The three-dimensional structure of trabecular bone ... - ResearchGate

Timothy M. Ryan* 

Department of Anthropology, 

The University of Texas at 

Austin, Austin, Texas 78712, 

U.S.A. Email: 

tmryan@duke.edu 

Richard A. Ketcham 

Department of Geological 

Sciences, The University of 

Texas at Austin, Austin, 

Texas 78712, U.S.A. Email: 

ketcham@mail.utexas.edu 

Received 30 October 2001 

Revision received 

28 January 2002 

and accepted 29 January 

2002 

Keywords: trabecular bone, 

high resolution X-ray 

computed tomography, 

strepsirrhines. 

The three-dimensional structure of 

trabecular bone in the femoral head of 

strepsirrhine primates 

It has been hypothesized for over a hundred years that trabecular 

bone plays an important structural role in the musculoskeletal system 

of animals and that it responds dynamically to applied loads through 

growth. The objectives of this study are to quantify the threedimensional 

structure of femoral head trabecular bone in a sample of 

extant strepsirrhines and to relate patterns of interspecific variation to 

locomotor behavioral differences. The bone volume fraction (BV/TV) 

and fabric anisotropy of trabecular bone in the femoral heads of 

Cheirogaleus major, Avahi laniger, Galago senegalensis, Galago alleni, 

Loris tardigradus, Otolemur crassicaudatus, and Perodicticus potto were 

quantified in three dimensions using serial high-resolution X-ray 

computed tomography scan data. A volume based method was used 

to quantify the structural anisotropy in three cubic samples located 

inside the central portion of the femoral head. Significant structural 

differences were found between the predominantly leaping galagines 

and indriids and the nonleaping lorisines and cheirogaleids. The 

leapers in general have relatively anisotropic trabecular bone. The 

galagines display a unique pattern of decreasing bone volume and 

increasing anisotropy moving from the superior to the inferior half of 

the femoral head. By contrast, the nonleaping taxa possess relatively 

uniform and isotropic bone throughout the femoral head. The 

differences in femoral head trabecular structure among these taxa 

seem to be related to locomotor behavioral differences, reflecting 

variation in the use and loading of the hip joint during normal 

locomotion. 

2002 Published by Elsevier Science Ltd. 

Journal of Human Evolution (2002) 43, 1–26 

doi:10.1006/jhev.2002.0552 

Available online at http://www.idealibrary.com on 

Introduction 

Locomotor behavior and the loads produced 

during locomotor activity are important 

factors determining the structure and form 

of the bony skeleton. Research focused on 

the morphology and structure of long bone 

joints and diaphyses has demonstrated the 

relationships among morphology, locomotor 

behaviors, and the loads engendered during 

particular behaviors (Burr et al., 1982; 

Schaffler et al., 1985; Burr et al., 1989; 

*Current address: Duke University Primate Center, 

Division of Fossil Primates, 1013 Broad Street, 

Durham, North Carolina 27705, U.S.A. 

Demes & Jungers, 1989, 1993; Ruff, 1989; 

Demes et al., 1991; Ruff & Runestad, 

1992; Runestad, 1997). Relatively little 

work, however, has been focused on either 

the structure or the variation in trabecular 

bone in primates and other mammals and its 

relationship to other morphological and 

locomotor differences (Ward & Sussman, 

1979; Oxnard & Tang, 1981; Thomason, 

1985; Rafferty & Ruff, 1994; Oxnard, 1997; 

Rafferty, 1998; Swartz et al., 1998; 

Macchiarelli et al., 1999; Fajardo & Müller, 

2001). 

Trabecular bone consists of a complex, 

interconnected network of bony rods and 

0047–2484/02/070001+26$35.00/0 2002 Published by Elsevier Science Ltd.

2 T. M. RYAN AND R. A. KETCHAM 

plates with a variable three-dimensional 

arrangement throughout the skeleton. It was 

Meyer, working with the engineer Culmann 

in 1867, who first noted a relationship 

between trabecular bone morphology and 

skeletal loads, and Wolff later expanded on 

these ideas, postulating a direct mathematical 

relationship between bone form and skeletal 

loads (Hayes & Snyder, 1981; Roesler, 

1981, 1987). Many subsequent studies have 

provided good evidence of the structural and 

mechanical importance of trabecular bone 

(Lanyon, 1974; Hayes & Snyder, 1981; 

Radin et al., 1982; Carter et al., 1989; 

Biewener et al., 1996). Histomorphometric 

methods have been used on both histologic 

sections and, more recently, on highresolution 

X-ray computed tomography 

(HRXCT) scans to determine the exact 

structure of trabecular bone in two and three 

dimensions (Odgaard, 1997). Much of this 

work has been conducted to understand the 

mechanisms of age- and disease-related 

bone loss in humans, and has demonstrated 

the relationship of architectural components, 

such as anisotropy and volume fraction, 

to the mechanical and structural 

behavior of trabecular bone (Van Rietbergen 

et al., 1995, 1996). 

Interspecific structural variation in 

trabecular bone in primates and other mammals 

indicates that some differences in 

trabecular structure can be related to 

locomotor behavioral differences (Ward & 

Sussman, 1979; Oxnard & Yang, 1981; 

Thomason, 1985; Rafferty & Ruff, 1994; 

Oxnard, 1997; Rafferty, 1998; Swartz et al., 

1998; Macchiarelli et al., 1999; Fajardo & 

Müller, 2001). Most notably, Oxnard & 

Yang (1981; Oxnard, 1997) used optical 

fourier transforms to assess differences in 

the trabecular structure in the lumbar vertebrae 

of hominoids. They found that relatively 

fine-scale behavioral differences could 

be resolved and that the trabecular structure 

corresponded to the inferred loading 

patterns of different locomotor behaviors. 

Rafferty (1998) analyzed the trabecular 

structure in the femoral neck of a broad 

range of primates and found that taxa 

engaging in significant climbing behavior 

possess trabeculae distributed relatively 

evenly throughout the neck. By contrast, 

those taxa engaging in quadrupedal and 

leaping behaviors have trabecular bone arising 

mainly from the inferior neck, reflecting 

the more predictable loading conditions 

engendered during these behaviors. Fajardo 

&Müller (2001) found important structural 

differences in the femoral neck trabecular 

bone between various primate taxa with 

different locomotor behaviors using 

HRXCT data. 

The most important aspect of these comparative 

studies is that they have related 

interspecific differences in trabecular structure 

to locomotor and functional differences 

on both large scales (e.g., suspensory versus 

quadrupedal: Rafferty, 1998) and small 

scales (e.g., among Pongo, Pan, and Gorilla: 

Oxnard & Yang, 1981). With the exception 

of the work by Fajardo & Müller (2001), 

studies of trabecular bone variation across 

primates have not attempted to quantify the 

anisotropy, connectivity, or exact structure 

of trabecular bone in either two or three 

dimensions. Traditional methods of quantifying 

trabecular bone structure have 

required destructive thin sectioning of bone 

specimens. However, recent technological 

advances in computed tomography now 

allow for nondestructive access to the internal 

morphology of specimens of any size 

(Flannery et al., 1987; Feldkamp et al., 

1989; Denison et al., 1997; Fajardo & 

Müller, 2001; Ryan, 2001). 

The purpose of the present study is to 

quantify the three-dimensional structure of 

trabecular bone in the femoral head of several 

small strepsirrhine primates. The work 

of Rafferty & Ruff (1994) on trabecular 

density in the femoral head of catarrhine 

primates suggests that articular surface area 

and internal trabecular morphology are

FEMORAL HEAD TRABECULAR STRUCTURE 

3 

Table 1 

Taxonomic sample 

Taxon 

n 

Body mass 

(g)* 

Locomotion† 

Avahi laniger 4 1175 Vertical clinging and leaping 

Cheirogaleus major 3 400 Quadrupedalism 

Galago alleni 2 273 Vertical clinging and leaping 

Galago senegalensis 10 283 Vertical clinging and leaping 

Loris tardigradus 10 267 Slow quadrupedalism/climbing 

Otolemur crassicaudatus 12 1150 Quadrupedalism, some leaping 

Perodicticus potto 11 1230 Slow quadrupedalism/climbing 

*Body sizes taken from Smith & Jungers (1997). 

