A new method of comprehensive static histomorphometry applied on human lumbar vertebral cancellous bone

Bone Vol. 27, No. 1 July 2000:129 –138

A New Method of Comprehensive Static Histomorphometry Applied on Human Lumbar Vertebral Cancellous Bone J. S. THOMSEN, E. N. EBBESEN, and Li. MOSEKILDE Department of Cell Biology, Institute of Anatomy, University of Aarhus, Aarhus, Denmark

Key Words: Histomorphometry; Vertebral body; Bone structure; Aging; Fracture; Spine.

The aim of the present study was to assess age-related changes in the human spine by use of established static histomorphometry, and to determine how these static histomorphometric measures are interrelated in human cancellous bone tissue. The material comprised normal human lumbar vertebral bodies (L-2) from 12 women (19 –96 years) and 12 men (23–91 years) selected from a larger autopsy material to give an even age and gender distribution. In addition, L-2 from three female subjects (80, 88, and 90 years) with a known vertebral fracture of L-2 were considered. Approximately 9-mm-thick frontal (mediolateral) slices were embedded in methylmetacrylate, stained with aniline blue, and scanned into a computer with a flatbed image scanner at a high resolution (2400 dpi). With a custom-made computer program the following static histomorphometric measures were determined: trabecular bone volume; marrow space star volume; bone space star volume; anisotropy of bone and marrow phase (star length distribution method); node-strut analysis (node:terminus ratio); trabecular thickness; trabecular number; trabecular separation; and trabecular bone pattern factor. In addition, connectivity density was determined (by the ConnEulor method). All 11 histomorphometric measures, except bone space star volume and the two measures of anisotropy, showed a significant correlation with age. Marrow space star volume (r ⴝ 0.82) and trabecular bone volume (r ⴝ ⴚ0.81) showed the highest correlation with age. Furthermore, it was found that all of the histomorphometric measures were correlated, to different degrees. Trabecular bone volume correlated significantly with all ten histomorphometric measures, whereas the two anisotropy measures were poorly correlated to the other measures. Finally, we found the histomorphometric values in this study to be in excellent accordance with various previously published results from studies of human trabecular vertebral bone, the sole exception being marrow space star volume, which was probably due to the small (artificial) region of interest (ROI) that was used in the earlier studies. In conclusion, the new method applied herein allows for easy assessment of age-related changes and also for assessment of relationships between histomorphometric measures in human vertebral cancellous bone. (Bone 27:129 –138; 2000) © 2000 by Elsevier Science Inc. All rights reserved.

Introduction Analyses of histologic sections in relation to aging and treatment efficacy have focused mainly on the iliac crest; fewer studies have performed static histomorphometry on human vertebral bodies. Some of the studies carried out during the last three decades on static histomorphometry of the human spine are summarized in Table 1. Each of these studies focused on a limited number of different static histomorphometric measures. Recent investigations of the iliac crest have revealed that some of the histomorphometric measures were correlated.11,12,15,49 This leads to the question of whether similar close relationships exist between the static histomorphometric measures in cancellous bone from other anatomic sites, particularly vertebral cancellous bone, which undergoes a loading pattern very different from the loading pattern of the iliac crest. The aim of this investigation was to apply the established static histomorphometric methods to sections from human vertebral bodies originating from female and male subjects over a wide age range, and to examine age-related changes and the relationships between the different static histomorphometric measures. The present study examines almost all available static histomorphometric measures carried out on the same material. Furthermore, we present a method for easy image acquisition that, to the best of our knowledge, has not been used before in connection with histomorphometric analyses. This study is a part of the “Danish In Vitro Bone Study” (DAVIBO). Data from the DAVIBO study concerning the iliac crest7,23,49 and biomechanics and densitometry of the third lumbar vertebral body have been published previously.20 –22 Materials and Methods Bone Specimens From a large body of normal autopsy material, a subset of lumbar vertebral bodies (L-2) from 12 women (aged 18.5–96.4 years) and 12 men (aged 22.6 –90.8 years) was selected.20 –22 The subjects were chosen so as to provide an even age and gender distribution in the age range of approximately 20 –90 years. In addition, L-2 from three female subjects (aged 80.0, 87.5, and 89.6 years) with a known vertebral fracture of L-2 were included in the study for comparison with individuals without fractures. All vertebral bodies were evaluated by normal X-ray

Address for correspondence and reprints: Dr. Jesper Skovhus Thomsen, Department of Cell Biology, Institute of Anatomy, University of Aarhus, DK-8000 Aarhus C, Denmark. E-mail: [email protected] © 2000 by Elsevier Science Inc. All rights reserved.

