The Wolff’s Law On Bone Remodeling And Transformation, Part II

Sorry for the recent absence of new posts for the last 3-4 days. I took an extended break from the website but I am back now and will be getting more posts out. This post is the 2nd of two major articles I will use to talk about the Wolff’s Law of bone remodeling.

This article I have found and will post below shows that the old law of Wolff is not as scientifically valid as I thought. The article was written for the  AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY in 2006.

The critical thing about this article as that it completely objectively looks at how correct Wolff’s Law applies to actual bone loading. The hind leg loading of rodents are looked at again and we can see that this article can be used to analyze the feasibility and effectiveness of the Lateral Synovial Joint Loading technique.

The Link to the Document HERE. As always, I will highlight the most important parts of the article.

Who’s Afraid of the Big Bad Wolff?: ‘‘Wolff’s Law’’ and Bone Functional Adaptation

Christopher Ruff,1* Brigitte Holt,2 and Erik Trinkaus3

1Center for Functional Anatomy and Evolution, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205
2Department of Anthropology, University of Massachusetts, Amherst, Massachusetts 01003 3Department of Anthropology, Washington University, St. Louis, Missouri 63130-4899


ABSTRACT ‘‘Wolff’s law’’ is a concept that has some- times been misrepresented, and frequently misunder- stood, in the anthropological literature. Although it was originally formulated in a strict mathematical sense that has since been discredited, the more general concept of ‘‘bone functional adaptation’’ to mechanical loading (a designation that should probably replace ‘‘Wolff’s law’’) is supported by much experimental and observational data. Objections raised to earlier studies of bone functional adaptation have largely been addressed by more recent and better-controlled studies. While the bone morpholog- ical response to mechanical strains is reduced in adults relative to juveniles, claims that adult morphology reflects only juvenile loadings are greatly exaggerated. Similarly, while there are important genetic influences on bone development and on the nature of bone’s response to mechanical loading, variations in loadings themselves are equally if not more important in deter- mining variations in morphology, especially in compari- sons between closely related individuals or species. The correspondence between bone strain patterns and bone structure is variable, depending on skeletal location and the general mechanical environment (e.g., distal vs. proximal limb elements, cursorial vs. noncursorial ani- mals), so that mechanical/behavioral inferences based on structure alone should be limited to corresponding skele- tal regions and animals with similar basic mechanical designs. Within such comparisons, traditional geometric parameters (such as second moments of area and section moduli) still give the best available estimates of in vivo mechanical competence. Thus, when employed with appropriate caution, these features may be used to reconstruct mechanical loadings and behavioral differ- ences within and between past populations.

The idea that bone form reflects in some way its mechanical loading history during life is fundamental to many paleontological and bioarchaeological studies of skeletal material. While physical context and material culture give clues to past behavior, analysis of the skele- tons themselves is the most direct way to reconstruct individual behavior, and to explore intra- and interpopu- lational differences in behavior (e.g., Larsen, 1997; Drucker and Henry-Gambier, 2005; Scott et al., 2005). Reconstructions of body size and shape from skeletal remains are also dependent to some degree on assumed relationships between mechanical loadings and bone morphology (Ruff, 1995, 2003; Delson et al., 2000; Auer- bach and Ruff, 2004). The phenomenon of bone adapta- tion to imposed mechanical loadings is often loosely referred to as ‘‘Wolff’s law,’’ although as noted by others (Bertram and Swartz, 1991; Cowin, 2001b; Pearson and Lieberman, 2004; and see below), there are problems with this representation. Regardless of semantic issues, the general concept that bone adapts to its mechanical environment during life, and therefore that differences in morphology can be used to investigate differences in past mechanical environments, is widely accepted among paleoanthropologists and bioarchaeologists.

Several recent studies, however, beginning with the often-cited review by Bertram and Swartz (1991), called into question at least portions of ‘‘Wolff’s law’’ as it is generally understood (Forwood and Burr, 1993; Demes et al., 1998, 2001; Lovejoy et al., 2002, 2003; Ohman and Lovejoy, 2003; Lieberman et al., 2004; Pearson and Lie- berman, 2004). A number of issues have been raised, including the precise meaning of the ‘‘law,’’ the validity of the experimental evidence for bone functional adapta- tion, correspondence between in vivo strain measure- ments and bone structure, the genetic vs. environmental determinants of bone form, age dependency of bone func- tional response to loading, and whether skeletal mor- phology is mechanically ‘‘ideal.’’ Because the general con- cept of bone functional adaptation is so pervasive in bio- logical anthropology and indeed biology (Roesler, 1987), it is important to carefully evaluate these issues/objec- tions and their implications for current research approaches. We do so here, and attempt to clarify both the limits and potential of bone structural analyses. The emphasis here is on cortical bone distribution in long bone diaphyses, in part because most of the above stud- ies also focused on this aspect of skeletal form, and because this has been a very active area of anthropologi- cal research over the past several decades (e.g., Endo and Kimura, 1970; Kimura, 1971; Lovejoy et al., 1976; Jungers and Minns, 1979; Lovejoy and Trinkaus, 1980; Ruff and Hayes, 1983; Schaffler et al., 1985; Trinkaus and Ruff, 1989; Demes and Jungers, 1993; Ruff et al., 1993; Runestad, 1997; Trinkaus et al., 1999; Stock and Pfeiffer, 2001; Holt, 2003; Weiss, 2003; Beauval et al., 2005; Carlson, 2005). This list is not exhaustive; in fact, we make no attempt here to provide an encyclopedic review of recent literature on this general topic, which is voluminous (e.g., Martin et al., 1998; Cowin, 2001a; Pearson and Lieberman, 2004). Rather, we confine our- selves to key works that are specifically relevant to addressing the issues posed above and that provide his- torical context for the ideas of concern.