†Locomotor behaviors taken from Walker (1969), Crompton (1984), Glassman & 

Wells (1984), Gebo (1987), Nash et al. (1989) and Oxnard et al. (1990). 

independent of one another. Their findings 

suggest that the external structure is driven 

mainly by the mobility demands of the joint, 

and that the underlying trabecular architecture 

is largely determined by the magnitude 

and orientation of the loads passing through 

the joint. Because the internal and external 

morphology of the femoral head are determined 

by both weight-bearing and mobility 

demands, the femoral head represents a 

good element to use for investigations of the 

structure and function of trabecular bone. It 

is proposed here that the three-dimensional 

architecture of trabecular bone in the proximal 

femur, including its anisotropy and density, 

is correlated with the loads engendered 

in the hip joint during specific locomotor 

behaviors. 

Materials and methods 

Data collection and image processing 

The taxa used in this study are listed in 

Table 1. Skeletal specimens were obtained 

from the American Museum of Natural 

History (New York), the National Museum 

of Natural History (Washington), the Peabody 

Museum of Natural History (Yale), 

and the Museum of Comparative Zoology 

(Harvard). All were wild-shot adults with no 

apparent pathologic conditions. One femur 

from each individual was selected for scanning 

based on availability and condition. 

There are two main size groups within the 

sample and the locomotor behaviors cover a 

series from specialized leapers (G. senegalensis, 

G. alleni, A. laniger) through occasional 

leapers (O. crassicaudatus) and generalized 

quadrupeds (C. major) to slow climbers and 

suspensory forms (L. tardigradus, P. potto) 

(Walker, 1969, 1979; Crompton, 1984; 

Glassman & Wells, 1984; Gebo, 1987; Nash 

et al., 1989; Oxnard et al., 1990). Because 

sex data were not available for all of the 

individuals in the sample and the taxa are 

monomorphic, both sexes were pooled for 

the current analysis. Despite the monomorphism, 

however, the increased calcium 

demands on the female skeleton during various 

stages of life history present another set 

of variables affecting skeletal structure and 

the levels of intraspecific variation. These 

factors are not addressed in the current 

study. 

All specimens were scanned at the High- 

Resolution X-ray Computed Tomography 

Facility at the University of Texas at Austin 

(UTCT; http://www.ctlab.geo.utexas.edu). 

The details of HRXCT are covered by 

Flannery et al. (1987) and Ketcham & 

Carlson (2001). HRXCT scanners operate 

on the same principles as conventional 

medical computed axial tomography (CAT) 

scanners, and produce analogous data.


HRXCT employs higher-energy X-rays to 

penetrate denser material, and small X-ray 

focal spot and detector sizes to increase 

resolution to


5 

Figure 1. Anatomical terminology used in the current paper. 

especially in animals with distinctly divergent 

femoral head morphologies such as galagines, 

lorisines, cheirogaleids, and indriids. Nevertheless 

it is important at least to attempt to 

develop systematic VOI selection methods 

that can produce volumes that are generally 

homologous in size and location across different 

individuals. Anatomical terminology is 

potentially confusing when applied exclusively 

to the femoral head without reference 

to other features. The terminology used here 

for describing the selection of VOIs and for 

referring to the VOIs is detailed in Figure 1. 

The human terms ‘‘superior’’ and ‘‘inferior’’ 

are used to refer to the position in the femoral 

head relative to the long axis of the femur. 

The human terminology was deemed to be 

least confusing of those available even though 

it is not the most appropriate for nonhuman 

primates. 

Prior to extracting the VOIs, each femoral 

head dataset was rotated so that all femora 

were oriented in the same way. Each femur 

was rotated so that the posterior surface was 

oriented towards the top of the image, the 

anterior surface towards the bottom, the 

medial to the right, and the lateral to the left. 

The amount of rotation necessary for each 

femur was calculated in Adobe Photoshop 

using the mid-line slice within the femoral 

head in the superoinferior axis. This image 

was manually rotated until the posterior 

surface was aligned parallel with the top 

edge of the image. Once the degrees of 

rotation were determined for each femur, 

the batch processing function in Photoshop 

was used to reorient all of the images for 

each femur in the sample. 

Three separate VOIs were extracted 

for the current study. The first was one 

large VOI defined as a cubic volume in the 

center of the femoral head. This central 

cubic volume was defined based on three 

measured femoral head dimensions: (1) the 

maximum anteroposterior breadth, (2) the 

maximum mediolateral breadth, and (3) 

the maximum superoinferior height. From 

these measurements a central point was 

determined. First, the CT slice that 

represented the superoinferior midpoint of 

the femoral head was determined. On this 

slice, lines were superimposed in the


Figure 2. VOI selection method. (a) The large central cubic volume is positioned so that its center lies at 

the intersection of the superoinferior, mediolateral, and anteroposterior planes inside the femoral head. 

The smaller cubic subsamples have an edge length equal to 75% of the edge length of the large central 

cube and are centered inside the large cube. (b) Shown are the positions of the two cubic subsamples (gray 

boxes) and the large central cube (white box) within the femoral head of a potto. The superior and inferior 

cubic subsamples are positioned within the head so that they share the superoinferior mid-line section as 

their bottom-most and top-most slice, respectively. The subsample cubes extend superiorly (white arrow) 

and inferiorly beyond the extents of the large cube. 

mediolateral and the anteroposterior directions 

[Figure 2(a)]. These lines were placed 

along the mid-line of the perpendicular 

dimension. The intersection of the lines 

represented the central point of the femoral 

head. This point also represented the center 

of the cubic VOI. 

Once the central point was found, the 

cubic VOI was determined. The side length 

of the cube was defined as 50% of the length 

of the shortest of the three measured dimensions 

which was usually the mediolateral 

breadth. Adobe Photoshop was used to extract 

the square cross-sections making up the 

cube from each slice. Using a batch processing 

function, it was possible to extract precisely 

sized and perfectly aligned sections 

from each slice with a set of pre-recorded 

processing actions. This procedure produced 

a series of square cross-sections representing 

a perfect cube with equal pixel 

dimensions and slice numbers. 

Two other cubic VOIs were extracted 

from each femoral head. These volumes 

were smaller than the large central cube and 

represented superior and inferior subsamples 

of the head [Figure 2(b)]. The superior 

and inferior subsamples shared the 

superoinferior mid-line as their inferior-most 

and superior-most slice, respectively. These 

cubes had an edge length equal to 75% of 

the edge length of the large central cube and 

were also centered on the mid-point of the 

large central cube. The subsample cubes incorporated 

some of the same volume as the 

large cube, but also extended both superiorly 

and inferiorly past the region encompassed 

by the central cube. These superior and 

inferior subsamples were used to explore 

the variation in trabecular structure across 

the femoral head. The VOI selection techniques 

employed here produced roughly homologous 

cubic VOIs from each individual. 

The cubic VOIs generated from these steps 

represented three cubes of trabecular bone 

occupying the same amount of relative 

space within the femoral head of each 

specimen.


7 

Three-dimensional measurement of trabecular 

bone structure 

Trabecular structure was quantified in three 

dimensions on each of the extracted VOIs 

using software developed at UTCT called 

QUANT3D. The QUANT3D software is written 

in the Interactive Data Language (IDL) 

v.5.3 (Research Systems, Inc.) and implements 

several commonly-used fabric 

anisotropy quantification techniques. 

The threshold value between bone and air 

within each individual’s large cubic VOI was 

calculated using the iterative method of 

Ridler & Calvard (1978) and Trussell 

(1979). In this method, for each iteration 

the mean grayscale values above and below a 

proposed threshold are calculated, and the 

mean of these two values is proposed as the 

threshold for the next iteration. Iteration 

continues until a stable solution is found. 

A more detailed discussion of this method, 

its application to HRXCT data, and its 

justification is provided in the Appendix. 

Using the cubic VOIs extracted from the 

femoral heads, the bone volume fraction and 

structural anisotropy were quantified from 

segmented three-dimensional reconstructions 

of the HRXCT scan data. The fabric 

characteristics of trabecular bone were 

quantified using a volume based technique 

known as the star volume distribution 

(SVD). SVD describes the distribution of 

material around a typical point in a structure. 