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Table 1. Some of the studies of vertebral trabecular bone by histomorphometry Study

Year

N

Histomorphometric methods

Arnold et al.5 Bromley et al.9 Atkinson6 Whitehouse54 Bergot et al.8

1966 1966 1967 1974 1988

96 92 68 3 61

Mosekilde34 Mosekilde36 Vesterby et al.52 Alexiades et al.2 Vesterby51 Diebold et al.19 Mellish et al.33 Vesterby et al.53 Dempster et al.18 Amling et al.3 Grote et al.26 Amling et al.4 Ritzel et al.43 Kneissel et al.31,b Cendre et al.10

1988 1989 1989 1990 1990 1991 1991 1991 1993 1994 1995 1996 1996 1997 1999

23 91 8 10 18 20 35 15 23 27 26 40 37 65 20

Trabecular thickness BV/TV,a T.Ar, B.Ar, and B.Pm BV/TV and number of transverse trabeculae BV/TV, trabecular thickness, Am.space, Ab.space, and B.Pm BV/TV, mean trabecular width, and mean trabecular spacing (using horizontal and vertical slices) Trabecular thickness and separation of vertical and horizontal trabeculae BV/TV and trabecular thickness and separation of vertical and horizontal trabeculae V*m.space and V*b.space BV/TV and trabecular thickness V*m.space and V*b.space BV/TV, Tb.Th, Tb.N, Tb.Sp, SV, and S/V Node-strut analysis BV/TV, V*m.space, V*b.space, and trabecular thickness BV/TV, Tb.Th, Tb.N, and Tb.Sp BV/TV, Tb.Th, Tb.N, Tb.Sp, and TBPf BV/TV and TBPf BV/TV and TBPf BV/TV, Tb.Th, Tb.N, and TBPf BV/TV, Tb.Th, Tb.N, Tb.Sp, and TBPf BV/TV, Tb.Th, Tb.N, Tb.Sp, and node-strut analysis

Histomorphometric measures that involve osteoid surfaces or osteoclastic surfaces are omitted. KEY: N, number of subjects in the study; SV, bone surface density, S/V, bone surface:volume ratio. See text for explanations of bone characteristics (“Histomorphometric methods” column). a Includes cortical bone. b Based on a medieval Nubian population.

procedure.20 –22 Vertebral bodies with fractures were identified from the lateral-projection X-ray images. The study was approved by the local ethics committee. Specimen Preparation Most of the soft connective tissue was removed from the intact vertebral bodies with a scalpel. After a thin midsagittal section was obtained, an approximately 9-mm-thick frontal (mediolateral) slice for histomorphometry was sawed from one half of the vertebra with a diamond precision-parallel saw (Exakt, Apparatebau, Otto Herrmann, Norderstedt, Germany). The 9-mm-thick slices were embedded in methylmetacrylate (Technovit 9100, Heraeus Kulzer, Wehrheim/Ts., Germany) and cut into 10-␮mthick sections on a Jung Model K microtome. A series of six consecutive 10-␮m-thick sections was cut, then ten 10-␮m-thick sections were removed, and finally a series of six consecutive 10-␮m-thick sections were cut. Four disector pairs28,48 (two sections separated by 10 ␮m) were selected from each individual. Due to section artifacts it was not always possible to select four disector pairs from each individual. In all, 98 disector pairs were used; that is, an average of 3.6 pairs per individual. All sections were stained with aniline blue (modified Masson trichrome), because this staining technique provides good contrast between the marrow and the bone phase. In all, 168 sections were used for calculations of histomorphometric measures, which is an average of 6.2 sections per individual. Image Acquisition The 10-␮m-thick aniline blue-stained sections were placed in a flatbed image scanner (Agfa Arcus II, Agfa-Gevaert AG, Leverkusen, Germany) with an integrated transparency scanning unit. The Agfa scanner was connected to a 333 MHz Intel Pentium II personal computer (Zitech Computer, Birkerød, Denmark). Images were acquired with Agfa FOTOLOOK 2.09 (Agfa-

