Li Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Fortune Link Triones Scitech Co., Ltd., Beijing, China Search for more papers by this author Yang Li Yang Li Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Search for more papers by this author Jing Zhang Jing Zhang Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Search for more papers by this author Fu Wang Fu Wang Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Department of Oral Basic Science, School of Stomatology, Dalian Medical University, Dalian, China Search for more papers by this author Ang Li Ang Li Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Key Laboratory of Shaanxi Province for Craniofacial Precision Medicine Research, College of Stomatology, Xi'an Jiaotong University, Xi'an, China Search for more papers by this author Lei Hu Lei Hu Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Search for more papers by this author Zhipeng Fan Zhipeng Fan Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Search for more papers by this author Shouqin Lü Shouqin Lü Center of Biomechanics and Bioengineering, Key Laboratory of Microgravity (National Microgravity Laboratory) and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China Search for more papers by this author Gang Ding Gang Ding Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Department of Stomatology, Yidu Central Hospital, Weifang Medical University, Weifang, China Search for more papers by this author Chunmei Zhang Chunmei Zhang Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Search for more papers by this author Jinsong Wang Jinsong Wang Department of Biochemistry and Molecular Biology, Capital Medical University School of Basic Medical Sciences, Beijing, China Search for more papers by this author Mian Long Mian Long Center of Biomechanics and Bioengineering, Key Laboratory of Microgravity (National Microgravity Laboratory) and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China Search for more papers by this author Songlin Wang Corresponding Author Songlin Wang [email protected] orcid.org/0000-0002-7066-2654 Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China Department of Biochemistry and Molecular Biology, Capital Medical University School of Basic Medical Sciences, Beijing, China Search for more papers by this author Author Information Xiaoshan Wu1,2, Jinrong Hu3,4, Guoqing Li1, Yan Li1,5, Yang Li1, Jing Zhang1, Fu Wang1,6, Ang Li1,7, Lei Hu1, Zhipeng Fan1, Shouqin Lü3,4, Gang Ding1,8, Chunmei Zhang1, Jinsong Wang9, Mian Long3,4 and Songlin Wang *,1,9 1Beijing Key Laboratory of Tooth Regeneration and Function Reconstruction, Capital Medical University School of Stomatology, Beijing, China 2Department of Oral and Maxillofacial Surgery, Xiangya Hospital, Central South University, Changsha, China 3Center of Biomechanics and Bioengineering, Key Laboratory of Microgravity (National Microgravity Laboratory) and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China 4School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China 5Fortune Link Triones Scitech Co., Ltd., Beijing, China 6Department of Oral Basic Science, School of Stomatology, Dalian Medical University, Dalian, China 7Key Laboratory of Shaanxi Province for Craniofacial Precision Medicine Research, College of Stomatology, Xi'an Jiaotong University, Xi'an, China 8Department of Stomatology, Yidu Central Hospital, Weifang Medical University, Weifang, China 9Department of Biochemistry and Molecular Biology, Capital Medical University School of Basic Medical Sciences, Beijing, China *Corresponding author. Tel:+86 010 57099478, E-mail: [email protected] The EMBO Journal (2020)39:e102374https://doi.org/10.15252/embj.2019102374 PDFDownload PDF of article text and main figures. Peer ReviewDownload a summary of the editorial decision process including editorial decision letters, reviewer comments and author responses to feedback. ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InMendeleyWechatReddit Figures & Info Abstract Renewal of integumentary organs occurs cyclically throughout an organism's lifetime, but the mechanism that initiates each cycle remains largely unknown. In a miniature pig model of tooth development that resembles tooth development in humans, the permanent tooth did not begin transitioning from the resting to the initiation stage until the deciduous tooth began to erupt. This eruption released the accumulated mechanical stress inside the mandible. Mechanical stress prevented permanent tooth development by regulating expression and activity of the integrin β1-ERK1-RUNX2 axis in the surrounding mesenchyme. We observed similar molecular expression patterns in human tooth germs. Importantly, the release of biomechanical stress induced downregulation of RUNX2-wingless/integrated (Wnt) signaling in the mesenchyme between the deciduous and permanent tooth and upregulation of Wnt signaling in the epithelium of the permanent tooth, triggering initiation of its development. Consequently, our findings identified biomechanical stress-associated Wnt modulation as a critical initiator of organ renewal, possibly shedding light on the mechanisms of integumentary organ regeneration. Synopsis Most mammals undergo replacement of deciduous teeth with permanent dentition during the postnatal development. Here, studies in miniature pigs and human samples suggest that eruption of the deciduous tooth triggers permanent tooth primordium maturation via mechanical stress release in the mandible. Dental lamina of the permanent tooth remains in a resting state until deciduous tooth erupts. Eruption-induced elease of mechanical stress inside the mandible activates permanent tooth initiation. Mechanical stress suppresses permanent tooth initiation via RUNX2-mediated regulation of Wnt pathway activity. Introduction Cyclical renewal of various integumentary organs, including hair, feathers, and teeth, is necessary for maintaining their function after wear or injury (Blanpain & Fuchs, 2014; Lai & Chuong, 2016; Lu et al, 2016). Transition from the resting to the initiation stage is critical for organ replacement and regeneration. For example, determining how to induce hair follicles to make the transition from the telogen (resting stage) to the anagen phase (initiation stage) without falling into the exogen phase (shedding phase) may enable the development of alopecia treatments. Although it is known that circulating hormones and molecules play important roles in the transition from one phase to another (Fuchs, 2015; Widelitz & Chuong, 2016), the mechanism of organ renewal initiation remains to be identified. The initiation of tooth development involves a series of interactions between the epithelium and the mesenchyme. It begins as the dental lamina (DL) invaginates into the mesenchyme and forms a tooth bud. After the epithelium folds into the mesenchyme, it grows into a cap and then enters the bell stage (Koussoulakou et al, 2009). Continuous tooth renewal occurs throughout the life span of many animals such as fish and reptiles (Huysseune, 2006; Handrigan & Richman, 2010; Handrigan et al, 2010; Wu et al, 2013). However, the teeth of large mammals—including humans—are replaced only once (Jarvinen et al, 2009; Jernvall & Thesleff, 2012). The dental lamina of permanent teeth (PT) can be detected at a very early embryonic stage, but the development of PT germs continues for about 6–12 years before eruption (Pansky, 1982). It is known that the dental lamina remains in the resting phase for a while before developing into a tooth bud (Fraser et al, 2006). However, little is known about how the resting dental lamina of the PT is initiated and regulated inside the mandible, largely because of the lack of suitable animal models. The miniature pig has a diphyodont dentition similar to that of humans. Thus, our group established a miniature pig model as a tooth development research platform (Wang et al, 2014, 2017; Li et al, 2015, 2018). Studies using large animal models have defined the developmental stages and established gene expression profiles of diphyodont dentition (Weaver et al, 1966; Tucker & Widowski, 2009; Buchtova et al, 2012; Sova et al, 2018). In this study, we investigated the mechanism by which tooth replacement is initiated using both the miniature pig model and human canine tooth germ samples. Results Morphology of the permanent pig canine tooth during the initiation stage We selected deciduous and permanent canine teeth as a model for observing the early stages of PT morphogenesis (Fig 1A–G). The successional dental lamina (SDL) of the permanent canine (PC) bud was connected to the outer enamel epithelium of the enamel organ of the deciduous canine (DC) on the lingual side at embryonic day 50 (E50) (Fig 1A). At E55, the SDL began to separate from the DC (Fig 1B). Hematoxylin and eosin (H&E) staining and immunostaining showed that the SDL contained medial and lateral layers (Fig EV1A and B). At E60, the SDL of the PC had separated from the DC. A space could be identified between the DC and PC (Fig 1C). The SDL remained resting until the start of the bud stage, when the DC started to