Intercept lengths are determined for 

each of some number of orientations 

through a point lying in bone (Figure 3). 

The intercept is the longest uninterrupted 

‘‘line’’ lying entirely within bone at a particular 

orientation. The determination of 

these intercept lengths is performed on some 

number of randomly positioned points lying 

within bone. This process is illustrated 

in Figure 3 for the two-dimensional 

situation using six orientations and two 

points. A fabric tensor is derived from the 

star volume distribution data using a 

weighted orientation matrix method. Three 

Figure 3. The SVD method shown in two dimensions. 

The white areas are trabecular bone and the black areas 

are marrow space. The gray radial ‘‘stars’’ demonstrate 

how intercept lengths are measured at several orientations 

at random points within the bone phase. L is the 

length of the longest intercept that lies entirely within 

bone at this particular orientation. The current study 

utilized 1000 random points and 1000 random orientations 

at each point. 

eigenvalues, τˆ1, τˆ2, τˆ3, and three eigenvectors, 

û 1 , û 2 , û 3 , describing the distribution 

of material are derived from the fabric 

tensor. The SVD and weighted orientation 

matrix methods as well as their application 

to trabecular bone studies were outlined by 

Cruz-Orive et al. (1992), Karlsson & Cruz- 

Orive (1993), and Odgaard et al. (1997). 

The calculation of the SVD and the use 

of the orientation matrix method are 

summarized in detail in the Appendix. 

Using the QUANT3D program, intercept 

lengths were measured for 1000 random 

orientations at 1000 random points lying 

within the bone phase for each VOI. The 

orientations were randomly distributed 

within a sphere with 0φ2π and 0sin 

θ1. The eigenvalues were used to calculate 

several indices of anisotropy. The 

degree of anisotropy (DA) was calculated as 

the primary eigenvalue divided by the 

tertiary eigenvalue (τˆ1/τˆ3). Benn (1994) 

defined two indices to describe fabric 

shape in sedimentary rock that are generally


Table 2 

Parameter 

Trabecular bone structural parameters 

Degree of anisotropy (DA) 

Isotropy index (I) 

Elongation index (E) 

Bone volume fraction (BV/TV) 

Equation 

useful for description of any fabric. The 

isotropy index, I, is the inverse of the DA as 

calculated above and the elongation index, 

E, is calculated as 1(τˆ2/τˆ1). Using these 

three indices it is possible to describe 

trabecular bone fabric characteristics across 

different individuals and to compare among 

the taxa. Bone volume fraction (BV/TV) was 

determined from each of the cubic volumes 

as the number of bone voxels divided by the 

total number of voxels. The equations used 

to calculate the fabric and bone volume 

fraction parameters used in the current 

study are summarized in Table 2. 

Statistical analyses were used to assess the 

significance of the results for BV/TV and 

DA using SPSS Release 10.0.5 for Windows 

(SPSS Inc.). Mann–Whitney U-tests were 

used in the comparison of results between 

each possible paired combination of species 

for each of the three cubic VOIs. Because 

the superior and inferior cubic subsamples 

were not independent, Wilcoxon Signed 

Ranks tests were used to compare the paired 

results for these samples within each species. 

Results 

HRXCT data 

Differences in the arrangement of trabecular 

bone across the femoral head from the 

superior half to the inferior half are clearly 

evident from the HRXCT scan data. Figure 

4 shows representative HRXCT scans for 

each species. Shown are three slices for each 

specimen: the mid-slice is at the mid-line of 

the superoinferior dimension, the superior 

slice is the top-most slice of the large central 

cubic sample, and the inferior slice is the 

bottom-most slice of the central cube. 

Quantitatively, differences are apparent 

between the arrangement of trabecular bone 

in the leaping and nonleaping species. The 

superior portion of the femoral head in all 

taxa is apparently relatively isotropic in at 

least the mediolateral/anteroposterior plane. 

The fabric characteristics for the leaping 

taxa change in the inferior half of the head, 

appearing much more anisotropic than the 

analogous regions in the nonleaping taxa. 

These apparent superoinferior structural 

differences are evident from the quantitative 

structural results. 

Test patterns 

Prior to analyzing three-dimensional 

trabecular bone structure in QUANT3D, several 

test patterns with known structural features 

were analyzed to assess the efficacy of 

the computer code. Tests were run to evaluate 

the software’s ability to correctly quantify 

BV/TV and anisotropy. In addition to 

these structural tests, a ‘‘sampling density’’ 

test of the effects of increasing numbers of 

points and orientations was run. 

BV/TV values were verified with several 

tests involving either synthetic data created 

with known BV/TV values or actual data in 

which BV/TV was determined by other 

means. Three three-dimensional test structures 

were used to assess the anisotropy 

quantification method. The basic unit 

for all three structures was a bar with 

square cross section and an 11:1 aspect 

ratio. In the first test the data consisted 

entirely of parallel bars, and yielded a DA 

value of 304·2 and an E value of 0·997, 

indicating as expected high anisotropy and 

elongation. The second test consisted


9 

Figure 4. Transverse cross-sectional HRXCT scans from the femoral heads of the six genera used in the 

current study. The superior slice is the top-most slice of the large central cube and the inferior slice is the 

bottom-most slice of the large central cube. The scale is 5 mm in each image. (a) Galago senegalensis; (b) 

Loris tardigradus; (c) Cheirogaleus major; (d)Otolemur crassicaudatus; (e) Perodicticus potto; (f) Avahi laniger. 

of beams crossing orthogonally in a set of 

parallel planes (i.e., a stacked set of 2D 

grids), resulting in a DA value of 137·6 and 

an E value of 0·002, indicating high anisotropy 

and no elongation. The third test consisted 

of beams in all three orthogonal directions 

in a three-dimensional grid, and 

resulted in a DA value of 1·06 and an E 

value of 0·007, correctly reflecting an isotropic 

structure. 

One Perodicticus potto cubic sample was 

used to test the effects of point and orientation 

numbers on the calculated DA values. 

The DA obtained for this cubic sample 

using 1000 random points and 1000 random 

orientations was 3·20. Doubling the 

number of points and orientations used 

resulted in a DA of 3·17, a difference of less 

than 1%. These results coupled with the fact 

that the 1000–1000 point and orientation


Table 3 

Summary statistics for bone volume fraction (BV/TV) 

Taxon n Mean S.D. CV Min Max 

Large cubic volume 

Avahi laniger 4 0·414 0·0534 12·90 0·354 0·465 

Cheirogaleus major 3 0·454 0·0197 4·35 0·441 0·477 

Galago 12 0·507 0·0342 6·76 0·459 0·553 

Loris tardigradus 10 0·415 0·0506 12·20 0·328 0·482 

Otolemur crassicaudatus 12 0·487 0·0226 4·65 0·447 0·523 

Perodicticus potto 11 0·448 0·0522 11·60 0·347 0·532 

Superior subsample 

Avahi laniger 4 0·443 0·0562 12·70 0·374 0·505 

Cheirogaleus major 2* 0·467 0·115 24·70 0·385 0·548 

Galago 12 0·542 0·0478 8·82 0·468 0·627 


Otolemur crassicaudatus 11† 0·562 0·0502 8·93 0·466 0·664 


Inferior subsample 

Avahi laniger 4 0·445 0·0618 13·90 0·388 0·516 


Galago 12 0·453 0·0630 13·90 0·328 0·559 




*Three Cheirogaleus specimens were scanned and used in the large VOI analyses. Due to some slight damage to 

one of these specimens in an area outside of the large cubic VOI but within the superior cubic subsample, only two 

were used for the subsample VOI analyses. 

†Twelve Otolemur specimens were scanned and used in the large VOI analyses. Due to some slight damage to 

one of these specimens in an area outside of the large cubic VOI but within the cubic subsamples, only eleven were 

used for the subsample VOI analyses. 

pairing is typical even for larger human 

specimens (Odgaard, 1997; Odgaard et al., 

1997) leads us to conclude that the use of 

1000 points and 1000 orientations is sufficient 

to accurately capture the structural 

features of trabecular bone for both the large 

and small specimens in the present sample. 

