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Keywords:

  • mandible development;
  • mathematical analysis;
  • micro-CT;
  • morphometrics;
  • thin-plate spline analysis

Abstract

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. Literature cited

Prenatal development of the mandible is an important factor in its postnatal function. To examine quantitatively normal and abnormal developmental changes of the mandible, we here evaluated morphological changes in mineralizing mandibles by thin-plate spline (TPS) including bending energy (BE) and Procrustes distance (PD), and by Procrustes analyses including warp analysis, regression analysis, and discriminant function analysis. BE and PD were calculated from lateral views of the mandibles of mice or of human fetuses using scanned micro-computed tomography (CT) images or alizarin red S-stained specimens, respectively. BE and PD were compared (1) between different developmental stages, and further, to detect abnormalities in the data sets and to evaluate the deviation from normal development in mouse fetuses, (2) at embryonic day (E) 18.5 between the normal and deformed mandibles, the latter being caused by suturing the jaw at E15.5, (3) at E15.5 and E18.5 between normal and knockout mutant mice of receptor tyrosine kinase-like orphan receptor (Ror) 2. In mice, BE and PD were large during the prenatal period and small after postnatal day 3, suggesting that the mandibular shape changes rapidly during the prenatal and early postnatal periods. In humans, BE of the mandibles peaked at 16–19 weeks of gestation, suggesting the time-dependent change in the mandibular shape. TPS and Procrustes analyses statistically separated the abnormal mandibles of the sutured or Ror2 mutant mouse fetuses from the normal mandible. These results suggest that TPS and Procrustes analyses are useful for assessing the morphogenesis and deformity of the mandible. Anat Rec, 2012. © 2011 Wiley Periodicals, Inc.

The mammalian mandible is a complex morphological structure formed by various morphogenetic components of different embryological origins. These morphogenetic components were assembled during development to form the final structure (Atchley,1993). The mandible originates from cells of the neural crest that migrate to the first mandibular arch and form the embryonic mesenchyme, which later develops into skeletal, dental, and connective tissues. The mesenchymal cells aggregate and produce condensations before undergoing differentiation to produce the morphogenetic components of the mandible (Atchley and Hall,1991). The mandible consists of two symmetrical halves (right and left), each formed by a dentary bone with four morphogenetic regions: the mandibular body (ramus) and three processes (coronoid, condylar, and angular).

Establishing normative expectations for experimentally induced changes in size and shape will be an important innovation in three-dimensional (3-D) micro-computed tomography (CT)-based morphological assessments, especially in quantifying differences in the values of those parameters between sets of developing mandibles as a primary aim. Nondestructive methods such as micro-magnetic resonance imaging (Pieles et al.,2007) and micro-CT (Johnson et al.,2006; Boughner et al.,2008; Nagase et al.,2008; Parsons et al.,2008; Hallgrimsson et al.,2009; Metscher,2009a,b) have been adapted to the 3-D visualization of embryonic morphology. In this capacity, micro-CT can play a prominent role in quantitative studies of mandibular growth and development.

A relatively recent technique, high-resolution micro-CT combined with morphometric analyses allows evaluation of the mandible and determination of the shape changes in bone morphology (Fajardo and Muller,2001). The use of geometric morphometry in the study of shape has caused a revolution in biometric analysis (Rohlf and Marcus,1993; Bookstein,1996), promoting advances in the knowledge and utilization of these multivariate statistical techniques. These methods were developed to analyze the differences in shape among samples based on anatomic landmarks defined by Cartesian coordinates and can give a quantitative account of shape-change; they have been used successfully in biological and clinical comparisons (Zelditch et al.,1992; Ferrario et al.,1993; Singh and Hay,1999; Hay and Singh,2000; Hay et al.,2000).

Morphometrics is the study of shape variation and its covariation with other variables (Bookstein,1991; Dryden and Mardia,1998). Morphological studies of subtle anomalies in the field of morphogenesis and tests for the developmental toxicity of new drugs, pesticides, or food additives have focused mainly on abnormal shape, that is, maldevelopment of bone and other parts. The majority of studies have focused on postnatal ontogenetic patterns, but an understanding of the ontogenetic pattern during the prenatal period is of particular importance because distinctive morphogenetic divergence is more concentrated at this stage (Ponce de León and Zollikofer,2001; Ackermann and Krovitz,2002; Vioarsdottir et al.,2002; Cobb and Ó Higgins,2004). Clinical observation suggests that, in some individuals, the shape of the mandible may change with age (Pessa et al.,2008).

In this study, mathematical analyses were performed on the morphometric data of not only the normal prenatal and postnatal mouse mandible but also those of mechanically stressed or genetically altered mice to test and develop a sensitive method to detect slight deviation from normal development. We also studied the developmental process of the human mandible in the fetal period, which is relatively rare due to the limited availability of fetal specimens. The purposes of this study were thus to elucidate the mandibular morphological changes during the normal and abnormal developmental processes and to apply an appropriate morphometric technique for the assessment of mandibular morphogenesis.

