Of mice, rats and men: Trabecular bone architecture in mammals scales to body mass with negative allometry

Journal of Structural Biology 183 (2013) 123–131

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Of mice, rats and men: Trabecular bone architecture in mammals scales to body mass with negative allometry Meir Max Barak a,b,⇑, Daniel E. Lieberman a, Jean-Jacques Hublin b a b

Department of Human Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA Department of Human Evolution, Max Planck Institute for Evolutionary Anthropology, Leipzig 04103, Germany

a r t i c l e

i n f o

Article history: Available online 30 April 2013 Keywords: Allometry Animal model Trabecular bone Histomorphometry Meta-analysis

a b s t r a c t Body mass (BM) in mammal species spans over six orders of magnitude. Although trabecular bone contributes to the mechanical properties of bones, we know much less about how trabecular bone scales with BM than about how cortical bone scales with BM. We therefore conducted a meta-analysis of the existing literature to test in rodents, humans and other mammals, predicted scaling properties between BM and several trabecular parameters: bone volume fraction (BV/TV), trabecular number (Tb.N), trabecular thickness (Tb.Th), trabecular separation (Tb.Sp), connectivity density (ConnD) and degree of anisotropy (DA). Our results show that BV/TV and DA are independent of BM and that Tb.N, Tb.Th and Tb.Sp scale with negative allometry relative to BM. Rodents appear to have relatively thicker and fewer trabeculae than humans, and we propose it that is due to a minimum thickness threshold ‘‘imposed’’ on mechanically functional trabeculae. Consequently, rodents (mice and rats) and humans demonstrate two distinct mechanisms to achieve variations in BV/TV. Although Tb.Th variation is the main contributing factor for differences in BV/TV in humans, Tb.N variation is the main contributing factor for differences in BV/TV in rodents. Our results also demonstrate no correlation between Tb.N and Tb.Th within each taxon (mice, rats and humans). Since rodents are a common animal model for research on bone biomechanics, the evidence that trabecular bone parameters scale and correlate differently in rodents than in humans suggests that care should be applied when extrapolating bone biomechanical results from small animals to large-bodied humans. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction Bone is a hierarchical composite material comprised in its lowest structural level of carbonated hydroxyapatite, collagen type I, several other non-collagenous proteins and water (Weiner and Wagner, 1998); in its highest structural level, bone is constructed of dense cortical and porous trabecular bone tissues (Weiner et al., 1999). Although all mammalian skeletal bones are practically identical as regard to their material components, their mechanical behavior differs both within and across species (Currey, 2003). While intra-species diversity is mainly due to heterogeneity in hydroxyapatite content and variations in cortical morphology and trabecular architecture (Currey, 2003; Fratzl and Weinkamer, Abbreviations: BM, body mass; BS/TV, bone surface to total volume (bone volume fraction); BV/TV, bone volume to total volume (i.e., bone volume fraction); ConnD, connectivity density; DA, degree of anisotropy; Tb.N, trabecular number; Tb.Sp, trabecular separation; Tb.Th, trabecular thickness. ⇑ Corresponding author at: Department of Human Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA. Fax: +1 617 496 8041. E-mail addresses: [email protected] (M.M. Barak), [email protected]. edu (D.E. Lieberman), [email protected] (J.-J. Hublin). 1047-8477/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jsb.2013.04.009

2007; Weiner and Wagner, 1998), differences across species are affected heavily by body mass (BM). It has been known since Galileo that forces act on the bones of small animals very differently than big animals, because bone strength scales to the power of two whereas mechanical loading scales to the power of three (Galilei, 1638). Consequently, as animals get bigger, their bones need to be more robust in order to withstand higher loads. Thus, whole bone scale their length and diameter relative to BM with close to isometry (/BM0.33; i.e., the slope of the regression between the log of bone length or diameter and the log of BM is close to 0.33) (Alexander et al., 1979; Biewener, 1983; Steudel and Beattie, 1993). As trabecular bone tissue contributes to the mechanical properties of whole bones (Barak et al., 2008, 2010; Brodetti and Hirsch, 1956; Pennycuick, 1967; Rockoff et al., 1969; Rogers and LaBarbera, 1993; Werner et al., 1988), one would also expect trabecular bone properties such as trabecular number (Tb.N), trabecular thickness (Tb.Th), and trabecular separation (Tb.Sp) to scale relative to BM with close to isometry. Despite the importance of scaling, few previous studies have looked at how trabecular bone parameters scale with body size across species. Mullender et al. (1996) compared bone volume