Bone volume fraction 

Summary statistics for BV/TV for each 

species used in this study are given in Table 

3. Due to the small sample size of G. alleni 

(two individuals) and the similarity in body 

size and locomotor behavior to G. senegalensis, 

these two taxa were pooled into one 

group for the purposes of this study. In the 

large central cube, Galago and Otolemur 

have the highest BV/TV and Loris and Avahi 

have the lowest. The results of Mann– 

Whitney U-tests for each paired species 

comparison are shown in Table 4. There are 

significant differences in BV/TV between 

each of the two galagine species and the 

other taxa. In addition, there is a significant 

difference between the mean BV/TV of 

Galago and Perodicticus. There appears to be 

no significant scaling component to BV/TV 

in these taxa. 

The superior subsample shows a similar 

trend with the galagines having the highest 

BV/TV, Loris the lowest, and the other taxa 

distributed between (Table 3). Both Perodicticus 

and Loris are significantly different 

from the galagines (Table 4). Avahi falls 

closer to the lorisines than to the galagines 

and is significantly different from Galago 

and Otolemur. The inferior subsample 

reflects a different trend in the BV/TV. The 

taxa are all much more similar, but the trend 

within the data is reversed. Among all the


11 

Table 4 

Results of Mann–Whitney U-tests for bone volume fraction (BV/TV) 

Taxon 

Avahi 

laniger 

Cheirogaleus 

major 

Galago 

Loris 

tardigradus 

Otolemur 

crassicaudatus 


Avahi laniger — 

Cheirogaleus major ns — 

Galago 2·789** 2·021* — 

Loris tardigradus ns ns 3·297*** — 

Otolemur crassicaudatus 2·547* 2·021* ns 3·363*** — 

Perodicticus potto ns ns 2·585** ns 1·969* 




Galago 2·547* ns — 

Loris tardigradus ns ns 3·824*** — 

Otolemur crassicaudatus 2·742** ns ns 3·732*** — 

Perodicticus potto ns ns 2·467* ns 2·856** 




Galago ns ns — 

Loris tardigradus ns ns ns — 

Otolemur crassicaudatus ns ns ns 2·183* — 

Perodicticus potto ns ns ns ns 2·988** 

*P


Table 5 

Summary statistics for degree of anisotropy (DA) 

Taxon n Mean S.D. CV Min Max 


Avahi laniger 4 3·65 1·61 44·2 1·46 5·31 

Cheirogaleus major 3 2·23 0·134 5·98 2·12 2·38 

Galago 12 2·90 0·753 26·0 2·02 4·34 


Otolemur crassicaudatus 12 2·85 1·01 35·3 1·84 4·89 



Avahi laniger 4 3·46 0·511 14·8 2·77 3·91 


Galago 12 2·19 0·662 30·2 1·26 3·32 





Avahi laniger 4 6·11 6·06 99·2 2·21 15·1 


Galago 12 4·17 1·35 32·3 1·92 7·35 




*Three Cheirogaleus specimens were scanned and used in the large VOI analyses. Due to some slight damage to 

one of these specimens in an area outside of the large cubic VOI but within the superior cubic subsample, only two 

were used for the subsample VOI analyses. 

†Twelve Otolemur specimens were scanned and used in the large VOI analyses. Due to some slight damage to 

one of these specimens in an area outside of the large cubic VOI but within the cubic subsamples, only 11 were 

used for the subsample VOI analyses. 

In this superior cubic subsample, Perodicticus 

actually has a higher mean DA than all of 

the other taxa except Avahi. 

In contrast to the superior cubic subsample, 

the inferior cubic subsample shows 

significant differences between the slowclimbing 

lorisines and the more leaping taxa. 

Loris has the lowest mean DA and is significantly 

different from Avahi, Galago, Otolemur, 

and Perodicticus. Although Perodicticus 

is not significantly different from Otolemur,it 

is significantly different from Galago. Cheirogaleus 

has relatively isotropic bone with a 

DA falling in the lorisine range. One interesting 

result to note is that for Avahi the 

mean DA is much higher than the mean DA 

for the other taxa. This result is mainly due 

to one of the four individuals having a very 

high DA value (15·10). Removing this outlier 

results in a mean of 3·11. This Avahi 

individual appears to possess more plate-like 

trabeculae in the inferior half of the femoral 

head which may be the main factor driving 

the significantly higher DA value. These 

results suggest that trabecular arrangement 

in Avahi laniger may be unusually variable 

between specimens. 

There does not appear to be any scaling 

effect on DA in these taxa for any of 

the three cubic VOIs. The DA values for the 

two smallest taxa fall on opposite ends of 

the spectrum, with Galago having one of the 

highest DA values and Loris having the 

lowest. Galago has DA values that are higher 

than both Perodicticus and Otolemur in the 

large and the inferior cubic samples. These 

relationships demonstrate that body size 

appears to be a relatively unimportant factor 

driving trabecular bone fabric anisotropy 

among these taxa.


13 

Figure 5. Comparison of species mean bone volume fraction values for superior and inferior cubic 

subsamples. The number above each pair of columns represents an index of the inferior subsample bone 

volume fraction divided by the superior subsample bone volume fraction. Asterisks denote results of 

Wilcoxon Signed Ranks tests with the following significance levels: *P


Table 6 

Results of Mann–Whitney U-tests for degree of anisotropy (DA) 

Taxon 

Avahi 

laniger 

Cheirogaleus 

major 

Galago 

Loris 

tardigradus 

Otolemur 

crassicaudatus 





Loris tardigradus ns ns 3·033** — 

Otolemur crassicaudatus ns ns ns 2·572** — 

Perodicticus potto ns ns ns 3·239*** ns 




Galago 2·547* ns — 

Loris tardigradus 2·687** ns ns — 

Otolemur crassicaudatus 2·872** ns ns ns — 

Perodicticus potto ns ns ns ns 2·003* 





Loris tardigradus 2·687** ns 3·693*** — 

Otolemur crassicaudatus ns ns ns 3·521*** — 

Perodicticus potto ns ns 3·200*** 2·958** ns 

*P


15 

Figure 6. Comparison of species mean degree of anisotropy values for superior and inferior cubic 

subsamples. The number above each pair of columns represents an index of the inferior subsample degree 

of anisotropy divided by the superior subsample degree of anisotropy. Asterisks denote results of Wilcoxon 

Signed Ranks tests with the following significance levels: *P


Figure 7. Primary (τˆ1) vs. tertiary (τˆ3) eigenvalues for superior cubic subsample. (a) Avahi laniger; 

Cheirogaleus major; Galago; Loris tardigradus; Otolemur crassicaudatus; Perodicticus potto. Open 

polygonal boxes surrounding Galago and Loris and closed polygonal boxes enclosing Otolemur and 

Perodicticus. 

assessed along with the differences between 

taxa. 

The different degrees of intraspecific variation 

in the two parameters suggests that 

there are potentially important differences 

between individuals in the use and loading 

of the hip joint during locomotion. The high 

intraspecific variation in bone volume fraction 

within Loris and Perodicticus suggests 

differences in the magnitudes of the loads 

engendered in different individuals. Such a 

situation might be expected in animals with 

a more irregular locomotor pattern as used 

by the lorisines. The fabric anisotropy 

appears to vary relatively more within the 

galagines, perhaps reflecting dissimilarities 

in the positioning of the femur during a leap 

that consequently affect the orientation of 

the loads acting on the femoral head. Otolemur 

has a very high coefficient of variation in 

the inferior cubic sample, according well 

with the presumed variability in their 

locomotor behavior across and within 

individuals. 

The sample sizes were relatively small for 

Cheirogaleus and Avahi, but the results from 

the current study suggest that variation in 

the trabecular structures within each of 

these taxa is similarly high. The degree of 

anisotropy values for the two Cheirogaleus 

individuals examined for the cubic subsample 

analysis reveal an interesting trend in 

trabecular structure. One individual has a 

superior degree of anisotropy value of 2·62 

and an inferior degree of anisotropy value of 

1·52, while the other individual has degree 

of anisotropy values of 1·60 and 2·87 for 

superior and inferior degree of anisotropy, 

respectively. The two individuals, therefore, 

show the exact opposite trends in trabecular 

anisotropy in the superior and inferior halves 

of the femoral head. Such variability could


17 

Figure 8. Primary (τˆ1) vs. tertiary (τˆ3) eigenvalues for inferior cubic subsample. Symbols as in Figure 7. 