Materials and methods

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. Literature cited

Animals

We maintained all mice at 22°C–24°C under a 12-hr light and 12-hr dark cycle at the Department of Experimental Animals, Center for Integrated Research in Science, Shimane University. Food and water were available ad libitum. All animal studies were approved by the Ethics Committee for Animal Experimentation of Shimane University, and the animals were handled according to institutional guidelines.

Jcl:ICR female mice (Clea, Tokyo, Japan) were used. We defined midnight on the day when we observed a vaginal plug as embryonic day (E) 0.0. After pregnant mice (from 14.5 to 18.5 gestational days) were deeply anesthetized with diethyl ether, fetuses from E14.5 to E18.5 were obtained, and the body weight (BW) (gm) and crown-rump length (CRL) (mm) were measured. Postnatal mice [postnatal day (P) 1 to P7] were sacrificed using ether anesthesia. Mice of other ages (P8-P14, P21, and P28) were deeply anesthetized with ether and decapitated. The heads of the postnatal mice (N = 64) and bodies of the fetuses (N = 20) were fixed with 10% formalin in 70% methanol solution overnight at room temperature, then dehydrated with 70% ethanol for 1 hr with an interval of 20 min before performing CT scan (Nagase et al.,2008).

Receptor tyrosine kinase-like orphan receptor (Ror) 2 gene is responsible for bone and cartilage growth. Mutations in this gene can cause skeletal disorder with shortening of bone and a dysmorphic facial appearance. As our study was dealing with the shape change of the mandible, this gene was chosen as a deforming factor. Ror2 mutant heterozygous (Ror2+/−) mice were maintained on a C57BL/6J background and crossed to generate Ror2+/+, Ror2+/−, and Ror2−/− fetuses (Takeuchi et al.,2000; Yamada et al.,2010). E15.5 (N = 38) and E18.5 (N = 50) fetuses were obtained, and we measured CRL and BW of six or more fetuses from six litters at each developmental age. Ror2+/+, Ror2+/−, and Ror2−/− fetuses (N = 5 for each) were identified by polymerase chain reaction (PCR) genotyping. A total volume of 20 μL for every sample was prepared for the final reaction. Then, 0.5 μL of each DNA product was amplified using Nova Taq DNA polymerase (Novagen, San Diego, CA) and primers by 35 cycles (94°C for 30 sec, annealing at 60°C for 30 sec, and extension at 72°C for 30 sec). Ten microliters of the reaction mixture was analyzed in 1.5% agarose gel in the presence of ethidium bromide.

Micro-CT Scan and 3-D Reconstruction

The heads of all the mice were imaged by a micro-CT scanner (Skyscan 1174, Kontich, Belgium) at 6–21 μm nominal resolution (50 kV, 800 μA, 1.00° rotation steps, an average of 5 frames and 25 min total exposure time), with a total of 184 slices per scan and checked for both accurate ring artifact reduction and random movement. The scans were reconstructed and cropped. A volumetric 3-D reconstruction for each sample was obtained from Volume Graphics (VG) Studio Max V 2.0 software from the set of scans (Fig. 1A–I). In addition, the volume (mm3) and surface area (mm2) of the mandibles were recorded.

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Figure 1. Micro-CT scan and 3-D reconstruction images of mouse mandibles. A (E15.5), B (E18.5) from prenatal stages and C (P7), D (P21) from postnatal stages of mouse mandible development. Due to TMJ movement restriction by exo utero surgery, the deformation of the mandible was observed in the sutured group at E18.5 (F) compared to those in the sham-operated group at E18.5 (E). Ror2+/+ (G), Ror2−/− (H) and Ror2+/− (I) mandibles at E18.5; the deviation of the mandible was observed in the Ror2−/− mandible (H) from those in the Ror2+/+ (G) and Ror2+/− (I) mandibles at E18.5. Scale bars = 1 mm. E and F, G, H, and I are at the same magnification, respectively.

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Exo Utero Surgery of Mouse Fetuses to Restrict Temporomandibular Joint (TMJ) Movement

Exo utero surgery was performed as described previously (Hatta et al.,1994,2002,2004; Habib et al.,2005,2007; Udagawa et al.,2006; Yamada et al.,2008; Jahan et al.,2010). Briefly, at E15.5, the pregnant dams were anesthetized with 50 mg/kg BW of pentobarbital. The abdominal wall was incised longitudinally at the mid-line from beneath the xiphoid process to the lower abdomen. Then detached the skin from the abdominal muscles, and a longitudinal incision of the anterior abdominal muscles was made along the uterine wall. Then, we pulled gently the intact right (or left) uterine horn out of the abdomen. Longitudinal incision was made on the myometrium at the counterpart of the placenta, and exposed the fetuses covered by the embryonic membrane. The umbilical cords of unnecessary fetuses were cut with scissors and remove the fetuses from the placenta. We left three or four fetuses in each horn of the uterus for manipulation. The fetuses' mandible and maxilla were fixed by an 8-0 nylon suture (Fig. 2A; sutured group). We also performed a sham operation by passing the needle from the mandible through the maxilla of some fetuses without making a knot (sham-operated group). After the operation, the fetuses together with the uterus were placed back in the abdominal cavity of the dam, and the incision on the abdominal muscle was sutured closed with 3- or 4-0 silk line; incision of the abdominal skin was closed by autosuture (MikRon 9 mm Autoclip Applier), and were allowed to develop exo utero till E18.5.