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fraction (BV/TV), Tb.N, Tb.Th and Tb.Sp in the femoral head of five different mammal species (rat, rabbit, Rhesus monkey, pig and cow). Although they did not study the scaling of these trabecular bone properties with BM, and only looked at trabeculae in 2-D, the study does compare them across species. Their results showed that the range of Tb.Th and Tb.N values were relatively small between species (150–190 lm and 2.1–3.1 trabeculae/mm for Tb.Th and Tb.N respectively), except for rats which were significantly different (77 lm and 6.5 trabeculae/mm for Tb.Th and Tb.N respectively). Another 2-D study by Swartz et al. (1998) also found only a very weak relationship between Tb.Th and BM in the humeral and femoral head in a large sample of mammal species, but they did find that Tb.Th scaled close to isometry with BM within bats. They concluded that as body size increases the total number of trabeculae within a bone rather than Tb.Th increases in order to maintain adequate surface area for calcium homeostasis. A final recent study to note is Doube et al. (2011), which CT scanned the femoral head and lateral condyle of 72 terrestrial mammalian, 18 avian and one crocodilian species, thus including species with estimated body masses between 6 g and 3400 kg. This study found that, among mammals, BV/TV did not scale with body mass while Tb.Th and Tb.Sp increased with BM. They did not measure Tb.N; however they did show that connectivity density (which is highly correlated to Tb.N) decreased with BM. Given the various unsolved questions regarding how trabecular bone scales with body mass, we designed a meta-analysis study to look at issues of scaling. The aims of our study are to address how trabecular bone scales with BM and to quantify the relationships between BV/TV, Tb.N. Tb.Th and Tb.Sp in different mammal species. Our first hypothesis, based on the few previous studies (Swartz et al., 1998; Doube et al., 2011), is that differences between mammal species in BV/TV and DA will not correlate to BM, while Tb.N, Tb.Th, Tb.Sp and Connectivity density (ConnD) will scale with negative allometry to BM. Secondly, we postulate that as BV/TV is determined by Tb.N and Tb.Th, the relation between BV/TV and Tb.N, and BV/TV and Tb.Th differs among mammals of varying size depending on the scaling of these trabecular bone properties with BM. Therefore, if our first hypothesis holds, Tb.N and Tb.Th may contribute differently to BV/TV in small vs. large mammals. Finally, we hypothesize that due to scaling, the relation between other trabecular bone properties also varies among mammals of different size (e.g. Tb.N vs. Tb.Th). 2. Materials and methods 2.1. Literature search and inclusion criteria In order to identify relevant studies to include in the meta-analysis, systematic computerized searches were performed indepen-

dently in Ovid and PubMed electronic databases for studies published prior to December 2010. The following search strings and keywords were used to search in the title and abstract of articles: [trabecula⁄], [cancellous], [(BV/TV) and (cancellous)], [(Tb.N) or (Tb.Th) or (Tb.Sp)]. Additional studies were identified by examining the reference lists of all articles identified. All on-line supplemental data was also inspected. Studies based on earlier data sets as well as duplicate experimental data sets were excluded. Studies were included based on the following criteria: (1) the manuscripts were published in peer-reviewed journals in English, (2) the manuscript presented original data, (3) the study included a distinct control group of healthy individuals with no bone pathologies or signs of osteoporosis (only data from healthy and normal control groups were included in our study), (4) the study control group included only mature individuals and excluded juvenile or aged subjects, which have significantly different trabecular bone properties due to immature and growing skeletons or deterioration of the bone structure and osteopenia respectively, (5) in order to avoid subjectivity, several studies that compared multiple age, sex and treatment groups were also excluded. In such studies, there is no single objective way to pool the data, as these analyses often find complex patterns and significant differences between various groups, (6) measurement resolution was published and was sufficient to measure the trabecular properties of the species studied (Table 1S, online supplementary material), (7) the average values of at least BV/TV, Tb.N, Tb.Th, Tb.Sp, ConnD or DA were provided or could be calculated. In six papers the values were measured from the provided plot using Paint.NET v3.5.10, an image editing software (dotPDN LLC, Kirkland, WA, USA), which enables quantification of data points from ordinates by superimposing a pixel grid on an enlarged image (see Tables 1–3). Applying these criteria yielded 51 papers on humans, 11 on nonhuman primates, 12 on rats, 9 on mice, 4 on cows, 3 on sheep, 2 on dogs, 2 on swine, 2 on rabbits, 1 paper on donkeys, 1 paper on horses and 1 paper on potoroos (a marsupial). Because some of these studies included more than one group eligible to participate in the meta-analysis – some papers contributed more than one data point. A complete summary of the studies included is given in the on-line supplementary material (Table 1S, online supplementary material). As our study is a meta-analysis of the existing literature (including almost 100 manuscripts and spanning nearly two decades) it is important to explicate the vast amount of data (244 data points), the methods used in the various studies, their sensitivities and limitations. The majority of data points included in our meta-analysis were measured using a microCT (196 data points, 80.3% of all data points). The rest of data points were measured using microMRI (another 3D-measurment technique; 14 data points, 5.7% of all data points), histology (a 2D-measurment technique; 32 data

Table 1 Regression parameters for trabecular bone properties relationship with body mass.

