, David B. Burr2, Neil A. Sharkey3 and David P. Fyhrie4
Orthopaedic Surgery, UC Davis Medical Center, Olga, WA, USA
Department of Anatomy and Cell Biology, Indiana University School of Medicine, Indianapolis, IN, USA
Kinesiology, Orthopedics and Rehabilitation, Pennsylvania State University, University Park, PA, USA
Orthopaedic Surgery, Biomedical Engineering, UC Davis Medical Center, Sacramento, CA, USA
Bone is exquisitely sensitive to its mechanical environment. The mechanisms by which this occurs from the biochemical to the organ level are explored in this chapter. Various models used to explain mechanical adaptation are also described. Cartilage is less adaptive, but several models have been proposed to explain how cartilage develops and adapts to loads.
KeywordsWolff’s lawMechanotransductionStrainMechanostatHabituationFluid flowDamage repairChondral modeling
Every change in the form and function of … bone[s] or of their function alone is followed by certain definite changes in their internal architecture, and equally definite secondary alterations in their external conformation, in accordance with mathematical laws. J. Wolff as quoted by Keith (1918).
The idea that bone structure is somehow controlled locally to suit its current mechanical function has become a central tenet of orthopaedic medicine and science. The goal of this chapter is to come to grips with this idea. As a scientific hypothesis, the putative ability of bone not only to repair itself, but to adapt to variations in imposed stresses, which we now know as Wolff’s Law, is an extremely appealing idea to engineer and biologist alike. However, developing this idea into a scientific theory supported by appropriate experimental results has proven to be a hefty scientific problem. In the following pages we take up this problem, trying to organize into a coherent theory the principal hypotheses and more recent experiments found in the literature on this subject. First, however, it is helpful to review the origins of Wolff’s law and the concepts that it represents.
6.2 The Historical Context
What is today called Wolff’s law incorporates several different concepts, most of which Wolff himself said nothing about. Following the lead of Roesler (1981, 1987), we focus on three key concepts that arose in the nineteenth century:
Optimization of strength with respect to weight
Alignment of trabeculae with principal stress directions
Self-regulation of bone structure by cells responding to a mechanical stimulus
The idea that bone senses and adapts to its mechanical environment is an old one. Julius Wolff wrote about the link between mechanics and architecture in the late 1800s and is routinely given credit for this idea, but he was certainly not the first to make the observation. Galileo (1638) pointed out the mechanical implications of the shapes of bones, as did other early writers (Monro 1976). Bell (1827) observed that cancellous bone structure had “reference to the forces acting on the bone.” Both he and Bourgery (Bourgery 1832) apparently recognized that trabecular bone architecture is influenced by mechanical forces, and thought that it maximized strength relative to the amount of material used. This relationship is the first important concept that we want to recognize: optimization of bone strength (or stiffness) with respect to its weight. This is vitally important because the density of bone tissue (about 2 g/cm3) is twice that of other tissues in the body. The metabolic cost of carrying about extra bone is very high. It is perhaps unlikely that Bell and Bourgery ever considered this; they may simply have been struck by the obviously exquisite structure of cancellous bone, which looks so efficient!
Ward (1838) compared the trabecular arrangement in the neck of the femur to a bracket designed to hold a street lamp to its post (Fig. 6.1). We now apply the name Ward’s triangle to the region of sparse trabecular struts corresponding to the central opening in this “bracket.” Ward’s comparison is significant because it is an early recognition that bone structure is analogous to structures engineered by people and that bone does not remain where it does not need to be.
We come now to the second key concept, which arose from a legendary conversation between Karl Culmann and Hermann von Meyer. The story goes that one day in 1866 Prof. Culmann, a well-known engineer, visited the laboratory of Prof. Meyer, an equally well-known anatomist, and happened to see a specimen of a proximal human femur that had been sectioned longitudinally to reveal its pattern of trabecular arcades. Culmann was immediately struck by the similarity of this pattern to that of the principal stresses within a crane structure which he had analyzed (Fig. 6.2 shows sketches of these two objects). He is said to have cried out “That’s my crane!” (Thompson 1992).1 The crane was actually named after Fairbairn, the Scots engineer who designed it. Its flowing, bonelike shape is typical of the trial-and-error designs common during the early industrial revolution in Great Britain. It is interesting to note that elasticity theory and the science of strength of materials were rapidly developing during this period of time. Augustin Cauchy had, in about 1822, discovered the existence of principal stresses, but decades passed before engineers began to make practical use of the concept. Culmann was one of the first to understand and use the concept of principal stress directions; he was one of several engineers from the continent who led the way in developing a mathematical theory of mechanics, which eventually refined the experimental approaches of British and American engineers. He had apparently been applying his graphical methods for calculating principal stress directions to Fairbairn’s crane. In any event, the similarity between the trabecular arcades and the stress trajectories is indeed striking. Clearly, however, the shapes and loads are substantially different for the crane and the femur. Not only that, but the femur is a discontinuous collection of bony struts filled with marrow, while the crane is a homogeneous structure. Principal stresses do not exist for a discontinuous structure. The significance of this was overlooked for a long time (Cowin 1997). We shall return to this issue several times in this chapter.
(Left) Principal stress trajectories in a Fairbairn crane as calculated by Culmann. (Right) The trabecular arrangement in a proximal human femur as sketched by von Meyer.
This conversation was noted by others interested in bone, including Wolff, and soon afterward he began to publish papers on this subject (Wolff 1869, 1870). His interpretations of cancellous architecture quickly rose to dominance. He accepted at face value the implications of the Culmann–Meyer stress-trajectory hypothesis and asserted that there was a mathematically perfect correspondence between trabecular architecture and principal stress trajectories. This similitude is what Wolff’s law meant to Wolff, and it is our second key concept.
Wolff went on to try to explain the trabecular structure within many pathologic specimens using this basic idea. In 1892, he published his famous book, Das Gesetz der Transformation der Knochen (The Law of Bone Transformation), which summarized his earlier writings.2 It must be appreciated, however, that while he spoke of mathematical rules governing trabecular architecture, he was not an engineer or mathematician, and never attempted to formulate a mathematical theory of “Wolff’s law.” Furthermore, he believed that bone was formed interstitially (i.e., cells pushed out new bone from within the calcified matrix—a physical impossibility), and had no understanding of bone modeling and remodeling as we know them.
Later, Koch (1917), an engineer as well as a physician, resolved some of the issues regarding the comparison of Culmann’s stress trajectories for the Fairbairn crane with a human femur. He calculated the stress trajectories in a human femur based on a reasonably accurate load applied to the head and geometry obtained from actual anatomic measurements. In doing so, he was able to demonstrate that trabecular orientations are, after all, similar to mathematical calculations of stress trajectories for a homogeneous structure of the same shape (Fig. 6.3).
We must return now to the nineteenth century, to note the emergence of the third key concept regarding the adaptation of bone to mechanical loading: the idea that this occurs via a self-regulating biologic mechanism. While it may seem obvious to you that this must be the case, that is only because you have been educated in an era when self-regulation is accepted as an essential part of biological organisms. That was not the case in the time of Wolff. It was in his century that Claude Bernard (1813–1878) introduced the idea of homeostasis to physiology: the concept that physiologic systems self-regulate so as to keep a critical internal variable constant. However, it was many years before the full significance of this concept came to be appreciated and accepted. Thus, it was still a fundamentally new idea when, in 1881, W. Roux, influenced by Darwin and others, hypothesized that organisms possess the ability to adapt to changes in their living conditions (Note that we are not speaking of evolution here, which involves long-term, genetic changes between one generation and the next, but changes in an individual during its lifetime, even day-to-day or minute-to-minute changes. Also, we are not speaking of adjusting to internal, physiologic changes, but to changes involving interactions with the external environment). Roux specifically proposed that the ability of bone to align trabeculae with stress trajectories was accomplished by cells forming and resorbing bone according to variations in a functional stimulus, in this case, a mechanical stimulus. While his imperfect understanding of biology and mechanics led him to make many mistakes in developing his theory, his concept of self-regulated functional adaptation governed by cell sensitivity to a functional stimulus was extremely important.