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Figure 2. A: Exo utero surgery. At E15.5, the abdominal cavity of the dam was surgically opened and fetuses covered with the embryonic membrane were exposed. Then the mandible and maxilla were fixed by suturing, while the umbilical cord and placenta were kept intact inside the amnion. Right panel: schematic representation of restrained jaw movement of mouse fetuses. Arrows indicate the suture fixation with 8-0 nylon (originally from Habib et al.,2005). BE: Alizarin red S-stained human fetal mandibles [B (CRL 97 mm), C (CRL 121 mm), D (CRL 146 mm), and E (CRL 178 mm)]. F: Landmarks depending on the anatomical points of view. Each landmark itself contains x- and y-coordinates of BE matrix, which changed during development; and all the landmarks together were used to calculate the total BE. G: Schematic representation of the landmarks. Demonstration of the landmarks represents the distances between the stages of development, and the sum of the squared distances between the landmarks is PD. Scale bars = 1 mm.

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As in our several previous studies (Hatta et al.,1994,2002,2004; Habib et al.,2005,2007; Jahan et al.,2010), we observed that the exo utero surgery as described caused no general growth retardation, and neither the CRL, BW, nor the mandibular morphology of the E18.5 sham-operated fetuses were significantly different from those of the E18.5 in utero normal fetuses. Therefore, we here show only the results of sham-operated fetuses, and not those of in utero normal fetuses, as the control.

Human Fetuses

The human fetuses used in this study were from the Kyoto collection, Kyoto University, (Nishimura,1975; Shiota,1991; Tanaka,1991; Otani et al.,2008; Udagawa et al.,2010; Zhang et al.,2011). All fetuses used in this study were obtained through collaboration with obstetricians in Japan, in accordance with Japanese laws. The study was approved by the Ethics Committee of Shimane University, Faculty of Medicine. More than 20 yr before this study, the fetuses were fixed in 10% formalin solution after abortion and preserved in glycerol with ethanol in equal proportion (1:1), with periodic replacement of fixative. Due to this fixation, which continued primarily for macroscopic studies and to lengthen the preservation time, the mandibles were not intact in all samples. We therefore carefully selected from the collection well-preserved mandibles (N = 29) of externally normal fetuses ranging from 52 to 212 mm in CRL (11–25 weeks of gestational age) for this study.

Alizarin Red S Staining of Human Fetuses

To detect mineral, the mandibles were stained by alizarin red S bone staining, which stains the calcified matrix associated with bone (Whitaker and Dix,1979; Young et al.,2000; Depew,2009; Zhang et al.,2011), with modifications as described below.

The fixed specimens were dehydrated by 70% ethanol and kept in acetone overnight to remove the fat. Then the specimens were incubated in 0.5% potassium hydroxide containing 0.1% alizarin red (Wako, Osaka, Japan) overnight at 37°C for 2–3 days until the color turned pink. Samples were digested in benzyl alcohol mixed with benzyl benzoate solution in the same ratio (1:1) until the tissue was cleared. Finally, samples were transferred gradually through 50% and 100% glycerol.

The specimens were photographed by digital camera (Canon EOS Kiss, Tokyo, Japan), and the images (Fig. 2B–E) were transferred to a personal computer for mathematical analysis. CT scan was not possible to perform in human specimens, as the space in micro-CT scanner was too small for all the human samples.

Mathematical Analysis

Landmarks of the mandible.

Landmarks are key points of correspondence. Therefore, they were defined in the same way on each mandible of a given type, for example, for all mandibles, corresponding points were chosen for landmarks (Fig. 2F), which were selected to be informative about particular characteristics of interest. We digitized some anatomical landmarks, which we assumed to be homologous. The landmarks were defined for the lateral view of the right mandible and are described as follows:

  • 1
    Tip of the coronoid process.
  • 2
    Anterior edge of the molar teeth row.
  • 3
    Antero-dorsal border of the incisive alveolus.
  • 4
    Antero-ventral border of the incisive alveolus.
  • 5
    Anteromost point on the ventral border at the ramus and body junction.
  • 6
    Tip of the angular process.
  • 7
    Most postero-inferior edge of the articular surface of the condyle.
  • 8
    Most postero-superior edge of the articular surface of the condyle.

The locations of these points on the mandible are depicted in Fig. 2F. The right hemi-mandible of each specimen [scanned (mouse) or stained (human)] was taken for analysis, and the x- and y-coordinates of each landmark were captured using tpsDig software (V 2.16, F. James Rohlf, Ecology and Evolution, SUNY, Stony Brook, NY).

Thin-plate spline (TPS) analysis. 

