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Functional determinants of bone structure: Beyond Wolff's law of bone transformation
Bane, 13,403-409, (1992) Printed in the USA. All rights reserved.
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8756-3282192 $5.00 + .OO 0 1992 Pergamon Press Ltd.
EDITORIAL: Functional Determinants of Bone Structure: Beyond Wolff’s Law of Bone Transformation C.
H.TURNER
Biomechanics and Biomaterials
Research Center and Orrhopaedic Surgery Department,
Charles H. Turner. Ph.D., IN 46202, U.S.A.
Address for corresoondence and retwints:
ClinicalDrive,
Rm 600, Indianapolis,
Director of Orthopaedic
Frost has suggested that functional loading controls bone mass and form as a thermostat controls temperature-by homeostatic regulation (i.e., by negative feedback). Yet, the literature contains many results that appear incompatible with the “mechanostat” hypothesis. We propose that a different type of regulatiowpigenetic-is important in many aspects of bone adaptation. Epigenetic regulation, as we describe it, involves positive feedback loops and promotes differentiation as it forces elements of a system to choose between two extreme levels called attractors. Our review of bone adaptation data suggests that lamellar bone formation is regulated homeostatically, whereas the formation of woven-Bhered bone or fracture callus is regulated epigenetitally, that is, woven hone formation is brought about by a positive feedback loop that stimulates osteoblasts to a state of greater individual activity. This positive feedback loop may involve transforming growth factor B (TGFB), for which autocrine induction has been demonstrated in viva, as well as other factors, including insulin-like growth factor (IGF) and prostaglandin E, (PGE,). The importance of this model is that it provides a mechanism for many unexplained nonlinear events that have heen observed in bone adaptation experiments. Furthermore, it provides insights into the genesis of woven bone, which is a critical step in the process of bone healing and regeneration. growth factor-beta-Bone
University, Indianapolis,
IN 46202,
U.S.A.
Research, Indiana University Medical Center, 541
are generally brought about by negative feedback loops, whereas epigenetic regulations occur through various mechanisms, including positive feedback loops. So which model is correct? The answer to this question is elusive because the available data tend to support the existence of both forms of regulation. As pointed out by Bertram and Swartz (1991), “those who seek to study skeletal response to load find a literature replete with confusing and often contradictory experimental evidence.” In this paper, we will explore the hypothesis that homeostatic regulation of bone structure occurs in growing bone and in the adult skeleton under normal usage; but epigenetic regulation (i.e., regulation by positive feedback) is more important during many phases of bone development and regeneration. It is further proposed that the circumstances in which epigenetic regulation is dominant may have great importance in bone healing and orthopaedic implantology.
Abstract
Key Words: Transforming tion-Bone loss.
Indiana
Biological Feedback Biological feedback processes can be separated into two broad categories: homeostatic regulation and epigenetic regulation (Thomas & D’Ari 1989). Thomas and D’Ari proposed that homeostatic regulation involves negative feedback loops, and epigenetic regulation is brought about predominantly by positive feedback loops. We will use this definition of epigenetic regulation throughout the paper. However, it should be noted that Thomas and D’Ari’s view is somewhat controversial because epigenetic regulation may occur through other mechanisms besides positive feedback. Homeostatic regulation drives the elements of a system to a steady-state point between two extremes. In bone, the regulated variable is the skeletal rigidity which is maintained at a level that is thought to provide minimum adequate structure (i.e., a structure that is adequate for functional needs but with minimal mass) (Alexander 198 1; Frost 1964; Turner 199 1). Functional strain measurements made on weight-bearing limbs of many species of animals have shown that peak strains fall within a narrow range, suggesting that the bone adapts so that peak strain* is homeo-
adapta-
Introduction A century ago, Julius Wolff proposed that bony architecture is dictated by the mechanical stresses placed upon it (Wolff 1892). Wolff’s novel idea caught on and today it is widely accepted that bone is a highly adaptive tissue that modulates mass and structure in response to its loading environment. Yet there is still considerable debate as to how bone adaptation should be modeled. Several authors have proposed that bone structure is homeostatically regulated (Frost 1964, 1983, 1987; Currey 1984; Cowin & Hegedus 1976; Cowin et al. 1985; Carter 1982; Fyhrie & Carter 1986; Hart & Davy 1989; Turner 1991), and others are proponents of epigenetic regulation (Rubin et al 1990; Weinans et al. 1992, Beaupre et al. 1990). These two models for regulation produce strikingly different results; homeostatic regulations
___________ *Although peak functional strain levels have been postulated as the signal that is regulated homeostatically, the actual mechanical parameter is, as yet, undefined. For instance, there is considerable evidence that suggests that bone is more sensitive to functional loads of greater frequency (O’Connor et al. 1982; McLeod & Rubin 1992). The frequency-dependent model of homeostatic regulation is supported by the studies by Uhthoff and Jaworski (1978) that have shown varying sensitivity to disuse at different skeletal sites. Dogs that had one forelimb immo-
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C. H. Turner: Functional
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system. and (c) positive feedback may force differentiation of cell phenotypes, leading to cell transformation (Thomas 1989).
Homeostatic
PGEz Treatment
Time (days)
Fig. 1. Bone formation rate in the tibia1 metaphysis of adult rats during and after prostaglandin
E, treatment
(Ke et al. 1991, used with permisafter which the rate was homeostatically regulated back to pretreatment
sion). A dose response effect of PGE, was observed, bone formation values.
