comparison of eight histomorphometric methods for measuring trabecular bone architecture by image...

Comparison of Eight Histomorphometric Methods forMeasuring Trabecular Bone Architecture by Image Analysison Histological SectionsDANIEL CHAPPARD,1 ERICK LEGRAND,2 CHRISTIAN PASCARETTI,2 MICHEL F. BASLE,1AND MAURICE AUDRAN2

1LHEA Laboratoire d’Histologie-Embryologie, CHU and Faculte de Medecine,49045 Angers Cedex, France2Service de Rhumatologie. CHU d’Angers, 49033 Angers Cedex, France

KEY WORDS: image analysis; bone; stereology; fractal geometry; connectivity; bone architec-ture; mathematical morphology; osteoporosis; male osteoporosis

ABSTRACT Osteoporosis is defined as a disease characterized by low bone mass and microarchi-tectural deterioration of trabecular bone leading to enhanced bone fragility. Various histomorphomet-ric methods have been described to measure bone architecture on histological sections. However, notall of the methods are strictly equivalent and some of them appear able to detect differences earlierin the course of the disease. We have compared 8 histomorphometric methods known to characterizethe architecture of trabecular bone in 154 male osteoporotic patients. Measurements were done ontransiliac bone biopsies: Trabecular number, thickness, and separation (Tb.N, Tb.Th, Tb.Sp);Trabecular Bone Pattern Factor (TBPf); Euler-Poincare’s number (E); Interconnectivity Index (ICI);strut analysis of the trabecular network with the ratio of nodes/free-end (N/F); star volume of thebone marrow (V*m.space) and trabeculae (V*Tb) and the Kolmogorov fractal dimension of the trabecularboundaries (D). Relationships between the various architectural parameters were studied byhierarchical cluster analysis. Linear, hyperbolic, and exponential correlations were found betweentrabecular bone volume (BV/TV) and architectural parameters. Cluster analysis demonstrates thelink between these architectural parameters. ICI, E, and TBPf, which reflect the amount ofopen/closed marrow cavities clustered together and appeared related to Tb.Sp, V*m.space which areindicators of the mean size of marrow cavities. Tb.Th, V*Tb and N/F flocked together as they reflectthe trabecular size. Tb.N and D segregated together and seemed to best describe the trabecularnetwork complexity. These histomorphometric techniques are correlated but correlations may belinear or nonlinear. Several histomorphometric techniques need to be used in parallel to appreciatethe pathophysiological mechanisms of osteoporotic states. Microsc. Res. Tech. 45:303–312, 1999.r 1999 Wiley-Liss, Inc.

INTRODUCTIONOsteoporosis is a widely prevalent disorder observed

in both genders. About 200 million people worldwideare supposed to be affected (Griffin, 1990). According torecent consensus conferences held in Hong Kong (1993)and Amsterdam (1996), osteoporosis is presently de-fined as a ‘‘disease characterized by a low bone massand microarchitectural deterioration of bone tissue,leading to reduced strength and enhanced bone fragil-ity’’ (Anonymous, 1991; Peck et al., 1993). Clinically,osteoporosis is associated with an increased risk ofvertebral and long bone fractures. Due to such aconsiderable health care cost, it is important to identifysubjects with increased risk for future fractures. Manyprospective studies have established a strong associa-tion between low bone mass and increased fracture risk(Cummings et al., 1993; Marshall et al., 1996; Melton etal., 1993). Dual energy X-ray densitometry (DXA) isactually recognized as the most valuable noninvasivemethod to measure bone mineral density (BMD). Inwomen, the risk of osteoporotic fracture increases byone and a half- to three-fold for each standard deviationdecrease of BMD (Cummings et al., 1993; Marshall et

al., 1996). For men, some studies indicate that the riskof fragility fractures increases as BMD declines but thestrength of this relation appears to be lower thanreported in women (Kanis et al., 1994). In addition,there is a considerable overlap in the BMD measure-ment between control and fractured patients. BMDalone does not completely explain the fracture risk andit is likely that factors other than bone mass can play akey role. Other noninvasive physical techniques suchas QCT (quantitative computer tomography) or MRI(magnetic nuclear imaging) have been proposed for theassessment of the skeletal status (Genant et al., 1996).However, they suffer from high costs and they expose tohigh ionizing radiation doses. Ultrasound measure-ments have been proposed to investigate bone qualitybut poor understanding of what is being measured bybroadband attenuation and speed of sound is still anopen question.