Gevaert AG, Leverkusen, Germany) and stored in the tagged image file format (TIFF) with CCITT group 4 compression. The images were captured with FOTOLOOK in the “line art” setting (i.e., 1 bit images) at a resolution of 2400 dpi, which is equivalent to a spatial resolution of 10.58 ␮m. The threshold between black and white was set to 75%. This setting was found by scanning the same bone section with different values of threshold (50%– 85% with steps of 5 percentage points). By comparing the resulting images with the bone section using a stereomicroscope (Olympus SZ-40, Olympus, Tokyo, Japan) the threshold of 75% was found to provide images that best matched the original section. The GNU IMAGE MANIPULATION PROGRAM (GIMP) (http:// www.gimp.org), running under the Linux operating system (Red Hat LINUX 5.1, Red Hat Software, Inc., Research Triangle Park, NC), was used to remove artifacts from the images. During the removal of artifacts, comparison was made between the computerized image and the section using the stereomicroscope. Figure 1 shows two examples of digitized images next to two adjacent 4-mm-thick sections. A custom-made computer program was created to perform the histomorphometric measurements. The program was written in C and ran under the Linux operating system on the PC. The high-image resolution resulted in very large images (typically 2800 ⫻ 3800 pixels). The computer program showed the images reduced to 25% of their original size so that a region of interest (ROI) could be drawn on the computer screen with a pointing device (e.g., a mouse). Thereafter, the polygon-shaped ROI was scaled by a factor of 4 so that it matched the original image size. Bone Histomorphometry Trabecular bone volume. The trabecular bone volume (BV/TV [B.Ar/T.Ar]) was obtained by counting the number of pixels representing the bone and marrow phases, respectively. The number of pixels representing the bone area was divided by the

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Figure 1. (Left) Images of 4-mm-thick nonembedded bone sections. The images are of sections adjacent to the embedded sections used for histomorphometry. (Right) Digitized images of 10-␮m-thick sections used for histomorphometry. Upper row: 32-year-old man; lower row: 90-year-old man. Original magnification: ⫻1.44.

sum of the number of pixels representing the bone and marrow area. The bone area (B.Ar), marrow area (Ma.Ar), and tissue area (T.Ar) could then all be computed, as the area of one pixel is 10.58 ␮m ⫻ 10.58 ␮m ⫽ 111.94 ␮m2. Star volume. The marrow space star volume51,52 (V*m.space) was obtained by implementing the “nucleator method”27 in the computer program, as previously described.49 Briefly, a series of randomly selected points in the marrow phase was selected. A line was followed in a random direction until it intercepted either a bone-marrow boundary or the ROI boundary. The euclidean length, ln, of the intercept line from the randomly selected point to the boundary was recorded and the star volume computed as: V *n ⫽

4␲ 3 ln 3

(1)

where l3n is the average over all intercept lengths raised to the power of 3. In all, 3000 randomly selected points were used, each with 36 different randomly selected intercept lines. Bone space star volume (V*b.space) was found in the same way, but with the randomly selected points chosen in the bone phase. Node-strut analysis. We implemented the node-strut analysis as described by Garrahan et al.24 A Hilditch skeletonization procedure1,32 was iteratively applied to the image, so the trabec-

ular network was “eroded” until it was only 1 pixel thick.1,24,32,33 The Hilditch skeletonization procedure was chosen because it is very insensitive to edge noise that gives rise to artificial skeleton branches. The skeletonization process is a topological invariant process and, therefore, the skeletonized network has the same topological properties as the unskeletonized network. (A topological invariant process is a homeomorphism; i.e., a deformation without tearing or folding that preserves the topological properties). On the skeletonized network, nodes (Nd) and termini (Tm) were identified automatically. A node is a point at which three or more trabeculae (struts) are joined, and a terminus is defined as a point at which a trabecula is not joined to any other trabecula.24 Both nodes and termini can be detected automatically from the skeletonized network by inspecting the local 3 ⫻ 3 neighborhood of a pixel. It has been argued that the node:terminus ratio (Nd/Tm) is a way of expressing the connectivity of the trabecular network.13 Consequently, we limited the node-strut analysis to computation of the node:terminus ratio. Trabecular bone pattern factor. Hahn et al. suggested a simple method to quantify the structure of two-dimensional (2D) sections called the trabecular bone pattern factor (TBPf).29 The theory behind the trabecular bone pattern factor is that many