statically regulated (Rubin & Lanyon 1984). Therefore, it has been proposed that peak strains (or some other index of functional loads) act as a negative feedback signal for bone cells (Frost 1964, 1983, 1987. Cowin & Hegedus 1976; Lanyon 1987: Turner 1991; Martin & Burr 1989). For the purpose of our analyses, it is important to consider the following characteristics of homeostatic regulation: (a) after homeostasis is achieved. the system will remain at or oscillate around a supposedly optimum value or set point, and (b) after the system is perturbed it should adapt such that the feedback signal (possibly strain) returns to the same steady-state value as before the perturbation. Epigenetic regulation tends to drive a system to one of multiple steady-state levels. For our purposes, we assume that epigenetic regulation is implemented by positive feedback loops. In a simple positive feedback system there are stable steady states at the extreme levels (Thomas & D‘Ari 1989). These steady states are called attractors because the system tends to be driven toward one or the other. Once an attractor state is reached the system will remain there until perturbed. More complex positive feedback systems, called multistationary, can have many attractor states. Epigenetic regulation is also called differentiative because it forces elements of the system to differentiate into two or more very different final states. For this reason, epigenetic regulation has been proposed as a driving force in the genesis of trabecular bone (Weinans et al. 1992). Although this result remains more mathematical curiosity than biological reality, epigenetic regulation is potentially very important during bone development. In this paper, several characteristics of epigenetic regulation are considered: (a) positive feedback often takes the appearance of a threshold (i.e., a large enough perturbation will cause the system to jump from one attractor state to another, thus activating the system) (b) a simple positive feedback loop has the added feature of “saturation” (i.e., after the system is perturbed sufficiently to cause a jump from the first to the second attractor state further increase in perturbation will have no further effect upon the
Regulation of Bone Structure
One of the simplest examples of homeostatic regulation is control of temperature by a thermostat. A thermostat corrects perturbations in temperature by activating cooling or heating processes until a steady-state (homeostasis) again is achieved. Frost has likened the process of bone adaptation to a thermostat (Frost 1964. 1987). In a direct reference to this analogy, he has coined the term “mechanostat” to describe the mechanism of functional adaptation of bone (Frost 1987). In this theory, mechanical signals within the bone tissue are the endpoints that are regulated by the system. These mechanical signals are maintained at a steadystate level or range of levels within a “physiological window” (Martin & Burr 1989). Frost’s model is one of homeostatic regulation and can be modeled as a simple negative feedback loop (Turner 1991). Homeostatic regulation of bone structure is active during skeletal growth. Keller and Spengler (1989) have shown that the peak strains within the femora of rats were unchanged over a period of 6 to 30 weeks of age, even though the rats’ body weights tripled. Biewener and coworkers (1986) have shown that peak strains in the tibiotarsus of growing chicks did not change over a period when body mass increased IO-fold. These results lead one to believe that peak strains are homeostatically controlled. It is important to note, however, that peak strain is only an index of functional loading, and may not be the actual parameter being regulated. The maintenance of homeostasis in the adult skeleton is most evident in studies of rats (Ke et al. 1991; Jee & Li 1990). Ke et al. demonstrated that the anabolic effects of prostaglandin EZ (PGE,) were not lasting once the treatment was withdrawn. PGEz treatment caused a dose-dependent increase in bone formation rate, yet after treatment was withdrawn, bone formation rate began to decrease and returned to pretreatment values 120 days after withdrawal of PGE, (Fig. I). This type of response is the hallmark of homeostatic regulation (i.e., the system is driven toward a single steady-state value regardless of starting point). Trabecular bone mass also decreased toward pretreatment values after PGE, withdrawal (Fig. 2). However, in the two highest dose groups the trabecular bone mass remained elevated over
____ bilized lost more bone mass in bones at the extremities as opposed to proxrmal locations. The third metacarpal of these dogs lost an average of 48% of its bone mass after 40 weeks of immobihzation. the radius lost 42%. the ulna lost 36% and the humerus lost 29% (the results of Uhthoff et al. 1985 show similar trends). The more distal weight-bearing banes are exposed to high-frequency loading components imparted by the impact with the ground. These high frequency components are diminished greatly as the load is transferred to more proximal bones, since the joints act as shock absorbers. Therefore. the most distal bones have adapted to a broader frequency spectrum of functional loads and, thus, are more sensitive to removal of functional loading.
Time After Withdrawal of PGEz (days) Fig. 2. Homeostatic
regulation of trabecular bone mass in the tibia1 metaphysis of adult rats after anabolic treatment with prostaglandin E, (adapted from Ke et al. 199 1) The gain in bone mass after treatment was dose dependent (doses of Clmglkg, 1 mglkg, 3 mglkg, and 6 mg/kg were administered), yet after withdrawal of treatment the bone mass returned to or near pretreatment values. The lines through the data represent logarithmic curve fits.
C. H. Turner: Functional
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Fig. 3. Homeostatic increase in bone mass in the distal femora of adult rats during overuse of the left hindlimb (the right hindlimb was bound so the rats walked on three legs). The values are plotted as the percentage of values from age-matched control animais. After about 10 weeks a new steady-state bone mass value is reached (illustrated by the grey band). The values in this plot were calculated from the data of Jee and Li (1990). Used with permission. pretreatment values even after 120 days of PGE,. This result can be interpreted in two ways: (a) the study didn’t allow enough time for the trabecular bone mass to reach pretreatment levels (this was the authors’ explanation; Ke et al., 1991)*, or there is “slop” in the negative feedback loop such that the steady-state value is really a range of values such that the system never quite reaches the original steady-state after a perturbation (Frost 1983; Turner 1991; Martin & Burr 1989). Further evidence for homeostatic regulation of bone structure is seen in bone adaptation to asymmetries in functional loading as reported by Jee and Li (1990). In these studies the right hindlimb of rats was immobilized so all of the body weight was supported on the left hindlimb. In response to this overload, trabecular bone mass of the left hindlimb appeared to adapt homeostatically to a new steady-state bone mass after about 10 weeks (Fig. 3). Similar asymmetries in bone mass have been observed in professional baseball pitchers (King et al. 1969) and tennis players (Jones et al. 1977).
Epigenetic Regulation of Bone Structure Positive feedback and woven bone formation The genesis of bone often is separated into two extreme categories: lamellar and woven-fibered bone formation (Jee 1983). These categories are not always distinct; often the lines between woven-fibered and lamellar bone are blurred into hybrid bone types called fibrolammelar or plexiform bone (Currey 1984; Martin & Burr 1989). These intermediate types of bone are difficult to categorize; functionally, they may resemble woven bone (Carter & Spengler 1978), but morphologically and developmentally they are distinct (Martin & Burr 1989). The following discussion will be limited to extreme categories of lamellar and woven bone with the understanding that the epigenetic model used here for woven bone formation may also apply, to a lesser extent, to plexiform bone formation. Lamellar bone is formed slowly and precisely on existing bone surfaces, it has a highly organized collagen structure, and becomes fully mineralized. Conversely, woven bone is formed rapidly, almost haphazardly, has a randomly and loosely organized collagen structure and, although it can become highly mineralized, tends to be less dense due to loose packing of collagen fibers and large porosities. Unlike lamellar bone, woven bone *Since the recovery of trabecular bone mass should follow an exponential decay function, it will never quite reach the original steady state.