Shape differences can be described by the differences in the coordinates of corresponding landmarks between the objects. The thin-plate spline (TPS) analysis describes shape change by interpolating between the relative displacements of discrete points, or landmarks, presumed to correspond between forms (Bookstein,1989b,1991; Swiderski,1993). TPS quantitatively analyzes shape change (Bookstein,1989b) using the theory of surface spline interpolations (Bookstein,1991) to express the differences between two landmark configurations as a continuous deformation (Fig. 2G; Mclntyre and Mossey,2003). TPS uses an interpolation function representing a mapping (Mclntyre and Mossey,2003) and maps the deformation in shape from one object to another (Bookstein,1991). TPS also produces a rigorous quantitative analysis of the spatial organization of shape change (Swiderski,1993; Franchi et al.,2001) by bending energy (BE) and Procrustes distance (PD). In this study, we used tpsSplin software (V 1.20, Ecology and Evolution) to calculate BE and PD.

Bending energy (BE)

BE can be defined as the energy that would be required to bend an infinitely thin metal plate over one set of landmarks so that the height over each landmark is equal to the coordinates of the homologous point in the other form (Bookstein,1989a; Franchi et al.,2001). In TPS analysis, the differences in two configurations of landmarks are expressed as a continuous deformation by using regression functions in which homologous points are matched between forms to minimize the BE (Fig. 2G; Richtsmeier et al.,1992; Franchi et al.,2001). BE represents the shape change of the mandible.

Procrustes distance (PD)

PD is the sum of the squared distances between analogous or corresponding landmarks. The squared PD is approximated by the minimum of the summed squared distances between corresponding points over the similarities (Bookstein,1997). The PD is a least-squares-type metric that requires a one-to-one correspondence between the shapes. The PD is determined as follows:

  • Compute the centroid of each shape.

  • Re-scale each shape to equal size.

  • Align with respect to the centroids.

  • Align with respect to orientation by rotation.

The squared PD between two shapes is the sum of the product of the squared point distances after alignment (Fig. 2G; Morshed and Zhu,2009). PD deals with the shape change of the mandible.

Calculation of BE and PD

BE and PD in the mandible were calculated between adjacent developmental stages in the human fetuses, for example, from a smaller CRL to the next-larger CRL, and in the mice, for example, from an earlier developmental stage to the subsequent one. The mandible at the earlier stage, for example, the smaller of two developmental stages, was chosen as a reference. Changes in BE and PD during development were examined by regression analysis (RA) using multiple samples of each stage.

To examine whether or not BE and PD can be useful for discriminating between normal and abnormal developments, we compared BE and PD in the mandible between the normal and the sutured group of mouse fetuses at E18.5, and between the wild-type (C57BL/6J) fetuses and the Ror2 knockout fetuses at E15.5 and E18.5. In these fetuses, we calculated BE and PD between one fetus and the others. For example, between the No. 1 fetus and Nos. 2, 3, 4, or 5 fetus; the No. 2 fetus and Nos. 1, 3, 4, or 5 fetus and so on; normal E18.5 and sham-operated E18.5; normal E18.5 and sutured E18.5; normal E15.5 and wild-type E15.5; normal E18.5 and wild-type E18.5; normal E15.5 and Ror2 knockout E15.5; and normal E18.5 and Ror2 knockout E18.5. We chose as a reference the fetus of which both summations of the squares of BE and PD were minimum.

We repeated taking the landmark coordinates and calculated BE and PD three times in each mandible, and used the mean of BE and PD for statistical analyses.

Procrustes analysis. 
Principal warps

Principal warps are the eigenfunctions of the BE matrix interpreted as actual warped surfaces over the surface of the original landmark configuration, and include partial and relative warps. Principal warps are ordered from least to most BE (smallest to largest eigenvalues), which corresponds to the least to most spatially localized deformation, and the corresponding eigenvalues are referred to as BEs. The purpose of these analyses was to transform the variation in shape for landmark data among more than two mandibles, as the method is extended to deal with curving edges with landmarks (Bookstein,1989a). It was possible, however, to output information to a file of mandibles onto the principal warps as variables. We used tpsRelw software (V 1.49, Ecology and Evolution) for the analysis in this study.

Partial warps

The partial warps are computed as eigenvectors of the BE matrix projected on the x-y-plane of the data. The partial warp scores are two-dimensional vectors that have x- and y-components, and express the contribution that each partial warp makes to the total deformation. The partial warp scores are the coefficients indicating the position of an individual, relative to the reference, along partial warps (Zelditch et al.,2004).

Relative warps

The relative warps are computed to summarize the variation among the mandibles (with respect to their partial warp scores) in as few dimensions as possible. Relative warps are the principal component axes of a multivariate space in which each point corresponds to a sample, and the axes are the inversely weighted principal warps of the BE matrix defined by a reference configuration of landmarks. The present analysis read a set of x-y-coordinates for a landmark of mandible and expressed their variation in terms of relative warps.

Discriminant function analysis (DFA)

After Procrustes fit of the raw data of the landmark coordinates, discriminant analysis was performed to classify the samples into groups. We used MorphoJ and examined the shape difference between groups by a T-square test, which is used in multivariate hypothesis test. The reliability of the discrimination was assessed by leave-one-out cross-validation.

