Architecture and mineralization of developing trabecular bone in the pig mandibular condyle
Article first published online: 7 JUN 2005
Copyright © 2005 Wiley-Liss, Inc.
The Anatomical Record Part A: Discoveries in Molecular, Cellular, and Evolutionary Biology
Volume 285A, Issue 1, pages 659–666, July 2005
How to Cite
Mulder, L., Koolstra, J. H., Weijs, W. A. and van Eijden, T. M.G.J. (2005), Architecture and mineralization of developing trabecular bone in the pig mandibular condyle. Anat. Rec., 285A: 659–666. doi: 10.1002/ar.a.20208
- Issue published online: 21 JUN 2005
- Article first published online: 7 JUN 2005
- Manuscript Accepted: 7 APR 2005
- Manuscript Received: 21 FEB 2005
- Inter-University Research School of Dentistry through the Academic Center for Dentistry Amsterdam
- bone histomorphometry;
- degree of mineralization;
- quantitative microcomputed tomography;
- mandibular condyle;
Architecture and mineralization are important determinants of trabecular bone quality. To date, no quantitative information is available on changes in trabecular bone architecture and mineralization of newly formed bone during development. Three-dimensional architecture and mineralization of the trabecular bone in the mandibular condyle from six pigs of different developmental ages were investigated with micro-CT. Anteriorly in the condyle, a more advanced state of remodeling was observed than posteriorly, where more active growth takes place. Posteriorly, the bone volume fraction increased with age (r = 0.87; P < 0.05) by an increase of trabecular thickness (r = 0.88; P < 0.05), while the number of trabeculae declined (r = −0.86; P < 0.05). Anteriorly, despite an increase in trabecular thickness (r = 0.97; P < 0.001), there was no change in bone volume fraction due to a simultaneous decline in trabecular number (r = −0.84; P < 0.05) and increase in trabecular separation (r = 0.95; P < 0.01). Posteriorly, rods were remodeled into plates as expressed by the structure model index (r = −0.97; P < 0.001), whereas anteriorly, a plate-like structure was already present in early stages. The trabecular structure had a clear orientation throughout the developmental process. The global degree of mineralization increased both anteriorly (r = 0.86; P < 0.05) and posteriorly (r = 0.89; P < 0.05). We suggest that the degree of mineralization does not depend on the bone volume, but on the thickness of the trabeculae as the mineralized centers of trabeculae were getting larger and more highly mineralized with age compared to their appositional layers. This indicates that besides apposition of new bone material on the surface of trabeculae, the mineralized tissue in their centers still changes and matures. © 2005 Wiley-Liss, Inc.
The trabecular architecture of bone adapts to the mechanical circumstances to which it is subjected during function. Besides architecture, the mechanical properties of trabecular bone depend on the degree and distribution of mineralization (Turner et al., 1990; Borah et al., 2000; Müller, 2003; Follet et al., 2004). The plates and rods of adult trabecular bone are composed of packets of remodeled bone of different ages and thus different degrees of mineralization (Parfitt et al., 1983). It has also been shown that tissue mineralization varies spatially within trabeculae of adult bone (Paschalis et al., 1997) as well as of fetal trabecular bone (Meneghini et al., 2003). Furthermore, these variations appeared to be consistent with the preexisting notions that formation of trabecular bone takes place on the surface of trabeculae, and that newly produced collagenous tissue becomes more mineralized and rigid with age (Ziv et al., 1996). So far, there is no quantitative information concerning the development of the architecture and mineralization properties of trabecular bone and both properties have not been interrelated.
After initial formation, fetal trabecular bone structure is likely to adapt to the mechanical environment in utero by remodeling. Besides, the mineralization of this structure will undergo changes. The supposedly rapidly developing structure of fetal trabecular bone and its mineralization would provide an interesting model to investigate the simultaneous changes of these two properties. The development of the trabecular architecture has been studied in the femur (Salle et al., 2002) and in the vertebra (Nuzzo et al., 2003). Both studies solely investigated the architecture of the trabecular bone and did not elaborate on the degree and distribution of mineralization. Thus far, no information is available on the degree and distribution of mineralization and its relation to the architecture of the developing trabecular bone. Knowledge regarding the development of trabecular bone architecture and its relation to mineralization will augment the understanding of normal trabecular bone development and delivers baseline data to which deviations can be compared. For instance, bone diseases such as osteoporosis and the influences of pathogenic drugs or noxious environmental conditions can be traced back to the fetal development of bones (Cooper et al., 2002; Javaid and Cooper, 2002). In addition, knowledge of the degree and distribution of mineralization will add to a more accurate estimation of the apparent mechanical properties of trabecular bone as investigated by, for example, finite-element models (van der Linden et al., 2001; Bourne and van der Meulen, 2004).