BV/TV DA Tb.N ConnD Tb.Th Tb.Sp

All Average All Average All Average All Average All Average All Average

Regression slope

Regression intercept

R Value

P value (linear correlation)

0.0092 0.0549 0.27 0.033 0.146 0.106 0.332 0.3 0.137 0.124 0.137 0.082

1.41 1.39 0.32 0.23 0.42 0.46 1.06 1.28 1.99 1.98 2.51 2.42

0.045 0.496 0.133 0.568 0.748 0.810 0.673 0.800 0.659 0.756 0.649 0.567

P = 0.476 P = 0.121 P = 0.135 P = 0.147 P < 0.01 P < 0.05 P < 0.01 P < 0.05 P < 0.01 P < 0.05 P < 0.01 P = 0.087

For each trabecular bone parameter 2 regressions were calculated: (1) the regression for all existing data points (Fig. 1), and (2) the regression for the average value for each species. Using either method does not change the scaling relationship between each trabecular bone parameter and body mass.

M.M. Barak et al. / Journal of Structural Biology 183 (2013) 123–131 Table 2 Key differences in the relationship between Tb.N, Tb.Th and BV/TV for humans, rats and mice.

Tb.N vs. BV/TV Regression slope Regression intercept r value P value (linear correlation) Tb.N range (D) Max effect on BV/TV

Human

Rat

Mouse

16.38 2.8 0.664 P < 0.01 0.6–2.1 (1.5) 24.6

7.29 0.01 0.827 P < 0.01 2.4–6.8 (4.4) 32.1

3.32 0.8 0.774 P < 0.01 3.1–7.8 (4.7) 15.6

Human 0.159 5.33 0.743 P < 0.01 83–296 (213) 33.9

Rat 0.227 13.5 0.426 P = 0.129 50–115 (65) 14.8

Mouse 0.184 11.44 0.353 P = 0.138 22–69 (47) 8.6

Tb.Th vs. BV/TV Regression slope Regression intercept r value P value (linear correlation) Tb.Th range, lm (D) Max effect on BV/TV

The maximum effect of Tb.N or Tb.Th on BV/TV was calculated by multiplying values range by the regression slope. Notice how Tb.Th has higher effect on BV/TV in humans (33.9 > 24.6) while Tb.N has higher effect on BV/TV in rats and mice (32.1 > 14.8 and 15.6 > 8.6 in rats and mice respectively). Statistically significant values (P < 0.01) are marked as bold

Table 3 Pearson partial correlation statistical test results between BV/TV and Tb.N and BV/TV and Tb.Th.

Human Rat Mouse

BV/TV-Tb.N

BV/TV-Tb.Th

P < 0.01 P < 0.01 P < 0.01

P < 0.01 P = 0.0245 P = 0.037

Pearson partial correlation statistical test results between BV/TV and Tb.N (left column, Tb.Th was kept constant), and BV/TV and Tb.Th (right column, Tb.N was kept constant). Statistically significant values (P < 0.01) are marked as bold

points, 13.1% of all data points), scanning electron microscopy (SEM, a 2D-measurment technique; one data point) and Archimedes’ principle (one data point). It is important to mention that not all trabecular bone properties were measured by every one of these techniques. For example, ConnD and DA were measured only by 3D-measurments techniques and almost solely using microCT scanning. Figure 1S (online supplementary material) demonstrates that excluding or including the histology and SEM data points did not change the relationship between the trabecular parameters and therefore did not significantly alter the results. Additionally, due to the different techniques used, the sensitivity of the measurements varied accordingly. Histology studies, though in 2D, are characterized by high measurement resolution in the order of several micrometers. The vast majority of microCT studies reported a high scanning resolution of 30–50 lm and below; a very few older studies reported values of 85 lm and above. MicroMRI studies reported scanning resolution ranging between 85 and 172 lm (only one data point for the later). One possible limitation of any meta-analysis is the use of data from various sources that used different techniques to extract data. Trabecular bone properties values from microCT scans may have been calculated differently due to the use of alternate software packages. Such information is especially important as some techniques may use the ‘parallel plate mode’ to calculate the trabecular bone parameters (Parfitt et al., 1983). In this model, one measures BV/TV and bone surface area, which are then used to calculate Tb.Th, Tb.Sp and Tb.N; hence, when using this model, these trabecular bone parameters are derived-from BV/TV and bone surface area, and are non-independent (Parfitt et al., 1983). In Table 1S (online supplementary material), papers that used the ‘parallel plate