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concave surfaces on the sections represent a well-connected 2D network, whereas a section containing many convex surfaces represents a poorly connected 2D network. The bone area (B.Ar) and the length of the bone-marrow interface (B.Pm) are measured. The binary bone image is then dilated by applying a median filter to the image. This filtration procedure results in a thickening of the trabecular structure by one pixel. The bone area (B.Ar⬘) and the length of the bone perimeter (B.Pm⬘) are then measured again. The trabecular bone pattern factor is defined as: TBPf ⫽

B.Pm ⫺ B.Pm⬘ B.Ar ⫺ B.Ar⬘

(2)

Well-connected 2D networks (i.e., networks with many concave surfaces) will result in low (and in some cases even negative) values of TBPf. Poorly connected 2D networks (i.e., networks with many convex surfaces) will result in high values of TBPf. The size of the dilation is defined as one pixel, and the resulting change in bone area and bone perimeter is therefore resolution dependent. This means that care should be taken when results are compared between experiments, but when the resolution is kept constant the results are fully comparable. Parallel-plate model. From area and length measurements the parallel-plate model calculates thickness and separation of the bone tissue assuming the tissue is equally distributed as parallel plates.40 Tb.Th is the thickness of the plates, Tb.N is the number of plates per unit length, and Tb.Sp is the separation between the plates. The trabecular thickness (mean trabecular plate thickness) is given by: Tb.Th ⫽

2000 B.Ar 1.199 B.Pm

(3)

Here, B.Ar denotes the area of the bone phase in the ROI, and B.Pm denotes the length of the bone-marrow interface. The factor value of 1.199 was found experimentally by Schwartz and 4 Recker to be better than the value of ␲ used for structures without 44 preferred spatial orientation. The empirically found factor of 1.199 was determined using iliac crest bone biopsies, which are less anisotropic than the vertebral bone sections investigated in this study. Therefore, the factor might have to be adjusted to produce accurate measurements when investigating bone tissue from sites other than the iliac crest. The trabecular number (mean trabecular plate density) is given by: Tb.N ⫽

1.199 B.Pm 2 T.Ar

(4)

where T.Ar denotes the total tissue area inside the ROI, and trabecular separation (mean trabecular plate separation) is given by:

the MIL method quantifies the orientation of the bone surface and not the bone volume, and suggested volume orientation (VO) distribution as a volume orientation measuring technique.38 Cruz-Orive et al. developed the star volume distribution (SVD) method from the star volume measure to quantify bone and marrow volume orientation.16 Smit suggested a method for measuring the mean bone length,45 which was later referred to as the star length distribution (SLD), as it is, in essence, a simplification of the star volume distribution.37,39,45– 47 Of these three volume orientation methods, we chose to present the results of the star length distribution as the representative measure of volume orientation, as the investigation by van Rietbergen et al. found that star length distribution, when correlated with elasticity (found by a finite-element model), gave the best fit.42 Briefly, intercept lines are found in the same way as for star volume, but, instead of using random directions, 180 equally distributed known directions are used. From the set of average intercept lengths (one for each direction) a so-called fabric tensor was calculated using the orientation matrix method.30,39 Eigenvalues ␭1 and ␭2 and eigenvectors were calculated for the 2 ⫻ 2 fabric tensor. Goulet et al. defined the degree of anisotropy as25: A⫽

冑

兩␭ 1兩 兩␭ 2兩

(6)

where 兩␭1兩 ⱖ 兩␭2兩. Connectivity density. The connectivity density (CD) describes the number of branching trabeculae minus the number of free ending trabeculae per tissue volume. A free ending trabecula is a temporary phenomenon, as a “perforated” trabecula is not load bearing and will thus be removed.36 A free ending trabecula is not identical to a “terminus.” (A free ending trabecula exists in three-dimensional [3D] space, whereas a “terminus” exists only as a “free ending object” on a 2D section of a 3D object.) The connectivity density was measured using the ConnEulor principle,28 where two adjacent histologic sections (a disector) are compared to provide 3D structural information. The CD is given as28,55: CD ⫽