405
can be formed de novo and generally precedes the formation of lamellar bone during bone development and growth (Jee 1983; Martin & Burr 1989). In the adult skeleton, woven bone formation is most commonly associated with pathological conditions, like severe Paget’s disease, stress fracture, and fluorosis. It is also the major component of fracture callus that provides the initial mechanical union of the fracture. The driving force behind woven bone formation is a mystery. Woven bone often is formed by osteoblasts that appear phenotypically the same as the cells that form lamellar bone, with one glaring exception: They produce large amounts of badly organized collagen instead of carefully aligning the fibers into lamellae. Interestingly, woven bone formation is relatively unaffected by hormonal regulation (Parfitt 1983), whereas lamellar bone formation is closely regulated by circulating hormones (Turner 1991; Frost 1987). We propose that positive feedback loops that can be activated by supraphysiological stimuli cause osteoblasts to pass through a threshold in activity and cause a transition from lamellar to woven bone formation. This type of regulation of cell activity has been proposed for other cell types (Thomas 1989), and it seems to fit with experimental evidence. For instance, the transition from lamellar to woven bone formation can be blocked if prostaglandin production is blocked (Aufdemorte et al. 1991). This suggests that prostaglandins, especially prostaglandin E,, play some part in the stimulation of woven bone formation. Mechanical loads and some osteoblastic products, including growth factors, stimulate the production of prostaglandin E, by osteoblasts (Somjen et al. 1980; Yeh & Rodan 1984; Binderman et al. 1984; Tashjian et al. 1982, 1985; Lemer 1991), which in turn can stimulate the production of insulin-like growth factor I, which further stimulates osteoblastic activity (McCarthy et al. 1991; Hock et al. 1988). The foregoing example provides no definitive proof, but suggests the possibility of positive feedback loops regulating osteoblasts. Furthermore, a number of growth factors are synthesized by osteoblasts during normal bone formation (Hauschka et al. 1986; Canalis et al. 1988). Many of these factors, in turn, have stimulatory effects upon osteoblastic activity (McCarthy et al. 1989; Canalis et al. 1989: Schmid et al. 1989; Pfeilschifter et al. 1990; Kasperk et al. 1990), supporting the potential for stimulation of osteoblasts by paracrine or autocrine feedback. One bone-derived growth factor for which autocrine induction has been documented is transforming growth factor p. TGFP expression is often associated with woven bone formation in vivo. For instance, during the early stages of fracture healing, osteoblasts in regions of woven bone formation show severalfold increases in expression and synthesis of TGFP (Joyce et al. 1990b), and TGFP expression is seen in regions of woven bone formation in the developing skeleton (Akhurst et al. 1990). High concentrations (2&200 kg/ml) of TGFP have been shown to cause subperiosteal woven bone formation in vivo (Noda & Camiliere 1989; Mackie & Trechsel 1990; Marcelli et al. 1990). Furthermore, TGFP has been shown to positively regulate its own expression in vivo (Joyce et al. 1990a) and in culture systems (Van Obberghen-Schilling et al. 1988). It also has been shown that some 25% of TGFP secreted by bone cells is in an active form, so it may create a positive feedback loop that promotes cell proliferation (Robey et al. 1987). Furthermore, cell division causes geometric amplification of the amount of TGFP present (Robey et al. 19871, thus increasing the positive feedback effect. This positive feedback may not occur at all concentrations of TGFP, because TGFP exhibits a biphasic effect on DNA synthesis of bone cells: Low concentrations (fg/ml) inhibit, whereas higher concentrations (>3 pg/ml) stimulate [3H]thymidine incorporation (Kasperk et al. 1990). This biphasic effect indicates that if cells are stimulated to produce higher concen-
C. H. Turner: Functional
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determinants
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trations of TGFP, they will stimulate their own proliferation and initiate a positive feedback loop, resulting in woven bone formation. Epigenetic
regulation
in bone adaptation
models
Several techniques have been developed to modulate in vivo mechanical loads on bone. They include overload of the radius by ulnar osteotomy (Goodship et al. 1979; Lanyon et al. 1982; Burr et al. 1989), external force application through implanted pins (O’Conner et al. 1982; Churches & Howlett 1982; Rubin & Lanyon 1984; Rubin & Lanyon 1985; Pead et al. 1988), and external force application using four-point bending (Turner et al. 1991). These studies were done on different animal species, including rats, rabbits, roosters, turkeys, dogs, sheep, and pigs. Of these models, all require prior surgical intervention, except the rat tibia overload model of Turner et al. (1991). Yet, there is one common element in these models-they all cause woven bone formation. It is our position that formation of woven bone formation occurring in the foregoing loading models is epigenetically regulated. For the most part, results from loading experiments support this contention. Lanyon et al. (1982) performed osteotomies on mature sheep and measured strains in the sheep’s radii immediately after osteotomy and 12 months after osteotomy. Immediately after osteotomy, tensile strains and compression strains in the radius were increased by 20% and 8%, respectively. Surprisingly, after 12 months the strains in the overloaded radius were reduced to 18% and 10% below those measured in age-matched nonsteotomized animals. The authors hypothesized that this overadaptation was caused because the bone’s goal was to reestablish original strain distributions instead of peak strain magnitudes. We offer another plausible hypothesis-epigenetic regulation. It is the nature of epigenetic regulation to drive a system toward an extreme value or attractor state. Therefore. a positive feedback loop activated by a osteotomy of the ulna would immediately drive the system toward maximal bone formation (i.e., woven bone formation). The amount of new bone formed should not necessarily correlate with the original strain levels that caused it (i.e., there is no a priori reason why the final attractor state should be the same as the original steady-state conditions). Perhaps the most compelling evidence for epigenetic regulation of woven bone formation is demonstrated by the study of Rubin and Lanyon (1984). In this study, adult roosters underwent a surgical procedure to functionally isolate the left ulna, after which Steinmann pins were placed in each end of the bone to allow externally applied loading. Loading was applied at 0.5 cycle per second for 0, 4, 36, 360, and 1800 cycles per day. Groups loaded for 36 or more cycles per day showed mineralization changes characteristic of woven bone formation. Comparison of the 36, 360, and 1800 cycle per day groups shows no increase in woven bone formation response with increased number of loading cycles (Fig. 4). Saturation of response with increasing stimulus is the hallmark of epigenetic regulation! Turner et al. (1991) showed a similar saturation effect after applying from 1 to 108 loading cycles to the tibiae of rats. Pead et al. (1988) demonstrated that a single burst of loading applied to the isolated avian ulna model produced periosteal thickening and woven bone formation seven days later. No other stimulus was applied in the interim period between the loading bout and the response. Interestingly, the salient feature of epigenetic regulation is that a transient change in the environment can result in a stable change of the state of the system, continuing long after the perturbation (Thomas & D’Ari 1989).