As noted by Cowin (2001b, p. 30–31), current usage of the term ‘‘Wolff’s law’’ usually involves only the general concept that ‘‘over time, the mechanical load applied to living bone influences the structure of bone tissue.’’ How- ever, he went on to point out that Wolff actually had something much more specific in mind, namely the for- mulation of strict mathematical rules governing this process, particularly with respect to the development of trabecular orientation in long bones (the ‘‘trajectorial theory’’), most famously expressed in the proximal femur. Wolff himself nicely summarized this argument in the introduction to his 1892 treatise (Wolff, 1892; translation in Wolff, 1986, p. 1): ‘‘Thus the law of bone remodeling is the law according to which alterations of the internal architecture clearly observed and following mathematical rules, as well as secondary alterations of the external form of the bone following the same mathematical rules, occur as a consequence of primary changes in the shape and stressing or in the stressing of the bones.’’

Many authors criticized Wolff ’s mathematical treat- ment of bone modeling/remodeling, which involved both engineering and biological misconceptions (for historical reviews, see Roesler, 1981, 1987; Martin et al., 1998; Cowin, 2001b). The ‘‘false premise in Wolff’s law’’ dis- cussed by Cowin (2001b) involves modeling real bones as solid, homogeneous, and isotropic structures subjected to static applied loads, which is strictly incorrect. However, neither Cowin (2001b) nor any of the other recent authors who critiqued Wolff’s law denied the importance of mechanical loading in the development of bone form, i.e., the more ‘‘general’’ version. This is an important point, since the two versions have sometimes been confused. For example, the critique by Cowin (2001b) (of the strict version) was cited by Currey (2002, p. 159) (again with reference to the strict version), who in turn was quoted by Ohman and Lovejoy (2003) in their more general critique of Wolff’s law. This confounding of the more general with the more specific version of the ‘‘law’’ unnecessarily con- fuses the issue: like many others, neither Cowin (2001b) nor Currey (2002) intended their critiques to imply a nega- tion of the general version; both authors have, in fact, spent most of their careers refining our knowledge of mechanically adaptive mechanisms in bone.

Given this potential confusion, it may be better to sim- ply discard the term ‘‘Wolff’s law’’ in its more general sense, as recommended recently by several authors (Martin et al., 1998; Cowin, 2001b; Pearson and Lieber- man, 2004). Following the original lead of Roux (1881), taken up by more recent investigators (Churches and Howlett, 1982; Cowin et al., 1985; Lanyon and Rubin, 1985), the term ‘‘bone functional adaptation’’ seems appropriate for this more general meaning. As summar- ized by Roesler (1981), the writings of Roux (1881) incor- porated two important principles: 1) organisms possess the ability to adapt their structure to new living condi- tions, and 2) bone cells are capable of responding to local mechanical stresses. Although not without their own problems (Roesler, 1981), the ideas of Roux (1881) encap- sulate much of the more general concept of bone func- tional adaptation as understood today. (In fact, as noted by Cowin (2001b), some researchers suggest renaming the more general version of Wolff’s law ‘‘Roux’s law.’’)

Figure 1 is a schematic diagram, taken from Lanyon (1982), of perhaps the simplest representation of bone functional adaptation in a more modern sense (see also Lanyon and Skerry, 2001). The bone modeling/remodel- ing stimulus is based on strain (not stress)—the actual physical deformation of the bone tissue—and acts through feedback loops. Increased strain (e.g., through an increase in activity level) leads to deposition of more bone tissue, which then reduces strain to its original ‘‘optimum customary level.’’ Decreased strain (e.g., through inactivity) leads to resorption of bone tissue, which again restores the original strain levels. Many other authors have embraced the general idea of a ‘‘cus- tomary’’ or ‘‘equilibrium’’ strain level window above which bone deposition is stimulated and below which resorption is stimulated (e.g., Carter, 1984; Frost, 1987; Turner, 1998), although there are many qualifications to and variations on this general model. One of the most important qualifications is that the ‘‘customary strain level’’ to which bone tissue is adapted is apparently not constant, but varies by skeletal location (Carter, 1984; Hsieh et al., 2001; Lanyon and Skerry, 2001; Lieberman et al., 2001; Currey, 2002) as well as by systemic factors such as age, disease state, hormonal status, and genetic background (Frost, 1987; Lee et al., 2003; Pearson and Lieberman, 2004; Suuriniemi et al., 2004). Also, the type of strain (its frequency and other characteristics), as well as the loading history of the bone cells, are important variables influencing the magnitude of bone response (Turner, 1998; Burr et al., 2002).

These complexities suggest that the general model shown in Figure 1 must be interpreted carefully and within specific contexts (e.g., comparisons between simi- lar skeletal regions in genetically similar animals), and that disentangling the effects of different loading compo- nents, such as load magnitude vs. frequency, may be very difficult from morphology alone. But increased com- plexity does not invalidate application of the general model, which is supported by much experimental evi- dence, reviewed below, with suitable caution (Lanyon and Skerry, 2001). In any event, arguments regarding the validity of the ‘‘strict’’ version of Wolff’s law must be distinguished from those concerning the nature of bone functional adaptation in general.