In the present study, the method of microcomputed tomography (micro-CT) was applied to investigate simultaneously the architectural and mineralization properties of developing trabecular bone. Recently, micro-CT has been established as an accurate and powerful tool for determining three-dimensional architectural parameters of young and adult trabecular bone in a nondestructive manner (Müller et al., 1996, 1998; Rüegsegger et al., 1996; Uchiyama et al., 1997). It has been proved applicable to investigate the changes in trabecular architecture during aging and postnatal development (Barbier et al., 1999; Ding, 2000; Nafei et al., 2000; Tanck et al., 2001; Wolschrijn and Weijs, 2004). In addition, it has been recently demonstrated that commercial micro-CT systems are not only capable of describing the architectural, but also the physical properties of trabecular bone, such as the degree and distribution of mineralization (Mulder et al., 2004).
An interesting piece of bone that has a rapid formation of trabeculae and that would provide a suitable model for developing trabecular bone is the mandibular condyle (Teng and Herring, 1995; Giesen and van Eijden, 2000). Moreover, the mandibular condyle is subjected to mechanical usage in utero: fetal swallowing and yawning (de Vries et al., 1982). In this study, the trabecular bone of the mandibular condyle of developing pigs was analyzed. Although a lot is known about the structure of the trabecular bone in the juvenile and adult mandibular condyle, it is unclear how this specific structure develops during fetal life. Extensive research has been performed on the fetal development of the mandibular condyle. However, these studies focused mainly on the cartilage part (Durkin and Irving, 1973; Hall, 1987; Copray et al., 1988; Ben-Ami et al., 1992; Shibata et al., 1996). The underlying endochondrally developing trabecular bone has received little attention.
MATERIALS AND METHODS
The mandibular condyles from six pigs (standard Dutch commercial hybrid race) of different developmental ages were used in this study. The fetuses had an estimated age of 65–70, 70–75, 82–87, and 95–100 days of gestation and were obtained from slaughtered sows in a commercial slaughterhouse. Fetal age was determined from the mean weight of the litter using growth curves (Evans and Sack, 1973). A newborn (112–115 days postconception) and a 2-week-old (130 days postconception) piglet were obtained from the experimental farm of the Faculty of Veterinary Medicine in Utrecht, The Netherlands, and were euthanized by an intravenous overdose of ketamine (Narcetan) after premedication. The specimens were obtained from other experiments that were approved by the Committee for Animal Experimentation of the Faculty of Veterinary Medicine, Utrecht, The Netherlands. They were stored at −20°C prior to assessment.
The mandibles were prepared by dissection from the heads and cut in half at the symphyseal region. No attempt was made at removing all the soft tissue. The condyles of the three oldest specimens had to be separated from the mandibular ramus in order to be able to analyze all specimens with the same resolution, which is limited by the diameter of the micro-CT specimen holders.
Three-dimensional reconstructions of the trabecular bone of the specimens were obtained by using a high-resolution micro-CT system (μCT 40; Scanco Medical, Bassersdorf, Switzerland). The condyles were mounted in cylindrical specimen holders (Polyetherimide; 20 mm outer diameter; wall thickness, 1.5 mm) and secured with synthetic foam. The specimens were completely submerged in 70% ethanol. The scans yielded an isotropic spatial resolution of 10 μm. A 45 kV peak-voltage X-ray beam was used, which corresponds to an effective energy of approximately 24 keV (Mulder et al., 2004). The micro-CT system was equipped with an aluminum filter and a correction algorithm, which reduced the beam hardening artifacts sufficiently to enable quantitative measurements of the degree and distribution of mineralization of developing bone (Mulder et al., 2004). The computed linear attenuation coefficient of the X-ray beam in each volume element (voxel) was stored in an attenuation map and represented by a gray value in the reconstruction. This attenuation coefficient can be considered proportional to the local degree of mineralization (Nuzzo et al., 2003).
To determine the architecture of the bone specimens, volumes of interest (approximately 1 mm3) were built up out of 10 × 10 × 10 μm3 voxels and segmented using an adaptive threshold, which was visually checked. In a segmented image, every voxel with a linear attenuation value below the threshold (assumingly representing soft tissue or background) was made transparent and voxels above this threshold (representing bone) were made opaque.