Loading Cycles per Day Fig. 4. Bone mineral change in the isolated avian ulna as a result of cyclic loading applied at 0.5 cycles per second with a magnitude of 2050 pstrain (Rubin & Lanyon 1984). Bone mineral content increases as a function of number of loading cycles until the response saturates at 36 cycles per day. Loading for 360 cycles per day and 1800 cycles per day does not increase the amount of new bone mineral above that achieved with 36 cycles of loading per day.
As discussed above, positive feedback often takes the appearance of a threshold where a large enough perturbation will cause the system to jump to a new attractor state. This characteristic applies nicely to the genesis of woven bone. This phenomenon is illustrated by experiments done in our laboratory in which external bending forces are applied to the tibiae of adult rats. In a recent study, we applied bending moments of 81, 99, 120, and 150 N-mm at 36 cycles per day for 12 days. There was proliferative woven bone formation at the periosteal surface in 14 or 24 rats subjected to bending force. The number of rats with woven bone increased in a stairstep pattern as the loading magnitude increased (Fig. 5) (Turner, manuscript in preparation). A threshold for the stimulation of woven bone formation is seen at a bending moment of about 110 N-mm (about 1800 pstrain) (Akhter et al. in press). In all cases woven bone formation was either on or off. For the bones where there was woven bone present, there was no positive correlation between the magnitude of applied load and the amount of woven bone formed 0, = 0.15). In contrast, Rubin and Lanyon (1985), using the isolated avian ulna model. found a positive linear relationship between the change in bone cross-sectional area and applied strain magnitude. However. they did not distinguish between animals that
0
20
40
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80
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120
140
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Bending Moment Applied to the Tibia (N-mm) Fig. 5. Bone formation response in rats’ tibiae exposed to daily fourpoint bending for 12 days. The vertical axis represents the percent increase in cross-sectional area of the mid-section of the tibia1 diaphysis. The number of rats that expressed a woven bone response in each loading group (out of a total of six) is shown in parenthesis. The asterisks represent groups that had significantly greater @ s 0.01, Wilcoxon signedrank) woven bone formation than contralateral control limbs. A threshold for the stimulation of woven bone formation is seen at a bending moment of about I IO Nmm (Copyright Charles H. Turner, all rights reserved).
C. H. Turner: Functional
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407
exhibited woven bone formation and those that did not. Judging from the large standard deviations in bone area change from Rubin and Lanyon’s high-strain groups (a2000 pstrain), it appears that some of the animals exhibited woven bone formation and others did not, which would be consistent with our results (Fig. 5). A Model for Bone Adaptation The proposed relationship between bone formation rate and functional strain stimulus consists of a region that is homeostatically regulated and another that is regulated epigenetically (Fig. 6). The homeostatic region of the relationship is linear with net bone formation driven to a value of zero. The epigenetic region drives the system to an attractor state with maximal activation of bone formation (i.e., woven bone formation). The transition between the two regions represents the threshold for the stimulation of woven bone formation. The proposed model (Fig. 6) is strikingly similar to that proposed by Carter (1982), with one exception. Carter proposed that a nonlinear response in bone loss occurred at extreme levels of disuse. Support for this nonlinear character of bone resorption was not found in the evidence reviewed above (e.g., Ke et al. 1991). This does not rule out the possibility of positive feedback loops controlling bone resorption under conditions of extreme disuse or nutritional deficiency. A biological interpretation of the model in Fig. 6 is this: Lamellar bone formation is homeostatically regulated, whereas woven bone formation is epigenetically regulated. The distinction between homeostatic and epigenetic regulation is nontrivial, as the control mechanisms behind these two processes are profoundly different. Therefore, it is not surprising that the osteoblastic activities associated with genesis of lamellar and woven bone are distinct. A further understanding of the mechanism of woven bone formation is vital to several clinical disciplines. Bone formation de now appears first as woven bone, which is later replaced by lamellar bone (Jee 1983; Martin & Burr 1989). The formation of a woven bone scaffold typically precedes lamellar bone formation around porous coated orthopaedic implants (Burr et al. 1991). Also, woven bone formation is a critical element in the fracture-healing process. The efficiency of woven bone formation has been shown to decrease with increasing age in the isolated avian ulna loading model (Rubin et al. 1992) and in a rodent fracture healing model (Bak & Andreassen
1989). It is possible that this age-related decrease in efficiency of woven bone formation is directly related to the decrease in osteogenic growth factors that occurs with age (Nishimoto et al. 1985; Syftestad & Urist 1982), as these growth factors may play a crucial part in the positive feedback that stimulates cell differentiation and woven bone formation. If this is true, it has implications in certain nutritional deficiencies. For instance, vitamin D deficiency decreases the osteoinductive potential of bone (Turner et al. 1988), possibly by decreasing deposition of TGFP by osteoblasts (Finkelman et al. 1991). In trabecular bone, aging causes perforation of structural elements and discontinuity of the bone structure (Pa&t 1984; Vesterby et al. 1989). Regeneration of these lost trabeculae cannot occur unless preceded by de now woven bone formation (Jee 1983). Therefore, treatment and restoration of vertebral trabecular bone in an osteoporotic skeleton requires woven bone formation in the marrow space. The only treatment shown to accomplish this is high-dose PGE, (Mori et al. 1990). Interestingly, PGE, also may be an important link in the positive feedback loop that initiates woven bone formation.
Acknowledgments: This study was supported by grants from the Whitaker Foundation and the National Institutes of Health (#AR40688). The author thanks David Burr for his helpful comments on an earlier draft of this manuscript.
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I+--
homeonatic
region e-n
epigenetic
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Functional strain stimulus Fig. 6. Proposed model for bone adaptation. The homeostatic region is characterized by negative feedback such that the system is driven toward a net bone formation rate of zero. The epigenetic region is characterized by positive feedback and is driven to an attractor state of maximal bone formation (i.e., woven bone formation). The transition between the two regions represents the threshold for woven bone formation (Copyright Charles H. Turner, all rights reserved).