A series of now-classic papers from the 1960s through the 1980s appeared to provide clear evidence for bone functional adaptation to mechanical loading and unload- ing, using various experimental animal models (e.g., Saville and Smith, 1966; Hert et al., 1969; Liskova and Hert, 1971; Chamay and Tschantz, 1972; Uhthoff and Jaworski, 1978; Goodship et al., 1979; Jaworski et al., 1980a; Woo et al., 1981; Churches and Howlett, 1982; Lanyon et al., 1982; Lanyon and Rubin, 1984), as well as observations of human athletes (e.g., Nilsson and West- lin, 1971; Jones et al., 1977) (for a comprehensive review, see Meade, 1989). However, in their critique, Bertram and Swartz (1991, p. 23) argued that much of this evi- dence was inherently flawed because of problems in experimental design: ‘‘While accepting that mechanical load has substantial influence on the development of form in bone, we argue that to date there is no direct evidence of its influence on the healthy mature appen- dicular skeleton that is not seriously compromised by complications arising from indirect effects of the investi- gative procedures on other aspects of the organism’s physiology.’’ The ‘‘complications’’ that Bertram and Swartz (1991) referred to involve inflammatory re- sponses due to surgical treatment, and repair phenom- ena (regeneration of injured tissue, or repair of stress fractures), none of which they considered to properly fall under ‘‘Wolff’s law.’’ With regard to the first of these fac- tors, it should first be noted that the studies above that included surgical intervention generally included surgi- cal controls, i.e., bones in which all surgical procedures except the change in mechanical loading had been car- ried out, although as Bertram and Swartz (1991) and others pointed out, it is still difficult to completely con- trol for all related effects. There is also some question as to whether woven bone, a typical response (at least at first) to sudden mechanical overload, is ‘‘normal’’ or ‘‘pathological’’ (see also Frost, 1988). However, with regard to this latter issue, Burr et al. (1989, p. 232), in a carefully controlled experiment that intentionally incor- porated some features of earlier experimental work, demonstrated that ‘‘woven bone can be a normal adap- tive response to an intense mechanical challenge, even in the absence of trauma or fatigue-induced damage.’’

Partly in response to such criticisms, a series of inves- tigators beginning in the early 1990s developed new ani- mal models that did not involve invasive surgical proce- dures (Turner et al., 1991; Torrance et al., 1994; Forwood et al., 1998). These models have since been used exten- sively to study various aspects of bone modeling/remodel- ing under altered mechanical loadings (e.g., Hsieh et al., 2001; Burr et al., 2002; Robling et al., 2002).

shows the results of one such experiment (Robling et al., 2002). In this experiment, the forearms of 6-month-old rats were dynamically loaded in compression, which cre- ates bending stresses in the midproximal region of the bone due to its natural curvature. At this age, the rats can be considered ‘‘adults,’’ since no further growth in bone length occurred over the 16-week experimental period. The extra loading produced an increase of 70– 100% in bending rigidity (second moment of area) in the plane of bending compared to control limbs, through increased periosteal bone apposition in regions under the highest bone strain (Fig. 2). Bone strength determined through direct mechanical testing after sacrifice in- creased 64–165%, depending on the loading schedule and strength parameter. Interestingly, these gains were not well-represented by changes in bone mineral content (BMC) or bone mineral density (BMD), the two most commonly measured outcomes of human exercise stud- ies. Conversely, changes in the relevant second moment of area (a geometric property) explained 92% of the var- iance in strength (ultimate force). Similar results were obtained by Warden et al. (2005), who also demonstrated greatly increased fatigue resistance after experimentally increased loading in the same animal model. These stud- ies noninvasively reproduced and extended similar results of earlier studies (e.g., Lanyon et al., 1982) demonstrat- ing the specificity of bone adaptation to changes in strain distributions, and also the primacy of geometric changes in such adaptations (Woo et al., 1981).

Bertram and Swartz (1991) also argued that much of the change in bone dimensions observed in human ath- letes, and commonly attributed to increased mechanical loading, was actually a repair process in response to ‘‘chronic fatigue damage,’’ and as such did not qualify as support for ‘‘Wolff’s law.’’ It could be debated whether repair of fatigue-induced microcracks is actually outside the realm of ‘‘normal’’ bone mechanical adaptation, since such repair has been hypothesized to be an important component of bone remodeling throughout life (Martin et al., 1998). Other more recent studies of human athletes and volunteers in exercise intervention studies also showed clear evidence of adaptive bone modeling/ remodeling without evidence of fatigue (or stress) frac- tures, as reviewed below. The varying response of bone to applied loading is probably best viewed as a contin- uum, involving in some cases rapid deposition of woven bone (which can subsequently be remodeled into lamellar bone), in some cases repair of microcracks, and in other cases direct deposition of lamellar bone, depending on the severity and suddenness with which the loading schedule is implemented (Rubin et al., 1995). Also, not all bone fea- tures may react similarly to applied loading: in Robling et al. (2002), the distal ulnar articulations of experimentally loaded groups developed osteophytic reactions, which is perhaps not surprising given the very ‘‘abnormal’’ way in which the carpus was loaded (Fig. 2), and possible con- straints on articular remodeling (Ruff et al., 1991; Lieber- man et al., 2001) (what this might indicate regarding mechanisms underlying osteoarthritis was not addressed by the authors). However, the response in the diaphysis was ‘‘normal’’ in terms of bone tissue appearance (Fig. 4 in Turner and Robling, 2004). In summary, while experi- mental and observational studies have their limitations, such studies have clearly demonstrated that functionally adaptive changes in bone structure can be brought about by manipulation of mechanical loadings, supporting the general model shown in Figure 1.


Given that bone adaptation to mechanical loadings very likely involves a response to strains (deformations) engendered by such loadings, direct measurement of bone strains in vivo using strain gauges can provide important information in evaluating adaptive mecha- nisms (e.g., Fig. 2B, although in this case, strains were calculated in a simulated in vivo loading) (Robling et al., 2002). Three recent studies documented in vivo strains in the long bones of macaques (Demes et al., 1998, 2001) and sheep (Lieberman et al., 2004), and concluded that strain patterns were not well-correlated with cross-sec- tional geometry of the bones, thereby casting doubt on whether cross-sectional geometry could be used to recon- struct mechanical loading history. Specifically, the bend- ing axes generally did not match well with the neutral axes of sections, or conversely, sections were not rein- forced in regions of maximum strain (Lieberman et al., 2004) made a number of other points, which are ad- dressed below). It should be noted that none of these studies examined the effects of exercise per se on bone modeling/remodeling, but rather the normal patterns of strain during locomotion in laboratory animals.