*Correspondence to: Daniel Chappard, MD, PhD, LHEA Laboratoired’Histologie-Embryologie, Faculte de Medecine, 49045 Angers Cedex, France.e-mail: [email protected]

Received 20 May 1998; accepted in revised form 15 January 1999

MICROSCOPY RESEARCH AND TECHNIQUE 45:303–312 (1999)

r 1999 WILEY-LISS, INC.

Normal trabecular bone is a natural biomaterial thatis constituted by a honeycomb network of trabeculae.Trabeculae are of two types: vertical or curved platesconnected by pillars (Parfitt et al., 1983). An increasedosteoclastic activity and/or a decreased osteoblasticactivity appear able to reduce bone mass similarly buttrabecular architecture can be altered in various ways(Kleerekoper et al., 1985). It has been now recognizedthat perforations of plates, rupture of connecting pil-lars, or thinning of trabeculae may occur in variousetiologies of osteoporosis. Postmenopausal osteoporosishas been well documented but male osteoporosis hasnot received the same interest (Chappard et al., 1996;Kleerekoper, et al., 1985). Several authors have tried toinvestigate trabecular architecture on bone biopsies byhistomorphometric techniques. Former studies in-cluded measurements of trabecular thickness and den-sity but they did not provide any information on theconnectivity of the network (Birkenhager-Frenkel etal., 1988; Parfitt, 1983). Recently, a great interest hasrisen for the quantitative description of the trabeculararchitecture of osteoporotic patients. In addition, newstereological methods are now available to providevaluable information on the connectivity of trabecularbone and branching complexity. However, several ofthem are time-consuming, tedious, or require specialsophisticated microscopical devices making them unus-able in routine laboratory practice (Thomsen et al.,1996; Vesterby, 1993). With the development of imageanalysis, several techniques can be adapted to modernsystems. In our laboratory, eight different stereologicalmethods were computed and used in a single home-made program. The aims of the present study were (1)to investigate if one technique is sufficient to character-ize trabecular architecture, and (2) to elucidate therelationships between these various morphometric pa-rameters.

MATERIALS AND METHODSBone Biopsies

One hundred and fifty-four biopsies obtained fromosteoporotic male patients have been selected for analy-sis. The age of the patients ranged from 19 to 79 years(mean 51.37 6 12.86 years). They had been admitted inthe department of rheumatology because they hadsuffered from vertebral crush fractures or because ameasure of bone density by DXA had shown a low bonedensity (lumbar T-score less than 3 standard deviations[SD]). Transiliac bone biopsies were obtained underlocal anesthesia, 2 cm below the iliac crest and 2 cmbehind the antero-superior iliac spine. The trephine

had a 7.5-mm internal diameter according to Frostrecommendations; it provides a large bone core suitablefor analysis since displacement and disruptions oftrabeculae are avoided (Frost, 1976). Similar bone coresare now prepared worldwide in the same way in allhistomorphometric laboratories; they comprise a cancel-lous surface area ranging from 60 to 112 mm2 depend-ing on the patient’s morphology (Recker, 1983). Speci-mens were processed undecalcified as previouslydescribed (Chappard et al., 1987, 1988). Patients wereincluded in the present study whatever the suspectedorigin of the osteoporosis. The series includes idio-pathic, alcoholic, corticosteroid-treated, and mastocyto-sis-related osteoporosis. For each patient, four nonse-rial sections (7µm thick, separated by 100µm) weredone, parallel to the long axis of the bone core. Onlypatients having a complete bone biopsy (i.e., with twocortices and no artefactual disruption of the trabecularnetwork) were included in the study. No attempt wasdone to perform inter-group comparisons because thestudy focused on the relationships between histomor-phometric techniques.