Procrustes ANOVA

Procrustes ANOVA is a method for assessing the relative amounts of variation among individuals (Klingenberg and Mclntyre,1998; Klingenberg et al.,2002). Procrustes ANOVA was used in studies of left-right asymmetry to assess the amount of measurement error. In this study, we used MorphoJ software (V 1.02d, Sun Microsystems, Santa Clara, CA) for the analysis.

Other Statistics

We applied a one-way analysis of variance (ANOVA) to compare the BW, CRL, volume, BE and PD of the mandibles among the Ror2+/+, Ror2+/–, and Ror2−/– fetuses; and we applied Student's t test to compare these values between sutured and sham-operated fetuses. All data in this study were represented as the mean (M) ± standard deviation (SD), where P < 0.05 was considered significant.

RESULTS

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. Literature cited

By using micro-CT scan and 3-D analyses, we obtained mandibular images to detect the developmental pattern, which is an important factor for mineralization.

Mice

CRL and BW

There was no significant difference in CRL and BW between sham-operated and sutured fetuses at E18.5 (data not shown), or among the Ror2+/+, Ror2+/–, and Ror2−/– fetuses at either E15.5 or E18.5 (Table 1), according to ANOVA.

Table 1. Average BW and CRL
 EmbryoBody weight (BW) (gm)Crown-rump length (CRL) (mm)
E15.5Ror2+/+0.41614.048
Ror2+/−0.42214.014
Ror2−/−0.40013.680
E18.5Ror2+/+1.25421.222
Ror2+/−1.19420.114
Ror2−/−0.99818.802
Macroscopic observation. 

The mandibular morphology does not appear to be significantly different among the Ror2+/+, Ror2+/−, and Ror2−/− fetuses at E15.5, or between the Ror2+/+ and Ror2+/− fetuses at E18.5. Cartilaginous mandible was gradually mineralized, and the first mineralization in mandibles was seen at E14.5.

Morphogenesis of the mandible during development. 

To analyze the morphogenesis of the mandible in mice, the volume, BE and PD were calculated. BE (Fig. 3C) and PD (Fig. 3D) were larger in the prenatal period than in the postnatal period especially after P3, whereas the volume of the mandible increased rapidly in the postnatal stages (Fig. 3A). Figure 3B showed that the summations of BE and PD, and gradients of tangents of the curve became smaller and smaller as the mice grew. BE and PD were thus decreased after birth; however, there was a small peak of BE (Fig. 3C) and PD (Fig. 3D) on P7.

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Figure 3. Growth curves of morphological development of mandibles in moue (AD) and human fetuses (E and F). A: The volume of the mouse mandibles increased more rapidly in postnatal stages than in prenatal stages. The growth curve of the mandibular volume was approximated by the power function [Volume = 0.0023 (day)2.6 – 2.4, R2 = 0.94]. (B) Summation of BE and PD, (C) BE, and (D) PD represent the shape change of the mandible in mice. The changes in BE and PD were approximated by the regression functions [BE = −3370 (day)−2.9 + 2.3; R2 = 0.93; PD = −94 (day)−1.6 + 1.5; R2 = 0.99]. BE and PD were decreased after birth, but there was a small peak on P7, indicated by arrows, (C, D). E and F: In the human fetuses, the BE rate was higher at 121–152 mm CRL (16–19 weeks of gestation) than in the other weeks, and the rate of PD did not show any peak. Dotted line: period of birth (A–D); duration of peak (E). R2 = coefficient of determination.

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CT scan and 3-D analysis. 

Using CT scan and 3-D reconstructed mandibles, we observed the deformation (both size and shape were altered) of the mandibles in the sutured group at E18.5 (Fig. 1F) compared with those in the sham-operated group at E18.5 (Fig. 1E), as well as the deviation (the anterior half of the mandibular body was shortened, but the entire shape was not altered) in the Ror2−/− group at E18.5 (Fig. 1H) from those in the other two groups (Ror2+/+ and Ror2+/−; Fig. 1G,I) at the same stage.2

Table 2. Comparison by discriminant function analysis
Difference between means
 ComparisonProcrustes distanceP-value
E15.5Ror2+/+ Ror2−/−0.08660.1047
Ror2+/+ Ror2+/−0.06710.0098
Ror2−/− Ror2+/−0.05430.4586
E18.5Ror2+/+ Ror2−/−0.11550.0002
Ror2+/+ Ror2+/−0.03310.0227
Ror2−/− Ror2+/−0.0882<0.0001

The sutured (Fig. 1F) and Ror2−/− mandibles (Fig. 1H) at E18.5 were shorter in length and thinner in width than those of the sham-operated (Fig. 1E), Ror2+/+ (Fig. 1I), and Ror2+/− fetuses (Fig. 1G) at E18.5, respectively.