erupt (Fig 1D and E). At E90, the DC had erupted and the enamel organ of the PC at the bud stage was localized beside the gingival sulcus near the top (Fig 1E). At postnatal day 0 (PN0), the PC had entered the cap stage (Fig 1F); at PN10, it had entered the bell stage (Fig 1G). To observe the morphological dynamics in other anterior teeth, we performed H&E staining on the third deciduous incisor from E50 to E100 and found similar processes of deciduous tooth eruption and permanent tooth initiation (Appendix Fig S1). Figure 1. Morphology and molecular map of the permanent canine germ during initiation stages in swine A–G. Hematoxylin and eosin (H&E) staining of the frontal sections of miniature pig mandible slices showing morphological changes during the permanent canine (PC) initiation stage from embryonic day 50 (E50) to postnatal day 10 (PN10); (A'–F') are magnifications of boxed regions in their corresponding figure panel. DC, deciduous canine; PC, permanent canine; SDL, successional dental lamina; n = 3. H. In situ hybridization (ISH) showing the expression pattern of Sox2 in the initiation stage from E50 to E90; right figure panels are magnifications of boxed regions in left panels. Dashed lines mark the position of the successional dental lamina (SDL); green arrowhead indicates positive staining of Sox2 at the tip of the SDL. n = 3. I. Immunofluorescence (IF) of Ki67 at the SDL at E60, E70, and E90; right figure panels are magnifications of boxed regions in left panels. n = 3. J. Semi-quantification and comparison of Ki67 expression levels during E60, E70, and E90 stages. n = 3. K. TUNEL assay showing the apoptosis status of the SDL at E60, E70, and E90; right figure panels are magnifications of boxed regions in left panels. n = 3. L. Diagram illustrating the initiation stage at E50 (attached SDL), E60 (detached SDL), E90 (bud stage), and PN10 (bell stage). OEE, outer enamel epithelium; IEE, inner enamel epithelium. Data information: Data represent the means ± SEM. *P < 0.05 (one-way ANOVA and Newman–Keuls post hoc tests). Scale bars = 100 μm. Download figure Download PowerPoint Click here to expand this figure. Figure EV1. Immunostaining and in situ hybridization (ISH) of the PC primordium from E50 to E90 A. Immunohistochemistry (IHC) of pan-cytokeratin from embryonic days 50 (E50) to E90 showing the dual layers of the epithelium in dental lamina and enamel organ. B. Immunofluorescence (IF) of pan-cytokeratin from E50 to E90 showing a similar pattern. C–E. ISH of Shh, Pitx2, and Pax9 during the initiation stage from E50 to E90. Dashed lines mark the position of the SDL or PC. Data information: n = 3 for all panels. Right figure panels are magnifications of the boxed regions in corresponding left panels. Scale bar = 100 μm. Download figure Download PowerPoint Next, with in situ hybridization (ISH), we found that Sox2, the epithelial stem cell marker, was expressed at the tip of the SDL at E60, marking the potential location of stem cells during the resting stage (Fig 1H). We also analyzed the expression patterns of other molecules including the epithelial markers Shh and Pitx2 and the mesenchymal marker Pax9 (Fig EV1C–E). We found that Shh expression was absent in both the primary and successional dental lamina (Fig EV1C and Appendix Fig S2). The proliferation of dental epithelium increased significantly when the tooth bud grew into the bud stage at E90 (Fig 1I and J). However, apoptosis of dental epithelium cells remained at low levels throughout the initiation stage (Fig 1K). In short, the SDL of the PC remained stationary after detachment from the DC germ and did not enter the bud stage until the DC erupted. The attached SDL, detached SDL, bud stage, cap stage, and bell stage could all be identified during PC development (Fig 1L). Difference in growth rate between the deciduous canine tooth and the alveolar socket During the PC initiation process, we observed rapid growth of the DC. To confirm that the growth rate of the DC differed from that of the surrounding alveolar socket, we made 3-dimensional reconstructions of the DC, PC, and alveolar socket at E60 and E90 based on H&E staining of serial frontal sections (Fig 2A and Appendix Fig S3). The width of the DC increased much more rapidly than that of the labial and lingual alveolar socket (Fig 2A and B). In addition, DC width relative to total alveolar socket width increased significantly (Fig 2C). Thus, the DC width growth rate was significantly higher than that of the alveolar socket before DC eruption. Figure 2. Differential growth rates of