Image AnalysisThe following abbreviations used hereafter to de-

scribe histomorphometric parameters have been pro-posed by the ASBMR committee (Parfitt et al., 1987).The symbols used to describe image analysis tech-niques will refer to Serra’s nomenclature (Serra, 1982).The histomorphometric analysis was done on a LeicaQuantimet Q570 image processor. The system isequipped with a CCD camera (Sony 930P), which isable to digitize images in a 512 x 512 pixel raster in 256gray levels. The analyzer can store 24 gray images,coded on 8 bits and 24 binary images; in addition, fivecolored bitplanes are used as overlays. Numerous math-ematical morphology functions are available throughan image-oriented language derived from the MicrosoftQBasic housed in a 486 PC compatible. Bone sectionsare placed on an X-ray light box after adjusting theillumination for uniformity across the light box (shad-ing process). A digitized image of a complete section isstored in the gray image processor at a magnification ofx6. After interactive thresholding, a binary image of thebony component is obtained. Artifacts created duringthe surgical and histotechnological steps are elimi-nated by both automatic and interactive procedures.Two lines are drawn manually on the binary imagefrom one cortex to the other in order to limit the upperand lower boundaries of the section. The trabecularnetwork is then disconnected from the endosteal sur-faces by an interactive procedure (Fig. 1). Basic histo-morphometric measurements can be obtained such ascortical thickness, cortical porosity, bone core width.Throughout this paper, the set Y will refer to the binaryimage of the cancellous space and is composed of ypixels, X is the set of trabeculae composed of x pixelsand the following relationships are X , Y; Xc is thecomplementary set of X in Y and represents the marrowspaces in such a way that Xc < X 5 Y and Xc > X 5 Ø.Trabecular bone volume (BV/TV) is derived from mea-surements of bone area (B.Ar is measured as the sum ofx pixels) and cancellous tissue area (T.Ar measured as

Abbreviations

X set of pixels in a binary imagex one pixel of the set XXc the complementary set of XS(X) the skeleton of XX the boundary set of XØ the empty setX< Y union of set X and set YX > Y intersection of set X with set YX ,Y the set X is included in set Yx [ X the pixel x belongs to X5a6 structuring element! dilatation of an image

304 D. CHAPPARD ET AL.

the sum of y pixels)

BV/TV 5 100 p B.Ar/T.Ar (1)

The following methods were computed to estimatethe spatial distribution of trabeculae, their connectivityand complexity.

Trabecular Thickness, Number, and Separa-tion. These parameters were derived from trabeculararea and perimeter (B.Ar and B.Pm) according toParfitt’s formulae (Parfitt, 1983).

Tb.Th 5 1.199 p B.Ar/2/B.Pm (2.1)

The factor 1.199 used for correcting section obliquitywas experimentally found to be better adapted totrabecular bone architecture at the ilium than 4/p.Trabecular number (Tb.N expressed in /mm) and tra-becular separation (Tb.Sp expressed in µm) were calcu-lated assuming that trabecular bone can be modellizedaccording to the parallel plate and bar model.

Tb.N 5 Tb.Ar p 10/Tb.Th (2.2)

Tb.Sp 5 1000/Tb.N 2 Tb.Th. (2.3)

Trabecular Bone Pattern Factor (TBPf). Thismethod was proposed by Hahn at al. (1992) and is

Fig. 1. a: Binary image of a transiliac bone biopsy after threshold-ing for bone tissue, elimination of debris, and separation of corticalbone (black) from trabecular bone (gray). In this picture, bone volume(BV/TV), trabecular thickness and densities are derived from measure-ments of trabecular area and perimeter. b: Determination of Euler-Poincare’s number The enclosed medullar cavities are identified indark-gray, trabeculae surrounding them are gray and the discon-nected trabeculae are black. c: Determination of the interconnectivityindex of marrow spaces after skeletonization The ‘‘trees’’ are black, thefree branches are dark-gray and the nodes are identified as s. d: Strutanalysis of the trabecular network after skeletonization The nodes areidentified as W, the node-to-node struts are black, the node-to-free-endstruts are dark gray, the free-end-to-free-end struts are light-gray, thecortical struts are middle-gray. e: The star volume of marrow spacesmeasured by the chord distribution method. A grid of parallel lines