⌺B ⫺ ⌺H ⫺ ⌺I 2 䡠 h 䡠 ⌺T.Ar

(7)

where B is the number of branching trabeculae (“bridges”), H is the number of “holes,” I is the number of “islands” (free ending trabeculae), and h is the distance between sections (i.e., from the top of the first section in the disector pair to the top of the other section in the disector pair). In this study, h ⫽ 20 ␮m. A similar method for quantification of the topological properties of three-dimensional structures from serial sections was proposed by DeHoff et al.17 Statistics

2,000 Ma.Ar Tb.Sp ⫽ 1.199 B.Pm

(5)

The assumption that the network consists of parallel plates is not necessarily fulfilled for vertebral bone structure from aged individuals. Whether the parallel-plate model gives results that have a direct physical interpretation when the model assumption breaks down is an open question. Star length distribution. Whitehouse54 suggested the computation of trabecular orientation by use of the mean intercept length (MIL) method.14,25,50 However, Odgaard et al. argued that

Linear regression analyses were performed using the leastsquares method on linear relationships.41 In the case of power relationships, both the independent and the dependent variables were logarithmically transformed, and then linear regression was performed on the transformed data, where we have that ln y ⫽ a ln x ⫹ b is the same relationship as y ⫽ Bxa, with B ⫽ eb. In the case of an exponential relationship, only the dependent variable was logarithmically transformed. In the case of power or exponential relationships, the Pearson’s r values presented were calculated from the linear regression on the logarithmically transformed data. In case of polynomial relationships the least-

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Figure 2. Histomorphometric measures in relation to age. (A) Trabecular bone volume; (B) marrow space star volume; (C) node:terminus ratio; and (D) trabecular bone pattern factor. Filled circles: men; open circles: women; open squares: women with fractures. Regression coefficients are shown in Table 2.

squares fit was obtained using the singular value decomposition (SVD) method.41 In such cases, Pearson’s r was calculated using: r2 ⫽ 1 ⫺

␹2

(8)

N

兺 ( y ⫺ y៮ )

2

i

i⫽1

Individuals with fractures were excluded from the statistical analysis. Men and women were pooled in the statistical analysis, because the number of subjects was too small to justify separate analyses by gender. Results Age-related Changes Figure 2 shows trabecular bone volume, BV/TV (Figure 2A), marrow space star volume, V*m.space (Figure 2B), node:terminus ratio, Nd/Tm (Figure 2C), and trabecular bone pattern factor, TBPf (Figure 2D), plotted as function of age. The trabecular bone volume showed a decline with age from 15% to 7% in the age interval of 20 –90 years (r ⫽ ⫺0.81). The V*m.space increased from 40 to 300 mm3 (r ⫽ 0.82), Nd/Tm decreased from 0.31 to 0.2 (r ⫽ ⫺0.52), and TBPf increased from 2.2 to 3.8 mm⫺1 (r ⫽ 0.60) over the same age interval. It was not possible to identify the three individuals with fractures on the basis of BV/TV or V*m.space alone, as all these data points were close to the regression line. However, it can be seen that the individuals with fractures had very high TBPf values, but also that two individuals without fractures had comparable values for TBPf. Figure 3 shows mean trabecular plate thickness, Tb.Th (Figure 3A), mean trabecular plate separation Tb.Sp (Figure 3B),