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model’ to calculate trabecular bone properties from their microCT scans are colored in blue while papers that calculated trabecular bone properties from their microCT scans independently from each other are colored in red. Our meta-analysis includes 158 microCT data points which were calculated independently, without the limitations of the ‘parallel plate model’ (83 data points using the Scanco in-house software, 45 data points using the QUANT 3D software, 17 data points using the Tri/3D BON software, 10 data points using the GE Healthcare in-house software and three data points which were calculated independently, but where the manuscript does not describe exactly what software was used), and 34 microCT data points which were calculated employing the ‘parallel plate model’ (23 points using the Skyscan software, and 11 points using the assumptions of the ‘parallel plate model, but where the manuscript does not describe exactly what software was used), (Table 1S, online supplementary material). It is worth mentioning that according to the Skyscan CTan software manual (page #9), although their Tb.N calculation is based on the ‘parallel plate model’ equation, they measure Tb.Th and Tb.Sp independently from each other and directly from the 3D volume; therefore their measurements could be considered a direct calculation from a 3D volume, and independent of the limitations of the ‘parallel plate model’. This decreases the number of microCT data points derived directly from the ‘parallel plate model’ even further to 11. Figure 2S (online supplementary material) further demonstrates for the human data points that excluding or including the microCT data points which were calculated using the ‘parallel plate model’ did not change the relationship between the measured trabecular bone parameters and therefore did not significantly alter the results (we compared only human data points since rats had no data points calculated using the ‘parallel plate model’ and mice had only one such data point). 2.2. Meta-analyses Data points were extracted from the studies and entered into Excel (Office Excel 2007, Microsoft Corporation, Redmond, WA, USA). Because the number of data points for all species beside humans was relatively small (e.g., for rats and mice we found 16 and 19 data points respectively) our meta-analysis did not consider sex since this will decrease group sizes even more, precluding robust statistical methods. For the same reason, the correlation between trabecular bone properties and BM was evaluated for all bones pooled together. The following bones (from these various species) were included in our meta-analysis: mandibular condyle (humans, nonhuman primates, sheep and rabbits), humerus (nonhuman primates), radius (humans), metacarpal bones (humans and nonhuman primates), vertebrae (humans, rats, mice, cows, swine and dogs), iliac crest (humans), femur (humans, nonhuman primates, rats, mice, cows, sheep, swine, dogs, donkeys and rabbits), tibia (nonhuman primates, rats, mice, cows, sheep and horses) and calcaneus (humans and potoroos). Table 1S (online supplementary material) gives a detailed account of the various bones sample. In order to test whether trabecular bone scales with isometry or positive/negative allometry relative to body mass we plotted the log of BV/TV, Tb.N, Tb.Th, Tb.Sp, ConnD and DA against the log of BM for all the species included in the meta-analysis. Plots were generated using R, version 2.15.2 (R Foundation for Statistical Computing, Vienna, Austria; www.r-project.org). Where animal BM was not given in the paper it was estimated at the species level from the literature (see Tables 2S and 3S, online supplementary material). In addition, the following relations were investigated and plotted: BV/TV relative to Tb.N, BV/TV relative to Tb.Th and Tb.Th relative to Tb.N. A regression line was computed and the slope of the line was calculated for humans, rats and mice (the other species had too few data points).

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2.3. Statistics Statistical tests for homogeneity of regressions were performed to test for differences in regression slopes between species (BV/TV vs. Tb.N and BV/TV vs. Tb.Th). If the slopes of two species were not significantly different they were further tested with ANCOVA to determine whether the two species adjusted means were significantly different. A significant difference indicates that the independent variable (Tb.N or Tb.Th) has a different contribution to BV/TV in the two species. Statistical significance was determined using 99% confidence intervals. Because both Tb.N and Tb.Th can affect BV/TV we performed a Pearson (linear) partial correlation analysis (Matlab 2008a, The MathWorks, Natick MA, USA) to measure the correlation between BV/TV and either Tb.N or Tb.Th, while holding other variables constant. Statistical significance was determined using two-tailed 99% confidence intervals. 3. Results 3.1. Scaling of trabecular bone with body size In order to examine scaling effects, Fig. 1 plots log-transformed relationships between BV/TV (Fig. 1a), DA (Fig. 1b), Tb.N (Fig. 1c), ConnD (Fig. 1d), Tb.Th (Fig. 1e) and Tb.Sp (Fig. 1f) against the BM of all the species included in the meta-analysis. These regressions indicate that BV/TV and DA are independent of body mass (r = 0.045 and P = 0.48 for BV/TV, Fig. 1a; and r = 0.133 and