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Date
Received:
Dale
Revised;
Date Accepted:
April 16, 1992 July 22, 1992 July 22, 1992
Copyright
8756-3282192 $5.00 + .OO 0 1992 Pergamon Press Ltd.
EDITORIAL: Functional Determinants of Bone Structure: Beyond Wolff’s Law of Bone Transformation C.
H.TURNER
Biomechanics and Biomaterials
Research Center and Orrhopaedic Surgery Department,
Charles H. Turner. Ph.D., IN 46202, U.S.A.
Address for corresoondence and retwints:
ClinicalDrive,
Rm 600, Indianapolis,
Director of Orthopaedic
Frost has suggested that functional loading controls bone mass and form as a thermostat controls temperature-by homeostatic regulation (i.e., by negative feedback). Yet, the literature contains many results that appear incompatible with the “mechanostat” hypothesis. We propose that a different type of regulatiowpigenetic-is important in many aspects of bone adaptation. Epigenetic regulation, as we describe it, involves positive feedback loops and promotes differentiation as it forces elements of a system to choose between two extreme levels called attractors. Our review of bone adaptation data suggests that lamellar bone formation is regulated homeostatically, whereas the formation of woven-Bhered bone or fracture callus is regulated epigenetitally, that is, woven hone formation is brought about by a positive feedback loop that stimulates osteoblasts to a state of greater individual activity. This positive feedback loop may involve transforming growth factor B (TGFB), for which autocrine induction has been demonstrated in viva, as well as other factors, including insulin-like growth factor (IGF) and prostaglandin E, (PGE,). The importance of this model is that it provides a mechanism for many unexplained nonlinear events that have heen observed in bone adaptation experiments. Furthermore, it provides insights into the genesis of woven bone, which is a critical step in the process of bone healing and regeneration. growth factor-beta-Bone
University, Indianapolis,
IN 46202,
U.S.A.
Research, Indiana University Medical Center, 541
are generally brought about by negative feedback loops, whereas epigenetic regulations occur through various mechanisms, including positive feedback loops. So which model is correct? The answer to this question is elusive because the available data tend to support the existence of both forms of regulation. As pointed out by Bertram and Swartz (1991), “those who seek to study skeletal response to load find a literature replete with confusing and often contradictory experimental evidence.” In this paper, we will explore the hypothesis that homeostatic regulation of bone structure occurs in growing bone and in the adult skeleton under normal usage; but epigenetic regulation (i.e., regulation by positive feedback) is more important during many phases of bone development and regeneration. It is further proposed that the circumstances in which epigenetic regulation is dominant may have great importance in bone healing and orthopaedic implantology.
Abstract
Key Words: Transforming tion-Bone loss.
Indiana
Biological Feedback Biological feedback processes can be separated into two broad categories: homeostatic regulation and epigenetic regulation (Thomas & D’Ari 1989). Thomas and D’Ari proposed that homeostatic regulation involves negative feedback loops, and epigenetic regulation is brought about predominantly by positive feedback loops. We will use this definition of epigenetic regulation throughout the paper. However, it should be noted that Thomas and D’Ari’s view is somewhat controversial because epigenetic regulation may occur through other mechanisms besides positive feedback. Homeostatic regulation drives the elements of a system to a steady-state point between two extremes. In bone, the regulated variable is the skeletal rigidity which is maintained at a level that is thought to provide minimum adequate structure (i.e., a structure that is adequate for functional needs but with minimal mass) (Alexander 198 1; Frost 1964; Turner 199 1). Functional strain measurements made on weight-bearing limbs of many species of animals have shown that peak strains fall within a narrow range, suggesting that the bone adapts so that peak strain* is homeo-
adapta-
Introduction A century ago, Julius Wolff proposed that bony architecture is dictated by the mechanical stresses placed upon it (Wolff 1892). Wolff’s novel idea caught on and today it is widely accepted that bone is a highly adaptive tissue that modulates mass and structure in response to its loading environment. Yet there is still considerable debate as to how bone adaptation should be modeled. Several authors have proposed that bone structure is homeostatically regulated (Frost 1964, 1983, 1987; Currey 1984; Cowin & Hegedus 1976; Cowin et al. 1985; Carter 1982; Fyhrie & Carter 1986; Hart & Davy 1989; Turner 1991), and others are proponents of epigenetic regulation (Rubin et al 1990; Weinans et al. 1992, Beaupre et al. 1990). These two models for regulation produce strikingly different results; homeostatic regulations
___________ *Although peak functional strain levels have been postulated as the signal that is regulated homeostatically, the actual mechanical parameter is, as yet, undefined. For instance, there is considerable evidence that suggests that bone is more sensitive to functional loads of greater frequency (O’Connor et al. 1982; McLeod & Rubin 1992). The frequency-dependent model of homeostatic regulation is supported by the studies by Uhthoff and Jaworski (1978) that have shown varying sensitivity to disuse at different skeletal sites. Dogs that had one forelimb immo-
403
C. H. Turner: Functional
determinants
of bone structure
system. and (c) positive feedback may force differentiation of cell phenotypes, leading to cell transformation (Thomas 1989).
Homeostatic
PGEz Treatment
Time (days)
Fig. 1. Bone formation rate in the tibia1 metaphysis of adult rats during and after prostaglandin
E, treatment
(Ke et al. 1991, used with permisafter which the rate was homeostatically regulated back to pretreatment
sion). A dose response effect of PGE, was observed, bone formation values.