with a 5 p/4 5 45° is intersected with the medullary spaces. Thelength of each chord is measured in this direction and so with gridswith angle a ranging from 0 to 2p. f: The star volume of trabeculaemeasured by the chord distribution method A grid of parallel lineswith a 5 2p/3 5 120° is intersected with the medullar spaces Thelength of each chord is measured in this direction and so with gridswith angle a ranging from 0 to 2p. g: The fractal dimension methoddetermined by the box counting algorithm. A chessboard-like grid ofdark-gray boxes and one of light-gray boxes (with e 5 2 pixels as sidelength) are intersected with the trabecular perimeter. The number ofsquare boxes is determined as N(2) 5 Ndark-gra boxes (2) 1 Nlight-gray boxes (2).h: The grids are now composed of boxes with e 5 16 pixels as side lengthThe number of square boxes is determined N(16) 5 Ndark-gray boxes (16) 1Nlight-gray boxes (16).

305TRABECULAR BONE ARCHITECTURE IN OSTEOPOROSIS

mainly based on the use of mathematical morphology inimage analyzer systems (Hahn et al., 1992). The ratio-nale of the method is supported by the observation thatin a well-connected structure, the concave surfaces areabundant; whereas convex surfaces are more numerousif the structure is disconnected. After acquisition of agiven binary image Y and determination of B.Ar andB.Pm, a dilatation of Y is performed (Y ! 5a6) where 5a6 isan octogon used as structuring element. The newvalues of bone area and perimeter (noted B.Ar2 andB.Pm2) are measured. TBPf is defined as:

TBPf 5 (B.Pm 2 B.Pm2)/(B.Ar 2 B.Ar2) (3)

In other words, when a trabecular network is highlydisconnected, the convex surfaces are increased and thedilatation process increases the perimeter drastically whilethe area is only moderately affected. This provides lowvalues of TBPf in a well-connected network and high valueswhen marked disconnection of trabeculae is present.

Euler-Poincare’s Number. The method consists incounting the number of enclosed medullar cavities andconnected trabeculae (Fig. 1b) (Compston, 1994). Thecardinal of X represents n, the total number of (discon-nected) trabecular profiles. Automatic recognition of

closed marrow cavities is obtained by a filling holeprocedure on X = X8. So X8 > X provides a set X88 , Xc

corresponding to marrow cavities whose cardinal is m.The Euler-Poincare’s number is simply obtained as:

E 5 n 2 m. (4)

The more connected the trabecular network, the lessis E. Negative values can be obtained in highly con-nected systems. E needs to be adjusted to T.Ar.

Interconnectivity Index (ICI). The method wasoriginally proposed by Le et al. (1992) to describe theconnectivity of porous biomaterials, such as corals, thatwere used as bone grafts. When applied to trabecularbone, connectivity of the marrow cavities can be appre-ciated by taking the skeletons of their profiles (i.e., thecentroids of maximal open discs included in the profile)(Fig. 1c). The algorithm works by thinning Xc. Since theskeletonization process is very sensitive to local varia-tions of the profile boundaries, which produce undesir-able dendrites, the skeleton was pruned using a condi-tional algorithm. Briefly, the terminal ends and thebranching nodes of the skeleton were identified andreconstruction allowed the elimination of the shortestbranches (less than 20µm). On the reconstructed skel-

Fig. 1. (Continued.)


eton S(Xc), the total number of nodes (N), node-to-nodebranches (NN), and node-to-free-end branches (NF)were determined. The number of ‘‘trees’’ (T) was alsoobtained, a tree being the structure composed of inter-connected node(s) with node-to-node and/or node-to-free-end branch. The interconnectivity index (ICI) of thebone marrow cavities is then defined as:

ICI 5 (N p NN)/(T p (NF 1 1)) (5)

Thus, the higher the level of connectivity of the marrowcavities (given by a high number of nodes and segmen-tal branches associated with a low number of trees), thehigher the ICI and, conversely, the higher the fragmen-tation of the bone trabecular network.