The fact that long bone diaphyses may be customarily bent in planes that are not equivalent to their directions of greatest bending rigidity or strength was noted previ- ously (Lanyon and Rubin, 1985). Together with the observation that long bone curvature often seems to increase rather than decrease strains in vivo, this formed the basis for theories that bone structure may be designed in some cases to confine strains to more pre- dictable patterns, rather than strictly to minimize strains (Lanyon and Rubin, 1985; Bertram and Biewener, 1988). This is not inconsistent with the model shown in Figure 1: some degree of bending could actually be beneficial to bone tissue by maintaining strains within the ‘‘optimum customary’’ window (Lanyon and Rubin, 1985). At the same time, potentially catastrophic strains in ‘‘unusual’’ orientations could be avoided. Because of their more read- ily available surfaces for attaching strain gauges, the dis- tal limb elements of cursorial animals (horses, sheep, and dogs) were most often used in these experiments (see also Lieberman et al., 2004). These skeletal locations are rela- tively ‘‘unprotected’’ medially and laterally by muscle ten- dons (one reason that they are more accessible for strain gauges) (e.g., see Piotrowski et al., 1983; Thomason, 1985). Thus, any unusual bending in the mediolateral plane (e.g., due to turning or walking over uneven ground) is probably less able to be modified by muscles, making this a more ‘‘dangerous’’ loading orientation for the bones. In these situations, it is not unreasonable to postulate a genetically selected difference in strain sensitivity thresh- olds that would favor the development of an elliptical cross section oriented to increase mediolateral (M-L) bending strength (Lanyon et al., 1982; Piotrowski et al., 1983; Nunamaker et al., 1989; Lieberman et al., 2004).

Of course, postulating genetic mechanisms that alter the ‘‘optimum customary’’ strain sensitivity of bone tis- sue argues against making comparisons between species that are not closely related, and for whom genetic selec- tion histories may have been significantly different: one would not want to use differences in cross-sectional shape between a human and horse long bone to recon- struct behavioral differences between them! In this respect, we fully concur with the caution by Demes et al. (2001, p. 264) ‘‘against broad behavioral conclusions derived from long bone cross-sectional shape.’’ However, comparisons within species or between closely related species who share the same basic body design and evolu- tionary history are much less likely to be confounded by such factors (see also Lieberman et al., 2004). In this regard, it is interesting that even in highly cursorial ani- mals, activity patterns appear to affect long bone cross- sectional geometry in predictable ways. Thoroughbred and standard-bred horses differ in cross-sectional geome- try of the third metacarpal (cannon bone), such that thoroughbreds, who are subjected to more rigorous train- ing of a type that specifically engenders high strains in the anteroposterior (A-P) plane, have more A-P strength- ened bones (Nunamaker et al., 1990). McCarthy and Jeffcoat (1992, p. 35), in an experimental study of young (yearling) thoroughbreds, also documented a site-specific effect of exercise in these animals: ‘‘In the unexercised group periosteal bone apposition occurred uniformly around the third metacarpal without selective enlarge- ment of any cortex. The increased thickness of the dorsal cortex in the exercised horses means that the bone is bet- ter able to withstand loading of this cortex where very high compressive strains can occur during locomotion.’’2 These results are consistent with the view that there is a basic structural model, in part genetically determined, of the horse third metacarpal that can then be modified by specific environmental (mechanical) stimuli (for a very similar argument, see Turner, 1998). This is very much analogous to comparisons of the same skeletal element within or between human populations with different behavioral characteristics (e.g., Ruff, 1987; Stock and Pfeiffer, 2001): because the basic underlying model is sim- ilar, variations in morphology are more likely to reflect variations in applied loading throughout life.

The above reasoning also argues for caution in extrap- olating results of strain gauge experiments between skel- etal locations or species with very different body plans and evolutionary histories. There is evidence that strain distributions in bones/species that are less specialized for cursorial locomotion more closely match traditional expectations of greater bone strength in directions of higher strain, especially during vigorous movement. Fig- ure 3 shows some of the results of Demes et al. (2001) on strains in the macaque tibial mid-diaphysis during walk- ing and galloping, and of Szivek et al. (1992) on strains in the greyhound femoral mid-diaphysis at various speeds (although the greyhound is certainly well-adapted for cursorial locomotion, its femur is surrounded by muscles in much the same way as a noncursorial ani- mal). In both cases, anterior and posterior strains in- creased with increasing speed. In the macaque tibia, the bending axis (the axis around which the bone is bent) during galloping moved to within 198 of the M-L axis, and to within about 138 of the neutral axis of the section (the axis about which bending rigidity is greatest) (Fig. 3A). That is, the greatest strains during galloping were experienced in almost the same direction as that of maxi- mum bending rigidity. In the greyhound femur, the bend- ing axis similarly rotated to a more M-L orientation (228 from the M-L axis) as speed increased from 0.61 to 2.44 m/sec, the former a slow walk and the latter a trot (Rubin and Lanyon, 1982) (Fig. 3B). While the neutral axes of sections were not calculated in this study, Szivek et al. (1992, p. 105–106) noted that during running, ‘‘the peak strain regions shifted to the anterior and posterior aspects of the bone… The shape of the cross section of the grey- hound femur at the mid-diaphysis (i.e., oblong) may be a result of this strain distribution while the dog performs.’’ Carter et al. (1981; see their Fig. 6) obtained very similar results for a mixed-breed dog moving at a speed between the two higher speeds shown in Figure 3B.