deciduous canine (DC) and alveolar socket and mechanical stress inside the mandible Three-dimensional reconstruction of serial H&E frontal sections of miniature pig mandibles at embryonic day 60 (E60) and day E90; deciduous canine (DC) in purple, permanent canine (PC) in yellow, and alveolar socket in green. The red, blue, and green arrows indicate the width of the labial alveolar socket, lingual alveolar socket, and DC, respectively. n = 3. DC and labial and lingual alveolar socket widths in the horizontal plane at the bottom of the PC during E60 and E90. n = 3. The proportion of DC width relative to the total alveolar socket width during E60 and E90. n = 3. Micro-CT imaging of the whole mandible at E60; boxed region is magnified in D' (top panel). (D') Mandible slice isolated with Geomagic software. White dashed lines mark DC. 3-D color map (left) after alignment of mandible slices before and after (sham) surgery showing a comparison of the surface points. Coronal sections through cusp tips (transparent squares, left) were selected for 2-D comparisons (middle); right panels are magnifications of yellow-boxed regions. The solid purple contour and dotted black contour indicate the pre- and post-surgery shapes, respectively. The distance between the two contours is the colored line segments showing the distance and direction of the movement. The colored ball in the 2-D comparison marks the position of the maximum displacement. The PC position is indicated in pink. n = 3. Dissected mandible slice with a "U" shape. In the cup model, the mandible slice was simplified as a cup according to its dimensions (unit, mm). Red arrows indicate the uniform force (stress) exerted on the inner wall of the mandible. The bottom of the cup was fixed to avoid rigid body motions. 3-D color map shows the extent of deformation based on the cup model established with ANSYS software. Probable range of mechanical stress inside the mandible evaluated by multiple simulation tests in which serial stress and Young's modulus were inputted into the cup model; the cup was set with the outer surface fixed (left, dr = 0 denotes that radial deformation of the outer surface equals 0) or the outer surface free (right). Deformation of the mandible walls under a series of stress levels with different Young's moduli. Data were obtained from multiple tests as in (I). Gray horizontal lines indicate upper and lower limit values of mean mandible wall displacement (79.74 and 36.48 μm, respectively); dashed colored lines indicate results of the free outer surface; solid colored lines indicate results of the fixed outer surface (with consideration of good linearity of the simulation results, the corresponding result points of the simulation series were omitted and replaced by solid or dashed colored lines for clarity); the actual stress value should be between the two extreme boundary conditions. Results show that the probable stress level ranged from 3 to 20 kPa. n = 3. Data information: Data represent the means ± SEM. Unpaired t-tests, *P < 0.05, **P < 0.01, ***P < 0.001. Download figure Download PowerPoint Biomechanical stress is generated inside the mandible Differential growth rates regulate organ development via mechanical stress or mechanical stress-linked molecular signals, indicating the existence of biomechanical stress inside tissues (Mao et al, 2013; Dowling et al, 2016; Pan et al, 2016; Hosseini et al, 2017; Qi et al, 2017). We therefore considered that mechanical stress may be present inside the mandible and that such mechanical stress can regulate PC initiation. We designed an experiment to determine the level of mechanical stress inside the mandible of a miniature pig prior to DC eruption. First, we made a cut to the gingiva overlying the DC of a fresh embryonic mandible to release any possible mechanical stress. Then, deformation of the mandible caused by this release of stress was measured using micro-CT (Fig 2D–E). Finally, the quantity of stress was determined based on the deformation and mechanical features of the mandible by establishing a "cup" model using the finite element analysis software (ANSYS) (Fig 2F–J). Briefly, the input mechanical variables included mechanical properties—represented by Young's modulus from measurements and Poisson's ratio from the literature (Korhonen et al, 2002; Tomkoria et al, 2004)—and different pressures exerted on the inner wall of the mandible (Fig 2G), starting from the preset initial values. The model output was the corresponding mandible deformation. These computed deformations were compared