In summary then, as Roesler (1987) has pointed out, nineteenth-century researchers provided us with three key concepts regarding bone’s ability to adapt to changing mechanical loads: bone structure optimizes strength with respect to the amount of material used; trabeculae line up with principal stress directions; and these things are accomplished by a self-regulating system of bone cells responding to a mechanical stimulus. Today, Wolff’s law remains a rather poorly defined “law,” but it more or less includes these three core principles.
6.3 Mechanical Adaptability and Evolutionary Adaptability
There has been considerable debate among engineers, biologists, and clinicians concerning the balance between genetics and mechanical adaptability in deciding the structures of bones. Some have argued that the anatomy and histology of a bone such as the human femur are determined primarily by genetic information expressed by various cells as they form the skeleton and maintain it throughout life. Others have come to believe that mechanical factors strongly influence the expression of the genetic plan carried by the cells. It is appropriate to consider the relationships between mechanical adaptability and evolutionary change as determinants of skeletal structure. This discussion is based on the ideas of Bateson (1963, 1987).
6.3.1 Somatic Versus Evolutionary Adaptation
The adaptation of bone to alterations in mechanical loading is an example of somatic change, that is, a change in body form or function that does not entail a genetic change and is therefore not passed on to succeeding generations. Somatic change is distinct from evolutionary change, which does involve a modification of the genome of the organism. A simple example of somatic change is obtaining a sun tan during a beach vacation; obviously, this does not alter the genetic code for skin color, and the tan is not passed on to the vacationer’s children. Nevertheless, somatic change plays an important role in evolution.
Bateson pointed out that the ability to adjust to environmental changes by somatic modification of body systems is essential to survival because evolutionary change operates relatively slowly, through chance mutations. In addition, somatic adjustments allow the organism to survive when a genetic mutation, which might ultimately have survival value, disrupts one or more body systems. Conversely, genetic adjustments to the somatic system itself allow the homeostatic range to be restored when a mutation has driven it to an extreme. Thus, evolution involves constant interaction between slow, haphazard genetic changes and rapid, predictable somatic changes. In short, somatic flexibility allows time for adaptive modifications of the genome to occur, and also helps the organism tolerate their adverse side effects.
Work in the burgeoning field of epigenetics has demonstrated that interactions between somatic and genetic adaptations are far more complex and inter-related than was once thought. We now know that it is possible for somatic changes to an organism to be passed on to subsequent generations, not through mutations in the genetic blueprint (DNA sequence) but through somatic events such as DNA methylation and histone modifications that change the expression of specific DNA sequences. The processes of epigenetics are well appreciated during growth and development as specialized cells differentiate along countless pathways, depending upon morphogens and other factors within their immediate environment. Subsequent daughter cells inherit the characteristics and phenotypes of their differentiated predecessors. This often occurs through an epigenetic process in which an enzyme called methyltransferase adds a methyl group to the carbon 5 position of cytosine (one of the four bases that comprise DNA) converting it to 5-methylcytosine. High levels of 5-methylcytosine alter local transcription patterns and cell phenotype. Going from cells to the whole organism, genetic imprinting occurs when these heavily methylated regions of the genome are passed from parent to offspring through the germline. This tends to silence expression of the allele from that parent in favor of expression of the other parent’s allele. Recent work suggests that epigenetics may play an important role in transgenerational adaptation to environmental factors. Cooney and colleagues (2002) found that feeding maternal mice methyl-supplemented diets strongly affected the distribution of coat color patterns in their offspring, and correlated with methylation of the sequences controlling its phenotypic expression. A pair of multi-generational studies in humans found associations between early paternal smoking and the body mass index of their sons, and even more striking, between the food supply of paternal grandfathers and the mortality risk ratios of their grandsons (Pembrey et al. 2006). It is not beyond the realm of possibility that epigenetic mechanisms play an important role in bone adaptation to environmental or lifestyle changes (e.g. diet, physical activity) in the individual during development and maybe even in subsequent generations (Grossniklaus et al. 2013).
126.96.36.199 A Non-skeletal Example
Consider, for example, what happens when the vacationer mentioned above goes instead to visit Machu Picchu, the ancient Incan ruins in the Peruvian Andes. After flying to Lima, the tourist’s next stop is the city of Cuzco with an elevation of 3700 m (12,000 ft). Picking up her backpack and heading for her hotel, she soon finds her heart pounding and her breath coming in gasps because of the thin air. Clearly, these are responses to the trouble her cells are having in getting enough oxygen. Her increased volume and rate of breathing and pumping blood are somatic changes allowing her to cope with the environmental changes. By the time she leaves Cuzco 2 days later to continue her journey to Machu Picchu itself, carrying her backpack no longer requires her heart and respiration rates to be adjusted upward so much because her hematopoietic system has produced more red blood cells. This second level of somatic adaptability requires more time to put in place, but much less metabolic energy than pumping blood and air faster.
However, more red blood cells per unit volume of blood (called hematocrit) is not the best physiologic adjustment for living permanently at high altitude, either. “Lowlanders” who go to high altitudes may suffer severe cardiovascular problems caused by the effects of increased hematocrit on the physical properties of their blood. Some individuals can adjust to living at high altitudes, but many cannot. However, groups of people have lived at high altitudes (principally in the Andes and Himalayan mountains) for many generations and appear to be free of altitude sickness. It is possible that these populations have experienced genetic changes, through differential reproductive success, which have adapted them to high altitudes in ways that avoid the problems associated with increased hematocrit (Cruz-Coke 1978).
188.8.131.52 Somatic Change in the Skeleton
Comparing bone’s mechanical adaptation to Bateson’s altitude adaptation example, the correlate to increased heart and respiration rates is an increased remodeling rate to repair load-induced microdamage. The correlate to increased hematocrit is periosteal and endosteal modeling to decrease the stresses in the bone. These skeletal responses can have problematic sequelae, just as the respiratory ones can. The increased rate of remodeling requires metabolic energy, and it introduces remodeling space porosity, which can increase strains and the damage formation rate. The formation of new bone on periosteal and endosteal surfaces also requires metabolic resources, and the additional bone mass must be carried about each day, at a very significant energy cost.
6.3.2 Somatic Versus Evolutionary Effects
Bateson’s point was that all evolutionary change involves endless somatic and genetic adjustments, which together achieve adaptations that would be impossible if only one or the other existed. Thus, it is shortsighted to debate which caused what, exactly. It is more important to learn how somatic and genetic changes interact in the skeleton, as they do in other organ systems. This kind of knowledge should ultimately be very useful in treating many bone injuries and diseases.
Box 6.1 Teleology and Adaptation, Optimization and Evolution
An engineer who has designed a structure can say, “The purpose of this strut is to reduce bending moments on this beam,” but we cannot analogously say that the purpose of a strut of trabecular bone is to reduce the bending moment on an adjacent trabecula. The difficulty lies with the word purpose. The attribution of purpose to physiologic mechanisms is called teleology, and in this text we have tried to avoid it. We might say instead, “a consequence of this trabecular strut is that bending moments on this adjacent trabecula are reduced.” This is not just an esoteric point of semantics, it is important in understanding the nature of biological adaptation, whether it is somatic or evolutionary.
In the course of natural selection a group of organisms produces a great many genetic variants, some of which are better adapted in the sense that they will leave more progeny in the next generation. By this mechanism, species evolve, and adaptations such as bone remodeling come into being and are preserved. The process is a passive and stochastic one: the concept of purpose does not enter into it.
There are two sides to biological adaptation—the organism and its environment. When the environment is noisy and unpredictable, the adaptive process has a more difficult problem to solve. For an example see: Crummett et al. (2013), Ng et al. (2013), Jansen et al. (2011) and Eranen et al. (2009). As we saw in Chap. 1, the mechanical environment of vertebrate bones is provided to a large extent by their own muscles; much of this loading is predictable and controllable. But the outside environment also directly loads bones, and these forces may be less predictable and controllable. If a creature walks on level ground all day, and at the end of the day steps unexpectedly into a hole, which of these is mechanically most significant in driving adaptation, the 20,000 cycles of gait or the one cycle of tripping that generates twice as much skeletal stress? Lanyon (1993) has favored the idea that skeletal adaptation is primarily an error-driven process, and it is the unusual loads that are most significant, but this important question has not been subjected to much research. More recent work by Currey and colleagues (2007) tends to suggest otherwise.