It should also be noted that in both of the studies depicted in Figure 3, the magnitude of maximum strain increased substantially in moving from a walk to a trot or gallop, as would be expected (Rubin and Lanyon, 1982). Because the stimulus for bone functional adaptation is dependent on strain rate, which in turn is dependent on strain magnitude and frequency (Turner, 1998), it is likely that more dynamic activities are far more osteogenic than slow walking (although small strains may also be osteo- genic; see Fritton et al., 2000). As observed by Rubin and Lanyon (1982, p. 206) in their now-classic review of in vivo strain gauge results, ‘‘The association which natu- rally exists between high peak strains and high strain rates will therefore result in bone architecture being pref- erentially influenced by the strains encountered during periods of vigorous, rather than more sedentary, activity’’ (see also Mikic and Carter, 1995). This is closely related to the ‘‘cellular accommodation’’ theory of Turner (1999), whereby bone cells are only stimulated by more ‘‘unusual’’ loadings. It can be presumed that galloping or trotting in the macaques and dogs included in Demes et al. (2001) and Szivek et al. (1992) was a relatively unusual, although certainly not unknown, activity compared to walking. The fact that the cross-sectional shape of both bones better corresponded with strains engendered during running may be a product of the higher strains produced by this more unusual, but still ‘‘characteristic’’ loading. This suggests that bone structure is correlated with activ- ity, and primarily vigorous activity.

In the other study by Demes et al. (1998; see also Demes et al., 2001), maximum strains in the macaque ulnar midshaft were always located closer to the medial and lateral cortices, regardless of speed of locomotion (although the location of peak strain moved slightly toward the anterior and posterior cortices during gallop- ing), while the bones were slightly stronger in the A-P direction. This would seem contrary to the scenario pre- sented above. However, unlike the tibia, the macaque ulna is part of a more ‘‘multifunctional’’ (Schaffler et al., 1985) forelimb complex that serves in a greater variety of roles, both locomotor and nonlocomotor, than do the hindlimb bones. Even during locomotion, the macaque forelimb experiences significant changes in applied load- ings, depending on substrate (Schmitt, 2003). Significant load-sharing with the radius, which is actually stronger than the ulna in cercopithecoids (Ruff, 2002), further complicates interpretations. In many ways, then, the loading environment of the macaque tibia is probably simpler and more predictable than that of the ulna, with more stereotypical positioning of the limb, muscle recruitment, and resultant strain patterns (e.g., peak strains in the macaque ulna actually declined from walking to galloping (Demes et al., 1998), which has not been reported in studies of other bones/species). In terms of behavioral reconstructions, interpretations of forelimb bone cross-sectional shape will be similarly complex, although overall forelimb relative to hindlimb strength proportions are still informative regarding general loco- motor behavior (Stock and Pfeiffer, 2001; Ruff, 2002).

We should also remember that, in adults at least, strain gauges measure deformations in bones that have already adapted to mechanical loading. As noted above, if the most osteogenic strains are those that occur under vigorous loadings such as running, the bone will adapt by altering its geometry accordingly, following the gen- eral model in Figure 1. The strains developed during less vigorous (but more common) loadings such as walking would thus be, in effect, ‘‘residual’’ strains that are insuf- ficient to stimulate modeling/remodeling (Turner, 1999). This could lead to misinterpretations of strain gauge data in terms of in vivo loadings. For example, if large A-P bending loads of certain limb bones occur during running that create large strains on the anterior and posterior surfaces, which in turn stimulate bone deposi- tion on those surfaces, then during walking (where A-P bending loads are probably much smaller), anterior and posterior surface strains will be small, and medial and lateral surface strains relatively larger. This does not, however, indicate that bending loads (even in walking) are typically larger in the mediolateral direction. Thus, one must be careful in extrapolating from strains to loads.

The strain gauge study in sheep by Lieberman et al. (2004) addressed two other issues relevant to interpreta- tions of long bone cross-sectional geometry: does the axis of bending of a long bone pass through the section cen- troid, and does this axis remain in a similar position throughout locomotion (stance)? Both questions were answered in the negative. The first result is similar to that obtained by other researchers or implied by their results (e.g., Carter et al., 1981; Rubin and Lanyon, 1982; Szivek et al., 1992). Because of the superimposi- tion of axial compressive on bending loads in most long bones, overall compressive strains are higher than ten- sile strains; the axis of bending (0 strain) correspond- ingly shifts toward the tensile side, thereby no longer passing through the section centroid (Fig. 3B; see also Fig. 2 in Lieberman et al., 2004). This is significant because geometric section properties that reflect bending rigidity and strength (second moments of area and sec- tion moduli) are typically calculated around axes that pass through the section centroid (e.g., Ruff and Hayes, 1983; Sumner et al., 1985). Thus, rigidity or strength estimates based on such properties will be in error, by as much as 30–50% (Lieberman et al., 2004). It should be noted, first, that these results do not affect past interpre- tations of the pure bending rigidity/strength of long bones; second moments of area and section moduli, as traditionally calculated, are still valid representations of such properties. What is strictly invalid is the implied assumption that in vivo loadings are, in fact, pure bend- ing loads. In studies that can be used to directly assess this assumption in vivo, the degree of deviation of bend- ing axes from section centroids can be quite variable, even at the same skeletal location and within the same species: between different phases of the stance cycle, dif- ferent animals, right and left limbs of the same animal, and even in repeated trials of the same limb of the same animal (e.g., Figs. 2 and 5 in Szivek et al., 1992). The bending axis may shift from one side of the section cen- troid to the other, depending on these factors (Szivek et al., 1992; Demes et al., 2001). In other words, there is no consistent ‘‘correction’’ factor that can be incorporated into section property analyses to account for these varia- ble deviations.

This is closely related to the second of the results of Lieberman et al. (2004): because of changes in ground reaction forces, limb positioning, and muscle forces dur- ing locomotion, bending axes cannot remain in exactly the same position relative to the cross section. This is clearly implied by earlier studies, such as Carter (1978), based on work originally reported by Lanyon et al. (1975), of strains in the human tibia during walking and jogging, in which longitudinal strains on one surface of the cortex shifted between tensile and compressive within one gait cycle. Because in this study, strain data were collected on only one surface (anteromedial), strain distributions cannot be determined; however, these results necessitate a major shift in the bending axis across the tibial cortex during gait. This is perhaps not surprising, given the variable position of the human tibia relative to the body’s center of gravity and chang- ing muscle actions during gait (Inman et al., 1981).