Characterization of the Trabecular Network.Assessment of trabecular connectivity using this methodhas been reported using manual or computed tech-niques based on image analysis (Mellish et al., 1991). Inour approach, X is skeletonized and pruned with thesame algorithms as described for ICI determination.On the skeleton of the trabeculae S(X), nodes, free-end,and the various types of trabeculae were characterizedand measured: node-to-node struts, node-to-free-endstruts,free-end-to-free-end struts, and cortex struts.Core boundary struts were not considered for measure-ment. Each type of strut is stored in a different overlaybinary plane of the image analyzer and allocated to adifferent color thus providing a visual characterizationof the whole trabecular network (Fig. 1d). In order toobtain a single parameter for easy handling, the node tofree-end ratio was determined (N/F) (Compston et al.,1987).

Star Volume of Marrow Spaces. Star volume ofmarrow spaces (V*m.space) was determined by the chorddistribution method described by Levitz and Tchoubar(1992) for porous glasses or cements. The method canbe summarized as follows: a series of grids were com-puted with parallel lines running with various angles a:p, p/2, p/3, p/4, p/6, 2p/3, 3p/4, and 5p/6. Each grid isstored on the hard disk and can be used as an image Za,which can be transferred to the binary planes of theimage analyzer when necessary. For each angle a, theintersection of Za with the binary image composed ofthe profiles of the marrow cavities is done. Thus, Za >Xc provides a set of linear segments (called chords)superimposed on the marrow spaces (Fig. 1e). Thecubed length of each chord 10

3 is then computed on thewhole section for a given a. In the same way, sets ofchords are obtained with each grid, so that all direc-tions from a 5 0 to 2p are explored very rapidly. Finally,all the cubed lengths of the chords in every a (Fig. 1e)are used in the calculation of the star volume:

V*m.space 5 p/3 p 103 (6)

Star Volume of Trabeculae. The measurement ofthe star volume of trabeculae (V*tb) is obtained in thesame way by superposition of the grids with the binaryimage of the trabeculae X (Fig. 1f).

Kolmogorov Fractal Dimension of the Trabecu-lar Network. On an histological bone section, thetrabecular perimeter can occupy a differing area of theplane due to folding, branching, etc. The fractal dimen-sion of the trabecular network can be measured by the

‘‘box counting method’’ applied on the image of thetrabecular boundaries X. A grid Ze composed of squareboxes (with e pixels as side length) and mimicking achess-board is over-imposed on the histological imageand X > Ze is obtained. The cardinal of this set, N1(e)corresponds to the number of boxes intersected with thetrabecular boundaries (Cross, 1994). The complemen-tary chess-board grid Ze

c is then used to count N2(e) in asimilar way after X > Ze

c. So N(e) 5 N1(e) 1 N2(e)representing the smallest number of boxes of side erequired to cover completely the trabecular boundariesreflects the perimeter examined with a e scale ratio.This step is repeated with e varying for 2 to 100 pixels(Fig. 1f,g) and data were plotted on a log-log graph (i.e.,log 5N(e)6against log 5e6). The relationship between pointsis measured by linear regression analysis using theleast square method. Because all dots are not aligned,the selection of valuable dots disposed on a straight linesegment was done with a probabilistic algorithm. Alloutliner points $ or # to one standard deviation withan a risk ,0.05 % were eliminated. The slope D of theregression line corresponds to the Kolmogorov fractaldimension.

For each parameter, the value obtained by averagingresults of the four sections was considered. The determi-nation of the fractal dimension and Euler-Poincare’snumber were obtainable in 103 patients only.

Statistical AnalysisStatistical analysis was performed using the Systatt

statistical, software release 6.0.1. All results are ex-pressed as mean 6 standard deviation. Correlationswere searched between parameters: linear correctionanalysis used Pearson’s r based on the model y 5 ax 1 bwhere y is the dependent variable and x the predictorvariable. When nonlinear relationships between twovariables appeared evident on graphic examination,polynomial (in x2 and x3), logarithmic (model: y 5 a .log (x) 1 b), hyperbolic (model: y 5 a 1 1/(b . x), andexponential (model: y 5 a . exp (b.x)) relationships werecomputerized. Finally, a multivariate procedure fordetecting groupings in variables was used. Clusteranalysis was done between all variables after standard-ization of data (i.e., providing an overall level andvariation comparable across measurements).