Open polygonal boxes surrounding Galago and Loris and closed polygonal boxes enclosing Otolemur and 

Perodicticus. 

be the result of variation in the locomotor 

behavior of individuals and could reflect 

fine-scale differences in the use of the 

hindlimb by particular animals. 

Similarly, variability within Avahi is probably 

quite high considering that one out of 

the four individuals displayed a unique 

trabecular pattern in the inferior femoral 

head with a degree of anisotropy value of 

15·1 as compared to 7·60 in the superior 

half of the head. Unfortunately, no information 

is available on the sex of this particular 

individual and aside from the unique 

trabecular pattern, there appears to be no 

other features distinguishing this specimen 

from the other Avahi in the sample. 

The high within-species variability 

observed here can be interpreted as a reflection 

of the mechanical significance of 

trabecular structure. Fine-scale structural 

differences between individuals suggest a 

tight association among the threedimensional 

trabecular architecture, the 

external mechanical loadings, and the locomotor 

behaviors of animals. Alternatively, 

the high intraspecific variation could also 

indicate that different primates are capable 

of behaving in similar ways (e.g., leaping, 

bridging) with very different trabecular 

structures. There seems to be no doubt that 

trabecular bone plays a significant structural 

role in the skeletal system and that its 

structure is influenced at least in part by 

the mechanical loads it experiences (Van 

Rietbergen et al., 1996; Odgaard et al., 

1997; Ulrich et al., 1999), but several other 

factors could contribute to the intraspecific 

variability in trabecular structure including 

sex, age, ontogeny, and locomotor individuality. 

No data were available on the sex of 

many of the individuals used in the current 

study so this factor was not considered. The 

potential importance of sexual dimorphism 

in trabecular structures should not be 

underestimated. The physiological stresses 

of pregnancy and nursing, differences in diet


Figure 9. Ternary shape diagram of isotropy index (τˆ3/τˆ1) and elongation index (1(τˆ2/τˆ1)) for the 

superior cubic subsample. Symbols as in Figure 7. Open polygonal boxes surrounding Galago and Loris 

and closed polygonal boxes enclosing Otolemur and Perodicticus. 

and resource utilization between males and 

females, and divergent locomotor frequencies 

all may contribute to intraspecific 

variation. In addition, because adult 

trabecular structure is the result of ontogenetic 

processes, developmental and agerelated 

differences in locomotion, habitat 

preference (e.g., size of preferred supports), 

and diet may be important factors contributing 

to the observed interindividual 

differences. 

Interspecific variation in trabecular structure 

Trabecular structure also shows significant 

interspecific variation. The most interesting 

difference between taxa is in the pattern of 

trabecular bone within a single individual’s 

femoral head. Lorisines display a more uniformly 

isotropic distribution across the femoral 

head from the superior to the inferior 

half while galagines have a relatively isotropic 

structure superiorly and a distinctly 

more anisotropic structure inferiorly. Significant 

differences between the trabecular 

architectures of the leaping galagines and 

the more quadrupedal and suspensory 

lorisines suggest that trabecular bone is 

significantly influenced by the unique 

loading conditions of particular locomotor 

behaviors. 

The two galagine species share a distinct 

pattern of trabecular arrangement within the 

femoral head, suggesting that leaping locomotion 

and the specific loads produced during 

leaping may be important factors driving 

the observed differences in bone structure. 

The trabecular bone in the central superior 

region of the femoral head is relatively isotropic 

and shows no real distinction from the 

trabecular structure of the lorisine taxa. In 

addition the superior region of the head has 

a high bone volume fraction in contrast to 

the lower values evident in the lorisines. 

Moving inferiorly in the head, though, the


19 

Figure 10. Ternary shape diagram of isotropy index (τˆ3/τˆ1) and elongation index (1(τˆ2/τˆ1)) for the 

inferior cubic subsample. Symbols as in Figure 7. Open polygonal boxes surrounding Galago and Loris and 

closed polygonal boxes enclosing Otolemur and Perodicticus. 

trabecular pattern in Galago and Otolemur 

becomes significantly less dense and more 

anisotropic. 

By contrast to the trabecular patterns in 

the galagines, the nonleaping lorisines have 

a more uniform and relatively isotropic distribution 

and arrangement of trabecular 

bone in the femoral head. The relatively 

uniform, isotropic trabecular architecture 

accords well with the types of loads that 

might be experienced during locomotion in 

these taxa. The slow quadrupedal, climbing, 

and suspensory behavior of the lorisines 

should produce a relatively diverse set of 

loads on the femoral head with a less 

stereotypical pattern than that found in 

animals that leap, leading to more isotropically 

distributed trabecular bone. 

Despite the overall similarities in the 

pattern of trabecular structure, there are 

some significant and interesting differences 

between Loris and Perodicticus in the structure 

of the femoral head trabecular bone. 

Loris has significantly more isotropic 

trabecular bone in the femoral head than the 

potto, especially in the inferior half of the 

head. Loris has the lowest degree of anisotropy 

values of all the taxa in the study and is 

significantly lower in both the central cubic 

volume and the inferior cubic subsample 

than Perodicticus, Otolemur, and Galago. Loris 

also has a significant increase in bone volume 

fraction from the superior to the inferior 

half of the head, a pattern not present in 

the larger-bodied lorisine. Perodicticus displays 

the same uniform, relatively isotropic 

trabecular pattern as Loris, but it is not as 

significantly isotropic inferiorly as Loris. The 

degree of anisotropy values for potto overlap 

significantly in the inferior portion with 

those of Otolemur and although both have 

different trabecular patterns within the


femoral head, there is no significant difference 

between the two in the degree of 

anisotropy in the inferior half of the head. 

Avahi presents an interesting case 

because this taxon appears to have certain 

features linking it to the leaping galagines 

and others that suggest a more lorisine or 

nonleaping trabecular pattern. Avahi has a 

relatively low bone volume fraction across 

the entire femoral head and does not display 

the decrease in bone volume fraction 

evident in the galagines. Leaving aside the 

one Avahi individual whose inferior 

trabecular bone is very anisotropic, Avahi 

shows a more uniform trabecular distribution 

from the superior to the inferior 

portion of the head similar to the pattern 

evident in the nonleaping lorisines. The 

mean degree of anisotropy for superior and 

inferior cubic samples in Avahi, however, 

are relatively high and are higher 

than in either Loris or Perodicticus. The 

ternary shape diagrams also show that 

Avahi displays a relatively uniform trabecular 

architecture throughout the femoral 

head. All four individuals plot in the same 

general region of the graphs for both the 

superior and the inferior subsamples unlike 

the lorisines and galagines which switch 

positions in the superior and inferior 

graphs. Avahi has a relatively uniform 

trabecular structure throughout the femoral 

head with low bone volume fraction and an 

anisotropic pattern. The overall arrangement 

of trabeculae, therefore, is distinct 

from both the leaping galagines and the 

slow quadrupedal lorisines. 

It is not clear exactly what either the 

intraspecific or interspecific variation in 

trabecular structure suggests about the 

mechanical design of the femoral head in 

these taxa. Little is currently known about 

the loads experienced at the hip joint during 

locomotion in these or any other mammalian 

taxa so conclusions regarding the 

structural and mechanical importance of 

the different trabecular structures is not 

presently possible. The experimental and 

theoretical work establishing a direct correlation 

between the fabric and bone volume 

characteristics and the elastic properties 

of particular trabecular bone specimens 

(Goulet et al., 1994; Odgaard et al., 1997; 

Kabel et al., 1999; Ulrich et al., 1999) provides 

a framework within which to consider 

some of the results of the current study. The 

intra- and interspecific variation in the 

trabecular architecture of the femoral head 

imply significant differences in the magnitudes 

and orientations of loads in the 

femoral head during locomotion both across 

individuals and across taxonomic groups. 