Thus, even with in vivo strain gauge data in hand, it is not possible to precisely define the position of the bending axis of a long bone section, because it varies constantly during use of the limb, both between and within individuals. Therefore, it is not possible to factor this into bone structural analyses, except perhaps in a general sense (Griffin and Richmond, 2005). In fact, it might be counterproductive to attempt to do so, at least quantitatively, because the particular choice of bending axis could bias results in unpredictable ways. Thus, it is probably advisable to continue to report section proper- ties (second moments of area and section moduli) relative to centroidal axes, with the understanding that these are only approximations of true bending rigidity and strength in vivo. In this respect, it is reassuring that Lieberman et al. (2004) obtained correlations of about 0.9 or better between section properties measured to centroidal axes and those measured to an average bending axis deter- mined experimentally. Also, since the main interest of many anthropological and paleontological studies is the relative importance of different types of mechanical load- ings, deviation of absolute estimated rigidities or strengths from actual values (even if such values were constant and could be determined) is of less concern, provided that the basic mechanical model is similar between the individuals being compared (see above).

Finally, as recognized by the investigators themselves, strains measured in laboratory animals moving on a treadmill at constant (and usually fairly low) speeds and in a straight line are not representative of the full range of variability present during normal activities (Lieberman et al., 2004), and only occasionally measure strains at the more important (see above) higher gait velocities. As noted by Dickinson et al. (2000, p. 105) in a wide-ranging review of animal locomotion, ‘‘In nature, unlike in the lab- oratory, straight-line, steady-speed locomotion is the exception rather than the rule.’’ Variable directionality of movement may explain, for example, why bones subjected primarily to A-P bending in typical treadmill exercises are still reinforced mediolaterally (Fig. 3, and see above). Mikic and Carter (1995, p. 465) were more explicit:

‘‘One difficulty that is encountered when using bone strain data in studies of functional adaptation is that reported data are often far from a complete record of strain over an experimental period. On the contrary, the reported results generally consist of a few average cyclic strain parameters that are extracted from a short period of recordings while an animal performs a very restricted task. Most inves- tigators agree, however, that a much more complete record of strain history is required to relate bone biology and morphology to strain. Such records should include the many diverse activities of the animal, including cage activity.’’

This is admittedly a very difficult task, and may not be totally achievable, even for animals in a controlled laboratory environment (but see Fritton et al., 2000, for example). Thus, researchers have turned to theoretical modeling approaches (extrapolated from available in vivo data) in an attempt to determine the influence of overall loading history on bone morphology (e.g., Carter, 1987; Beaupre et al., 1990; van der Meulen et al., 1993; Mikic and Carter, 1995). However, these observations empha- size some of the problems inherent in using data of this kind.

This is not to say that in vivo strain gauge studies cannot provide very valuable information: strain studies in animals have been critical in investigating general bone adaptive mechanisms (e.g., Fig. 2), and the few in vivo studies of strain in human (Lanyon et al., 1975; Burr et al., 1996; Aamodt et al., 1997; Carter, 1978) and nonhuman primate (Swartz et al., 1989; Demes et al., 1998, 2001) long bones helped clarify mechanical load- ings of these skeletal elements. Any morphological stud- ies should carefully consider such evidence and its impli- cations for reconstructing behavior. However, we also need to carefully consider the limitations of such data when applied to ‘‘real life’’ situations, i.e., the total load- ing history of a bone.


The pace of discovery of new genetic mechanisms underlying bone growth and development has increased dramatically over the past several decades (for recent reviews in the anthropological literature, see Chiu and Hamrick, 2002; Lovejoy et al., 2003; Pearson and Lieber- man, 2004). Building on these discoveries, Lovejoy et al. (2002, 2003) argued forcefully for the importance of genetic mechanisms in the determination of bone mor- phology, and conversely, the relative insignificance of ‘‘mechanoanabolism,’’ or the functional adaptation of bone to perceived mechanical stimuli during life. These arguments tend to dichotomize genetic and environmen- tal effects: ‘‘The most relevant issue for anthropologists is the degree to which adult bone structure is indicative of genetic background versus its history of load trans- duction’’ (Lovejoy et al., 2003, p. 101), with genetic influ- ences argued to be paramount: ‘‘External bone morphol- ogy now appears to be largely dictated by an integrated system of sequentially expressed gene arrays’’ (Lovejoy et al., 2002, p. 99). While we fully agree that a better understanding of bone developmental genetics is impor- tant for explaining the evolution of skeletal morphologi- cal variation (e.g., Shubin et al., 1997; Hallgrimsson et al., 2002; Hamrick, 2003), we believe that this rather polarized view is counterproductive: because genetic mechanisms are important does not mean that direct environmental stimuli are not; in fact, in certain respects, the two may be inseparable (Martin et al., 1998, p. 270–271; also see below). As shown above, it is obvious that mechanical loading during life can have a strong effect on variation in bone morphology. Minimiz- ing the importance of mechanical effects artificially restricts the scope of inquiry, and hinders attempts to provide a complete explanation for this variation.