RESULTSThe histogram frequency of BV/TV in the present

series of male osteoporotic patients appears in Figure 2.It is noticeable that only 92 out of the 154 patientspresented a BV/TV under 14%, which corresponds tothe spontaneous vertebral crush threshold defined byMeunier and coworkers (Meunier et al., 1973).Thesepatients were of the same age as the 67 ones withBV/TV above 14% (respectively, 49.6 6 11.2 years vs.52.6 6 13.7 years). No relationship could be foundbetween age and BV/TV (r 5 0.14).

Relationships Between BV/TV and ArchitecturalParameters

Table 1 illustrates the coefficients of correlation be-tween BV/TV and the architectural variables. For eachparameter, the best-fitted coefficient of correlation isindicated. A linear correlation was found with severalhistomorphometric parameters (e.g., Tb.Th, Tb.N, E,


N/F) (Fig. 3). Non linear relationships were foundbetween BV/TV and other architectural descriptorssuch as D, star volumes, ICI, and Tb.SP. Exponential orhyperbolic regressions were found to best describethese relationships (Fig. 4).

Interrelationships Between ArchitecturalParameters

Table 2 illustrates the matrix of correlation betweenarchitectural variables. Here again linear and nonlinear correlations were observed. Some relationshipsappear very strong such as N/F and ICI or Tb.N and D.

Cluster Analysis of Architectural ParametersThe analysis provides a tree with a unique ordering

in which every branch is lined up so that most similarvariables are closest to each other (Fig. 7). Variablesdescribing the same architectural characteristics ap-pear in the same cluster while variables exploringdissimilar ones appear in other clusters. In the presentstudy, variables measuring the same architectural angleappeared highly related: e.g., Tb.Th and V*Tb.

1. One can see that ICI, TBPf, and E form a firstcluster; these parameters reflect the amount ofclosed/open marrow cavities on the histological sec-

tions. This cluster is very rapidly joined by a branchcomposed of Tb.Sp and V*m.space, two parameters thatmeasure the mean size of marrow cavities. The linkamong these five parameters is very strong asevidenced by the short distance reached before com-bining in a single branch.

2. Another cluster is evidenced by a combination ofTb.Th and V*Tb, which are descriptors of the trabecu-lar dimensions. They are joined by N/F which alsoreflects the size of the trabecular struts.

3. Tb.N and D are joined and reflect the complexity ofthe trabecular network. Tb.N is not really a numberof trabeculae but reflects the probability for a testline to cross a trabecular profile on the section. Inthe same way, the fractal dimension is linked to the

Fig. 2. Histogram frequency of BV/TV in154 male osteoporotics. Note that 42% of thepatients have a BV/TV higher to 14% (arrow)corresponding to the spontaneous vertebralfracture threshold.

TABLE 1. Relationships between bone volumeand architectural parameters

rBest fitmodel P

Tb.Th (µm) 0.69 linear ,0.0001†Tb.N (/mm) 0.56 linear ,0.0001†Tb.Sp (µm) 0.78 hyperbolic ,0.0001†TBPf 0.85 exponential ,0.0001E 0.56 linear ,0.0001ICI 0.58 exponential ,0.0001N/F 0.76 linear ,0.0001V*m.space 0.70 hyperbolic ,0.0001V*Tb 0.50 exponential ,0.0001D 0.76 hyperbolic ,0.0001

†The relationships with these parameters are biased (see discussion in the text).

Fig. 3. Linear relationship between BV/TV and Tb.Th.


ability for the trabecular perimeter to fill up thesection area.

This cluster, describing the complexity, joins thesecond one describing the unit elements of the network.One can see that union of cluster 2 and 3 rapidly joinscluster 1 describing the marrow subpart of the biopsy.

DISCUSSIONThe intimate trabecular bone mass and microarchitec-

ture are determined by functional loads, which are theresultant of both muscular tensions and gravity. Accord-

ing to Wolff’s trajectorial law, trabecular plates have a3D arrangement parallel with the resultant tensilelines (Turner, 1992). Although low bone mass is animportant determinant of bone fragility, it is not thesole one and it has been suggested that the quality ofbone may play a role in the ultimate strength of theskeleton. There are also other predictors of fractures,such as the geometric properties of bone (hip axislength, cross-sectional area), the risk of falls, and thefall severity (Cummings et al., 1995; Faulkner et al.,1993). Bone quality comprises at least three parts (1)the nature of the organic and mineral phases of thematrix, (2) the structure (i.e., the molecular organiza-tion of either woven or lamellar), and (3) the microarchi-tecture (i.e., the arrangement of the matrix as a well-connected scaffold of plates and pilars.