Organisms that live in water inhabit a mechanical environment that is seemingly more predictable than the terrestrial one, which should allow for more metabolically efficient adaptation of their skeletons relative to land dwellers. But the buoyancy of water works against the adaptive advantage of a lighter skeleton in that a heavy skeleton balances low-density fat, resulting in an organism with an average density close to that of water, thereby facilitating aquatic locomotion. Conversely, birds (that is, flying birds, not terrestrial birds like chickens and ostriches) find exceptional adaptive value in a minimal-weight skeleton, which improves the efficiency of flight. Other factors contribute to the skeleton’s mechanical milieu as well, including pregnancy and other seasonal fluctuations in body weight, antler growth, hibernation, migration, and fighting among males. These factors must complicate the optimization of skeletal structure.
This chapter is devoted to discussing the proposition that the skeleton contains adaptive mechanisms that optimize its structure in some sense. Deterministic models (Nowlan and Prendergast 2005) suggest that bones do not evolve an optimal structure or properties from any one perspective, because there are competing interests (e.g. mechanical demand vs. mineral homeostasis vs. nutrient transfer vs. immune function), although they may approach optimal. It would therefore be a mistake to hypothesize that evolution is directed toward maximizing efficiency of structures. Evolution is directed toward maximizing genetic representation in subsequent generations, which in turn is associated with efficiency, but only rather loosely. Indeed, the physiques of many ancient relict species contain features that are hardly paragons of efficiency. Evolution can only modify the basic plan that exists. Take for instance the now well-known example of The Panda’s Thumb popularized by Gould (1980). It works quite well and is adapted to its role, but it is certainly not designed in a way an engineer would design it were she to start “from scratch.” The human knee joint, and the vertebral column, are two other examples, perhaps more immediate to those using this book.
6.4 What Is the Design Goal: What Does Bone Adapt to?
It is difficult to discuss mechanical adaptation of bone unless we can define the term “adaptation.” What does this really mean in the context of purely mechanical skeletal function? For the purposes of our following discussion we propose that bone structure (its shape and mass) is regulated to find the best (the optimum) solution to minimize both fracture risk and bone mass for the loadings that the bone experiences. The adaptation of bone is a somatic change, the limits of which are determined by the genome of the organism. We will show later that the unknown genetic potential for somatic change severely hampers the formulation of a generally applicable theory for the adaptation of bone to mechanical load.
Clearly, minimization of fracture risk is important in most bones, and minimizing bone mass allows the organism to reduce the metabolic energy required for its daily activities, increasing its ability to survive. Following the lead of Currey (1984), we speak of optimizing stiffness because bones need to support loads without bending too much, but they also need some flexibility for shock absorption and to avoid fracture. The optimal stiffness surely varies with the function of the particular bone. For example, Currey (1981) has discussed the divergent functions of three bones. The antlers3 of the male red deer require impact strength and energy-absorbing power; stiffness is deemphasized. The femoral cortex of the cow requires more stiffness. The tympanic bulla in the ear of the fin whale requires a high acoustic impedance and therefore very high stiffness. Table 6.1 shows how the elastic modulus and other attributes vary among the three bones. Although most bones would be more like the cow femur than antler or tympanic bulla in their function, the optimal stiffness obviously varies from bone to bone. It should be understood that this is only a trial hypothesis to serve as a benchmark for exploring this subject. At this point it seems clear that fracture risk and bone weight need to be minimized, but we shall see several alternative possibilities for the optimized variable in the following pages.
Material properties of three different bones
Red deer antler
Bending strength, MPa
Elastic modulus, GPa
Acoustic impedance, 109 kg/m2/s
Mineral content, % by weight
6.4.1 Optimization, Mechanical Adaptability, and Structure-Sensitive or Insensitive Properties
There is always a trade-off in nature; improvement in one property may be detrimental to another, and to maximize evolutionary fitness requires balance. In bone, this is reflected by the relationship between stiffness and toughness (or work to fracture), which are typically inversely related. Stiffer bones tend to absorb less energy prior to fracture (Currey 2004) and therefore optimizing stiffness does not necessarily mean that fracture risk will be reduced. Osteopetrosis is a good example. This is a condition in which the osteoclasts are not working well, so that bone is not resorbed as it should be (which also means that new bone cannot be formed by remodeling processes). The bone as a whole thus becomes more highly mineralized, and very stiff and strong. However, it has little capacity to absorb energy once it has passed the yield point, and therefore breaks rather easily.
Currey proposed that bone adapts to these competing needs by optimizing towards structure-insensitive mechanical properties (Currey et al. 2007). Structure-insensitive properties are those that are not greatly influenced by small flaws or inhomogeneities in the structure (Ashby 2004). These properties tend to be less variable across bones or species, than those that are structure-sensitive. For bone, structure-insensitive properties are those that determine properties in the pre-yield region of the stress-strain curve, such as elastic modulus and bending strength. Structure-sensitive mechanical properties are more greatly affected by structural inhomogeneities, and include toughness and work to fracture that will determine the energy expended in the post-yield region, as well as impact strength.
Evolutionarily, Currey argues, bone adapts to the more predictable, i.e. less variable, properties. Thus, stiffness would be deterministic, even at the expense of greater uncertainty in toughness. Mineral content and collagen cross-linking determine stiffness and toughness, albeit in an inversely proportional way. In the trade-off between stiffness and toughness, the fittest individuals would be those with the greatest certainty in pre-yield properties, even if this created less predictability in post-yield properties. From a structure-function standpoint, this makes a great deal of sense given that we spend most of our time loading our bones in the pre-yield range. It also makes sense in a self-repairing structure like bone, in which damage caused by unpredictable loads can eventually be repaired so that the animal can survive to reproduce another day.
6.5 How Does Bone Adapt: What Are the Signals and How Are They Transduced?
Mechanotransduction is a word used frequently by researchers in the field, but not often defined. It is a general term that can have a variety of meanings, depending on the context in which it is used. Mechanotransduction should be considered as a series of inter-related mechanical and biological events, rather than a single process. It was defined most clearly and thoroughly by Duncan and Turner (1995), who divided the sequence of events from the initial mechanical signal to the eventual biological effect into four stages: Mechanocoupling, Biochemical Coupling, Signal Transmission, and Effector Cell Response.
Mechanocoupling refers to the mechanical stimulus that initiates the events leading to a particular cellular response. We treat the potential “actors” in this play extensively in this chapter, concluding that strain may or may not have a direct impact on cellular response, but it certainly is the driving force behind fluid movements in bone that cause fluid shear stresses on osteocyte and canalicular membranes which in turn produce (although this is less likely to be significant) electrical potentials (streaming potentials) to which bone cells can respond. Fluid motion also modifies the diffusional mixing of extracellular signaling molecules which can affect cell behavior completely independently of fluid shear stress. Fluid mixing of the molecules is important because the concentration and the rate of presentation of signaling molecules changes cell response in complex and incompletely understood ways.
Once the mechanical stimulus has been perceived by the cell, it must transduce that mechanical signal into an intracellular biochemical response in the sensor cell (the osteocyte in bone) that has the potential to either transmit the signal to other cells or to initiate the recruitment and eventual maturation process that causes bone formation or resorption. This biochemical coupling may take several forms, and include physical changes to the cell (e.g. integrin—cytoskeleton-nuclear matrix deformations (Wang et al. 1993; Chen and Ingber 1999)), alterations in G-protein pathways, phosphorylation of proteins or regulation of mineral channels (e.g. calcium, phosphorus, or chlorine channels are common), or combinations of physical and biological regulation (e.g. stretch activated protein channels).
Once sensor cells, now commonly assumed to be osteocytes and bone lining cells (pre-osteoblasts), detect the signal and begin to respond, they must transmit this information to other cells that will actually do the work of making more bone, or removing it. Signal transmission may involve a host of autocrine and paracrine factors, but the messages themselves must be transmitted through a dendritic network that is much like the neural network in the brain (Turner et al. 2002). This transmission seems to require the help of connexins, in particular connexin-43, but probably also others.
