WEIGHT-BEARING BONES have evolved with the ability to

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1 JOURNAL OF BONE AND MINERAL RESEARCH Volume 16, Number 12, American Society for Bone and Mineral Research Mechanical Loading of Diaphyseal Bone In Vivo: The Strain Threshold for an Osteogenic Response Varies with Location YEOU-FANG HSIEH, 1 ALEXANDER G. ROBLING, 2 WALTER T. AMBROSIUS, 3 DAVID B. BURR, 1,2 and CHARLES H. TURNER 1 ABSTRACT Bone tissue responds to elevated mechanical loading with increased bone formation, which is triggered either directly or indirectly by the mechanical strain engendered in the bone tissue. Previous studies have shown that mechanical strain magnitude must surpass a threshold before bone formation is initiated. The objective of this study was to estimate the strain thresholds at three different locations along the ulna of adult rats. We hypothesized that the strain threshold would be greater in regions of the ulna habitually subjected to larger mechanical strains. New bone formation was measured on the periosteal and endocortical surfaces of the ulnar diaphysis in adult female rats exposed to controlled dynamic loading. Axial, compressive loading was applied daily at five different magnitudes for a period of 2 weeks. Bone formation rate (BFR) was measured, using double-label histomorphometry at the ulnar middiaphysis and at locations 3 mm proximal and 3 mm distal to the middiaphysis. Loading induced lamellar bone formation on the periosteal surface that was greater at the distal ulnar location and lower at the proximal location when compared with the middiaphysis. Likewise, peak strains on the periosteal surface were greatest distally and less proximally. There was a significant dose-response relationship between peak strain magnitude and periosteal new bone formation when the mechanically induced strain surpassed a threshold. The strain threshold varied from 1343 microstrain ( strain) proximally to 2284 strain at the midshaft to 3074 strain distally. Unlike the periosteal response to mechanical loading, there was not a clear dose-response relationship between applied load and bone formation on the endocortical surface. Endocortical strains were estimated to be <20% of periosteal strains and may not have been sufficient to initiate a bone formation response. Our results show that the osteogenic response on the periosteal surface of the ulna depends on peak strain level once a strain threshold is surpassed. The threshold strain is largest distally, where locomotor bone strains are typically higher and smallest proximally where locomotor bone strains are lower. (J Bone Miner Res 2001;16: ) Key words: rat, ulna, adaptation, mechanotransduction INTRODUCTION WEIGHT-BEARING BONES have evolved with the ability to adapt their shape and architecture to changes in the prevailing mechanical environment. Mechanical strain induced by dynamic loading plays an important role as a signal in triggering bone formation. Previous studies have indicated that mechanical strains must reach a specified magnitude before bone formation is initiated. (1 3) In addition, bone formation in response to dynamic mechanical 1 Department of Orthopedic Surgery, Indiana University School of Medicine, Indianapolis, Indiana, USA. 2 Department of Anatomy and Cell Biology, Indiana University School of Medicine, Indianapolis, Indiana, USA. 3 Department of Medicine, Indiana University School of Medicine, Indianapolis, Indiana, USA. 2291

2 2292 HSIEH ET AL. loading was shown to be correlated positively with peak strain magnitude when a threshold was surpassed. (2,3) However, the strain threshold for osteogenesis may vary along the proximal-distal axis of long bones. Indeed Mosley et al. (4) showed that dynamic axial loading applied to the ulnas of growing rats increased bone formation distally while suppressing bone formation proximally. The authors concluded that mechanical loading modulates growth-related modeling drifts in long bones and affects whole bone architecture. It is unclear whether site specificity of the loading response is present only during growth or is a phenomenon that also might be observed in adult long bones. Jaworski and Uhthoff (5) showed in adult dogs that the distal regions of weight-bearing limbs are more sensitive to disuse-related bone loss compared with proximal regions. In fact, the sensitivity of bone tissue to disuse-related bone loss is quite variable throughout the skeleton. (6) Non weight-bearing bones like the skull do not require mechanical loading to maintain their bone structure, whereas the tibia will lose a substantial amount of bone mass if subjected to disuse for several weeks. Turner proposed that bone mechanosensitivity accommodates according to its mechanical environment such that the strain threshold is greater in skeletal sites routinely exposed to larger mechanical strains. (7) Accordingly, we hypothesized that (1) strain thresholds for osteogenesis vary along the proximal-distal axis of long bones and (2) the strain threshold is highest where peak strain magnitudes in the bone tissue are high. We tested these hypotheses using the rat ulna loading model. Axial loading of the ulnas of growing rats