For a quantitative analysis of the architecture and the determination of the degree of mineralization, volumes of interest were chosen within four different regions of the condylar specimens to investigate the suspected heterogeneity. These regions were roughly located anterosuperiorly, anteroinferiorly, posterosuperiorly, and posteroinferiorly (Fig. 1).
To quantify the changes in architecture of the trabecular bone during development, several bone architectural parameters (BV/TV, bone volume fraction; Tb.N, trabecular number; Tb.Th, trabecular thickness; Tb.Sp, trabecular separation; Conn.D, connectivity density; SMI, structure model index; DA, degree of anisotropy) were calculated (Software Revision 3.2; Scanco Medical). The structure model index quantifies the characteristic form of the trabecular bone in terms of plate-like and rod-like trabecular elements. For an ideal plate-like and rod-like structure, this index is 0 and 3, respectively. The three principal directions of the trabecular structure were estimated by the mean intercept length (MIL) method and the degree of anisotropy is defined as the ratio between the maximal MIL and the minimal MIL (Hildebrand et al., 1999).
Degree and Distribution of Mineralization
The previously determined thresholds to separate bone from background were applied to the defined volumes of interest for the determination of the degree of mineralization. For this analysis, the voxels exceeding the threshold kept their original gray value. The outermost voxel layer characterized as bone was disregarded as this layer is likely to be corrupted by partial volume effects. The degree of mineralization was determined by comparing the average linear attenuation coefficient of the part of the reconstructed volume of interest, which had been characterized as bone, with reference measurements of a series of solutions with different concentration of the mineral K2HPO4 (Mulder et al., 2004). To investigate the degree of mineralization from the surface of the trabeculae to their centers, a specifically designed algorithm was used. Briefly, layers of bone-containing voxels were consecutively peeled from the surface of the reconstructed bone structure containing all the trabeculae. After a layer had been peeled off, its average degree of mineralization was calculated using the method mentioned.
Linear regression analysis was applied to assess changes in architectural parameters and mineralization with age for the different volumes of interest using SPSS (11.5.1 software SPSS). A test for the equality of two dependent correlations was applied. This was done in order to examine the equality between the correlation coefficients of a certain parameter with developmental age for the anterior and posterior regions. The correlation between the two regions was taken into account (Steiger, 1980). This is because the two investigated regions were taken from the same mandibular condyle and therefore should be treated as dependent samples. A P value of less than 0.05 was considered statistically significant.
The reconstructed images of the specimens clearly showed the orientation of the condylar development, as it grows in a backward and slightly upward direction (Fig. 1). Distinctly orientated bony spiculae could be observed at locations of rapid growth at the posterior and superior border of the condyle. More anteriorly in the condyle, these spiculae were less apparent and integrated with the trabecular structure. No solid cortex had been formed in any of the analyzed specimens. The cartilage covering the posterosuperior border of the actively growing mandible is not visible in these reconstructions. As no differences between inferior and superior regions were found (not shown), both anterior and posterior regions were combined to investigate anteroposterior differences.
An overview of the development of the trabecular structure in the condyle can be found in Figure 2, where trabecular bone of the posterior region of the mandibular condyles is compared for different ages. Figure 2 illustrates that during development there is an increase in the amount of bone and trabecular thickness and also a marked development of anisotropy of the trabeculae.
Quantitative changes in trabecular structure have been summarized in Figure 3. The amount of bone, expressed by the bone volume fraction (BV/TV), significantly increased with age in the posterior (r = 0.87; P < 0.05) but not in the anterior region. The increase in bone volume fraction in the posterior region could be attributed to an increase in trabecular thickness (Tb.Th; r = 0.88; P < 0.05), which outweighed a simultaneous decrease in trabecular number (Tb.N; r = −0.86; P < 0.05). No significant changes were found for trabecular separation (Tb.Sp) in the posterior region. In the anterior region, the bone volume fraction did not change; a decrease in trabecular number (r = −0.84; P < 0.05) and an increase in trabecular separation (r = 0.95; P < 0.01) were compensated by an increase in thickness (r = 0.97; P < 0.001) of the trabeculae. The posterior region displayed a decrease in the structure model index (SMI; r = −0.97; P < 0.001), indicating a change from rods to plates. Anteriorly, the trabeculae had a plate-like structure, which remained unchanged during the investigated ages. The connectivity density (Conn.D) decreased significantly in the anterior region (r = −0.92; P < 0.01) as well as the posterior region (r = −0.95; P < 0.01). No changes in the degree of anisotropy (DA) with age were found in the anterior region, whereas in the posterior region, the trabeculae became increasingly more orientated with age (r = 0.92; P < 0.01). Investigation of differences between correlation coefficients of the anterior and posterior region for each individual parameter yielded significant results for the bone volume fraction, trabecular separation, structure model index, and degree of anisotropy. This means that there is a difference between these regions in the way that these parameters relate to age.