The shift in structure from the superior to 

the inferior half of the femoral heads of 

Galago and Otolemur suggests that unique 

loading conditions are at work in these taxa 

which could be related to loads produced 

during leaping locomotion. The high 

volume fraction and isotropic structure 

superiorly and the significantly anisotropic 

structure inferiorly in galagines suggests that 

loads affecting the superior portion of the 

head are somehow qualitatively different 

from the loads affecting the inferior part of 

the head. 

Interestingly, the bone volume fraction is 

relatively high for all the taxa in this study 

compared to most values reported in the literature 

for humans and other mammals 

(Whitehouse, 1974, 1975; Goldstein et al., 

1993; Lipkin, 1996; Teng et al., 1997; Ulrich 

et al., 1999). In a survey of the results of other 

studies on a variety of skeletal elements, the 

bone volume fraction for both human and 

nonhuman taxa ranged from 0·023 to 0·464 

with a mean of 0·230 (standard deviation: 

0·134). Limiting the comparison to published 

results from the femur alone yields a bone 

volume fraction in the femoral head ranging 

from 0·08–0·35 (Whitehouse, 1974, 1975; 

Ulrich et al., 1999). 

The divergence between the current 

study and the other published work is most 

probably the result of both methodological


21 

and taxonomic differences. The current 

study calculated the bone volume fraction 

directly from the three-dimensional volume 

while most other studies use stereological 

estimation or point-counting methods on 

two-dimensional sections to obtain an estimate 

of the bone volume in three dimensions. 

The variability in trabecular structure 

within a single individual demonstrated in 

the current study suggests that such estimation 

procedures may not be accurate unless 

multiple two-dimensional sections are used. 

In addition to these methodological differences, 

there are differences in the taxonomic 

groups and skeletal elements used in the 

different studies. In most cases the studies 

examined human trabecular bone structures 

from a variety of bones including the femoral 

head, vertebral bodies, calcaneus, and 

humerus among others (Whitehouse, 1974, 

1975; Zhu et al., 1994; Link et al., 1998; 

Ulrich et al., 1999). Very few studies have 

made use of nonhuman primates or other 

animals as small as the strepsirrhines used in 

this study (but see Kinney et al., 1995; 

Lipkin, 1996). We note, however, that 

Fajardo & Müller (2001) studied trabeculae 

in the proximal femur of several catarrhine 

primates using HRXCT and obtained 

bone volume fraction values ranging from 

0·46–0·77, which is consistent with our 

results. 

The high volume fraction values in all the 

taxa in the current study indicate either that 

the loading at the femoral head is significantly 

higher, necessitating a denser and 

stiffer trabecular network, or that there is 

some scaling effect with the taxa used in this 

study having relatively larger and more 

dense trabeculae than that found in humans 

and other large mammals. The focus of this 

study was not to examine the allometric 

relationships between trabecular bone structure 

and body size, but some interesting 

insights can be gleaned from the results. 

Considering both bone volume fraction and 

fabric anisotropy, there appears to be no 

significant relationship between body size 

and trabecular structure, either in bone volume 

fraction or fabric anisotropy, in these 

strepsirrhine taxa. These results corroborate 

the finding of Swartz et al. (1998) who 

found no significant relationship between 

trabecular size and body size. 

Summary and conclusions 

The purpose of this study was to quantify 

the three-dimensional structure of trabecular 

bone in the femoral head of several 

strepsirrhine taxa. A volume-based technique 

was used to characterize the anisotropy 

of the three-dimensional lattice of 

trabecular bone in the central part of the 

head and the bone volume fraction of the 

trabecular bone within the head was quantified 

in three dimensions. In addition, the 

variation in trabecular morphology within 

different regions of the head was investigated 

by quantifying the anisotropy and the 

bone volume fraction in smaller cubes positioned 

superiorly and inferiorly inside the 

femoral head. 

Trabecular structure in the femoral head 

differs according to locomotor behavior. 

The leaping galagines, who probably have 

more stereotypical hip joint loadings, have a 

distinct trabecular pattern in the femoral 

head with isotropic bone in the superior half 

of the head and more anisotropic bone in the 

inferior half of the head. By contrast, the 

slow quadrupedal and suspensory lorisines 

have a uniformly isotropic trabecular architecture 

throughout the femoral head. The 

trabecular structure in the femoral head of 

Avahi is relatively anisotropic throughout, 

suggesting that he femoral loads in this 

leaper are different than those in the galagine 

leapers. Although the sample size was 

small, the Cheirogaleus trabecular structure 

appeared more similar to the nonleaping 

taxa in this study. The locomotor signal 

held by the trabecular bone supports other 

findings of differences among these taxa


especially between the leaping galagos and 

the nonleaping lorises in terms of their femoral 

anatomy and the functional significance 

of divergent femoral morphologies. The 

large amount of intraspecific variation in all 

of the taxa indicates that trabecular structure 

is pliable and potentially affected by 

small differences in the behaviors and 

lifestyles of animals. 

In conclusion, trabecular bone structure 

in the femoral head of strepsirrhine primates 

reflects differences in locomotor behavior 

and the loading conditions engendered during 

specific behaviors. This is the first analysis 

of its kind to map in three dimensions the 

trabecular bone structure of the femoral 

head of strepsirrhines and it demonstrates 

the utility of high-resolution X-ray computed 

tomography for the analysis of the 

functional differentiation of the locomotor 

skeleton in primates and other mammals. 

Acknowledgements 

We would like to thank John Kappelman, 

Brigitte Demes, Friderun Ankel-Simons, 

and Erik Seiffert for their helpful comments 

on earlier versions of this manuscript. We 

also thank three anonymous reviewers 

whose comments greatly improved this 

manuscript. We thank the collections managers 

and curators at the National Museum 

of Natural History, the American Museum 

of Natural History, the Peabody Museum of 

Natural History, and the Museum of Comparative 

Zoology who kindly loaned specimens 

in their care for this work. This project 

was supported by grants to TMR from 

the National Science Foundation (BCS- 

9908847) and the Leakey Foundation. 

References 

Benn, D. I. (1994). Fabric shape and the interpretation 

of sedimentary fabric data. J. Sediment. Res. A64, 

910–915. 

Biewener, A. A., Fazzalari, N. L., Konieczynski, D. D. 

& Baudinette, R. V. (1996). Adaptive changes in 

trabecular architecture in relation to functional strain 

patterns and disuse. Bone 19, 1–8. 

Burr, D. B., Piotrowski, G., Martin, R. B. & Cook, 

P. N. (1982). Femoral mechanics in the lesser bushbaby 

(Galago senegalensis): structural adaptations to 

leaping in primates. Anat. Rec. 202, 419–429. 

Burr, D. B., Ruff, C. B. & Johnson, C. (1989). Structural 

adaptations of the femur and humerus to arboreal 

and terrestrial environments in three species of 

macaque. Am. J. phys. Anthrop. 79, 357–367. 

Carter, D. R., Orr, T. E. & Fyrhie, D. P. (1989). 

Relationships between loading history and femoral 

cancellous bone architecture. J. Biomech. 22, 231– 

244. 

Crompton, R. H. (1984). Foraging, habitat structure, 

and locomotion in two species of Galago. In(P.S. 

Rodman & J. G. H. Cant, Eds) Adaptations for 

Foraging in Nonhuman Primates, pp. 73–111. New 

York: Columbia University Press. 

Cruz-Orive, L. M., Karlsson, L. M., Larsen, S. E. & 

Wainschtein, F. (1992). Characterizing anisotropy: a 

new concept. Micron microsc. Acta 23, 75–76. 

Demes, B. & Jungers, W. L. (1989). Functional differentiation 

of long bones in lorises. Folia primatol. 52, 

58–69. 

Demes, B. & Jungers, W. L. (1993). Long bone crosssectional 

dimensions, locomotor adaptations and 

body size in prosimian primates. J. hum. Evol. 25, 

57–74. 

Demes, B., Jungers, W. L. & Selpien, K. (1991). Body 

size, locomotion, and long bone cross-sectional 

geometry in indriid primates. Am. J. phys. Anthrop. 

86, 537–547. 

Denison, C., Carlson, W. D. & Ketcham, R. A. (1997). 