with those from measurements to estimate the pressure (Figs 2D–J and EV2, Appendix Figs S4 and S5, and Appendix Supplementary Methods). Click here to expand this figure. Figure EV2. Mechanical test and establishment of the cup model A–D. Testing Young's moduli of the samples. (A) Mandible bony piece (mandible side wall piece) prepared for the test (0.2–0.3 mm in thickness). (B) Diagram of the testing principle of nanoindentation for Young's modulus determination using the Piuma Chiaro Nanoindenter. The indenter (tip) applies force onto the sample (mandible bony piece in A) and records the force applied and the indentation depth (sample deformation). (C) Normal force spectrum from which valid experimental data were extracted. The red line signifies that the probe was engaging before reaching max deformation (Dmax); blue line indicates that the probe retreated after reaching Dmax. (D) Distribution of the typically measured Young's moduli of the samples. Red line indicates the fitting results of the Gaussian model. E–G. Gradient densities of the mesh (sparse, medium, and dense) were tested to determine the optimal mesh density of the cup for the computation. (E, E') The deformation is not symmetrical although it is clear in the sparse group. (F, F' left, G, and G') The medium and dense groups show similar deformation after exerting a force on the inner wall. (F') Series of Poisson's ratios, including 0.15 (not shown), 0.35 (left), and 0.48 (right), were tested. Dmax values of the three cases were 1, 1.21, and 1.37 after normalizing the data. Download figure Download PowerPoint To measure deformation after the release of stress, micro-CT images of the E60 mandible before and after surgery were obtained and aligned to generate a 3-dimensional color map indicating the extent of deformation (Fig 2D and E). The mean (± SEM) inward displacement of the outside compact bone was 36.48 ± 4.04 μm and that of the inside spongy bone was 79.74 ± 6.07 μm. In the control group, the size of the mandible slices before and after sham surgery was nearly identical, indicating almost no deformation (Fig 2E). To estimate the range of stress inside the mandible at E60, we used ANSYS 15.0 to establish the cup model, in which a "cup" mimics the U-shaped mandible slice (Fig 2F–H; Quanyu et al, 2017). In this model, the open ends of the cup were expanded as simulated stress was applied to the inner wall (Fig 2G and H). The 3-dimensional color spectrum indicates the degree of deformation from low to high (blue to red). The optimal mesh density of the cup for the computation was established based on density tests (Fig EV2E–G). In our model, the mandible was set as a homogeneous and elastic continuum for simplicity, in which Young's modulus and Poisson's ratio were required to run the simulations. To obtain Young's modulus of the mandible, a microdissected mandible slice was chopped into small pieces (Figs 2F and EV2A) on which Young's modulus was measured using a nanoindenter (Fig EV2B and C). It was found that Young's modulus ranged from 0.1 to 0.6 MPa, with a peak value of 0.23 MPa (Fig EV2D). As it is difficult to measure Poisson's ratio of such small samples experimentally, the impact of different Poisson's ratios on mandible deformation was evaluated via simulation tests and the results showed small changes in mandible deformation under different ratios (0.15, 0.35, and 0.48 were tested) (Fig EV2F'); Poisson's ratio of 0.35 was ultimately used for all simulations (Appendix Supplementary Methods). The 0.35 value is the medium value of cartilage Poisson's ratio (0.15–0.45) (Korhonen et al, 2002) and is within the common range in similar simulations (Tomkoria et al, 2004). Deformation of the mandible was simulated when forces and two mechanical parameters (Young's modulus and Poisson's ratio) were included in the model. Based on the maximum deformation of the mandible walls, a stress value range of 3–20 kPa was obtained for E60 mandibles after a series of simulations (Fig 2I and J). To inspect whether gradual stress changes occur during development, a series of simulations using the mean Young's modulus of E60, E65, and E75 mandibles were performed and stress value ranges of 8.2–15.1, 6.8–8.6, and 10.8–12.7 kPa were obtained for E60, E65, and E75 mandibles, respectively (Fig EV2B–D, Appendix Figs S4 and S5, and Appendix Supplementary Methods). In conclusion, mechanical stress inside the mandible was maintained from E60 to E90 prior to DC eruption. Biomechanical stress determines the
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