Degree and Distribution of Mineralization
Figure 2 shows a clear global increase in the degree of mineralization of trabeculae with age and a gradient of increasing mineralization from the surfaces toward the centers of the trabeculae. The global degree of mineralization increased significantly with age (anterior r = 0.86, P < 0.05; posterior r = 0.89, P < 0.05; Fig. 3). In the anterior region, the highest degrees of mineralization were observed. No significant differences were found in correlation coefficients between the anterior and posterior region, indicating that all regions mineralized at a similar rate. The three-dimensional distribution of attenuation values of reconstructed trabeculae revealed that mineralization was higher in the centers of the trabeculae than near their surfaces (Fig. 4). Besides this, a steeper gradient in the degree of mineralization from the surface to the center was observed in the oldest specimen as compared to the youngest one. In the oldest specimen, a relatively large constant region of highly mineralized bone in the centers of the trabeculae was present, which could also be confirmed in the two-dimensional cross-section through a section of trabecular bone (Fig. 4). The degree of mineralization of the outermost layers of trabeculae was nearly equal in the anterior and posterior regions of all examined ages.
To our knowledge, this is the first quantitative descriptive study of the concurrent changes in trabecular bone architecture and mineralization of newly formed bone during development. The data were obtained quickly, accurately, and in a nondestructive manner using a commercially available desktop micro-CT system. The resolution was sufficiently high to analyze the early development of trabecular bone. Fetal pigs of gestational age 65–70 days and older were chosen for this study as younger specimens did not have clearly discernable trabecular bone in the condylar head in the micro-CT reconstructions. It must be mentioned that only six specimens were used. However, the strong correlations found in this study justify this choice and rules out any coincidence based on interindividual variation.
It was shown that there is a considerable difference between anterior and posterior regions within the developing condyle. The posterior region exhibited an increasing bone volume fraction and every sign of an actively developing region. The anterior region, on the other hand, showed a more advanced state of remodeling with no increase in bone volume fraction. The increase in bone volume fraction in the posterior region with age can be attributed to an increase in trabecular thickness and an unchanged trabecular separation despite a decline in trabecular number. A decline in structure model index in the posterior region indicated an ongoing change from rod-like trabeculae to a more plate-like shape. Along with complete disappearance of rod-like trabeculae, merging of two or more rods into plates is a likely cause for the decline in trabecular number, which in turn supposedly caused the observed decrease in connectivity density. A fall in trabecular number and rise in thickness was also observed anteriorly. As simultaneously the trabecular separation increased, the bone volume fraction remained unchanged. The decline in trabecular number was in this case likely to be caused by removal of complete trabecular elements as no change in structure model index was observed. It did, however, cause a decrease in connectivity density (Fig. 3). The anteroposterior differences could be largely explained by the fact that the trabecular bone had been formed earlier anteriorly than posteriorly and thus that remodeling had been going on for a longer period of time anteriorly.
The values for the architectural parameters of the trabecular bone in the pig mandibular condyle corroborate more with those of the developing human femur than those of the developing human vertebra. Bone volume fraction and trabecular thickness and separation in the present study (BV/TV, 20–38%; Tb.Th, 35–80 μm; and Tb.Sp, 80–180 μm) were low compared to values found for the vertebra (BV/TV, 30–54%; Tb.Th, 84–118 μm; and Tb.Sp, 155–321 μm) (Nuzzo et al., 2003), but in agreement with values for the femur (BV/TV, 24–34%; Tb.Th, 71–98 μm) (Salle et al., 2002). This indicates that the development of the condyle resembles the development of the trabecular bone in long bones. It should be mentioned, however, that the age range chosen in this study resembled that of the femur study closer than that of the vertebra study.