Finally, effector cells that actually produce the response must mature and go to work. In bone, these are the osteoclasts and osteoblasts. How they are controlled is the subject of other chapters in this book (see Chaps. 2 and 3). It is worth emphasizing, though, that they do not work in a vacuum generated only by the information provided by the sensor cells, but are regulated during their activities by hormones, other metabolic products, by noncollagenous matrix proteins and by communication among themselves.
In this chapter, we will concentrate mostly on the first step in the mechanotransduction process, mechanocoupling, and to a lesser degree on signal transmission, as the other steps are largely complex biological processes, outside the scope of this text. If cells adapt bone to mechanical loads by responding to a mechanical stimulus, it is obviously important to know what that stimulus is and to be able to measure it. One attractive suggestion, supported by many experiments, is that bone adapts to strain. Cells attached to bone surfaces may “feel” the displacements of the surface and respond to them. Strain is also an appealing variable from the point of view of minimizing fracture risk. We will see in Chap. 7 that yield strains are reasonably constant for bone. Therefore, keeping strains near a point well below the yield strain should maintain a margin of safety against monotonic, creep, and fatigue failure. Finally, if stiffness is to be optimized in some sense, the fact that strain is a measure of bone stiffness under a given load (e.g., body weight) may be significant. These features and others make it easy to see why strain is targeted as the prime functional stimulus, and why measurement of bone strains in vivo has been such an important component of the experimental work aimed at bone adaptation.
6.5.1 Measurement of Strain in Living Animals
Until the advent of in vivo strain gauging techniques, the adaptation of bone to mechanical loading could not be effectively analyzed because bone’s “mechanical environment” could not be quantitatively assessed at a level commensurate with cellular activity. Lanyon and Smith (1969, 1970) reported the first measurement of in vivo bone strains in animals when they implanted uniaxial strain gauges on the medial tibial cortex in sheep. They found mean longitudinal surface strains of 260 microstrain during walking and a 16 % increase when the animals were trotting.
Subsequent to this, Lanyon (1971, 1972) applied strain gauges to the thoracic and lumbar vertebrae in sheep. He reported average peak surface strain ranges in thoracic vertebrae during walking of 142 microstrain (με), increasing 25 % to 187 με during trotting. Cochran (1972, 1974) applied strain gauges to the tibia and ulna in dogs, measuring strains in the tibia between 103 and 665 με, depending on the load and the anatomical position of the strain gage. The mode of the strain, compressive or tensile, was not specified. Shortly after this, Barnes and Pinder (1974) and Turner et al. (1975) added the radius, tibia, metacarpus, and metatarsus of horses to this list. Lanyon et al. (1975) demonstrated that strain magnitudes in the human tibia during locomotion were similar to those in bones of other animals.
6.5.2 Principal Stresses, Strains and Trabecular Orientations
About this time, Lanyon began to use rosette strain gauges,4 permitting the measurement of principal strain directions. Applying these gauges to the calcaneus of a sheep, Lanyon (1973, 1974) demonstrated that the principal orientations of trabeculae coincided with the principal compressive and principal tensile strain directions. Later, Hayes and Snyder (1981) conducted an intensive study of the human patella which concluded that its trabecular orientations are highly correlated with principal stress directions, as determined by finite element analysis. Although this study did not examine in vivo strains on the patella, both studies suggest that the proposed “trajectory criterion” of Culmann, Meyer, and Wolff is essentially correct and trabeculae do align themselves with the continuum level principal stress (or strain) directions (i.e., the principal directions in a homogenous model structure).
There have been several efforts to understand mathematically the trajectory criterion for cancellous bone by combining properties of the stress (or strain) with properties of cancellous bone structure and/or cancellous bone mechanical properties. Cortical bone (Dempster and Liddicoat 1952) and cancellous bone (Harrigan and Mann 1984) were experimentally demonstrated to be mechanically anisotropic and probably to be essentially orthotropic—having three orthogonal principal material axes similar to the three principal axes of stress. If cancellous bone is an orthotropic material, then if one aligns the largest principal modulus (stiffness) with the largest magnitude of principal stress and so on down to the smallest principal modulus and stress, the elastic energy put into the material by an arbitrary stress is minimized (Fyhrie and Carter 1986). This suggests that trabecular orientation is a result of elastic energy minimization through alignment of the material properties with the applied stress (There are some constraints on the size of the shear moduli in that theory). It was also demonstrated experimentally that the orientations of the surfaces of the trabeculae could be modeled fairly accurately as a second rank tensor called the mean intercept length (MIL) and that the orientations of the principal axes of the MIL tensor matched the orientation of the orthotropic material properties of the bone (Cowin 1985). As a result, there are three mathematical objects that one can consider aligned in cancellous bone in order to try and explain the trajectory criterion: (1) the principal directions of the orthotropic material properties, (2) the principal directions of the mean intercept tensor and (3) the principal stress (or strain) directions. These alignments can be condensed into the rule that trabecular orientation (i.e., orientation of the mean intercept ellipsoid) matches the orientation of the principal stresses (Cowin 1986) and, with additional arguments, that their orientation is driven by the goal (an optimization) to make the principal apparent axial strains all the same (Turner 1992).
All of these ideas for mathematically explaining the orientation of cancellous bone with loading result in solely orthogonal networks of trabeculae because all of the principal axes that are being aligned are orthogonal. Unfortunately, trabeculae don’t always meet orthogonally—for example, the two main portions of the trabecular network in the proximal femur meet at an angle different from ninety degrees. This was recognized early (von Meyer 1867) but was improperly rejected by arguing that early work on the theory of elasticity predicted orthogonal stresses (Wolff 1892) [For the philosophers among our readers, this was a triumph of the Platonic Ideal (mathematical theory) over Aristotelian Materialism (anatomical data)]. Non-orthogonality of trabeculae was mathematically explained by a superposition of multiple loading cases at both the average (Carter et al. 1989) and trabecular level (Mullender et al. 1994), but the underlying biological mechanisms for the sensation and correction of trabecular orientation to loading are still not known.
184.108.40.206 Peak Strains Are Similar Across Species
Subsequently, Rubin and Lanyon (1982) surveyed their own work and that of others and published the data shown in Table 6.2. These data show that when an adult animal’s musculoskeletal system is functioning at a high physiologic level (e.g., a dog is running or a bird is flying), peak periosteal strains usually lie between 2000 and 3000 με. The fact that measured strains were nearly equivalent on different bones and in different animals supported the hypothesis that the skeletons of all animals are adapted to control strain.
Peak functional strains in various animal bones
Biewener et al. (1983)
O’Conner et al. (1982)
Lanyon et al. (1982)
Goodship et al. (1979)
Rubin and Lanyon (1984)
There are at least two notable exceptions to the data in Table 6.2. First, strains on the human tibia at a site where stress fractures occur have not been observed to exceed 2000 με, even during strenuous activity by Special Forces soldiers (Burr et al. 1996). More recent experiments, however, show that strains in excess of 3000 με can be generated during jumping activities, which may explain why “shin splints” are a relatively common injury among basketball players. See Yang et al. for a comprehensive review of in vivo bone strain measurements in people (Yang et al. 2011). Second, thoroughbred racehorses generate 5000–6000 με on the surface of their metacarpal (cannon) bone when running at racing speeds. However, these horses are special animals, bred and trained to run exceptionally fast while they are still juveniles. Strains of this magnitude probably only occur in young animals (or people) in which bone turnover is rapid and many osteons are still mineralizing.
6.5.3 Compressive Strains Are Larger than Tensile Strains
Because compressive strains in a long bone are usually superimposed on bending strains, the neutral axis is shifted and the peak compressive strains are usually greater than the peak tensile strains (Fig. 6.4).5 Lanyon et al. (1982) demonstrated that the ratio of (the absolute values of) peak compressive strain to peak tensile strain on the sheep radius varies between 1.45 and 2.34, and tensile strain was never greater than compressive strain during normal locomotion. In fact, tensile strain was always less than, and compressive strain was always greater than, 1000 με. Even after osteotomy of the adjacent ulna, the tensile strain on the radius was less than 1000 με. High fidelity cadaver simulations of human gait suggest that this phenomenon also holds true in the weight bearing bones of humans. Such experiments enable comprehensive but otherwise prohibitively invasive assessments of bone strain through placement of rosette gauges at multiple sites on a single bone (Goodwin and Sharkey 2002; Peterman et al. 2001). Results from studies focused on the tibia under loading conditions representative of normal walking nicely illustrate the greater compressive strains experienced in the posterior aspect of the tibial diaphysis relative to the tensile strains present on its anterior aspect (Fig. 6.5).