Three-dimensional quantitative textural analysis of 

metamorphic rocks using high-resolution x-ray tomography: 

Part I. Methods and techniques. J. Metamorph. 

Geol. 15, 29–44. 

Fajardo, R. J. & Müller, R. (2001). Three-dimensional 

analysis of nonhuman primate trabecular architecture 

using micro-computed tomography. Am. J. phys. 

Anthrop. 115, 327–336. 

Feldkamp, L. A., Goldstein, S. A., Parfitt, A. M., 

Jesion, G. & Kleerekoper, M. (1989). The direct 

examination of three-dimensional bone architecture 

in vitro by computed tomography. J. Bone Miner. 

Res. 4, 3–11. 

Flannery, B. P., Deckman, H. W., Roberge, W. G. & 

D’Amico, K. L. (1987). Three-dimensional x-ray 

microtomography. Science 237, 1439–1444. 

Gebo, D. L. (1987). Locomotor diversity in prosimian 

primates. Am. J. Primatol. 13, 271–281. 

Glasbey, C. A. (1993). An analysis of histogram-based 

thresholding algorithms. CVGIP-Graph. Model. Im. 

55, 532–537. 

Glassman, D. M. & Wells, J. P. (1984). Positional and 

activity behavior in a captive slow loris: a quantitative 

assessment. Am. J. Primatol. 7, 121–132. 

Goldstein, S. A., Goulet, R. & McCubbrey, D. (1993). 

Measurement and significance of three-dimensional 

architecture to the mechanical integrity of trabecular 

bone. Calcified Tissue Int. 53, S127–S133.


23 

Goulet, R. W., Goldstein, S. A., Ciarelli, M. J., Kuhn, 

J. L., Brown, M. B. & Feldkamp, L. A. (1994). The 

relationship between the structural and orthogonal 

compressive properties of trabecular bone. J. Biomech. 

27, 375–389. 

Hayes, W. C. & Snyder, B. (1981). Toward a quantitative 

formulation of Wolff’s Law in trabecular bone. 

In (S. C. Cowin, Ed.) Mechanical Properties of Bone, 

pp. 43–68. New York: The American Society of 

Mechanical Engineers. 

Kabel, J., van Rietbergen, B., Odgaard, A. & Huiskes, 

R. (1999). Constitutive relationships of fabric, 

density, and elastic properties in cancellous bone 

architecture. Bone 25, 481–486. 

Karlsson, L. M. & Cruz-Orive, L. M. (1993). Application 

of the star volume distribution to characterize 

structural anisotropy of a duplex stainless steel. In 

Stereology in Materials Science: Demonstration of 

Some Methods. Thesis. Stockholm: Royal Institute of 

Technology. 

Ketcham, R. A. & Carlson, W. D. (2001). Acquisition, 

optimization and interpretation of x-ray computed 

tomographic imagery: applications to the geosciences. 

Comput. Geosci. 27, 381–400. 

Kinney, J. H., Lane, N. E. & Haupt, D. I. (1995). In 

vivo, three-dimensional microscopy of trabecular 

bone. J. Bone Miner. Res. 10, 264–270. 

Kittler, J. & Illingworth, J. (1985). On threshold selection 

using clustering criteria. IEEE T. Syst. Man Cyb. 

SMC-15, 652–655. 

Kothari, M., Keaveny, T. M., Lin, J. C., Newitt, D. C., 

Genant, H. K. & Majumdar, S. (1998). Impact of 

spatial resolution on the prediction of trabecular 

architecture parameters. Bone 22, 437–443. 

Lanyon, L. E. (1974). Experimental support for the 

trajectorial theory of bone structure. J. Bone Jt. Surg. 

56B, 160–166. 

Leung, C. K. & Lam, F. K. (1996). Performance 

analysis for a class of iterative image thresholding 

algorithms. Pattern Recogn. 29, 1523–1530. 

Link, T. M., Majumdar, S., Lin, J. C., Newitt, D., 

Augat, P., Ouyang, X., Mathur, A. & Henant, H. K. 

(1998). A comparative study of trabecular bone 

properties in the spine and femur using high 

resolution MRI and CT. J. Bone Miner. Res. 13, 

122–132. 

Lipkin, E. W. (1996). Regional histomorphology of 

cancellous bone in Macaca fascicularis. Am. J. Primatol. 

39, 179–187. 

Macchiarelli, R., Bondioli, L., Galichon, V. & Tobias, 

P. V. (1999). Hip bone trabecular architecture shows 

uniquely distinctive locomotor behaviour in South 

African australopithecines. J. hum. Evol. 36, 211– 

232. 

Nash, L. T., Bearder, S. K. & Olson, T. R. (1989). 

Synopsis of Galago species characteristics. Int. J. 

Primatol. 10, 57–80. 

Odgaard, A. (1997). Three-dimensional methods for 

quantification of cancellous bone architecture. Bone 

20, 315–328. 

Odgaard, A., Kabel, J., van Rietbergen, B., Dalstra, M. 

& Huiskes, R. (1997). Fabric and elastic principal 

directions of cancellous bone are closely related. J. 

Biomech. 30, 487–495. 

Oxnard, C. E. (1997). From optical to computational 

fourier transforms: the natural history of an investigation 

of the cancellous bone structure of bone. In 

(P. Lestrel, Ed.) Fourier Descriptors and their Applications 

in Biology, pp. 379–408. Cambridge: Cambridge 

University Press. 

Oxnard, C. E. & Yang, H. C. L. (1981). Beyond 

biometrics: studies of complex biological patterns. 

Symp. Zool. Soc. Lond. 46, 127–167. 

Oxnard, C. E., Crompton, R. H. & Lieberman, S. S. 

(1990). Animal Lifestyles and Anatomies: The Case of 

the Prosimian Primates. Seattle: University of 

Washington Press. 

Radin, E. L., Orr, R. B. & Kelman, J. L. (1982). Effect 

of prolonged walking on concrete on the knees of 

sheep. J. Biomech. 15, 487–492. 

Rafferty, K. L. (1998). Structural design of the femoral 

neck in primates. J. hum. Evol. 34, 361–383. 

Rafferty, K. L. & Ruff, C. B. (1994). Articular structure 

and function in Hylobates, Colobus, andPapio. Am. J. 

phys. Anthrop. 94, 395–408. 

Ridler, T. W. & Calvard, S. (1978). Picture thresholding 

using an iterative selection method. IEEE T. Syst. 

Man Cyb. SMC-8, 630–632. 

Roesler, H. (1981). Some historical remarks on the 

theory of cancellous bone structure (Wolff’s Law). 

In (S. C. Cowin, Ed.) Mechanical Properties of Bone, 

pp. 27–42. New York: The American Society of 

Mechanical Engineers. 

Roesler, H. (1987). The history of some fundamental 

concepts in bone biomechanics. J. Biomech. 20, 

1025–1034. 

Ruff, C. B. (1989). New approaches to structural 

evolution of limb bones in primates. Folia primatol. 

53, 142–159. 

Ruff, C. B. & Leo, F. P. (1986). Use of computed 

tomography in skeletal structure research. Yearb. 

phys. Anthrop. 29, 181–196. 

Ruff, C. B. & Runestad, J. A. (1992). Primate limb 

bone structural adaptations. A. Rev. Anthrop. 21, 

407–433. 

Runestad, J. A. (1997). Postcranial adaptations for 

climbing in Loridae (Primates). J. Zool. 242, 261– 

290. 

Ryan, T. (2001). The structure and function of 

trabecular bone in the femoral head of strepsirhine 

primates. Ph.D. Dissertation, The University of 

Texas at Austin. 

Schaffler, M. B., Burr, D. B., Jungers, W. L. & Ruff, C. 

B. (1985). Structural and mechanical indicators of 

limb specialization in primates. Folia primatol. 45, 

61–75. 

Smith, R. J. & Jungers, W. L. (1997). Body mass 

in comparative primatology. J. hum. Evol. 32, 523– 

559. 

Spoor, C. F., Zonneveld, F. W. & Macho, G. A. 

(1993). Linear measurements of cortical bone and 

dental enamel by computed tomography: applications 

and problems. Am. J. phys. Anthrop. 91, 469– 

484.