Another factor that must be carefully considered in this context is variability between different types of skel- etal features in the extent to which they are environ- mentally modifiable during life. For example, long bone articular size appears to be less affected by changes in mechanical loading than cross-sectional diaphyseal size (Ruff et al., 1991; Lieberman et al., 2001). The great majority of developmental genetic studies of the skeleton examined variation in gross morphological features (e.g., patterns of limb element organization); bone ‘‘size’’ fea- tures such as mass, volume, and length; or bone ‘‘den- sity’’ (usually not true tissue density). Heritability esti- mates for bone mineral content (BMC) and bone mineral density (BMD), the most commonly measured bone parameters, average about 60–70% in humans, but if covariation with body mass is accounted for, this falls to about 50% (for an excellent review, see Prentice, 2001). However, such skeletal traits do not provide estimates of mechanically relevant parameters (Sievanen et al., 1996; van der Meulen et al., 2001). Volkman et al. (2003, 2004) carried out a more relevant study in which they assessed genetic effects on cross-sectional geometric and other mechanical properties of the mouse femur, using quanti- tative trait loci (QTL) analysis. They found evidence for complex genetic control of these characteristics, but at a low level: genetic markers accounted for only 3–22% of trait variances. They discussed several possible path- ways through which genes may influence bone structure: 1) a direct influence on bone size and shape (i.e., directed activity of osteoblasts and osteoclasts); 2) an indirect effect on factors such as body weight, muscle strength, and activity level, which in turn alter mechanical load and thus bone structure; and 3) an effect on responsive- ness of bone to applied mechanical loading (i.e., ‘‘set points’’ in a ‘‘mechanostat’’-like mechanism; see Frost, 1987; Martin et al., 1998, p. 270–271). The interaction between genetic and environmental effects is prominent in the second two of these proposed mechanisms. Other investigators, in fact, demonstrated varying mechano- sensitivity in different mouse strains (Kodama et al., 2000; Robling and Turner, 2002).

Many other recent studies found evidence for some heritability of various bone structural traits, sometimes sex-linked (e.g., Peacock et al., 2005, and references therein). It is important to note that these studies do not provide estimates of actual genetic determination of traits, however (Prentice, 2001), and that as noted above, final adult morphology is likely to be a complex product of genetic-environmental interactions. A good example of this is the interaction between the gene(s) encoding for the estrogen receptor a (ER-a) and physical exercise: both the receptor and increased mechanical loading are necessary to increase bone mass (Lee et al., 2003; Suuriniemi et al., 2004). As Lanyon and Skerry (2001, p. 1938) pointed out, ‘‘although systemic influ- ences may modify mechanically adaptive processes, they cannot substitute for them,’’ i.e., regardless of genetic background, appropriate mechanical loading is necessary to develop normal adult form. This was demonstrated in experiments early in the last century in which bones iso- lated from mechanical loading during growth still devel- oped the general features of their normal counterparts, but not the specific morphological details (Murray, 1936). The major evolutionary features of skeletal morphology (e.g., what makes a horse skeleton different from a human skeleton) may be principally genetic, but what makes one horse (or one human) skeleton different from another is likely to be a product of both genetics and environment, with different skeletal features more or less environmentally modifiable. Thus, understanding both genetic and environmental influences is critical to understanding morphological variation.


Another issue discussed by Bertram and Swartz (1991) was the apparent age-specificity of bone response to changes in mechanical loading, particularly a reduction in mechanical loading (e.g., Jaworski et al., 1980b), which might argue against a universally applicable ‘‘Wolff’s law.’’ Bertram and Swartz (1991, p. 267) also noted a distinction between modification of growth pat- terns and functional adaptation in the ‘‘mature’’ skele- ton: ‘‘It appears to us that many of the adjustments of bone form associated with mechanical loads result from the interaction of load with the developmental/growth process, which in bone normally persists into young adulthood (mid-20’s or later in human studies).’’ It is important to recognize that the ‘‘growth’’ period, as they defined it here, includes early adulthood, extending be- yond adolescence as usually defined. This would corre- spond to the ‘‘positive’’ period of skeletal growth where bone mass is normally increasing, even though growth in bone length has largely ceased (Riggs and Melton, 1992).

Forwood and Burr (1993) reviewed earlier animal and human exercise studies across different age groups. They concluded that while the main function of mechanical loading in the adult skeleton was to conserve or main- tain existing bone, ‘‘exercise can, in fact, add small amounts to bone mass of the adult skeleton,’’ on the order of a few percent, although this adaptation ‘‘is mod- est when compared with that in growing bone’’ (Forwood and Burr, 1993, p. 100). They also noted that very inten- sive exercise can stunt growth in growing bones. Pearson and Lieberman (2004) reviewed the evidence for a reduc- tion in osteogenic potential on a cellular level with aging. It should be noted, however, that the most drastic reductions occur in aged or senescent adult cells, so this factor may not be as applicable to comparisons between juveniles and young adults.

With respect to anthropological reconstructions of past behavior, the key question raised by these studies is: to what extent is the morphology of adult bones indicative of the mechanical loading of these bones during adult- hood? This question can be subdivided into two related questions: first, can mechanical loading significantly change bone morphology after the childhood and adoles- cent years, and second, regardless of the answer to the first question, is adult bone morphology still informative with regard to adult loadings?

The first question can be answered in the affirmative, although it is also apparent that the bone response to mechanical stimuli is more marked in juveniles than in adults (Forwood and Burr, 1993; Turner et al., 2003). Part of the problem with evaluating bone sensitivity to mechanical loading in adults is that the response is probably slower than in juveniles; thus, long-term longi- tudinal studies may be necessary to clearly document effects. Many prospective exercise studies of human adults also have problems in study design, including nonrandomization of subjects, poor compliance, small samples, failure to control for other confounding effects, and failure to measure effects at the actual site of skele- tal loading (Kerr et al., 1996), all of which may contrib- ute to inconsistency of results across studies (Pearson and Lieberman, 2004). One of the best-controlled studies in older adults was by Kerr et al. (1996), who examined the effects of weight-training on BMD at several skeletal sites in postmenopausal women (mean age, 58 years at start of program) over a period of 1 year. The weight- training, three times per week, was carried out on either the right or left upper and lower limbs, with the opposite limb serving as an internal control, thus inherently accounting for systemic variables such as genetic influ- ences, diet, hormonal status, and body weight. Their results for the distal radius are shown in Figure 4. As with many such studies in adults, the effects were rela- tively small (an average gain of 2.4% on the exercised side, compared to a loss of 1.4% on the control side), but significant. Statistically significant positive effects of exer- cise were also seen in the hip region. Interestingly, exer- cises aimed at increasing strength (higher weights, lower number of repetitions) had a more positive effect than those aimed at increasing endurance (lower weights, more repetitions). This suggested that the magnitude of loading (or rate of change in magnitude of loading) was more important than the number of loading cycles, which agrees with some animal experimental results (see refer- ences above).