induces bone formation on the periosteal surface, (4,8) suggesting that this loading model is appropriate for the study of periosteal bone formation in response to mechanical loading in adult rats. In this study, we measured the periosteal surface strains and osteogenic responsiveness of the periosteal and endocortical surfaces at different locations along the ulnas in adult rats subjected to cyclic axial loading. We then estimated the strain threshold for osteogenesis at each of three diaphyseal locations middiaphysis and 3 mm proximal and distal from the middiaphysis. MATERIALS AND METHODS FIG. 1. Schematic diagram of the ulna loading system. The forearm is held in cups between the flexed carpus and the olecranon. The ulna is loaded through the carpal joint and overlying soft tissues. Also shown are the locations where bone formation parameters and bone strains were measured. Eighty-four adult female Sprague Dawley rats (7 8 months old) with a mean ( SEM) body weight of 308 g ( 15 g) were used for this study, 4 rats for the determination of the relationship between mechanical strain on the ulna and applied load and 80 rats for measurement of mechanical strain induced bone formation. The animals were housed 2 rats to a cage with a 12 h/12 h light/dark cycle. They were given water and a standard rat laboratory diet ad libitum and monitored daily. The procedures performed throughout the experiments followed the guidelines of the Indiana University Animal Care and Use Committee. For load-strain calibration experiments, each rat was killed and then the shaft of the right ulna was exposed and single element strain gauges (EA DJ; Measurements Group, Raleigh, NC, USA) were bonded with cyanoacrylate adhesive to the medial ulnar surface 3 mm proximal and distal to the midshaft. Then, loading was applied to the ulna through the flexed carpus and olecranon process (Fig. 1) as described by Torrance et al. (8) using a loadcontrolled electromagnetic loading device constructed by Forwood et al. (9) Strains were measured using a strain gauge conditioner and amplifier (2200 system; Measurements Group) for peak loads of 5, 10, 15, and 20N at a frequency of 2 Hz applied for approximately 10 cycles. This loading regimen allowed us to discern any dose-response relationship between load magnitude and ulnar strain. The strain data collected 3 mm distal and proximal to the midshaft were combined with the strains measured at the medial surface of the midshaft that we reported previously. (10) Bending was induced because of the inherent curvature of the ulna, resulting in compressive strains on the medial surface and tensile strains on the lateral surface. (10) The ratio of compressive to tensile strain magnitude in the adult rat ulna is (10) This ratio is higher than that measured in growing rat ulnas (1.23 (4) ), suggesting that the adult ulna has less curvature than the immature ulna. In the adult ulna, the proportion of strain caused by bending was about 80% and the remaining 20% was caused by axial compression. This result is consistent with strain measurements in long bones of animals during locomotion, which show that 80 90% of the peak strain is caused by bending. (11,12) The in vivo rat ulna loading experiments were completed in two phases. For the first phase, the rats were assigned randomly to five loading groups with peak loads of 6.5 (group 1, n 8), 10.5 (group 2, n 8), 14.5 (group 3, n 8), 18.5 (group 4, n 8), and 22.5N (group 5, n 8). After

3 BONE FORMATION IN THE ADULT RAT ULNA completing the first phase, we learned that 22.5N caused fracture in all of the ulnas after several bouts of loading. Consequently, no rats were loaded at 22.5N in the second phase. Group sizes for the second phase were group 1, n 8; group 2, n 8; group 3, n 8; group 4, n 16; and group 5, n 0. Loading was applied as a haversine waveform to the right forelimb of rats under ether anesthesia for 10 days during a 12-day period at 2 Hz for 360 cycles/day. The left ulnas served as contralateral controls. This loading regimen allowed us to discern a dose-response relationship between strain magnitude and bone formation. Between loading sessions, rats were allowed normal cage activity. Intraperitoneal injections of calcein (7 mg/kg) were given to the rats on day 5 and day 12. All rats were killed on day 16. The right and left ulnas were removed for histomorphometry. At the end of the experiment the right and left ulnas of each rat were dissected, freed of soft tissue, and fixed in 10% neutral buffered formalin for 48 h. Then, the bone specimens were washed, dehydrated in ascending concentrations of ethanol, and embedded undecalcified in methyl methacrylate (MMA; Delaware Diamond Knives, Wilmington, DE, USA). Transverse sections (50 m thick) were cut through the middiaphysis of the ulna and 3 mm proximal and distal to the middiaphysis using a diamond wire saw (Histo-Saw; Delaware Diamond Knives). Three sections per ulna were analyzed microscopically using reflected UV light at a magnification of 150. Histomorphometric indices of bone formation were measured using the Bioquant semiautomatic digitizing system (R & M Biometrics, Nashville, TN, USA) attached to a Nikon Optiphot fluorescence