Most long bones are loaded in combined bending and compression, producing an asymmetric stress distribution in which compressive stresses are greater than tensile stresses.
Axial strain profiles at two anterior (R1 and R2) and two posterior (R5 and R6) sites of the tibial shaft, illustrating compressive loading superimposed with bending. The relationship between vertical ground reaction force (vGRF) and tibial strains during stance is also readily apparent. The left ordinate axis has units of microstrain (με) and the right ordinate axis corresponds to the dashed vGRF profile, with units of Newtons (Peterman et al. 2001).
220.127.116.11 What Aspects of Strain Regulate Adaptation?
The pioneering studies by Lanyon and others to measure strains on the surface of bones during activity provide some guidelines about which features in the strain environment may be critical to the adaptive response. The experiments of Lanyon and Rubin in particular showing that strain magnitude seems constrained within relatively strict boundaries are convincing that the magnitude of strain is a component of the signal. The uniformity of peak strain across species, and the correspondence between trabecular orientation and principal strain directions—are strong evidence that strain magnitude is one regulator of skeletal adaptation to the mechanical environment.
The principle of uniformity of peak strain implies a threshold-driven process. To further identify the relevant magnitudes of strain that could elicit a response, Turner et al. (1991) developed a rodent model in which bone formation rate (BFR) in the tibia could be measured in response to application of different magnitudes of strain generated in four point bending. Turner et al. (1994) loaded a series of rat tibiae at strains from 400 to 2000 με, and found no difference in BFR in the loaded tibia when compared to the contralateral nonloaded tibia when strains were less than 1050 με. When strains were greater than this, bone formation increased monotonically by sevenfold as strain increased to 2000 με. The idea that bone formation was linearly related to strain magnitude was not a new one, but the experimental demonstration that there was a threshold, and about where that threshold lay, was a new observation.
Nine years earlier, Rubin and Lanyon (1985) performed a similar experiment in which they applied loads to avian forelimbs from zero (unloaded, and in disuse) to 4000 με and noted a linear increase in cortical bone area related to increasing strain. They did not identify a threshold for response in their earlier experiment, but presented a linear response over the entire range of loads. In more recent work, this group has continued to assert this linearity of response over the range of strains and activities, from disuse, to very rigorous loads involving high strains with adaptation by woven bone (Sugiyama et al. 2012). However, when their data are viewed more closely, it becomes clear that there is a threshold for response, and that this threshold occurs slightly above 1000 με, just as in the Turner experiment using rats (Fig. 6.6). Although presented as loads rather than strains, their more recent data also suggest a threshold driven process because mean values for cortical and cancellous bone areas and volumes do not change substantially when peak loads (in mice) are less than 6 N. These studies appear to validate the idea of a threshold for adaptive response, and imply that this threshold may be similar across species.
The concept of a regulatory threshold is consistent with the view that the osteocyte-canalicular system performs as a neural (Turner et al. 2002) or “small world” (Gross et al. 2004) network that connects osteocytes with osteoblasts and lining cells to enhance mechanical signals. As Gross points out, such networks exhibit threshold-related behavior, and also have the capacity, once the threshold has been reached, to synchronize the signal, which effectively can amplify it. This does not necessarily mean, however, that the strain threshold is exactly the same at all locations on bones. In fact, the idea of a “neural network” involving osteocytes suggests the opposite: the capacity for learning and memory, as in a true neuronal network. Using the rat ulnar loading model, Hsieh et al. (2001) showed that bone formation was initiated at strain thresholds that varied from about 1300 to 3000 με along the length of the ulna. These thresholds correlated to regions of the ulna that were normally under higher strain, suggesting that bone tissue habitually receiving higher mechanical strains can become less responsive to loading, i.e. the system “remembers” its local loading history and responds accordingly. In other words, cells accommodate (or habituate) to their routine loading history and probably their hormonal environment, and only respond when the perceived stimulus is outside what they normally experience. The biological mechanism for such an accommodation has not been determined, but may reside in the osteocyte network (Turner et al. 2002).
Box 6.2 Cellular and Acellular Bone
Not all bone contains an osteocyte network. It has been known since the middle part of the nineteenth century that bone in some fish is acellular, although cells may be present during skeletal development. It may be, however, that fish have limited need for cellular signaling to repair bone damage. Being in an aquatic environment certainly lowers gravitational forces associated with muscle contraction. Nevertheless, muscle contraction requires calcium and so fish must use other mechanisms for systemic calcium regulation, and indeed they do. During development, humans develop a structure called the ultimobranchial body, which is eventually incorporated into the thyroid gland. Cells from this structure give rise to C cells in the thyroid gland that produce calcitonin, which helps to regulate plasma calcium levels. Fish also have an ultimobranchial body that produces calcitonin. When calcitonin is administered to fish with osteocytes, plasma calcium levels decrease. However, when calcitonin is administered to fish without osteocytes, plasma calcium does not change. To see reviews of this work, refer to Parenti (1986). This suggests that osteocytes are important for the systemic regulation of calcium in the blood, which they must perform by signaling other cells to resorb bone to release calcium stored there or stop resorbing when circulating Ca++ levels become too high. When osteocytes are not present, those signals are not generated and plasma calcium is invariant. Moss (1962) performed an interesting experiment to demonstrate differences in fracture repair between fish with cellular and those with acellular bone. Moss fractured the jaws of both kinds of fish, and observed the repair process under normal conditions in an aquatic environment with normal levels of calcium. In fish both with and without cells, fracture healing occurred via endochondral ossification by the formation of a large cartilage callus that subsequently calcified. When a similar experiment was performed in water that had no calcium salts in it, the fish with cellular bone healed and mineralized normally, but those with acellular bone failed to calcify the cartilage callus. Again, this suggests that fish without cellular bone are not able to internally regulate their calcium balance as do fish with osteocytes. These studies demonstrate the capacity of osteocytes to signal other cells, and the critical role played by osteocytes in metabolic regulation, but do not speak to the exclusivity of osteocytes in transducing mechanical signals. In this regard, there is preliminary evidence that acellular fish bone may have the capacity to form new bone in response to experimentally imposed mechanical loading, suggesting other, perhaps more primordial, mechanisms of mechanotransduction that function independent of osteocytes (Shahar et al. 2013). Regardless of eventual conclusions, cellular and acellular fish bone provides a natural model to further investigate the regulatory pathways responsible for bone growth and maintenance.
Thus, bone adaptation can be considered a location-specific and error-driven process. This has formed the basis for a number of computational models that attempt to predict bone’s modeling and remodeling behavior, including those devised by Cowin (Cowin and Hegedus 1976; Cowin and Nachlinger 1978), Hart and Davy (Hart and Davy 1989), Carter and Beaupre (Beaupre et al. 1990a, b), and Frost (Frost 1987b). For this to be true, of course, the opposite must also be demonstrated: loss of a mechanical signal should result in bone loss.
6.5.4 Canine Disuse Experiments
Uhthoff and Jaworski (1978) and Jaworski and Uhthoff (1986) studied the effects of disuse in growing dogs by casting one of their forelimbs for 40 weeks. The metacarpal diaphyseal bone loss in growing dogs was characterized primarily by reduced formation and increased resorption on the periosteal surface, indicating that the normal periosteal bone formation accompanying growth was inhibited or converted to resorption. Relative to the contralateral control bone, bone mass decreased rapidly at first, then more slowly. After 40 weeks of immobilization, it was asymptotically approaching about half the bone mass of the contralateral control bone. When the cast was removed after 32 weeks of immobilization, about 65–70 % of the deficit in bone mass was recovered in 28 weeks. In the diaphysis, this occurred both through endosteal apposition and through additions of woven bone to the periosteal surface. When the experiment was repeated in older dogs, bone loss occurred primarily at the endosteal surface and through increased intra-cortical porosity (Jaworski et al. 1980). There was no effect on periosteal diameter. Older dogs were less able to recover lost bone following remobilization, recovering only 40 % of the lost diaphyseal bone. In older dogs, remobilization stopped the endosteal bone loss and caused apposition of small amounts of lamellar bone to the periosteal surface.