statically regulated (Rubin & Lanyon 1984). Therefore, it has been proposed that peak strains (or some other index of functional loads) act as a negative feedback signal for bone cells (Frost 1964, 1983, 1987. Cowin & Hegedus 1976; Lanyon 1987: Turner 1991; Martin & Burr 1989). For the purpose of our analyses, it is important to consider the following characteristics of homeostatic regulation: (a) after homeostasis is achieved. the system will remain at or oscillate around a supposedly optimum value or set point, and (b) after the system is perturbed it should adapt such that the feedback signal (possibly strain) returns to the same steady-state value as before the perturbation. Epigenetic regulation tends to drive a system to one of multiple steady-state levels. For our purposes, we assume that epigenetic regulation is implemented by positive feedback loops. In a simple positive feedback system there are stable steady states at the extreme levels (Thomas & D‘Ari 1989). These steady states are called attractors because the system tends to be driven toward one or the other. Once an attractor state is reached the system will remain there until perturbed. More complex positive feedback systems, called multistationary, can have many attractor states. Epigenetic regulation is also called differentiative because it forces elements of the system to differentiate into two or more very different final states. For this reason, epigenetic regulation has been proposed as a driving force in the genesis of trabecular bone (Weinans et al. 1992). Although this result remains more mathematical curiosity than biological reality, epigenetic regulation is potentially very important during bone development. In this paper, several characteristics of epigenetic regulation are considered: (a) positive feedback often takes the appearance of a threshold (i.e., a large enough perturbation will cause the system to jump from one attractor state to another, thus activating the system) (b) a simple positive feedback loop has the added feature of “saturation” (i.e., after the system is perturbed sufficiently to cause a jump from the first to the second attractor state further increase in perturbation will have no further effect upon the
Regulation of Bone Structure
One of the simplest examples of homeostatic regulation is control of temperature by a thermostat. A thermostat corrects perturbations in temperature by activating cooling or heating processes until a steady-state (homeostasis) again is achieved. Frost has likened the process of bone adaptation to a thermostat (Frost 1964. 1987). In a direct reference to this analogy, he has coined the term “mechanostat” to describe the mechanism of functional adaptation of bone (Frost 1987). In this theory, mechanical signals within the bone tissue are the endpoints that are regulated by the system. These mechanical signals are maintained at a steadystate level or range of levels within a “physiological window” (Martin & Burr 1989). Frost’s model is one of homeostatic regulation and can be modeled as a simple negative feedback loop (Turner 1991). Homeostatic regulation of bone structure is active during skeletal growth. Keller and Spengler (1989) have shown that the peak strains within the femora of rats were unchanged over a period of 6 to 30 weeks of age, even though the rats’ body weights tripled. Biewener and coworkers (1986) have shown that peak strains in the tibiotarsus of growing chicks did not change over a period when body mass increased IO-fold. These results lead one to believe that peak strains are homeostatically controlled. It is important to note, however, that peak strain is only an index of functional loading, and may not be the actual parameter being regulated. The maintenance of homeostasis in the adult skeleton is most evident in studies of rats (Ke et al. 1991; Jee & Li 1990). Ke et al. demonstrated that the anabolic effects of prostaglandin EZ (PGE,) were not lasting once the treatment was withdrawn. PGEz treatment caused a dose-dependent increase in bone formation rate, yet after treatment was withdrawn, bone formation rate began to decrease and returned to pretreatment values 120 days after withdrawal of PGE, (Fig. I). This type of response is the hallmark of homeostatic regulation (i.e., the system is driven toward a single steady-state value regardless of starting point). Trabecular bone mass also decreased toward pretreatment values after PGE, withdrawal (Fig. 2). However, in the two highest dose groups the trabecular bone mass remained elevated over
____ bilized lost more bone mass in bones at the extremities as opposed to proxrmal locations. The third metacarpal of these dogs lost an average of 48% of its bone mass after 40 weeks of immobihzation. the radius lost 42%. the ulna lost 36% and the humerus lost 29% (the results of Uhthoff et al. 1985 show similar trends). The more distal weight-bearing banes are exposed to high-frequency loading components imparted by the impact with the ground. These high frequency components are diminished greatly as the load is transferred to more proximal bones, since the joints act as shock absorbers. Therefore. the most distal bones have adapted to a broader frequency spectrum of functional loads and, thus, are more sensitive to removal of functional loading.
Time After Withdrawal of PGEz (days) Fig. 2. Homeostatic
regulation of trabecular bone mass in the tibia1 metaphysis of adult rats after anabolic treatment with prostaglandin E, (adapted from Ke et al. 199 1) The gain in bone mass after treatment was dose dependent (doses of Clmglkg, 1 mglkg, 3 mglkg, and 6 mg/kg were administered), yet after withdrawal of treatment the bone mass returned to or near pretreatment values. The lines through the data represent logarithmic curve fits.
C. H. Turner: Functional
determinants
of bone structure
Fig. 3. Homeostatic increase in bone mass in the distal femora of adult rats during overuse of the left hindlimb (the right hindlimb was bound so the rats walked on three legs). The values are plotted as the percentage of values from age-matched control animais. After about 10 weeks a new steady-state bone mass value is reached (illustrated by the grey band). The values in this plot were calculated from the data of Jee and Li (1990). Used with permission. pretreatment values even after 120 days of PGE,. This result can be interpreted in two ways: (a) the study didn’t allow enough time for the trabecular bone mass to reach pretreatment levels (this was the authors’ explanation; Ke et al., 1991)*, or there is “slop” in the negative feedback loop such that the steady-state value is really a range of values such that the system never quite reaches the original steady-state after a perturbation (Frost 1983; Turner 1991; Martin & Burr 1989). Further evidence for homeostatic regulation of bone structure is seen in bone adaptation to asymmetries in functional loading as reported by Jee and Li (1990). In these studies the right hindlimb of rats was immobilized so all of the body weight was supported on the left hindlimb. In response to this overload, trabecular bone mass of the left hindlimb appeared to adapt homeostatically to a new steady-state bone mass after about 10 weeks (Fig. 3). Similar asymmetries in bone mass have been observed in professional baseball pitchers (King et al. 1969) and tennis players (Jones et al. 1977).
Epigenetic Regulation of Bone Structure Positive feedback and woven bone formation The genesis of bone often is separated into two extreme categories: lamellar and woven-fibered bone formation (Jee 1983). These categories are not always distinct; often the lines between woven-fibered and lamellar bone are blurred into hybrid bone types called fibrolammelar or plexiform bone (Currey 1984; Martin & Burr 1989). These intermediate types of bone are difficult to categorize; functionally, they may resemble woven bone (Carter & Spengler 1978), but morphologically and developmentally they are distinct (Martin & Burr 1989). The following discussion will be limited to extreme categories of lamellar and woven bone with the understanding that the epigenetic model used here for woven bone formation may also apply, to a lesser extent, to plexiform bone formation. Lamellar bone is formed slowly and precisely on existing bone surfaces, it has a highly organized collagen structure, and becomes fully mineralized. Conversely, woven bone is formed rapidly, almost haphazardly, has a randomly and loosely organized collagen structure and, although it can become highly mineralized, tends to be less dense due to loose packing of collagen fibers and large porosities. Unlike lamellar bone, woven bone *Since the recovery of trabecular bone mass should follow an exponential decay function, it will never quite reach the original steady state.