Morphometric study of the normal and deformed mandibles. 
Detection of the difference between sutured and sham-operated mandibles

There was no significant difference in the length (Fig. 4A), width (Fig. 4B), or ratio of length to width (Fig. 4C) between sutured and sham-operated mandibles at E18.5. There was a significant difference in PD (P < 0.05) between them by Student's t test (Fig. 4E), whereas there was no significant difference in BE (Fig. 4D). DFA showed the significant difference in PD between them (P < 0.05) and all samples in both groups were correctly classified, whereas only sham-operated group was correctly classified and no significant difference was observed in BE (data not shown).

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Figure 4. Morphometric study of abnormal mandibles at E18.5 in relation to the TMJ movement restriction by exo utero surgery. There was no significant difference in the length (A), width (B), or ratio between length and width (C) between sham-operated (sham) and sutured mandibles at E18.5. There was a significant difference in PD (E), but no significant difference in BE (D), between them. (F) Principal warps analyses separated the two groups, which correspond to the morphological changes associated with the deformation. In the relative warp analyses with α = 0 (equal weights for all partial warps) and α = 1 (greater weight for larger-scale partial warps), the first two relative warp axes account for 82% (relative warp 1 = 54% + relative warp 2 = 28%) and 91% (relative warp 1 = 70% + relative warp 2 = 21%), respectively, of the total shape variation. N = 3 for each group; * P < 0.05. Solid circles show the sham-operated plot. Blank squares plot the sutured group. Longitudinal dotted line is the centroid line.

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The partial and relative warp analyses showed the separation of the sham-operated and sutured groups. This separation corresponds to the morphological changes associated with the deformation (Fig. 4F).

Procrustes ANOVA showed that the amount of measurement error was significantly small (P < 0.001) in the sham-operated and sutured groups (data not shown).

Detection of the differences between Ror2+/+, Ror2+/−, and Ror2−/− mandibles

There was a significant difference in mandibular length between Ror2+/+ and Ror2−/− fetuses (P < 0.05; Fig. 5A), and in the ratio of the length to the width of the mandible between Ror2+/+, Ror2+/−, and Ror2−/− fetuses at E18.5 (P < 0.05; Fig. 5C).

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Figure 5. Morphometric study of the Ror2 mutant mandibles at E15.5 and E18.5. There was a significant difference in the length (A) of the mandible at E18.5 between Ror2+/+ and Ror2−/− fetuses, and in the ratio of the length to the width (C) of the mandible at E18.5 among Ror2+/+, Ror2+/−, and Ror2−/− mandibles. However, there was no significant difference in the width (B) among them at E18.5. The volumes of the mandibles at both E15.5 (D) and E18.5 (E) were reduced significantly more in the Ror2−/− mandible than in the Ror2+/+ and Ror2+/− mandibles; and the volume of the Ror2+/− mandibles at E18.5 was also significantly reduced compared with the Ror2+/+ mandibles (E). N = 5 for each group; * P < 0.05.

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Volume was significantly reduced in the Ror2−/− mandibles compared to the Ror2+/+ and Ror2+/− mandibles at both E15.5 and E18.5 (P < 0.05; Fig. 5D,E). The volume of Ror2+/− mandibles was also significantly reduced compared to the Ror2+/+ mandibles at E18.5 (P < 0.05; Fig. 5E). In contrast, BE and PD both were significantly increased in the Ror2−/− mandibles compared with Ror2+/+ and Ror2+/− mandibles at E18.5 (P < 0.05; Fig. 6C,D), while there were no significant differences in the BE and PD among them at E15.5 by ANOVA (Fig. 6A,B). DFA showed the significant difference in PD among Ror2+/+, Ror2+/−, and Ror2−/− (P < 0.05), and 100%, or 60%, or 80% of mandibles at E18.5 were correctly classified between Ror2−/− and the other groups, or between Ror2+/+ and the other groups, or between Ror2+/− and the other groups, respectively (data not shown). Significant difference was also observed in BE among Ror2+/+, Ror2+/−, and Ror2−/− (P < 0.05), and 100% of mandibles at E18.5 were correctly classified between Ror2+/+ and the other groups, or 100% between Ror2−/− and the other groups, or 60% between Ror2+/− and the other groups (data not shown).

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Figure 6. Morphometric analysis about shape changes in the Ror2 mutant mandibles. BE (C) and PD (D), both were significantly increased in the Ror2−/− mandibles compared with the Ror2+/+ and Ror2+/− mandibles at E18.5, while there were no significant differences in the BE (A) and PD (B) among them at E15.5. N = 5 for each group; * P < 0.05.

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The ordination scatter plot by the partial and relative warps showed that Ror2−/− mandibles were highly divergent from Ror2+/+ and Ror2+/− mandibles at E18.5 (Fig. 7B). The Ror2+/+ and Ror2+/− groups had very similar morphological characteristics at E18.5 (Fig. 7B). The scatter plot at E15.5 (Fig. 7A) did not show any separation among the Ror2+/+, Ror2+/−, or Ror2−/− groups.