6.5.5 The Mechanostat and the Equilibrium Strain Range
Frost (1987a, 1986) attempted to put these ideas about how bone adapts together into a conceptual model, integrating the concepts to define not only when a response would occur, but the nature of the response (resorption or formation) and the location of the response on one of the four bone envelopes. He likened the modulation of bone adaptation to strain to a home thermostat, and therefore termed his conceptual model “The Mechanostat.”
The mechanostat theory begins with the concept that there is a minimum effective strain which must be exceeded to excite an adaptive response (Fig. 6.6). However, instead of simply postulating that strains below a certain threshold will evoke no response, Frost suggests that there is an equilibrium range of strain values which will evoke no response. Strains above this range evoke a positive adaptive response (increased bone), and strains below this range cause a negative adaptive response (loss of bone). Others have suggested similar physiologic ranges, sometimes called “dead zones” or “lazy zones.” In this framework, the minimum effective strain becomes the upper limit of the equilibrium strain range, or the strain beyond which an augmenting adaptive response is initiated. There would also be a lower strain limit defining the strain below which bone loss would occur. The thresholds separating these zones or ranges are termed “setpoints.” These setpoints are determined by many factors in the hormonal and metabolic environment, and so cannot be viewed as fixed at a particular strain level. At very high strains, there is another setpoint which defines the strain range within which damage is severe enough to elicit a repair response. This can be either a remodeling response to repair internal damage to the bone matrix—microdamage—or rapid deposition of woven bone on external surfaces, such as is seen in a stress fracture.
Frost’s mechanostat theory asserts that modeling and remodeling have opposite responses to loading that pushes strains above or below the equilibrium range:
Increased loading……. modeling is increased and remodeling is inhibited.
Decreased loading…… modeling is inhibited and remodeling is increased.
The logic behind this algorithm is as follows. While the inhibition of remodeling by high strain may seem “backwards” because of the long-held concept that increased loads or strain stimulate “remodeling” to increase bone strength, it must be remembered that we are using the strict definition of remodeling, which does not include modeling. Now, think first of cortical bone. Osteonal remodeling increases porosity as a result of the remodeling space and the new Haversian canals created. It is therefore desirable that osteonal remodeling should be depressed by overload and stimulated by disuse. However, in those cases in which loads are so high that bone is damaged, it is desirable not to reduce remodeling, but to stimulate a repair reaction. We now know that the mechanostat theory is not entirely correct because remodeling is indeed activated at very high loads, when bone is damaged and dying osteocytes produce signals that recruit osteoclasts to remove the damage. It is also reasonable that mechanical overload should activate modeling to adapt the bone to future, similarly high, loads and, as we have seen, this has been observed experimentally in many different models.
It is important to understand that an identical mechanical strain can elicit a different response if the setpoint for response is altered. For example, if the setpoint to activate remodeling were raised, the bone could perceive that normal physical activity was decreased when it was not, activating an inappropriate remodeling response causing loss of bone. This may be in part what occurs in postmenopausal osteoporosis. With the loss of the estrogen stimulus, the lower setpoint for remodeling is higher, causing a loss of bone from endocortical, trabecular and intracortical surfaces even in the presence of normal activity and normal strains. Parathyroid hormone (PTH) is well-known to increase osteoblast sensitivity to a mechanical load (Ryder and Duncan 2001; Li et al. 2003; Kim et al. 2003). When given intermittently, as in therapies for osteoporosis, it elicits bone formation directly on endocortical and trabecular surfaces, i.e. a modeling response. Thus, the upper threshold to stimulate modeling is lowered, making the bone “see” usual strains from normal activity as an error signal.
6.5.6 Mechanical Compensation and the Roles of Bone Modeling and Remodeling
The competing architectural demands of remodeling and modeling show that mechanical adaptation occurs at both the structural level and at the tissue level, and these processes must be somehow coordinated. Shape and size changes are effected on external (i.e., periosteal and endosteal) bone surfaces, where there is more modeling than remodeling during growth, and less capacity for change in adults (Frost 1986). On the other hand, changes in material properties are effected on internal (i.e., Haversian and trabecular) bone surfaces. Internal bone surfaces are governed primarily by remodeling throughout life (Frost 1986).
The gross anatomy (i.e., the shape and size) of a bone is in large part determined during growth. Modeling serves to sculpt the bone to suit both the genetic plan and the demands of current mechanical usage. In adults, modeling is reduced in rate and extent, so that alterations of bone geometry require much more time (or a mechanical stimulus large enough to produce woven bone). This restriction is important with respect to joints as well as bones. An adult who greatly increases the loads on his skeleton is, in principle, more likely to acquire osteoarthritis than a juvenile because his bones have insufficient capacity to alter their metaphyseal size to reduce joint stresses (Frost 1994).
The mechanical properties of the bone material are matched to mechanical usage by remodeling. Unlike modeling, remodeling rates can be substantially increased in adults by various events, including changes in mechanical loading. But the purpose of remodeling is to maintain bone and to repair material damage, not to change gross architecture; large architectural adaptations to mechanical loading can only be effected by modeling processes. This limitation of remodeling is significant because it is practically impossible to substantially increase the strength or stiffness of cortical bone by remodeling, there being no large voids to be filled. Therefore, in adults it is much easier to reduce cortical bone strength than to increase it.
Because of these competing goals of modeling and remodeling, in both health and disease there are compensatory modifications of structure and material that maintain or adapt the bone to its mechanical environment. For example, postmenopausal osteoporosis involves loss of cancellous bone mass in the spine, which reduces the failure stress of the vertebral bodies. However, in men there is a concurrent increase in vertebral diameter that prevents the structural strength from being reduced to the same extent as the material strength (Mosekilde and Mosekilde 1990). A similar phenomenon occurs in long bone diaphyses (Martin and Atkinson 1977; Martin et al. 1980; Ruff and Hayes 1988; Ahlborg et al. 2003) and the neck of the femur (Beck et al. 1993), although others (Poole et al. 2010) have shown a more complex re-distribution of bone with age in the femoral neck. This form of compensation does not occur as effectively in women, for reasons that are not entirely clear. In part the difference between men and women may be related to both size differences and material property differences. Cancellous or intra-cortical bone loss in smaller bones requires greater compensatory periosteal bone formation to maintain a given stiffness than it does in larger bones. Moreover, reduced total bone stiffness during aging, which can be caused by the increased rate of remodeling at the menopause in women, requires a much greater periosteal response to maintain stiffness than does a similar percentage loss of bone mass (Jepsen and Andarawis-Puri 2012). For example, a 2 % reduction in bone apparent modulus might require twice as much apposition on the periosteal surface to maintain stiffness, as does a 2 % reduction in bone mass.
These adaptive functions between structure and material occur even during serious pathologic episodes, resulting in the strongest structure that circumstances allow. For example, human femurs drastically alter their cross-sectional geometry (by modeling of the periosteal and endosteal surfaces) to compensate for the poor material quality and large bending stresses arising from curvatures produced by rickets. Another example is shown in Fig. 6.7, which shows silhouettes of young (left) and old (right) femoral midshaft cross sections. The neutral axis for bending during gait is approximately from the top (anterior) to the bottom (posterior) of the sections. Note that the increased porosity associated with aging is more apparent in endosteal regions and quite striking near the neutral axis, where the resulting reduction in the bone’s failure stress has minimal effect on torsional and bending strength.
Midshaft cross sections of femur from a woman in her thirties (left) and from a woman in her nineties (right).