405
can be formed de novo and generally precedes the formation of lamellar bone during bone development and growth (Jee 1983; Martin & Burr 1989). In the adult skeleton, woven bone formation is most commonly associated with pathological conditions, like severe Paget’s disease, stress fracture, and fluorosis. It is also the major component of fracture callus that provides the initial mechanical union of the fracture. The driving force behind woven bone formation is a mystery. Woven bone often is formed by osteoblasts that appear phenotypically the same as the cells that form lamellar bone, with one glaring exception: They produce large amounts of badly organized collagen instead of carefully aligning the fibers into lamellae. Interestingly, woven bone formation is relatively unaffected by hormonal regulation (Parfitt 1983), whereas lamellar bone formation is closely regulated by circulating hormones (Turner 1991; Frost 1987). We propose that positive feedback loops that can be activated by supraphysiological stimuli cause osteoblasts to pass through a threshold in activity and cause a transition from lamellar to woven bone formation. This type of regulation of cell activity has been proposed for other cell types (Thomas 1989), and it seems to fit with experimental evidence. For instance, the transition from lamellar to woven bone formation can be blocked if prostaglandin production is blocked (Aufdemorte et al. 1991). This suggests that prostaglandins, especially prostaglandin E,, play some part in the stimulation of woven bone formation. Mechanical loads and some osteoblastic products, including growth factors, stimulate the production of prostaglandin E, by osteoblasts (Somjen et al. 1980; Yeh & Rodan 1984; Binderman et al. 1984; Tashjian et al. 1982, 1985; Lemer 1991), which in turn can stimulate the production of insulin-like growth factor I, which further stimulates osteoblastic activity (McCarthy et al. 1991; Hock et al. 1988). The foregoing example provides no definitive proof, but suggests the possibility of positive feedback loops regulating osteoblasts. Furthermore, a number of growth factors are synthesized by osteoblasts during normal bone formation (Hauschka et al. 1986; Canalis et al. 1988). Many of these factors, in turn, have stimulatory effects upon osteoblastic activity (McCarthy et al. 1989; Canalis et al. 1989: Schmid et al. 1989; Pfeilschifter et al. 1990; Kasperk et al. 1990), supporting the potential for stimulation of osteoblasts by paracrine or autocrine feedback. One bone-derived growth factor for which autocrine induction has been documented is transforming growth factor p. TGFP expression is often associated with woven bone formation in vivo. For instance, during the early stages of fracture healing, osteoblasts in regions of woven bone formation show severalfold increases in expression and synthesis of TGFP (Joyce et al. 1990b), and TGFP expression is seen in regions of woven bone formation in the developing skeleton (Akhurst et al. 1990). High concentrations (2&200 kg/ml) of TGFP have been shown to cause subperiosteal woven bone formation in vivo (Noda & Camiliere 1989; Mackie & Trechsel 1990; Marcelli et al. 1990). Furthermore, TGFP has been shown to positively regulate its own expression in vivo (Joyce et al. 1990a) and in culture systems (Van Obberghen-Schilling et al. 1988). It also has been shown that some 25% of TGFP secreted by bone cells is in an active form, so it may create a positive feedback loop that promotes cell proliferation (Robey et al. 1987). Furthermore, cell division causes geometric amplification of the amount of TGFP present (Robey et al. 19871, thus increasing the positive feedback effect. This positive feedback may not occur at all concentrations of TGFP, because TGFP exhibits a biphasic effect on DNA synthesis of bone cells: Low concentrations (fg/ml) inhibit, whereas higher concentrations (>3 pg/ml) stimulate [3H]thymidine incorporation (Kasperk et al. 1990). This biphasic effect indicates that if cells are stimulated to produce higher concen-
C. H. Turner: Functional
406
determinants
of bone structure
trations of TGFP, they will stimulate their own proliferation and initiate a positive feedback loop, resulting in woven bone formation. Epigenetic
regulation
in bone adaptation
models
Several techniques have been developed to modulate in vivo mechanical loads on bone. They include overload of the radius by ulnar osteotomy (Goodship et al. 1979; Lanyon et al. 1982; Burr et al. 1989), external force application through implanted pins (O’Conner et al. 1982; Churches & Howlett 1982; Rubin & Lanyon 1984; Rubin & Lanyon 1985; Pead et al. 1988), and external force application using four-point bending (Turner et al. 1991). These studies were done on different animal species, including rats, rabbits, roosters, turkeys, dogs, sheep, and pigs. Of these models, all require prior surgical intervention, except the rat tibia overload model of Turner et al. (1991). Yet, there is one common element in these models-they all cause woven bone formation. It is our position that formation of woven bone formation occurring in the foregoing loading models is epigenetically regulated. For the most part, results from loading experiments support this contention. Lanyon et al. (1982) performed osteotomies on mature sheep and measured strains in the sheep’s radii immediately after osteotomy and 12 months after osteotomy. Immediately after osteotomy, tensile strains and compression strains in the radius were increased by 20% and 8%, respectively. Surprisingly, after 12 months the strains in the overloaded radius were reduced to 18% and 10% below those measured in age-matched nonsteotomized animals. The authors hypothesized that this overadaptation was caused because the bone’s goal was to reestablish original strain distributions instead of peak strain magnitudes. We offer another plausible hypothesis-epigenetic regulation. It is the nature of epigenetic regulation to drive a system toward an extreme value or attractor state. Therefore. a positive feedback loop activated by a osteotomy of the ulna would immediately drive the system toward maximal bone formation (i.e., woven bone formation). The amount of new bone formed should not necessarily correlate with the original strain levels that caused it (i.e., there is no a priori reason why the final attractor state should be the same as the original steady-state conditions). Perhaps the most compelling evidence for epigenetic regulation of woven bone formation is demonstrated by the study of Rubin and Lanyon (1984). In this study, adult roosters underwent a surgical procedure to functionally isolate the left ulna, after which Steinmann pins were placed in each end of the bone to allow externally applied loading. Loading was applied at 0.5 cycle per second for 0, 4, 36, 360, and 1800 cycles per day. Groups loaded for 36 or more cycles per day showed mineralization changes characteristic of woven bone formation. Comparison of the 36, 360, and 1800 cycle per day groups shows no increase in woven bone formation response with increased number of loading cycles (Fig. 4). Saturation of response with increasing stimulus is the hallmark of epigenetic regulation! Turner et al. (1991) showed a similar saturation effect after applying from 1 to 108 loading cycles to the tibiae of rats. Pead et al. (1988) demonstrated that a single burst of loading applied to the isolated avian ulna model produced periosteal thickening and woven bone formation seven days later. No other stimulus was applied in the interim period between the loading bout and the response. Interestingly, the salient feature of epigenetic regulation is that a transient change in the environment can result in a stable change of the state of the system, continuing long after the perturbation (Thomas & D’Ari 1989).