P = 0.135 for DA, Fig. 1b). Both Tb.N and ConnD demonstrate a significant negative correlation with BM (r = 0.748 and P < 0.01 for Tb.N, Fig. 1c; and r = 0.673 and P < 0.01 for ConnD, Fig. 1d), while Tb.Th and Tb.Sp exhibit a significant positive correlation with BM (r = 0.659 and P < 0.01 for Tb.Th, Fig. 1e; and r = 0.649 and P < 0.01 for Tb.Sp, Fig. 1f). Since slopes that are smaller than 0.33 (or larger than 0.33 in cases of negative correlation) are significantly below the expectations of isometry, Tb.N (slope = 0.146), Tb.Th (slope = 0.137) and Tb.Sp (slope = 0.137) scale to body mass with negative allometry. Table 1 summarizes all the numeric data presented in Fig. 1. Table 1 also presents the regression slope, intercept and r values, and the P values when each species was represented only by one value (the average of all data points for each species). The trend of the slopes (and hence the scaling) does not change when using all data points vs. just the average data points. Furthermore, correlation significance (or lack of significance in the case of BV/TV and DA) does not differ either. The sole difference when switching from all data points to the average data points is that Tb.Sp scaling with BM fail short of being significant (P = 0.087; although the relationship remains negative allometry with similar slope intercept and r values; Table 1).The reason for this is the very small number of average data points (10, one for each species) compared to the original 176 data points. 3.2. Correlation between Tb.N, Tb.Th and BV/TV Fig. 2 shows the relation between BV/TV and Tb.N (Fig. 2a), and BV/TV and Tb.Th (Fig. 2b) for the various mammals included in our

Fig. 1. Log-transformed scaling relationships between body mass (BM) and BV/TV (a), DA (b), Tb.N (c), ConnD (d), Tb.Th (e) and Tb.Sp (f) for all the species included in the meta-analysis (Bovine – red triangles, canine – cyan squares, equine – black squares, human – red squares, mouse – black triangles, ovine – green diamond, swine – brown circles, Potoroo – black circles, primate – blue triangles, rabbit – orange triangles and rat – light green squares). Regressions equations and r values are presented for each case. There is no correlation between BV/TV and DA, and BM (Fig 1a and b), a negative correlation between Tb.N and ConnD, and BM (Fig 1c and d) and a positive correlation between Tb.Th and Tb.Sp, and BM (Fig 1e and f).

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Fig. 2. BV/TV as a function of Tb.N (a) and Tb.Th (b) for the different mammal species and nonhuman primates (Bovine – black circle with an ‘X’ over it, canine – black square with a ‘+’ sign over it, human – gray squares, mouse – black triangles, ovine – black star, swine – grey asterisk, Potoroo – black circles, primate – black ‘+’ sign, rabbit – upsidedown gray triangle and rat – open black circles). The data points for nonhuman primates, bovines, ovines, canines and swine are all within the range of human values. No linear regression was computed for these species as they were too few in number (the nonhuman primates include multiple species; see Table 2S).

meta-analysis. The data points for nonhuman primates, bovines, ovines, canines, rabbits and pigs are all within the range of human values and different from rats and mice for both Tb.N vs. BV/TV (Fig. 2a) and Tb.Th vs. BV/TV (Fig. 2b). No linear regression was computed for species other than humans, rats and mice because samples sizes were too small (the nonhuman primates include multiple species; for a detailed account of the various species see Table 2S). When focusing on humans, mice and rats, it is clear that they differ in the relationship between Tb.N and BV/TV (Fig. 3). The relationship between Tb.N and BV/TV is significantly different comparing humans to rats and humans to mice (ANCOVA, P < 0.01, P < 0.01), but not when comparing rats to mice (ANCOVA, P = 0.07). This indicates that mice and rats share a similar relationship between Tb.N and BV/TV which is different than humans. In humans, Tb.N scale steeply relative to BV/TV (regression slope of 16.38 and P < 0.01) but the values only range between 1 and 2 trabeculae per millimeter (Table 1S); this means that although Tb.N increase rapidly with BV/TV, the possible accumulated effect on BV/TV is limited (Table 2). In contrast, in rodents Tb.N scales more moderately relative to BV/TV (regression slopes of 3.32 and 7.29 in mice and rats respectively and P < 0.01; Table 2) yet the range of possible values and the accumulated effect on BV/TV is much larger (approximately between 2 and 8 trabeculae/mm; Table 1S). Similarly, there is a significant difference between mice, rats and humans in the relationship between Tb.Th and BV/TV (Fig. 4). The relationship between Tb.Th and BV/TV is significantly different comparing humans to rats and humans to mice (ANCOVA, P < 0.01, P < 0.01), but not when comparing rats to mice (ANCOVA, P = 0.15). This result indicates that mice and rats share a similar relationship between Tb.Th and BV/TV, which is different than humans. Tb.Th in rodents is low, not highly variable (20–70 and 50– 110 lm and regression slopes of 0.184 and 0.227 in mice and rats