18.104.22.168 Cellular Habituation: Do Cells Get Tired?
The idea that bone adaptation is threshold-related (strain magnitude) and error-driven (strain magnitude and distribution) led to the notion that as long as bone is loaded above its threshold, or in an unusual direction, cells will continue to respond until bone adaptation (which after all, takes some time to achieve) lowers the strain magnitude to below some response “setpoint” (in Harold Frost’s terminology). We know that bone responds to a very few number of cycles if the strain magnitude is high enough, and may not respond at all to many cycles of loading if the strain is insufficient to achieve a certain threshold. But what if bone is repeatedly loaded above the strain threshold, will that threshold eventually be insufficient to cause a cellular response? In other words, do cells themselves “adapt” to strain magnitude and become de-sensitized to it over a period of time?
Experiments suggest that cells do become less sensitive, and that the timeline and/or number of loading cycles in which this occurs can be quite short. The idea that cells may become less responsive was embedded in the early experiments of Rubin and Lanyon (1984), but because those experiments were focused on the initiation of bone adaptation, the process of habituation was not recognized from these experiments.
The Rubin and Lanyon experiments showed that, if the strains were sufficiently high, bone loss could be prevented with only 4 cycles/day of loading, and bone formation (in modeling mode on periosteal surfaces) would be stimulated with only 36 cycles per day. These experiments also showed, however, that bone formation was no greater when bone was loaded 100 cycles/day, or 1800 cycles per day at the same strains, clearly showing that just increasing the number of cycles applied did not stimulate the cells to work harder. Other studies following the early Rubin and Lanyon experiments, using different experimental designs and different animal models, suggested that when bone is loaded to about 1000 με, the adaptive response saturates within about 200–400 loading cycles (Umemura et al. 1997) (Fig. 6.8). These findings led Robling and Turner (Robling et al. 2000, 2001a, b) to use the four point tibial bending model in rats to deliver identical numbers of load cycles each day (i.e., an identical energy input), but to vary the timing of load delivery. They either delivered the load as 360 cycles at one time, or divided those 360 loading cycles into 2, 4 or 6 bouts of 180, 90 or 60 cycles in each bout, separated by different periods of time over the course of a single day. One would expect that, without cell saturation, it wouldn’t matter how the 360 cycles were delivered, since the amount of energy imparted to the system in each case was identical. However, these experiments showed that it did matter, and that bone formation rates (BFR/BS) were significantly increased when the load was delivered in bouts of 60 or 90 cycles each over the course of the day, compared to a group in which the 360 cycles were delivered at one time.
The relationship between bone formation and the number of load cycles per day based on experiments in roosters (, Rubin and Lanyon 1984), rats subjected to jumping exercise (○, Umemura et al. 1997) and four point tibial bending in rats (▵, Turner et al. 1994b). In combination, these data demonstrate that a small number of loading cycles creates the signals necessary for bone formation. Additional loading cycles do not increase the amount of bone formation or bone mass.
Box 6.3 Adaptation to Load Versus Evolutionary Adaptation
In the theory of evolution an adaptation (or adaptive trait) is a trait of an organism that has a current functional role. In evolutionary theory adaptation refers both to the trait and to the evolutionary process that led to the adaptation. For a theory of how bone responds to load the word adaptation means that the organism is using phenotypic plasticity to improve bone function. The two meanings of the word adaptation are similar, however, evolutionary adaptation changes the genotype and load adaptation is a somatic (phenotypic) adjustment that (as far as we know today) is not heritable. For bone adaptation the implication is that the bone is improved (in some sense of the word) by the somatic changes. This idea of improvement of the bone in response to loading is a theory, albeit one with substantial experimental support. Current experimental results do show that many of the changes in bone in response to loading should reduce the risk of fracture by, for example, increasing the cortical width in a bent bone or by reducing the curvature of an axially loaded long bone. However, this is not to say that all of the changes of bone in response to load make it better mechanically—for example, a blow on the shin can injure the periosteum and cause formation of a permanent bony lump that doesn’t appear to have any mechanical function, but may have a biological function in repairing tissue damage. Therefore, in general, changes of a bone in response to changed loads seem to make the bones mechanically better, but sometimes they do not. On balance, most of the responses to loading do seem to be “for the better” so it is not wrong to call the process bone adaptation as long as any load related changes that are mechanically irrelevant (or are mechanically maladaptive) are not forgotten or ignored.
These data convincingly demonstrate that cells habituate rather quickly to repeated loading (a relief to those of us who don’t care to run 5 miles a day to maintain our bone health). At compressive strain levels of approximately 1500 με, cell accommodation to load occurs within the first 100–200 load cycles (because the loading cycles were delivered at 2 Hz, this represented less than 2 min. of cyclic loading). However, these experiments did not demonstrate the length of the refractory period. How long does it take cells to become re-sensitized to loads once they have become saturated? A second set of experiments was designed in which all groups were given 4 bouts of 90 cycles per bout, and the time between the bouts varied from 30 min to 8 h (Robling et al. 2001b). Bone formation rate was maximized when bouts were separated by 4–8 h (Fig. 6.9). However, re-sensitization did not occur all at once, but was a gradual process that extended beyond the 8 h inter-loading period used in these experiments. Inter-loading periods longer than 8 h were not examined, but extrapolating data from the shorter periods suggests that return to full response may require as long as 12 h (Fig. 6.9).
Bone cells have a refractory period following loading, and only gradually recover their full sensitivity to subsequent loads. Osteoblasts recover most of their responsiveness to loads within about 8 h, but extrapolation from that data indicates that full recovery may not occur for about 12 h following a loading session (Robling et al. 2001b).
Related studies have been performed using low strain, high frequency vibrations applied to mesenchymal stem cells (MSC) in culture (Sen et al. 2011). In this case, refractory periods of 1–3 h between loading bouts enhanced the response of the MSCs, more so with the longer refractory period. This effect appeared to be independent of the magnitude or the frequency of the loading stimulus, further suggesting that strain magnitude may not be the predominant stimulus for bone adaptation. Taken as whole, these results have significant implications for the design of training and exercise programs intended to enhance skeletal health. On the one hand, skeletal health can be maintained or improved by several short periods of exercise over the course of the day. It is also true that, if skeletal health is the goal, injuries such as stress fractures can be avoided by designing training programs that include modest amounts of exercise. However, it should be kept in mind that short bouts of exercise are insufficient for proper maintenance of cardiovascular fitness.
6.5.7 Optimization and the Mathematical Basis of Wolff’s Law
Our assumption for this discussion is that bone structure is regulated to find the optimum solution to minimize both fracture risk and bone mass for the loadings that the bone experiences. A mathematical difficulty in this formulation is that we do not specify whether this is a “global” or a “local” optimum for the bone. A local optimum is a state of bone mass and geometry that is “better than any close-by.” That is, small changes in the mass or structure make the bone worse (higher fracture risk or greater bone mass) for the loading experienced. A global optimum is (not to be too specific) the best local optimum in the whole range of the possible variation of the system—as an example, the absolute minimum fracture risk for the given loads. The fact that bone could have more than one local minimum means that a real (as opposed to a mathematical) bone may not reach the “best solution” during adaptation because the changing tissue could easily fall into a local optimum where any further changes would be stopped because all perturbations of the tissue from the local optimum make it worse with-respect-to the load to which it is adapting.
Experiments performed by Robling et al. (2002) suggest that this could be happening in real bones. Using an experimental approach similar to that previously described, rat ulnae were given 360 loading cycles, either delivered at one time or in 90 cycle “bouts” four times throughout the day 3 days per week, for 16 weeks. They discovered that bones exposed to 360 cycles at one time never achieved the strength or mass of those that were loaded in shorter bouts. After 4 months, bone formation rate (BFR/BS) was threefold higher in the group which received the loads in bouts with fewer cycles. In terms of the remodeling cycle, 4 months in a rat is about equivalent to 1.5–2 years in a human, certainly sufficient time for bone to fully adapt to the mechanical stimulus. Although stiffness as a specific endpoint was not investigated, bone mineral content, whole bone areal bone mineral density, cross-sectional area and rigidity in the direction of bending at the midshaft were all 40–50 % greater in animals that received the loads in smaller doses. This is a remarkable result—an identical input of mechanical cycles resulted in two different “optimal” structures.