anisotropy of bone space, Ab.space (Figure 3C), and connectivity density, CD (Figure 3D), plotted as a function of age. From Figure 3 it can be seen that Tb.Th showed a decrease from 100 to 87 ␮m (r ⫽ ⫺0.38), Tb.Sp an increase from 400 ␮m to 1000 ␮m (r ⫽ 0.77), Ab.space a nonsignificant increase from 1.3 to 1.4, and CD a decrease from 5.5 to 2.5 mm⫺3 (r ⫽ ⫺0.62) over the age interval 20 –90 years. It should be noted that the difference in Tb.Th between young and old individuals was not very pronounced (i.e., the slope of the regression line was low). Furthermore, the slope of the regression line for Ab.space (Figure 3C) was not significantly different from zero (p ⫽ 0.091), indicating that, over the age range studied, there was no general change of Ab.space with age. However, the resulting fit-line was nevertheless drawn. The regression coefficients for correlations between the 11 static histomorphometric measures and age are shown in Table 2. Relationships Between Histomorphometric Measures Figure 4A shows V*m.space plotted as a function of BV/TV. There was a high correlation between V*m.space and BV/TV (r ⫽ ⫺0.88). Figure 4B shows TBPf as a function of BV/TV. These two histologic measures were highly correlated, with r ⫽ ⫺0.79. Trabecular bone pattern factor is plotted against the node:terminus ratio in Figure 4C. TBPf and Nd/Tm was highly correlated through a power function (r ⫽ ⫺0.95). Figure 4D shows CD as a function of BV/TV. BV/TV and CD were correlated, with r ⫽ 0.58. Note that the two individuals with the highest values of CD (i.e., the individuals with the most complex trabecular bone structure) were women. All the static histomorphometric measures studied in this investigation were correlated. The correlation coefficients and

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Figure 3. Histomorphometric measures in relation to age. (A) Mean trabecular plate thickness; (B) mean trabecular plate separation; (C) anisotropy of the bone space; and (D) connectivity density. Filled circles: men; open circles: women; open squares: women with fractures. Regression coefficients are shown in Table 2.

the function type that gave rise to the strongest correlation for each relationship are shown in Table 3. Discussion In this study we showed that there was an age-related decline in vertebral trabecular bone density (BV/TV) from 15% to 7% in the age range 20 –90 years. Bromley et al. found a decline from approximately 20% to approximately 13% in the same age range, but their measurements also included cortical bone.9 Mosekilde Table 2. Correlation coefficients in relationships between histomorphometric variables and age Variable

r

Relation

Figure

BV/TV V*m.space V*b.space Nd/Tm TBPf Tb.Th Tb.N Tb.Sp Am.space Ab.space CD

⫺0.81 0.82 n.s. ⫺0.52 0.60 ⫺0.38 ⫺0.77 0.77 n.s. n.s. ⫺0.62

linear exponential — exponential linear linear linear exponential — — linear

2A 2B — 2C 2D 3A — 3B — 3C 3D

p ⬍ 0.05 considered significant. n.s., not significant. See text for explanations of bone characteristics (“Variable” column).

found a decline in BV/TV from 14% to 7%35; Dempster et al. from 18% to 5%18; and Grote et al. from 16% to 6%26 in this age range. Therefore, the decline in BV/TV with age found in this study is in very good agreement with the previous studies indicating BV/TV’s dependency on age over a wide age range. We found that marrow space star volume (V*m.space) increased from approximately 40 to 300 mm3 (in the interval of 20 –90 years) in the vertebral body, with a maximum value of 750 mm3. Vesterby found a change from approximately 0 mm3 to approximately 140 mm3 in the same age range,51 and Vesterby et al. found a change of approximately 0 mm3 to approximately 100 mm3 in the age range 20 –75 years.52 There was a large discrepancy between the values found in the present study and those found in the aforementioned papers.51,52 The reason for this is that the two studies by Vesterby used a much smaller (artificial) ROI and then averaged over a number of ROIs in one section, whereas we computed V*m.space using an ROI that spanned the entire section (half vertebra). We previously showed that, for bone specimens with low BV/TV (as was the case for vertebral bone section in the older age groups), the computation of V*m.space was highly dependent on the size of the ROI.49 The result of using a too-small ROI is an underestimation of V*m.space. In this study we found that the node:terminus ratio (Nd/Tm) decreased from 0.31 to 0.2 over the age interval studied. Mellish et al. and Cendre et al. reported only Nd/TV and Tm/TV, so a direct comparison with the results from the present study is not possible.10,33

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Figure 4. Relationship between histomorphometric measures. (A) Marrow space star volume as function of trabecular bone volume; (B) trabecular bone pattern factor as a function of trabecular bone volume; (C) trabecular bone pattern factor as a function of node:terminus ratio; and (D) connectivity density as a function of trabecular bone volume. Filled circles: men; open circles: women; open squares: women with fractures. Regression coefficients are shown in Table 3.