respectively) and does not correlate with BV/TV (P = 0.138 and P = 0.129 for mice and rats respectively; Table 2), whereas Tb.Th in human is higher, more variable, and scales moderately relative to BV/TV (Tb.Th of 80–300 lm, regression slope of 0.159 and P < 0.01; Table 2). Table 2 summarizes key differences in how Tb.N and Tb.Th scale with BV/TV. The ANCOVA statistical test results and the linear regression slope differences in each species, which indicate a significant difference between humans and rodents, combined with the range of Tb.N and Tb.Th values (Table 2), together suggest that mice and rats achieve higher BV/TV with a different strategy than humans. A bone with higher BV/TV demonstrates a stronger tendency to have higher Tb.N values in rodents and higher Tb.Th values in humans (by ‘‘higher BV/TV’’ we refer to a higher value of one bone compared to another, not a BV/TV increase in one specific bone as a modeling response to higher loads). This means that when presented with two human bones, it is possible to predict that the bone with the higher BV/TV has thicker trabeculae compared to the bone with the lower BV/TV, but it is unpredictable solely from the BV/TV parameter whether the bones will also differ in Tb.N. In contrast, if the bones will belong to a mouse or a rat, it is possible to predict that the bone with the higher BV/TV will have more trabeculae compared to the bone with lower BV/TV, but it is unpredictable whether they will also differ in Tb.Th. As Tb.N and Tb.Th are not correlated (Fig. 5), these two strategies seem to be independent. Because many of the variables studied here are not independent, Table 3 presents the results of a partial correlation analysis. In rodents Tb.N, but not Tb.Th, is significantly and independently correlated with BV/TV. Contrary, in humans, both Tb.N and Tb.Th have significant, independent correlations with BV/TV. These results further support a different relationship between Tb.N and Tb.Th to BV/TV in rodents compared to humans.

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Fig. 3. (a) Relationship between Tb.N and BV/TV for humans (black squares), mice (an X over a circle) and rats (gray triangles). Regressions equations and r values are given for each of the three species. Humans present a significantly different relationship between Tb.N and BV/TV (steeper slope) compared to rats and mice, while rats and mice present a non-significant different relationship between Tb.N and BV/TV. This indicates that increasing Tb.N in rats and mice contributes much less to BV/TV compared to humans. (b) Minimum convex polygon plots (the smallest possible convex polygon around all data points) for humans, rats and mice. Note how rats and mice polygons are oriented more horizontally compared to humans, further demonstrating a difference in Tb.N and BV/TV relationship.

3.3. Correlation between Tb.N and Tb.Th There is no correlation between Tb.N and Tb.Th within each taxon (r values are 0.092, 0.108 and 0.189 and p values are 0.41, 0.713 and 0.467 for humans, rats and mice respectively; Fig. 5). For example, as Tb.N increases from 1 to 2 trabecula/mm (practically the entire range of Tb.N values in humans, Table 1S), Tb.Th increases only by 11.2 lm, and an increase of one trabecula/mm in mice corresponds to a minute decrease of 1.5 lm in Tb.Th. These results indicate that within a specific species, Tb.N and Tb.Th are independent.

4. Discussion As postulated, our meta-analysis results indicate that BV/TV and DA are independent of body mass, and that even though BM affects Tb.N, Tb.Th and Tb.Sp, these parameters do not scale with isometry but with negative allometry (Fig. 1). All in all, our scaling results suggest that small rodents have relatively thicker and fewer trabeculae with relatively more separation than one would predict from humans and other larger mammals. In addition, our results demonstrate that there is a clear difference in the relationship between BV/TV vs. Tb.N and Tb.Th in mice, rats and humans. Although Tb.Th is the main influence on BV/TV variations in humans, Tb.N is the main determinant of BV/TV variations in small rodents (Figs. 3 and 4, and Tables 2 and 3). Because Tb.N and Tb.Th are independent (Fig. 5) this difference signifies two distinct mechanisms by which large and small mammals achieve variations in BV/TV. In agreement with our meta-analysis results, Cotter et al. (2009) found that BV/TV and DA were independent of BM across several

primate species. Similarly, Doube et al. (2011) found that among mammals BV/TV did not scale with BM while Tb.Th and Tb.Sp increased with BM. Remarkably, both Doube et al. (2011) and the current study found that Tb.Th and Tb.Sp scale with negative allometry to BM and that the scaling values are very close to each other. We found a slope of 0.137 for both Tb.Th and Tb.Sp while Doube et al. (2011) found a slope of 0.155 for Tb.Th and 0.147 and 0.135 for Tb.Sp (Femoral head and femoral condyle respectively). However, as Doube et al. scanned only a few animals from each species they pooled all mammal species together. Therefore, contrary to our study, they could not test whether the relationship between BV/TV and Tb.N or Tb.Th varied between smaller and larger mammals. Mullender et al. (1996) also found that rats had different Tb.N and Tb.Th values compared to larger mammals. They postulated that Tb.Th and Tb.N differ with respect to each other in the rat because of the lack of growth plate fusion in this species. Because of this difference, one expects rats to develop relatively more new secondary trabeculae, which are typically thinner compared to primary trabeculae. These findings support our results that small rodents use a different mechanism to control trabecular bone properties. Contrary to our finding, Swartz et al. (1998) found only a very weak relationship between Tb.Th and BM in the humeral or femoral head of mammal species in which BM ranged six orders of magnitude. A possible difficulty with this study however, was that for each animal they measured only a small number of transverse trabeculae in the metaphysis (below the growth plate). These trabeculae were not near the joint surface, where loads are applied, and they measured only transverse trabeculae, which are less load bearing than vertical trabeculae in bones which are loaded mainly axially (Fields et al., 2011; Shi et al., 2010). Furthermore, Swartz and colleagues’ samples were biased towards smallbodied mammals: of the 66 individuals they measured, 63 were

