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 Department of Human Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA b Department of Human Evolution, Max Planck Institute for Evolutionary Anthropology, Leipzig 04103, Germany article info Article history: Available online 30 April 2013 Keywords: Allometry Animal model Trabecular bone Histomorphometry Meta-analysis abstract Body mass (BM) in mammal species spans over six orders of magnitude. Although trabecular bone con- tributes 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), trabec- ular thickness (Tb.Th), trabecular separation (Tb.Sp), connectivity density (ConnD) and degree of anisot- ropy (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 trabec- ulae 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 contribut- ing factor for differences in BV/TV in humans, Tb.N variation is the main contributing factor for differ- ences 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 bio- mechanics, 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 low- est 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, 2007; Weiner and Wagner, 1998), differences across species are af- fected 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 (/BM 0.33 ; 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 tra- becular bone properties such as trabecular number (Tb.N), trabec- ular 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 1047-8477/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jsb.2013.04.009 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: mbarak@fas.harvard.edu (M.M. Barak), danlieb@fas.harvard. edu (D.E. Lieberman), hublin@eva.mpg.de (J.-J. Hublin). Journal of Structural Biology 183 (2013) 123–131 Contents lists available at SciVerse ScienceDirect Journal of Structural Biology journal homepage: www.elsevier.com/locate/yjsbi