microscope (Nikon USA, Garden City, NJ, USA). Bone formation parameters of the endocortical and periosteal surfaces included mineralizing surface (MS/BS, %), which represents the percentage of bone surface that is actively forming bone, defined as the sum of the length of doublelabeled bone surface and half of the length of single-labeled bone surface divided by the total bone surface; mineral apposition rate (MAR, m/day) defined as the average distance between the subsequent calcein green labels divided by the time interval between the calcein injections; and bone formation rate (BFR/BS, m 3 / m 2 per year), which represents the volumetric rate of new bone formation, calculated as the product of MAR and MS/BS. Mechanically induced bone formation was represented in terms of the relative bone formation parameters, that is, relative BFR (rbfr/bs), relative mineralizing surface (rms/bs), and relative MAR (rmar), which were determined by subtracting the bone formation parameters measured for the left ulna from those measured for the right ulna. In addition, the sections from group 4 were analyzed by region (Fig. 2). Bone formation parameters were measured at the medial and lateral surfaces, where largest compressive and tensile strains occurred, and at the cranial and caudal surfaces, where strains were smallest. The regions where these measurements were made and their proximity to the strain gauge location on the medial surface are shown in Fig. 2. Simple regression analysis (Statview; SAS Institute, Cary, NC, USA) was performed to determine the relationship between load magnitude and ulnar strain. Wilcoxon 2293 FIG. 2. The location of the strain gauge on the medial surface and locations of the quadrants where bone formation measurements were made (boxes) on the rat ulna cross-section (midshaft). signed rank tests were performed for each loading group to determine significant differences in bone formation parameters between right (loaded) and left (control) ulnas. The nonparametric Wilcoxon test was chosen over the parametric paired t-test because the variances for some bone formation parameters were unequal for right and left ulnas. An analysis of variance (ANOVA) was performed to determine the effects of loading magnitude on the bone formation parameters, that is, BFR/BS, MS/BS, and MAR, for the left (control) and right (loaded) ulnas and for relative bone formation parameters (loaded minus control). A repeated measures ANOVA and paired t-tests (and nonparametric Wilcoxon tests) were used to compare rbfr/bs for the different quadrants (i.e., cranial, caudal, medial, and lateral) of the ulnar cross-section. In addition, a repeated measures ANOVA and paired t-tests (and nonparametric Wilcoxon tests) were used to compare rbfr/bs at different diaphyseal locations (i.e., proximal, distal, and midshaft). To examine the differences in strain thresholds for osteogenesis at the three locations along the ulnar diaphysis, we completed two separate regression analyses. The first analysis allowed us to test whether the relationship between peak compressive strain and rbfr was statistically different at the three diaphyseal locations. We used a quadratic model of the form y a b(x d i ) c(x d i ) 2 where x is the peak compressive strain, d i is the shift in strain threshold at the different locations, and y is rbfr. We assumed d i was zero for the proximal location. This model was fit using the nonlinear least squares routine (PROC NLIN) in SAS version (13) This model was compared with simple quadratic regression, that is, all d i s are zero, using an approximate ƒ test. Approximate CIs about the estimated d i were used for pairwise comparison of thresholds. A Bonferroni adjustment for multiple comparisons was made by examining approximate 98.33% (100 5/3%) CIs. Although the quadratic model allowed us to test whether changes in strain thresholds were significant, it did not provide clear values for strain thresholds. An additional analysis to estimate strain threshold values was completed by fitting data to a segmented regression model: y a b(x 1 x c )x 2, where y is rbfr, x 1 is peak compressive strain, and x c is the cut

4 2294 HSIEH ET AL. FIG. 3. The compressive strain magnitude on the medial surface induced by axial loading of the ulna increased linearly with applied load and varied with diaphyseal location (mid, midshaft; prox, proximal). Linear regressions of the data were highly significant (p ) for all locations (r ). Values are means SEM. point joining segment 1 with segment 2. If peak strain is x c, y a, and if peak strain is x c, y (a b)(x 1 x c ). The terms a and b are constants estimated by regression analysis. Using this model, x c represents the strain threshold for osteogenesis. Values of x c were varied until the curve fit (as determined by r value) was maximal. The x c was determined for each of the three diaphyseal locations. RESULTS The compressive strain measured on the medial surface increased linearly with applied axial load and varied with diaphyseal location such that strains were greater at the distal location and lower at the proximal location when compared with the middiaphysis (Fig. 3). Regressions of the data were highly