Scanning electron microscopy, a powerful tool toexplore the 3D microarchitecture of bone, is not usefulin routine practice (Boyde and Jones, 1996; Whitehouseet al., 1971). The need to clean bone and removemedullar cells prior to analysis limits the diagnosticinterest of this technique for clinical purposes. Recon-struction of the 3D trabecular network from serialhistological sections has been proposed by our groupand others to investigate some metabolic bone diseasesbut the method is time-consuming and does not providequantitative results (Chappard et al., 1991; Nigg et al.,1997). Reconstruction of the 3D microarchitecture bymicroCT scans appears to be a very interesting ap-proach (Muller et al., 1996; Odgaard and Gundersen,1993). Algorithms for direct measurement of 3D connec-tivity are under development but this technology ispresently limited by the cost of the hardware (Odgaard,1997; Parfitt, 1983; Smit et al., 1997). Recent data haveshown that 3D analysis will certainly supplant 2Dmeasurements for research purposes. However, severalcomparatives studies have reported that several 2Dand 3D measurements are well correlated (Kazama et

Fig. 4. Hyperbolic relationship between BV/TV and V*m.space.

Fig. 5. Linear relationship between TbTh and D (Fractal dimen-sion).

Fig. 6. Hyperbolic relationship between N/F and ICI.


al., 1998; Odgaard and Gundersen, 1993). Before the1980s, little attention was paid by histomorphometriststo trabecular architecture; bone volume, estimated by

BV/TV, was the most used parameter. Then, trabecularmorphology was conventionally described on the basisof microscopic inspection or by direct measurement of

TABLE 2. Interrelationships between architectural parameters

Tb.Th

Tb.N † Tb.N

Tb.Sp † 0.79§exponential Tb.Sp

TBPf 0.67linear

0.66linear

0.69linear TBPf

E 0.53exponential NS NS 0.77

linear E

ICI 0.38log

0.44exponential

0.49linear

0.82linear

0.64hyperbolic ICI

N/F 0.51linear

0.43linear

0.46linear

0.82linear

0.83hyperbolic

0.82hyperbolic N/F

V*m.space NS 0.76log

0.81linear

0.79linear NS 0.54

linear0.53

exponential V*m.space

V*Tb0.80

linear NS NS 0.69linear

0.45linear NS 0.41

linear NS V*Tb

D NS 0.81linear

0.83linear

0.66linear NS 0.46

linear0.45

linear0.58

linear NS

†The relationships with these parameters are biased (see discussion in the text). NS 5 non significant with any method. In all results mentioned with P , 0.0001, theabsolute values of the coefficient of correlation are provided.

Fig. 7. Cluster analysis of architecturalparameters.


the width of trabecular profiles (Aaron et al., 1985;Birkenhager-Frenkel, et al., 1988). Several histomorpho-metric parameters were derived from trabecular areaand perimeter measurements (i.e., trabecular thick-ness, density, and separation) (Parfitt, 1983; Parfitt etal., 1983). Correlations between bone volume and theseparameters were found to be linear but were somewhatbiased, since all parameters were derived from thesame basic measurements as shown in equations 1 to2.3 (Chappard et al., 1988; Kleerekoper et al., 1985;Weinstein and Hutson, 1987).

Recently, several histomorphometric techniques basedon Euclidean geometry have been reported to measuretrabecular connectivity (Compston, 1994). Other tech-niques such as fractal analysis have also been appliedto measure the complexity of trabecular bone (Fazzalariand Parkinson, 1996; Weinstein and Majumdar, 1994).Many biological objects observed in nature are typicallycomplex, irregular in shape, roughness, or branching.They possess a remarkable invariance under changes ofthe scale of magnification and are often referred to asself-similar objects. They can incompletely be describedby Euclidean geometry. The fractal geometry is becom-ing increasingly popular in biology to describe complexobjects such as cell boundaries, vascular patterns, orrespiratory trees (Cross, 1994, 1997; Mandelbrot, 1983).Profiles of bone trabeculae can also be described byfractal geometry (Cross, 1997; Fazzalari and Parkin-son, 1996; Weinstein and Majumdar, 1994).