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Fig. 4. (a) Relationship between Tb.Th and BV/TV for humans (black squares), mice (an X over a circle) and rats (gray triangles). Regressions equations and r values are given for each of the three species. Rats and mice present a non-significant different relationship between Tb.Th and BV/TV, and a significant different relationship between Tb.Th and BV/TV (steeper slopes) compared to humans. This indicates that increasing Tb.Th in humans contributes much less to BV/TV compared to rats and mice. (b) Minimum convex polygon plots (the smallest possible convex polygon around all data points) for humans, rats and mice. Note how rats and mice polygons are oriented more vertically compared to humans, further demonstrating a difference in Tb.Th and BV/TV relationship.

Fig. 5. Correlation between Tb.N and Tb.Th for humans (black squares), mice (an X over a circle), and rats (gray triangles). Regressions equations and r values are given for each of the three species. No correlation was found between Tb.N and Tb.Th. These results indicate that within a specific species, Tb.N and Tb.Th are independent.

65 kg or less, and the remaining three were 530 kg (two horses) and 40,000 kg (a humpback whale). These three large-bodied samples, which had relatively ‘‘thinner’’ trabeculae, affected their results by reducing the effect of BM on Tb.Th, and therefore should not have been grouped with the small-bodied mammals. BV/TV is the primary determinant of trabecular bone strength and stiffness (Borah et al., 2000; Kabel et al., 1999; Ryan et al., 2010). Consequently, bones with higher BV/TV are expected to be subjected to higher stresses. As BV/TV is determined by Tb.N and Tb.Th, bones with higher BV/TV may have more trabeculae, thicker trabeculae or a combination of both parameters. All things being equal, one expects increasing Tb.Th rather than Tb.N to have several advantages for achieving higher BV/TV. First, thicker trabeculae are stronger. Second, thicker trabeculae have more bone material per trabecula and therefore a lower strain energy density,

and a greater ability to dissipate loading energy efficiently. Third, because osteoclasts resorb bone only on the trabecular surface (Parfitt, 1994), for the same amount of BV/TV, few thicker trabeculae will have reduced BS/TV (bone surface to total volume) compared to many thinner trabeculae. Hence, it is predicted that due to lower trabecular surface, fewer osteoclasts (and subsequently osteoblasts) will be activated during remodeling. However, if scaling of BV/TV with Tb.N and Tb.Th differs between humans and rodents (Figs. 3 and 4), then varying Tb.Th relative to body mass may have disadvantages in small mammals such as rodents. As body mass varies from large mammals to small rodents, bone volume changes by orders of magnitude whereas Tb.Th varies only 3-4-fold (Doube et al., 2011; Mullender et al., 1996; Swartz et al., 1998). The likely major reason that trabecular thickness scales poorly with body mass is that there is a minimum thickness threshold for

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functional trabeculae. Resorption lacunae created by osteoclasts range in depth between 30 and 50 lm regardless of body size (data are scarce but exist for rats and humans) (Cowin, 2001; Eriksen et al., 1985; McNamara et al., 2006; Mulvihill et al., 2008), meaning that osteoclast activity will cut very thin trabeculae in two, destroying their mechanical functionality. Reviewing Tb.Th values for rats and mice (Table 1S) reveals that a plausibly substantial percentage of trabeculae in rats and practically almost all trabeculae in mice are close to this lower threshold. Consequently, in rodents and other small mammals, Tb.Th must be relatively thicker (i.e., are ‘‘overbuilt’’) and therefore stronger compared to larger mammals. Any small increase in strength from thicker trabeculae would be minuscule and outweighed by other possible disadvantages such as an extreme decrease in space between trabeculae (Tb.Sp) which could affect bone marrow hematopoietic performance and other poroelastic functions. Another possible reason that increased trabecular thickness may be disadvantageous in rodents is the importance of strain magnitude to bone maintenance (i.e., a minimum threshold of strain magnitude is necessary to maintain the trabecular bone tissue) (Huiskes et al., 2000; Huiskes, 2001). Loading bones causes deformation, and since trabeculae are relatively thicker in rodents they may experience lower strains per volume of bone (a hypothesis that may be tested using micro finite element models). Given evidence that bone turnover is stimulated by strain (Burger and Klein-Nulend, 1999; Burger et al., 2003), relatively thicker trabeculae in small mammals might inhibit normal mechanical signals generated from habitual loading, which are necessary to stimulate bone turnover. Finally, there may be advantages for small mammals such as rodents to have higher Tb.N relative to body mass. Because small mammals have little, finite bone space, the absolute number of mechanically functional trabeculae may be much smaller in small mammals compared to larger animals. If small mammals had a few, thick trabeculae as opposed to more thin trabeculae, then even a failure of only several trabeculae could extensively affect bone mechanical properties (albeit thicker trabeculae will probably fail at higher loads). Achieving higher BV/TV with more trabeculae (rather than fewer thicker trabeculae) may therefore allow small rodents to maintain a reasonable safety factor. One way to further quantify the difference between humans and rodents would be to compare ConnD and bone surface density (defined as bone surface area to total volume; BS/TV). Thicker and fewer plate-like trabeculae (more common in humans than rodents) will be characterized by a higher BS/TV and lower ConnD, while thinner and more plentiful rod-like trabeculae (more common in mice and rats than humans) will be characterized by a lower BS/TV and higher ConnD. Furthermore, surface properties such as BS/TV could elucidate other differences between humans and rodents in regards to non-mechanical functions of trabecular bone (e.g. maintaining mineral homeostasis). Unfortunately, these parameters are seldom measured in human trabecular tissue (especially BS/TV) and practically never in rodents. There are several possible limitations to this meta-analysis. As we were limited by available data, it is not clear at what body size threshold species switch from a strategy of having thicker vs. more trabeculae. Because most studies have used only mice, rats and humans, there is a large unfilled gap in body size between under 1 kg and around 60 kg. However, several studies from dogs and rabbits suggest that this transition occurs at very low body masses, probably around 1 kg or less (Goldstein et al., 1993; Liu et al., 2010; Mullender et al., 1996). Another question this study did not address is how additional factors such as the role of cortical bone, locomotor mode and joint loading direction may affect trabecular bone properties differences and their mechanical importance between the studied species. Mice and rats are quadrupeds, which mean they load their joints in different orientations and with less