Concerning trabecular bone pattern factor, we found an increase from 2.2 to 3.8 mm⫺1 at 20 –90 years. Grote et al. found that TBPf was 1.7 mm⫺1 at the age of 20 years and 3.5 mm⫺1 at the age of 90 years.26 However, as explained in Materials and Methods, it is difficult to compare TBPf between different studies, as the TBPf measurement is inherently resolution dependent. Despite the comparison difficulties, the values of TBPf

found in our study are in accordance with the values found by Grote et al.26 We found that trabecular thickness, as determined by the parallel-plate model, decreased from 100 to 87 ␮m from 20 to 90 years of age. The belief that there is a gender-related difference in trabecular thickness due to different mechanisms in agerelated bone loss (mainly perforations for women and thinning

Table 3. Correlation coefficients r in the relationships y ⫽ f(x) between the different histomorphometric variables y variable x variable

V*m.space

V*b.space

Nd/Tm

TBPf

Tb.Th

Tb.N

Tb.Sp

Am.space

Ab.space

Connectivity density

BV/TV V*m.space V*b.space Nd/Tm TBPf Tb.Th Tb.N Tb.Sp Am.space Ab.space

⫺0.88b — — — — — — — — —

0.39b n.s. — — — — — — — —

0.76b ⫺0.52b 0.40b — — — — — — —

⫺0.79b 0.57b ⫺0.48b ⫺0.95b — — — — — —

0.60c n.s. 0.91b 0.52b ⫺0.61c — — — — —

0.91a ⫺0.93b n.s. 0.65a ⫺0.63b n.s. — — — —

⫺0.92b 0.93b n.s. ⫺0.66b 0.66b n.s. ⫺1.00b — — —

0.48d n.s. n.s. n.s. n.s. n.s. n.s. n.s. — —

⫺0.33c n.s. n.s. ⫺0.37c n.s. n.s. ⫺0.35c n.s. 0.63a —

0.58b ⫺0.69b n.s. n.s. n.s. n.s. 0.72b ⫺0.71b n.s. n.s.

The fit functions indicated are the functions that gave the highest correlation coefficients. p ⬍ 0.05 considered significant. See text for abbreviations. n.s., not significant. See text for explanations of bone characteristics. Linear relation. bPower relation. cExponential relation. dPolynomial relation.

a

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for men) cannot be addressed by this study due to the relatively small sample. However, the slope of the fit-line was barely significantly different from zero (p ⫽ 0.0323). This means that the decrease in Tb.Th with age was not pronounced. In the age range 20 –90 years, Arnold et al. found trabecular thickness to vary from approximately 160 ␮m to approximately 100 ␮m, where they measured the thickness “directly.”5 Dempster et al. found a decrease from 110 to 80 ␮m,18 and Ritzel et al. noted a decrease from approximately 140 ␮m to approximately 120 ␮m,43 where both studies used the parallel-plate model. The trabecular thickness found in this study is in good agreement with the results of Dempster et al., but smaller than the values found by Arnold et al. This discrepancy can, to some extent, be explained by the difference in the procedure for determination of the trabecular thickness. If the assumptions of the parallel-plate model are not fulfilled—that is, the structures contain many rods (seen in the sections as dots) and a few plates (seen in the sections as lines)—the length of the bone perimeter (B.Pm) will be longer for a given bone area (B.Ar) than if the structure consists entirely of plates. Equation 3 thus gives rise to an underestimation of mean trabecular thickness. In this study, where we used the parallel-plate model to estimate trabecular thickness, it was not possible to distinguish between the thickness of horizontal and vertical trabeculae. So, a comparison with studies that have conducted separate measurements on horizontal and vertical trabeculae8,34,35 is not possible. However, a comparison of trabecular separation in relation to age can be performed, and this shows very similar results (increase from approximately 400 to 1000 ␮m).34,35 We note that the high correlation found between Tb.N and Tb.Sp (r ⫽ ⫺1.00) is partly artificial, due to the fact that equations 4 and 5 contain almost identical information. A high correlation is thus to be expected. The increase in anisotropy with age was not found to be significant. However, this might be due to the relatively few subjects used in this study. A study with a greater sampling data would have the power to clarify this issue. Although the present study included too few individuals to make a formal, statistically meaningful comparison between genders, it is nonetheless striking that there seem to have been no gender-related differences in the age relationships of the histomorphometric measures. However, further studies involving more individuals are needed before a definite conclusion can be reached. Likewise, concerning the individuals with a known fracture, although there were too few individuals to make any firm conclusions, these individuals deviated surprisingly little from the fit-lines. Again, however, with a sample size of only three, this might simply be coincidental (nevertheless, this is a very interesting indication and merits further study). The present study was done in a cross-sectional manner, and caution should be taken when examining age-related changes in histomorphometric measures. Furthermore, the functional fits are valid only inside the age interval from which the data were obtained. It would therefore be incorrect to use, for example, the BV/TV-age curve below the age of 20 years. Concerning relationships between static histomorphometric measures, we have found that there was a very strong correlation between BV/TV and V*m.space (r ⫽ ⫺0.88) in vertebral trabecular bone, which is very similar to what we found previously in iliac trabecular bone (r ⫽ ⫺0.91).49 We also found BV/TV and TBPf to be highly correlated through a power relationship (r ⫽ ⫺0.79). This is in agreement with the results of Amling et al., where a nonlinear relationship between BV/TV and TBPf was found with 兩r兩 ⫽ 0.76 for control subjects and 兩r兩 ⫽ 0.81 for osteoporotic subjects.3 However,