By using several of these histomorphometric meth-ods, we were able to characterize the microarchitec-tural changes associated with corticosteroid-inducedosteoporosis in the male (Chappard et al., 1996). Wehave reported nonlinear correlations (either exponen-tial, logarithmic, or hyperbolic) between BV/TV andseveral architectural parameters in this particular typeof male osteoporosis. This was also confirmed in an-other series of osteoporotic patients (Legrand et al.,1996, 1997) and by other groups (Croucher et al., 1996;Thomsen et al., 1998). The same findings were encoun-tered in this large cohort of male osteotoporotics. How-ever, some parameters such as N/F and Euler-Poin-care’s number are linearly correlated with BV/TV. Ourresults suggest that a hyperbolic correlation was foundto best fit BV/TV and D (r 5 0.76, the linear coefficientbeing at 0.71). A linear correlation was described byFazzalari and Parkinson (1996). The exponential rela-tionships between BV/TV and connectivity parametersand the fact that fractures seemed more frequent ingroups of patients with the more altered 3D parametersconfirm the important role played by bone architecturein bone strength (Aaron et al., 1985; Kleerekoper et al.,1985; Legrand et al., 1997). When the relationshipsbetween these architectural parameters themselvesare considered, nonlinear relationships are also fre-quently observed but it is not a general rule. This couldexplain the discrepancies observed between connectiv-ity descriptors: some of them can be more early alteredthan others according to the causes of the osteoporosisas previously shown (Chappard et al., 1996).

The cluster analysis was performed on the eightarchitectural descriptors in this large cohort of maleosteoporotic patients to understand the links betweenthese parameters. Cluster analysis is a multivariateprocedure for detecting the natural groupings in data

(Tuckey, 1997). Because the eight methods provideresults in various order of magnitude, data were stan-dardized before computing (i.e., results were put on acommon scale). Three groups of clusters can be identi-fied: one describing the size of the trabeculae (Tb.Th,N/F, and V*Tb), one describing the medullar cavities (ICI,E, Tb.S, TBPf, and V*m.space), and the latter correspond-ing to the branchings of trabeculae (Tb.N and D). Allclusters are finally regrouped over a short distance,confirming their relative interdependence. Results ob-tained in this large series of patients are very similar tothose described in a preliminary study based on fifty-five osteoporotics (Chappard et al., 1997).

In osteoporotic states, the trabecular network can bealtered in various ways: deep resorption lacunae causedby hyperactive osteoclasts may perforate plates orremove entirely thin trabecular rods, the apposition ofbone structure units with a reduced width may lead to aprogressive thinning of trabeculae. In addition, themechanisms may combine in the natural course of thedisease. These pathophysiological mechanisms havebeen elucidated in a variety of bone diseases: e.g.,post-menopausal osteoporosis (Kleerekoper et al., 1985;Parfitt, 1983; Vedi et al., 1996), primary hyperparathy-roidism (Parisien et al., 1990); alcoholic osteoporosis(Chappard, et al., 1991); corticosteroid-induced osteopo-rosis (Chappard et al., 1996; Dempster, 1989); andfluoride therapy (Zerwekh et al., 1997). It is now clearthat a limited loss of bone volume (appreciated byBV/TV) can be accompanied by microarchitecturalchanges that may reduce strength to a greater extentthan it would suggest (Silva and Gibson, 1997). Archi-tectural characteristics are now taken into account inbiomechanics equations, and computer simulations haveconfirmed the importance of minute alterations of thenetwork upon bone strength (Jensen et al., 1990; Siffertet al., 1996). In routine clinical practice, several histo-morphometric techniques must be used in parallel toexplore the various components of the trabecular bonearchitecture and to explore the pathophysiologicalmechanisms of bone loss in a given patient.

ACKNOWLEDGMENTSThe authors thank Mrs. Nadine Gaborit and Isabelle

Gaudry for technical assistance.

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