Swartz, S. M., Parker, A. & Huo, C. (1998). Theoretical 

and empirical scaling patterns and topological 

homology in bone trabeculae. J. Exp. Biol. 201, 

573–590. 

Teng, S., Choi, I. W., Herring, S. W. & Rensberger, J. 

(1997). Stereological analysis of bone architecture in 

the pig zygomatic arch. Anat. Rec. 248, 205–213. 

Thomason, J. J. (1985). The relationship of trabecular 

architecture to inferred loading patterns in the third 

metacarpals of the extinct equids Merychippus and 

Mesohippus. Paleobiology 11, 323–335. 

Trussell, H. J. (1979). Comments on ‘‘Picture thresholding 

using an iterative selection method’’. IEEE T. 

Syst. Man Cyb. SMC-9, 311. 

Ulrich, D., van Rietbergen, B., Laib, A. & Ruegsegger, 

P. (1999). The ability of three-dimensional structural 

indices to reflect mechanical aspects of trabecular 

bone. Bone 25, 55–60. 

Van Rietbergen, B., Weinans, H., Huiskes, R. & 

Odgaard, A. (1995). A new method to determine 

trabecular bone elastic properties and loading using 

micromechanical finite-element models. J. Biomech. 

28, 69–81. 

Van Rietbergen, B., Odgaard, A., Kabel, J. & Huiskes, 

R. (1996). Direct mechanics assessment of elastic 

symmetries and properties of trabecular bone architecture. 

J. Biomech. 29, 1653–1657. 

Whitehouse, W. J. (1974). The quantitative morphology 

of anisotropic trabecular bone. J. Microsc. 

101, 153–168. 

Whitehouse, W. J. (1975). Scanning electron micrographs 

of cancellous bone from the human sternum. 

J. Pathol. 116, 213–224. 

Walker, A. (1969). The locomotion of the lorises, with 

special reference to the potto. E. Afr. Wildl. J. 7, 1–5. 

Walker, A. (1979). Prosimian locomotor behavior. In 

(G. A. Doyle & R. D. Martin, Eds) The Study of 

Prosimian Behavior, pp. 543–565. New York: 

Academic Press. 

Ward, S. C. & Sussman, R. W. (1979). Correlates 

between locomotor anatomy and behavior in two 

sympatric species of Lemur. Am. J. phys. Anthrop. 50, 

575–590. 

Zhu, M., Keller, T. S., Moeljanto, E. & Spengler, D. 

M. (1994). Multiplanar variations in the structural 

characteristics of cancellous bone. Bone 15, 251–259. 

Appendix 

Thresholding algorithm 

The threshold algorithm used in this study is 

described by the equation (Trussell, 1979): 

where T k is the proposed threshold at the 

kth iteration, b is the brightness level (i.e., 

grayscale), n(b) is the number of occurrences 

of b in the image, and N is the 

number of gray values in the histogram. In 

QUANT3D, the initial threshold used is the 

midpoint between maximum and minimum 

grayscale values within the VOI, and the 

solution usually converges within four 

iterations. For this study, the threshold 

value was calculated independently for 

each individual’s large central cubic VOI 

and was then used for all three VOIs for that 

individual. 

This thresholding method effectively postulates 

that the data consist of two endmember 

phases represented by a roughly 

normal distribution of grayscale values, and 

that the most appropriate division between 

the two is the midpoint of their means. Both 

assumptions are reasonable for HRXCT 

data. The principal complicating factor is 

the partial-volume effect, in which pixels 

near material boundaries will have grayscale 

values representing a blurred volumetric 

average of the end-member components 

(e.g., Ketcham & Carlson, 2001). Because 

of the thinness and high surface area of 

trabecular bone, the majority of its mass lies 

close to a boundary, potentially preventing 

the true grayscale range of end-member 

bone from being realized in the images. The 

high resolution of our data ameliorates this 

effect, however. 

The thresholding method of Ridler & 

Calvard (1978) and Trussell (1979) has 

been used by several researchers and its 

accuracy and utility have been assessed 

(Glasbey, 1993; Leung & Lam, 1996). In a 

study comparing iterative methods using 

several thousand synthetic and real images, 

Leung & Lam (1996) found that this 

method performed best against other thresholding 

methods using objective standards 

such as precision, consistency, and approximation 

of the ‘‘correct’’ or ideal threshold 

(for synthetic images). In a more limited


25 

study Glasbey (1993) compared the 

performance of several iterative and noniterative 

algorithms and found that although 

some other methods were slightly better, 

this method performed well based on the 

accuracy with which the calculated 

thresholds matched the true thresholds 

for 654 bimodal histograms of known 

structure. 

The problems that have been noted with 

this algorithm center on the fact that inaccurate 

threshold values may be generated 

with certain histogram distributions in 

which the ‘‘valley’’ between the peaks representing 

each phase may not be deep enough 

for the algorithm to make a distinction 

between those phases (Kittler & Illingworth, 

1985). Our data do not suffer from this 

feature. 

There are several benefits in using this 

iterative thresholding technique over some 

of the more traditional methods. First, the 

iterative approach as implemented here 

takes the entire three-dimensional volume 

and all grayscale values within it into consideration 

in determining the optimal threshold 

value. Other methods use a more laborintensive 

and less comprehensive approach 

that does not consider an entire image or an 

entire three-dimensional array of images 

(Ruff & Leo, 1986; Spoor et al., 1993). 

Second, the method used here is consistent 

and precise, producing repeatable and regular 

results both within one specimen and 

across an entire sample (Leung & Lam, 

1996). In addition, the iterative method is 

automated, greatly reducing the potential 

for human error in the calculation of the 

threshold values. We verified our implementation 

through qualitative examination of 

the images and the calculated thresholds. 

Although this technique was not validated 

against quantitative measurements, the benefits 

of the method cited above and the 

positive results of the previous analyses outweigh 

any potential problems associated 

with this method. 

Star volume distribution 

The star volume distribution describes the 

distribution of material around a typical 

point in a structure. The mean volume as a 

function of orientation is known as the star 

volume component and is calculated as 

follows (Odgaard, 1997; Odgaard et al., 

1997): 

where υ V (ω) is the star volume component 

as a function of orientation ω, n is the 

number of points used, and L i is the length 

of a measured intercept through point i at 

orientation ω (Cruz-Orive et al., 1992; 

Karlsson & Cruz-Orive, 1993). The star 

volume distribution is the variation of the 

star volume component with orientation. 

The star volume distribution data are used 

to derive a fabric tensor using a weighted 

orientation matrix method. 

Given an orientation j defined by azimuth 

φ j and elevation θ j , the corresponding unit 

vector a j with direction cosines (x j , y j , z j )is 

given by (sin θ j cos φ j , sin θ j sin φ j , cos θ j ). 

The orientation matrix T is then compiled 

by summing over all orientations: 

The fabric tensor S is obtained by dividing 

this matrix by the sum of its eigenvalues. 

The fabric tensor conveys the moment of 

inertia M in any direction u through the 

relation: 

M=u(IS)u, (4) 

where I is the identity matrix. The fabric 

tensor is solved for its eigenvectors û 1 , û 2 , 

û 3 and eigenvalues τˆ1, τˆ2, τˆ3, which respectively 

estimate the orientation and relative


magnitudes of the primary, secondary and 

tertiary axes of the material in the measured 

structure. They can also be visualized as the 

axis directions and radii of an ellipsoid in 

three dimensions, with the radii indicating 

the relative material continuity along the 

three principal axes. We note that the 

second-order tensor solution by definition 

calculates three orthogonal axes, whereas 

the principal material directions in a skeletal 

mesh structure need not be orthogonal. 

The possibility therefore exists that the 

material axes defined by the eigenvalues and 

eigenvectors may not completely capture the 

actual preferred orientation of the trabecular 

fabric. However, analyses have demonstrated 

that volume-based methods such 

as SVD do accurately and effectively 

characterize the predicted mechanical 

response of trabecular bone (Odgaard 

et al., 1997; Kabel et al., 1999; Ulrich et al., 

1999), providing confidence that the true 

underlying problem is being addressed 

adequately.

The three-dimensional structure of trabecular bone ... - ResearchGate

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?