The explanation for there being two results was that cells become desensitized following relatively short periods of stimulation, and require a period of recovery before they can fully respond again (Robling et al. 2002). Another possible explanation is that the loading with shorter groups of cycles found a different local optimum because the bone perceived the two loadings as different. The bone does not have any particular long-term agenda, but only a series of short-term goals that reduce its risk of breaking. But the experiments raise a series of other important questions: If bone loading continued in short bouts, would the bone continue to respond, and for how long? Which cell populations become desensitized—the sensors (osteocytes) or the effectors (osteoblasts)? These are all exciting questions that remain to be answered by biologists and engineers.
6.5.8 Some Final Thoughts on Optimization, Adaptation and the Scientific Method
We have placed much of the previous discussion of bone’s response to load in the context of an “adaptation” or the seeking of an optimal state for the bone structure under the given loads. The idea of optimization of a mechanical structure is very seductive both for explaining the adaptation of bone to mechanical loading and, in fact, for explaining the process of evolution. It is unfortunate that it is wrong for both! The problems with this idea were beautifully presented by the celebrated evolutionary theorists Stephen Jay Gould and Richard C. Lewontin in a highly notable paper from 1979 (Gould and Lewontin 1979). In that paper they strongly questioned the idea of “natural selection as so powerful and the constraints upon it so few that direct production of adaptation through its operation becomes the primary cause of nearly all organic form, function, and behavior.” Viewed in this light, bone will adapt by finding an acceptable solution to a biological problem, but this solution may not be the one an engineer would devise as optimal, either in the short term or in the long-term.
The weakness of a bone adaptation theory that uses the concept of optimality is an assumption that natural selection is so strong that it produces a set of genetically defined mechanisms that result in mechanically optimal somatic adaptations of bone to applied load. In other words, optimization theories for bone adaptation are weak for the same reasons that optimization arguments are weak in evolutionary theory. In general, when an optimization theory is proposed as a broad explanation for the adaptation of bone to load it generally ignores the biological constraints or, more frustratingly, acknowledges and then ignores them.
Taken to the extreme, one might think that any use of optimization principles for understanding bone changes in response to load would be completely useless. Fortunately for the engineer interested in bone, optimization isn’t completely useless; instead it provides a useful ideal case that can be used to help build experiments. For example, in the previous section some of the concepts of optimization were used to better understand the experiments of Robling et al. (2002) who deliberately tested whether “identical loadings” (i.e., same number of cycles of the same kind) applied with different timing would produce the same biological result. The researchers formulated an experiment that could test whether the two loading scenarios were truly the same in terms of the adaptive response they elicited—with the underlying assumption (inherent to optimization) that there is a single “best” result for identical loads. Their experiment worked well because the results were not the same, leading to the conclusion that the loading scenarios were perceived as different by the real biological system, despite any interesting thoughts related to structural optimization based purely on mechanical input.
So we see that a theoretical construct for bone adaptation (that could be formulated as an optimization theory) was used to design a successful and very informative experiment on real bones. But what if the two outcomes had been the same? Could the experimenters then claim that bone uses an optimization scheme to find the single best solution? The answer is a resounding no because despite having used some ideas from optimization approaches to create the initial hypothesis it is a scientific mistake to use the results of an experiment to proclaim as truth the reasoning that led to the hypothesis on which the experiment was based. Remember that a scientific hypothesis can only be falsified and cannot be shown to be correct. This is because the result of any test of that hypothesis is only valid for the conditions under which the test is run. If the hypothesis cannot be invalidated, that does not suggest that it is universally true, nor does it suggest that we have even measured the proper outcomes.
A second less appreciated and perhaps more conceptually difficult reason is that even if a hypothesis is in fact true, the idea or reasoning leading to the stated hypothesis is totally irrelevant. To make a joke to illustrate this second point—an immigrant Indiana Leprechaun could have told Robling et al. that the bone adaptation results would be the same for the two loadings (Begorrah!). Despite magical intervention to create the hypothesis, the experiment would still be valid and falsify the hypothesis in a meaningful manner. And if the results had been same (i.e. the hypothesis was not rejected) the researchers could not have claimed with certainty that it was due to leprechauns, magic, biological optimization or any other reason. In this feeble joke, you can identify optimization theory with the leprechaun—whatever the outcome of the experiment, the source of the original hypothesis is not relevant and the validity of optimization isn’t verified. So, maybe the hypothesis is correct—but the source for the hypothesis (leprechaun or optimization) falls outside of the scientific method. This difficulty underlies all theories that are accepted as true natural laws. Even the extremely validated and useful Newton’s laws of motion give us only a hypothesis that the sun will rise in the east tomorrow. Even if it rises tomorrow (and forever after for the remaining history of our species) that doesn’t mean that the sun is governed by Newton instead of Ra—because why we think it will rise doesn’t have anything to do with whether what we think is true or false. For all practical purposes, of course, theories and rules that make many correct predictions (many correct hypotheses) are eventually acceptable as scientific truths; but even the extremely useful Newton’s laws of motion aren’t correct—ask the shade of Dr. Einstein. For optimality based bone adaptation theories there are more exceptions to the rules than there are to Newton’s—so all theories approaching bone’s response to load from that direction should be used carefully as tools rather than accepted as truths.
22.214.171.124 Statics and Dynamics in Bone Adaptation
The experiments explored in this chapter have demonstrated that very few load cycles are necessary to maximize bone’s adaptive response. However, they also showed that there is a lower limit of loading below which bone is lost. That means that one single loading event is not sufficient to prevent bone loss. Taken to its natural extreme, a single loading event is the same as one statically applied load, suggesting that dynamic loading is required to generate an adaptive response in bone. This, in-turn, suggests that bone adaptation is a rate-related phenomenon. We already know that bone is responsive to strain magnitudes that exceed local thresholds or setpoints. Is bone also sensitive to strain rate and if so, what rate is optimal, what are the thresholds (if any), and what is the relationship between strain rate and strain magnitude?
It has been known for 50 years or more that bone does not respond to a static load unless, as in the case of orthodontia, a dynamic load is imposed on top of the static load. Static loads, even those that are quite high, do not elicit any adaptive response. Early experiments by Hèrt in 1969 first suggested that dynamic loads were necessary for bone to respond. Later, this was underscored by Lanyon and Rubin (1984), who applied static loads to the avian ulna for 2 months and observed bone loss endocortically and increased intracortical porosity, changes identical to those found in immobilized animals. Dynamic loads at equivalent peak strain increased net bone formation periosteally, and prevented loss both endocortically and within the cortex. Mosley and Lanyon (1998) followed this work by investigating low, moderate and high strain rates using the rat ulnar axial loading model. In this work, they found that low strain rate loading suppressed the normal periosteal bone formation response, whereas high strain rate loading significantly increased the amount of periosteal new bone. These were growing animals, however, and other studies have shown that low to moderate impact loads can maintain skeletal mass and reduce the amount of loss during aging
Lanyon and Rubin (1984) observed that when no loading was applied over an 8-week period, the ulna suffered endosteal resorption and increased osteonal remodeling. Compressive static loading to 2000 με for the same period of time led to a similar result, but the same strains applied dynamically at 1 Hz produced a 24 % increase in cortical area, primarily from woven bone formation on the periosteal surface. Subsequently, Rubin and Lanyon (1985) did a dose-response experiment for 1 Hz loading in a bending mode such that peak compressive strains were about twice the magnitude of the tensile strains. When 100 cycles/day were applied at peak strains from 0 to 4000 με, there was a linear relationship between cortical area after 8 weeks and peak strain magnitude (% change in area = −15.3 + 0.015 × (peak microstrain), with R 2 = 0.69). Setting the left side of this equation equal to zero indicates that an equilibrium loading for maintenance of bone mass (zero change in area) would be 100 cycles/day at about 1000 με. This was an important benchmark. These investigators did another frequently cited experiment (Rubin and Lanyon 1984) in which 2050 με was applied at 0.5 Hz in daily loading bouts of 4, 36, 360, and 1800 cycles. It turned out that only 4 cycles/day were sufficient to maintain bone mass at this strain magnitude. After 4 weeks of loading, each of the three higher numbers of cycles produced the same increase in bone mass, about 40 ± 10 %, indicating that the woven bone response was an all-or-nothing phenomenon.