Loading Cycles per Day Fig. 4. Bone mineral change in the isolated avian ulna as a result of cyclic loading applied at 0.5 cycles per second with a magnitude of 2050 pstrain (Rubin & Lanyon 1984). Bone mineral content increases as a function of number of loading cycles until the response saturates at 36 cycles per day. Loading for 360 cycles per day and 1800 cycles per day does not increase the amount of new bone mineral above that achieved with 36 cycles of loading per day.
As discussed above, positive feedback often takes the appearance of a threshold where a large enough perturbation will cause the system to jump to a new attractor state. This characteristic applies nicely to the genesis of woven bone. This phenomenon is illustrated by experiments done in our laboratory in which external bending forces are applied to the tibiae of adult rats. In a recent study, we applied bending moments of 81, 99, 120, and 150 N-mm at 36 cycles per day for 12 days. There was proliferative woven bone formation at the periosteal surface in 14 or 24 rats subjected to bending force. The number of rats with woven bone increased in a stairstep pattern as the loading magnitude increased (Fig. 5) (Turner, manuscript in preparation). A threshold for the stimulation of woven bone formation is seen at a bending moment of about 110 N-mm (about 1800 pstrain) (Akhter et al. in press). In all cases woven bone formation was either on or off. For the bones where there was woven bone present, there was no positive correlation between the magnitude of applied load and the amount of woven bone formed 0, = 0.15). In contrast, Rubin and Lanyon (1985), using the isolated avian ulna model. found a positive linear relationship between the change in bone cross-sectional area and applied strain magnitude. However. they did not distinguish between animals that
0
20
40
M
80
,m
120
140
10”
Bending Moment Applied to the Tibia (N-mm) Fig. 5. Bone formation response in rats’ tibiae exposed to daily fourpoint bending for 12 days. The vertical axis represents the percent increase in cross-sectional area of the mid-section of the tibia1 diaphysis. The number of rats that expressed a woven bone response in each loading group (out of a total of six) is shown in parenthesis. The asterisks represent groups that had significantly greater @ s 0.01, Wilcoxon signedrank) woven bone formation than contralateral control limbs. A threshold for the stimulation of woven bone formation is seen at a bending moment of about I IO Nmm (Copyright Charles H. Turner, all rights reserved).
C. H. Turner: Functional
determinants
of bone structure
407
exhibited woven bone formation and those that did not. Judging from the large standard deviations in bone area change from Rubin and Lanyon’s high-strain groups (a2000 pstrain), it appears that some of the animals exhibited woven bone formation and others did not, which would be consistent with our results (Fig. 5). A Model for Bone Adaptation The proposed relationship between bone formation rate and functional strain stimulus consists of a region that is homeostatically regulated and another that is regulated epigenetically (Fig. 6). The homeostatic region of the relationship is linear with net bone formation driven to a value of zero. The epigenetic region drives the system to an attractor state with maximal activation of bone formation (i.e., woven bone formation). The transition between the two regions represents the threshold for the stimulation of woven bone formation. The proposed model (Fig. 6) is strikingly similar to that proposed by Carter (1982), with one exception. Carter proposed that a nonlinear response in bone loss occurred at extreme levels of disuse. Support for this nonlinear character of bone resorption was not found in the evidence reviewed above (e.g., Ke et al. 1991). This does not rule out the possibility of positive feedback loops controlling bone resorption under conditions of extreme disuse or nutritional deficiency. A biological interpretation of the model in Fig. 6 is this: Lamellar bone formation is homeostatically regulated, whereas woven bone formation is epigenetically regulated. The distinction between homeostatic and epigenetic regulation is nontrivial, as the control mechanisms behind these two processes are profoundly different. Therefore, it is not surprising that the osteoblastic activities associated with genesis of lamellar and woven bone are distinct. A further understanding of the mechanism of woven bone formation is vital to several clinical disciplines. Bone formation de now appears first as woven bone, which is later replaced by lamellar bone (Jee 1983; Martin & Burr 1989). The formation of a woven bone scaffold typically precedes lamellar bone formation around porous coated orthopaedic implants (Burr et al. 1991). Also, woven bone formation is a critical element in the fracture-healing process. The efficiency of woven bone formation has been shown to decrease with increasing age in the isolated avian ulna loading model (Rubin et al. 1992) and in a rodent fracture healing model (Bak & Andreassen
1989). It is possible that this age-related decrease in efficiency of woven bone formation is directly related to the decrease in osteogenic growth factors that occurs with age (Nishimoto et al. 1985; Syftestad & Urist 1982), as these growth factors may play a crucial part in the positive feedback that stimulates cell differentiation and woven bone formation. If this is true, it has implications in certain nutritional deficiencies. For instance, vitamin D deficiency decreases the osteoinductive potential of bone (Turner et al. 1988), possibly by decreasing deposition of TGFP by osteoblasts (Finkelman et al. 1991). In trabecular bone, aging causes perforation of structural elements and discontinuity of the bone structure (Pa&t 1984; Vesterby et al. 1989). Regeneration of these lost trabeculae cannot occur unless preceded by de now woven bone formation (Jee 1983). Therefore, treatment and restoration of vertebral trabecular bone in an osteoporotic skeleton requires woven bone formation in the marrow space. The only treatment shown to accomplish this is high-dose PGE, (Mori et al. 1990). Interestingly, PGE, also may be an important link in the positive feedback loop that initiates woven bone formation.
Acknowledgments: This study was supported by grants from the Whitaker Foundation and the National Institutes of Health (#AR40688). The author thanks David Burr for his helpful comments on an earlier draft of this manuscript.
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I+--
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Functional strain stimulus Fig. 6. Proposed model for bone adaptation. The homeostatic region is characterized by negative feedback such that the system is driven toward a net bone formation rate of zero. The epigenetic region is characterized by positive feedback and is driven to an attractor state of maximal bone formation (i.e., woven bone formation). The transition between the two regions represents the threshold for woven bone formation (Copyright Charles H. Turner, all rights reserved).
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Date
Received:
Dale
Revised;
Date Accepted:
April 16, 1992 July 22, 1992 July 22, 1992