Another observation apparent in Figure 4 is that a shorter-term study of a few months would not have picked up the significant effect of the exercise treatment. This factor should be kept in mind when evaluating results of shorter-term exercise studies in humans, or in other large, relatively long-lived mammals. Because of variable exigencies such as subject compliance and reten- tion (in human studies) and caretaking expenses (in ani- mal studies), these investigations are commonly carried out over short periods relative to total lifespan. This also has more general implications regarding interpretations of mechanical loading effects in adults: response to load- ing may be slower than in juveniles, but the total adult period available for functional adaptation is longer; thus, cumulative effects (positive or negative) may be larger than would be predicted by short-term studies.

This point was emphasized in a recent long-term longi- tudinal study of young adult female soccer players (Valdimarsson et al., 2005). The subjects averaged 18 years of age at the beginning of the study and were fol- lowed for 8 years, a long time period compared to most prospective studies. Bone mineral content and density of the whole body and BMD at various anatomical locations were evaluated using dual X-ray absorptiometry (DXA) at baseline and at follow-up. A control group of non- athletes of similar age was also followed over the same time period. In players who remained active throughout the period, BMC and BMD increased, and differences from controls increased (from 4% greater at baseline to 9–12% greater at the end in the total body, and from 7% at baseline to 14% greater in the leg; our calculations). Players who had retired from play during the follow-up period began with higher values than controls, but then showed no further increase over controls. Valdimarsson et al. (2005, p. 910) noted that while ‘‘exercise in adult- hood has been described as at best conferring BMD ben- efits of a few percentage points . . . this notion is only  supported by short-term prospective controlled studies spanning, at best, 24 months.’’ The age period evaluated in this study can appropriately be termed ‘‘postadoles- cent’’ (there was no change in height among the active players), but it does fall within the early adult ‘‘develop- mental/growth’’ period as defined by Bertram and Swartz (1991) (see above).

The bilateral asymmetry model used by Kerr et al. (1996) was also exploited in a series of studies of the playing and nonplaying upper limbs of athletes in racket sports. In one such study (Kannus et al., 1995), the age- dependence of exercise effects was specifically addressed by comparing bilateral asymmetry in upper limb BMC of adult ‘‘national-level’’ female tennis and squash players who had started playing at ages varying from young childhood to young adulthood. All individuals had played for at least 5 years, and the number of years of training was not a significant covariate. A progressively greater effect on bilateral asymmetry was seen in individuals who had started playing earlier: in the humeral shaft, the earlier starters averaged 20–24% asymmetry, while the older starters averaged 8–10% asymmetry. This result has been repeatedly cited as providing evidence for the age-specificity of mechanical loading on bone (Fig. 6 in Turner and Robling, 2003; Fig. 12 in Pearson and Lieberman, 2004; but note misattribution of data to another study), and it does appear to demonstrate a declining response after early adolescence. However, it is also noteworthy that even the oldest starters in this study, averaging 34 years of age when they began play- ing, still had about three times greater bilateral asym- metry than the controls included in the study. Thus, even in this age range, increased mechanical loading appears to significantly increase bone mass. Because the study was cross-sectional in design, it is not possible to say for sure how much bone was actually gained during the playing period. However, from an anthropological perspective, the greater asymmetry in the older-starting players would be correctly interpreted as reflecting greater asymmetric use of the upper limbs during adult- hood.

As noted earlier, BMC and BMD are not true mechani- cal characteristics, and their interpretation can be con- founded by nonconcordant and nonlinear changes in sub- periosteal and endosteal breadths during growth and young adulthood (Frisancho et al., 1970; Ruff et al., 1994; Petit et al., 2004). Significant changes in bone strength can occur with relatively small changes in BMC or BMD (Robling et al., 2002; Warden et al., 2005). A number of studies incorporated more mechanically rele- vant properties into evaluations of exercise effects in human subjects, using the upper limb bilateral asymme- try model. Ruff et al. (1994) and Trinkaus et al. (1994) reanalyzed radiographic data originally collected by Jones et al. (1977) for male and female professional ten- nis players (mean age, 25 years; mean starting age, 10 years). Median asymmetry in the polar second moment of area, J (a measure of bending/torsional rigidity), of the mid-distal humeral shaft was 57%, compared to median asymmetries near 10% in recent ‘‘normal’’ popu- lations. We also found an age effect, with players who started playing earlier showing more asymmetry due to greater subperiosteal expansion. However, the individual in the sample who started playing the latest (a male who started playing at age 19 years) still showed asym- metry in J of 31%. Haapasalo et al. (2000), using periph- eral quantitative computed tomography (pQCT), found mean bilateral asymmetries of 39–46% in second moments of area of the humeral midshaft in male Finn- ish ‘‘national top-level’’ tennis players (mean age, 30 years; mean starting age, 10 years). No evidence for any exercise effect on cortical bone density was found, i.e., mechanical adaptation to increased loading appeared to be all geometric (paralleling animal exercise studies, e.g., Woo et al., 1981). Kontulainen et al. (2002), also using pQCT, measured bilateral asymmetry in geometry and bone density of the upper limb bones in a subset of the same sample studied by Kannus et al. (1995). Mean asymmetry in a strength index that combined J and bone density of the humeral midshaft was about 26% in