Comparison with results from the mandibular condyle of juvenile pigs suggests that the trabecular bone in the condyle remains subject to extensive modeling and remodeling during further postnatal development. This is probably due to continuous changes of mechanical usage of the temporomandibular joint after birth (Langenbach and van Eijden, 2001). After birth, trabecular thickness and trabecular separations increase up to 180 and 280 μm, respectively, while trabecular number decreases to 2.9 mm−1 (Teng and Herring, 1995). The net result is that the bone volume fraction does not change after birth. The fetal (and older) specimens illustrated that the trabecular bone in the fetal condyle is already strongly oriented as the obtained degrees of anisotropy were generally above 2.0. It was suggested (Teng and Herring, 1995) that the orientation of the trabeculae in the posterosuperior direction was simply a reflection of the growth pattern in juvenile pigs. This might also be a likely explanation for the strongly oriented trabecular structure in the mandibular condyles investigated in this study. However, besides the fact that the trabecular orientation might be a reflection of a growth pattern, it has also been demonstrated that mechanical loading of bone during development (Goret-Nicaise, 1981; Burger et al., 1991) might be a determinant of the morphology of the developing trabecular bone.
We found that the global degree of mineralization of fetal trabecular bone increases with gestational age, and that the highest values were found anteriorly (Fig. 3). It is noticeable that anteriorly, the increase in degree of mineralization during development was not accompanied by an increase in bone volume fraction. We suggest that the degree of mineralization does not depend on the bone volume, but on the thickness of the trabeculae as the highly mineralized centers of trabeculae are getting larger with age (Fig. 3). The fact that mineralization increases from the surface of the trabeculae toward their centers indicates that bone remodeling in trabecular bone takes place at the surface of trabeculae. Therefore, the bone in the centers of trabeculae is older than that on the surface and consequently more highly and more maturely mineralized. The observed distribution of mineralization in individual trabeculae is consistent with observations in the condyles of the distal femur of mature rabbits (Morgan et al., 2002; Bourne and van der Meulen, 2004) obtained with a similar peeling algorithm. We also found that the bone in the center of the trabeculae became more highly mineralized with age, while the appositional layers had the same degree of mineralization throughout the age range studied. This indicates that besides apposition of new bone material on the surface of trabeculae, the mineralized tissue in their centers still changes and matures (Fig. 4). The net result of this process is an increasing degree of mineralization of the entire trabecular structure. It should be realized that the estimated degree of mineralization of the most superficial layers would be underrated by partial volume effects if these layers were taken into account while determining the average degree of mineralization of the structure. As trabecular elements of various thicknesses exist within one volume of interest, not all trabecular elements are peeled at the same rate. For instance, when a thin trabecular element is completely peeled, a thicker trabecular element is still in the process. Therefore, the distance from the trabecular surface in Figure 4 should be considered as the average distance from the trabecular surface for the volume of interest.
In conclusion, investigation with micro-CT of the changes in the trabecular bone of the developing mandibular condyle revealed regional differences concerning the trabecular architecture. The degree and distribution of mineralization, on the other hand, seemed to be quite independent of location and did not coincide with bone volume (anteriorly), but more with the trabecular thickness. A gradient in the degree of mineralization was observed between the centers of individual trabeculae and their outer surfaces, indicating bone growth by apposition. With age, the centers became more highly mineralized and larger and thus clearly suggesting a relationship between trabecular thickness and degree of mineralization.
The authors thank Irene Aartman from the Department of Social Dentistry and Dental Health Education of Academic Center for Dentistry Amsterdam for her assistance with the statistical tests. Appreciation also goes out to Jet de Jonge from the Department of Functional Morphology, Faculty of Veterinary Medicine, Utrecht University, for providing the specimens and to Geerling Langenbach for critically reading the manuscript.
- 1999. The visualization and evaluation of bone architecture in the rat using three-dimensional X-ray microcomputed tomography. J Bone Miner Metab 17: 37–44. , , , , , , , , .
- 1992. Structural characterization of the mandibular condyle in human fetuses: light and electron microscopy studies. Acta Anat 145: 79–87. , , .
- 2000. Evaluation of changes in trabecular bone architecture and mechanical properties of minipig vertebrae by three-dimensional magnetic resonance microimaging and finite element modeling. J Bone Miner Res 15: 1786–1797. , , , , , , , , , .
- 2004. Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CT-attenuation. J Biomech 37: 613–621. , .
- 1991. Modulation of osteogenesis in fetal bone rudiments by mechanical stress in vitro. J Biomech 24: 101–109. , , .
- 2002. The fetal origins of osteoporotic fracture. Calcif Tissue Int 70: 391–394. , , , , , .