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Figure 7. Scatter diagrams of the mandibular orientation among the groups. Orientation of the scatter plots by the partial and relative warps separated the Ror2−/− mandibles from Ror2+/+ and Ror2+/− mandibles at E18.5 (B). However, the scatter plot at E15.5 (A) did not show any separation, probably because the mandibles were less mineralized at this stage. In the relative warp analyses with α = 0 and α = 1, the first two relative warp axes accounted for 89% (relative warp 1 = 53% + relative warp 2 = 36%) and 96% (relative warp 1 = 69% + relative warp 2 = 27%) at E15.5 (A), and 93% (relative warp 1 = 83% + relative warp 2 = 10%) and 94% (relative warp 1 = 81% + relative warp 2 = 13%) at E18.5 (B), respectively, of the total shape variation. Red triangulated plots for Ror2+/+, solid circled plots for Ror2+/−, and green squared plots for Ror2−/− mandibles. The longitudinal dotted line is the centroid line.

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In DFA of the shape, the mandibles were discriminated between Ror2−/− and the others (P < 0.01), or between Ror2+/+ and Ror2+/− groups (P < 0.05) at E18.5, whereas they were discriminated only between Ror2+/+ and Ror2+/− fetuses at E15.5 (P < 0.01; Table 2). By cross-validation, 100% of mandibles were correctly classified between Ror2−/− and Ror2+/+ or between Ror2−/− and Ror2+/− groups at E18.5, while 80% was correctly classified between Ror2+/+ and Ror2+/− at E15.5 and E18.5 (data not shown). Procrustes ANOVA showed that the amount of measurement error was significantly small in both the Ror2 mutant E15.5 (P < 0.0001) and Ror2 mutant E18.5 (P < 0.0001) groups (data not shown).

Human Fetuses

Morphogenesis of the mandible during development. 

To analyze the morphogenesis of the mandible in human fetuses, BE and PD were calculated. The rate of BE was higher in 121–152 mm CRL (16–19 weeks of gestation) than in those of the other weeks, whereas the rate of PD did not show any peak (Fig. 3E,F). These changes were approximated by the regression functions [BE = 72 sin (0.0006 CRL – 0.036) + 0.35 sin (0.066 CRL – 3.09) + 0.25 sin (0.13 CRL – 4.7), R2 = 0.98 (Fig. 3E); PD = 4.2 exp {(CRL – 214/69)2}, R2 = 0.98] (Fig. 3F).

DISCUSSION

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. Literature cited

In this study, we demonstrated that morphometric and mathematical analyses based on micro-CT images and alizarin red S-stained specimens detected normal and abnormal morphological changes during the development of the mandible.

The mandibular growth pattern is characterized by intramembranous ossification of the mandibular body and endochondral ossification of the condyle (Lee et al.,2001). The mammalian mandible is a complex morphological structure consisting of multiple morphogenetic components that form the final structure (Atchley,1993). Because the development of the mandible is a continuous process in the prenatal period, there is a possibility of maldevelopment or abnormal changes of morphology in the mandibular body or in the processes. However, no investigation has yet been made to elucidate mathematically the abnormal morphological development of the mandible during the prenatal period. In this regard, we provide evidence that our present methods were sensitive and specific enough to differentiate the deformation and deviation of the mandible from normal development. The present findings on mandibular development have implications about both bone morphogenesis and clinical orientation.

In this study, we used micro-CT to image all mouse fetal and postnatal mandibles, and used the images in a geometric morphometric analysis to quantify mandibular morphology. CT-based volume measurements were performed in all mouse specimens. But the CT-based length measurements were performed in the sham-operated and sutured mandibles at E18.5; and Ror2+/+, Ror2+/−, and Ror2−/− mandibles at E18.5. Tomographic images are inherently volumetric and automatically aligned and size-calibrated, so they are directly useful for quantitative studies and theoretical modeling of development (Metscher,2009b).

The length, area, and volume have been used to compare the structure between two objects. These methods are suitable to compare the size between the objects, but not the shape because the configuration of multiple landmarks cannot be examined. The shape of a biological structure such as the mandible is a function of the relative position of the landmarks (Rohlf,2002). Triple-ratio can be used to examine the ratio among the contiguous four lengths between the objects in the sense of conformality (Lundh et al.,2011); however, triple-ratio is difficult to be used to compare the multidimensional shape, which is represented by the coordinates of multiple landmarks, between the objects. By the mathematical analysis used in the present study, we can compare the shape of the mandible between the individuals, but not the size. The emphasis on the shapes of biological structures is based on the observation that, of the two components of form (size and shape), shape is multidimensional and provides a good deal of information about the historical (evolutionary) processes responsible for the observed diversity (Rohlf and Bookstein,1987; Smith and Patton,1988; Patton and Smith,1990; Atchley and Hall,1991; Atchley et al.,1992; Raff,1996).

The simplest approach would be the direct analysis of the coordinates of superimposed specimens. Alternatively, if one were interested in looking at shape differences on different geometric scales and visualizing shape differences as deformations, one could analyze the partial-warp scores matrix with the uniform component appended. One of the purposes of this study was to illustrate the application of a statistical methodology of multivariate morphometrics (Marcus,1990) to the graphically oriented methods of geometric morphometrics for landmark data. The TPS is simply a convenient function with which to capture changes in landmark configurations and to display differences as the smoothest possible transformation grid. Compared with the approaches used in this study, there seem to be no alternative methods available that permit such straightforward yet statistically efficient morphometric analysis and visualization of the results. Nevertheless, as geometric morphometrics is an indirect method of measuring parameters (Bookstein,1991), a combination of RA, principal warps, and DFA were used in this study to provide a better representation of shape-change.