relative force per unit body mass than in bipedal humans. Moreover, due to lower BM and relatively thicker cortical shells (Bagi et al., 1997; Barak et al., 2010; Eswaran et al., 2006; Fazzalari et al., 2006), the stresses experienced by trabecular tissue of rodents are much smaller, which may influence how mechanically important trabecular tissue is in these species. It is possible that the relatively thicker cortex in small rodents is at least partially the reason for the Tb.N negative allometry relationship (i.e., mice and rats have fewer trabeculae than we predict because their cortex caries more of the loads compared to humans). Another limitation of this study is the relatively small number of data points available for rats and mice (16 and 19 respectively), compared to humans (109). Nevertheless, the number of data points for rats and mice were sufficient to test for statistical significance. The conclusions they yield are supported by the fact that all data points within a species formed a continuum and were in the same range (without any outliers), indicating that they represent the true range of values in the population. The small number of data points available for rats and mice also forced us to group different mice and rat strain together. The various strains of mice and rats are given in Table 4S (online supplementary material). Nevertheless, in the single paper that addressed the issue of trabecular bone properties relationship between different mouse strains, Tommasini et al. (2005), Fig 3b and Table 4S) showed that three different mouse strains (A/J, C57BL/6J, and C3H/HeJ) had similar slopes when plotting the relationships between BV/TV and Tb.Th, and BV/TV and Tb.N. This indicates that pooling different strains together, as in our meta-analysis, should not affect the correlations between BV/TV, Tb.N and Tb.Th. Finally, because of the small number of available data points the sex of the animal was not considered and all bones were pooled (despite the large number of available data point for humans, the number of data points per bone was not sufficient for a robust statistical analysis). Because different bones are subjected to different loads this may add some noise to our results, yet there is no previous study or any a priori reason to believe that the properties of trabecular bones correlate with each other differently between different bones within the same species. In addition, due to the relatively small number of available data we also included some datapoints from histological measurements. These measurements comprised only a small number of the data (13.1%, see Table 1S, online supplementary material) and these measurements did not alter the slope and strength of correlations between the trabecular bone properties (see Fig 1S, online supplementary material); thus we consider this issue to have no significant effect over our results. In conclusion, this meta-analysis finds that Tb.N, Tb.Th and Tb.Sp scale to BM with negative allometry while BV/TV and DA are independent of BM. Furthermore, our results indicate that Tb.N and Tb.Th are correlated with BV/TV differently in rodents and humans. Tb.N variation is the main contributing parameter to differences in BV/TV in mice and rats whereas Tb.Th variation is the main contributing parameter to differences in BV/TV in humans. These differences appear to be the result of a minimum thickness threshold ‘‘imposed’’ on mechanically functional trabeculae causing trabeculae to be relatively thicker in small rodents compared to humans (larger mammals). As mice and rats are the most common animal model for human bone research, our findings that trabecular bone parameters scale and correlate differently in rodents than in humans indicate that special care should be applied when interoperating and extrapolating trabecular bone biomechanical results across these species. Acknowledgments This study was supported by the Minerva Stiftung Gesellschaft für die Forschung mbH (a subsidiary of the Max Planck Society,

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