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Grote et al. found the relationship between BV/TV and TBPf to be linear, with 兩r兩 ⫽ 0.80 for individuals ⬍45 years and 兩r兩 ⫽ 0.76 for individuals ⬎45 years.26 In this study, we found that the histomorphometric measure that correlates best with the connectivity density is the mean trabecular plate density (Tb.N) (r ⫽ 0.72). This is in contrast to what we found previously in the iliac crest, where the histomorphometric measure that correlated best to connectivity density was trabecular bone volume.49 This difference could be explained by the overall structure of the vertebral and iliac trabecular bone; that is, the vertebral trabecular bone is closer to fulfilling the assumption of parallel plates than is the trabecular structure of the iliac crest. We can conclude from our investigation into the relationships between the histomorphometric measures of the iliac crest49 and the vertebral body that it is generally not possible to use one of the investigated histomorphometric measures as a generic substitute for connectivity density. The correlations are too dependent on the type of cancellous bone under investigation. The present study applied an image-acquisition technique that is new in connection with bone histomorphometry. The combination of aniline blue staining and a high-quality transparent image scanner is an efficient and fast method for acquiring high-resolution images of almost unlimited size (the size of the image scanner and the amount of available computer memory set the upper limits for the image size) and, to the best of our knowledge, this study is the first to correlate several histomorphometric measures with each other in human vertebral cancellous bone. Nevertheless, the present work has several limitations and shortcomings: (i) the number of individuals was too small to be able to investigate gender-related differences; (ii) the number of individuals with fractures was too low to draw any conclusions concerning differences in histomorphometric measures between vertebrae with fractures and vertebrae without fractures; and (iii) a comparison with compressive strength of whole lumbar vertebral strength and trabecular bone strength would be needed to establish how well the histomorphometric measures correlate with bone strength, and whether any of the histomorphometric measures can increase the predictive power of bone density on vertebral bone strength. In conclusion, we found the histomorphometric values in this study to be in excellent accordance with the various previously published results concerning human trabecular vertebral bone, with the sole exception being marrow space star volume, but this is probably due to the small (artificial) ROIs that were used in the earlier studies. Acknowledgments: The authors gratefully acknowledge the employees of the Department of Pathology, Odense University Hospital, and the Department of Forensic Medicine, Odense University, for collecting the specimens. Birthe Gylling-Jørgensen and Inger Vang Magnussen are gratefully acknowledged for their assistance in preparing the histologic sections. Gøsta Dam Jensen is acknowledged for his assistance in making the special devices for serial section staining. Michael Hewitt is gratefully acknowledged for revising this manuscript. The investigation was supported by the Danish Medical Research Council (No. 9503020).

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Date Received: December 17, 1999 Date Revised: February 21, 2000 Date Accepted: March 8, 2000