TPS analysis in this study was performed to provide information about mandibular shape changes in relation to mandibular maturation in growing normal subjects of mice and human fetuses. These findings indicate that significant modifications in the shape of the mandible take place in the prenatal stages of mouse development. TPS analysis has also been found effective for detecting abnormality, which depends significantly on the development of the mandible. TPS analysis appears to be particularly efficient for the description and statistical evaluation of shape variations occurring during mandibular growth and development.

This study has shown not only age-related but also stress-related changes in the morphological characteristics of the mandible. Many studies have been published regarding the morphological changes of the mandible during normal development (Bodner et al.,1998; Franchi et al.,2001; Lee et al.,2001; Ramaesh and Bard,2003; Radlanski et al.,2003; Monteiro and Reis,2005; Tagliaro et al.,2006,2009; Pessa et al.,2008; Leamy et al.,2008). However, it remains unclear how to precisely detect abnormal morphology. In this study, we investigated mathematically the morphogenetic patterns of the mandible in mice during normal and abnormal development considering the interrelationship of size and shape changes. The shape of the mandible and its alterations during development are typical and complicated, and it should be very interesting to observe the abnormal patterns that form as a result of any kind of stimulation or intervention. Mathematical methods can quantitatively analyze the global shape characteristics of the mandible, independently from its size or spatial orientation (Ferrario et al.,1999) for functional implementation. In this regard, this is the first reported mathematical study to combine mouse experiments with observation of human specimens to determine the morphogenesis of the mandible and to detect the abnormal development responsible for its deformation and deviation.

Prenatal TMJ movement restriction using the exo utero development system (Habib et al.,2005,2007; Jahan et al.,2010) is a very strong form of mechanical stimulation to produce disharmony in the development of the mandible. This restriction of jaw movement clearly led to the morphological deformation of the mandible in the E18.5 sutured fetuses, and morphometric analysis in particular revealed a significant increase in the PD in the sutured group. The relative warp analysis revealed a clear separation of the sutured group from the sham-operated group.

Ror2 has been demonstrated to play essential roles in developmental morphogenesis, and Ror2−/− mice exhibit short snouts with cleft palates (Schwabe et al.,2004) and shortened intestines (Yamada et al.,2010). Thus, the Ror2−/− mouse mandibles were expected to be malformed. The present CT scan and 3-D reconstruction of the mandible clearly demonstrated altered mandibles in the Ror2−/− group. By morphometric analysis, we detected not only a reduction in the volumes of the Ror2−/− mandibles at both E15.5 and E18.5, but also the morphological changes at E18.5 by calculating the BE and PD. In addition, DFA and relative warp analyses revealed the morphological differences in the mandibles between Ror2+/+ and Ror2−/− fetuses at E18.5, or Ror2+/+ and Ror2+/− fetuses at E15.5. These morphometric analyses detected the slight deformity of the Ror2+/− mandible shifted from the Ror2+/+ mandible. We found no significant difference in the BE and PD among the Ror2+/+, Ror2+/−, and Ror2−/− groups at E15.5, probably because the mineralization process was still at the early stage. There was thus a reduced possibility of shape changes, although there was still a tendency toward shape change. These findings revealed that Ror2−/− mandibles at E18.5 are significantly deviated from Ror2+/+ and Ror2+/− mandibles, suggesting that these methods are very sensitive and specific at detecting abnormal development of the mandible during fetal development.

Evaluation of the development of the mandible is one of the most potent tools for studying the clinical orientation of the mandible, for example, facial asymmetry, malocclusion, and prognathism or retrognathism. Clinical observation has suggested that midfacial profiles are established early in fetal development and are maintained postnatally (Mooney and Siegel,1986; Tollaro et al.,1994; Singh et al.,1998), and that the mandibular ramus grows faster than the rest of the body; mandibular growth patterns differ significantly in successive developmental periods (Bareggi et al.,1995; Lee et al.,2001). Youth and facial attractiveness are closely linked to the size and shape of the mandible (Perrett et al.,1994,1998; Pessa et al.,2008). The results of this study are important to clinicians' ability to detect the abnormal development of the mandible prenatally for early intervention to minimize functional impairment. This is because the perception of development is based on shapes, and disharmony in mandibular development causes some difficulties in contour, such as in mastication, tooth alignment, and facial expression. The techniques presented here would also be useful as sensitive and specific methods for toxicity testing. The methodological framework established in this study will thus contribute to future morphological studies.

In conclusion, our study shows that these mathematical methods are effective for elucidating the morphological development of the mandible as well as for detecting abnormality during development.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. Literature cited

The authors thank all the members of the Department of Developmental Biology, Faculty of Medicine, Shimane University, for their essential cooperation.

Literature cited

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. Literature cited