- 1988. The role of condylar cartilage in the development of the temporomandibular joint. Angle Orthod 58: 369–380. , , .
- 1982. The emergence of fetal behaviour: I, qualitative aspects. Early Hum Dev 7: 301–322. , , .
- 2000. Age variations in the properties of human tibial trabecular bone and cartilage. Acta Orthop Scand 292(Suppl): 1–45. .
- 1973. The cartilage of the mandibular condyle. Oral Sci Rev 2: 29–99. , .
- 1973. Prenatal development of domestic and laboratory mammals: growth curves, external features and selected references. Anat Histol Embryol 2: 11–45. , .
- 2004. The degree of mineralization is a determinant of bone strength: a study on human calcanei. Bone 34: 783–789. , , , .
- 2000. The three-dimensional cancellous bone architecture of the human mandibular condyle. J Dent Res 79: 957–963. , .
- 1981. Influence des insertions des muscles masticateurs sur la structure mandibulaire du nouveau-né. Bull Assoc Anat 65: 287–296. .
- 1987. Earliest evidence of cartilage and bone development in embryonic life. Clin Orthop 225: 255–572. .
- 1999. Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from spine, femur, iliac crest, and calcaneus. J Bone Miner Res 14: 1167–1174. , , , , .
- 2002. Prenatal and childhood influences on osteoporosis. Best Pract Res Cl En 16: 349–367. , .
- 2001. Mammalian feeding motor patterns. Am Zool 41: 1338–1351. , .
- 2003. Rietveld refinement on X-ray diffraction patterns of bioapatite in human fetal bones. Biophys J 84: 2021–2029. , , , , .
- 2002. Density versus depth from trabecular surface measured by quantitative micro-CT. Trans Orthop Res Soc 27: 110. , , .
- 2004. Accuracy of microCT in the quantitative determination of the degree and distribution of mineralization in developing bone. Acta Radiol 45: 769–777. , , .
- 1996. Morphometric analysis of noninvasively assessed bone biopsies: comparison of high-resolution computed tomography and histologic sections. Bone 18: 215–220. , , , , .
- 1998. Morphometric analysis of human bone biopsies: a quantitative structural comparison of histological sections and micro-computed tomography. Bone 23: 59–66. , , , , , , .
- 2003. Bone microarchitecture assessment: current and future trends. Osteoporosis Int 14: S89–S99. .
- 2000. Properties of growing trabecular ovine bone: II, architectural and mechanical properties. J Bone Joint Surg Br 82: 921–927. , , , , .
- 2003. Microarchitectural and physical changes during fetal growth in human vertebral bone. J Bone Miner Res 18: 760–768. , , , , , .
- 1983. Relationships between surface, volume, and thickness of iliac trabecular bone in aging and in osteoporosis: implications for the microanatomic and cellular mechanisms of bone loss. J Clin Invest 72: 1396–1409. , , , , , .
- 1997. FTIR microspectroscopic analysis of normal human cortical and trabecular bone. Calcif Tissue Int 61: 480–486. , , , , .
- 1996. A microtomographic system for the nondestructive evaluation of bone architecture. Calcif Tissue Int 58: 24–29. , , .
- 2002. Human fetal bone development: histomorphometric evaluation of the proximal femoral metaphysis. Bone 30: 823–828. , , , , .
- 1996. A histological study of the developing condylar cartilage of the fetal mouse mandible using coronal sections. Arch Oral Biol 41: 47–54. , , , , .
- 1980. Tests for comparing elements of a correlation matrix. Psychol Bull 87: 245–251. .
- 2001. Increase in bone volume fraction precedes architectural adaptation in growing bone. Bone 28: 650–654. , , , .
- 1995. A stereological study of trabecular architecture in the mandibular condyle of the pig. Arch Oral Biol 40: 299–310. , .
- 1990. The fabric dependence of the orthotropic elastic constants of cancellous bone. J Biomech 23: 549–561. , , , , .
- 1997. A morphometric comparison of trabecular structure of human ilium between microcomputed tomography and conventional histomorphometry. Calcif Tissue Int 61: 493–498. , , , , , .
- 2001. Trabecular bone's mechanical properties are affected by its non-uniform mineral distribution. J Biomech 34: 1573–1580. , , , .
- 2004. Development of the trabecular structure within the ulnar medial coronoid process of young dogs. Anat Rec 278A: 514–519. , .
- 1996. Microstructure-microhardness relations in parallel-fibered and lamellar bone. Bone 18: 417–428. , , .