significant (p ) for all locations (r 0.88 for middiaphysis, r 0.95 for distal, and r 0.84 for proximal). The ulnas of all rats loaded to 22.5N fractured after approximately 180 cycles (first day of loading), with a peak compressive strain of 6790 microstrains ( strain) at the site of fracture (slightly distal to the ulnar midshaft). The ulnas of 5 of 24 rats loaded to 18.5N fractured at approximately 3000 cycles (ninth day of loading), with a corresponding peak compressive strain of 5610 strain near the site of fracture (also slightly distal to the ulnar midshaft). Histomorphometric data were obtained from 14 to 15 rats in groups 1, 2, 3, and 4, respectively. Nine rats were excluded from this study because of specimen damage, missing calcein labels, or death from an overdose of ether. Neither periosteal nor endocortical bone formation parameters for the left (control) ulnas were different among the loading groups (p ). Axial loading 10N induced new bone formation on the periosteal surface at the midshaft of the ulna (Table 1; Fig. 4). All bone formation parameters at the midshaft and distal locations were significantly greater than those at the proximal location (p 0.05). There was very little osteogenic response on the endocortical surface of the ulna (Table 1). There was no clear dose-response relationship between applied load and bone formation on the endocortical surface. There was significant evidence (p ) that the strain thresholds for periosteal BFR differed by diaphyseal location. For the proximal location, the estimated model is x x 2 (the overall model was highly significant, p ). The change in threshold value between midshaft and proximal locations is estimated as 169 strain (95% CI, 547 and 885), between distal and proximal locations is estimated as 1212 strain (95% CI, 457 and 1967), and between distal and midshaft locations is estimated as 1043 strain (95% CI, 648 and 1437). After adjusting for multiple comparisons, the significant differences between distal and proximal and between distal and midshaft locations remained. Using a segmented regression curve fit, the threshold strain values for the proximal, midshaft, and distal diaphyseal locations were estimated to be 1343, 2284, and 3074 strain, respectively (Fig. 5). All segmented regression models were highly significant (p ) with good fits (r ). Mechanically induced bone formation was significantly greater (p 0.05) on the medial surface compared with other surfaces (Fig. 6). Although less than that on the medial surface, new bone formation on the lateral surface was enhanced by mechanical loading, particularly at the midshaft and distal sites (p 0.05). There was no consistent loading effect on bone formation at the cranial or caudal surfaces. On average, mechanically induced BFR varied significantly with location (p 0.05); it was greatest distally and least proximally. BFR roughly corresponded to the peak strains on the surfaces, which were estimated from strain gauge data using beam-bending equations. Absolute strain magnitudes were highest on the medial surface (distal, 5610 strain; midshaft, 4000 strain; proximal, 2010 strain), lower on the lateral surface (distal, 3667 strain; midshaft, 2614 strain; proximal, 1313 strain), and lower still on the cranial and caudal surfaces (distal, 972 strain; midshaft, 693 strain; proximal, 349 strain [estimated values]). DISCUSSION Our results show that periosteal bone formation at the ulnar diaphysis increases in proportion to peak strain level after a strain threshold is surpassed. In addition, we found that the strain threshold for osteogenesis varies with diaphyseal location on the ulna. The threshold strain for osteogenesis varied from 1343 strain proximally to 3074 strain distally along the diaphysis. Our hypothesis that strain thresholds correlate with peak strain levels along the ulna was supported by the data. The distal diaphyseal location (3 mm distal to the midshaft), which had a greater threshold strain for bone formation, exhibited the highest periosteal strain in response to axial loads. Similarly, the proximal diaphyseal location (3 mm proximal to the midshaft), which had a smaller threshold strain for bone forma-

5 BONE FORMATION IN THE ADULT RAT ULNA 2295 TABLE 1. AVERAGE BONE FORMATION PARAMETERS FOR THE PERIOSTEAL AND ENDOCORTICAL SURFACES OF THE MIDSHAFT OF THE RAT ULNA AS A RESULT OF AXIAL LOADING Group applied load MS/BS (%) MAR ( m/day) BFR/BS ( m 3 / m 2 /year) Periosteal 6.5N Right 33.1 (22.9) 0.78 (0.51) (104.4) Left 24.6 (15.3) NS 0.87 (0.40) NS 48.2 (68.5) NS 10.5N Right 36.8 (15.9) 1.29 (0.70) (145.0) Left 27.0 (15.8) p (0.45) p (60.5) p N Right 59.1 (21.6) 2.13 (1.14) (282.7) Left 29.5 (12.8) p (0.49) p (37.0) p N Right 74.7 (14.8) 2.51 (1.37) (409.5) Left 28.6 (13.8) p (0.29) p (39.6) p Endocortical 6.5N Right 5.0 (7.9) 0.07 (0.25) 5.9 (21.2) Left 8.3 (13.6) NS 0.30 (0.58) NS 30.0 (68.3) NS 10.5N Right 8.1 (14.9) 0.37 (0.68) 32.9 (94.8) Left 5.9 (13.9) NS 0.33 (0.61) NS 28.6 (86.1) NS 14.5N Right 16.6 (24.7) 0.50 (0.86) 64.4 (118.4) Left 8.3 (16.1) p (0.70) NS 41.4 (83.9) NS 18.5N Right 5.5 (9.9) 0.37 (0.69) 25.0 (62.0) Left 1.9 (2.8) NS 0.0 (0.0) p (0.0) p 0.05 Histomorphometric parameters measured were MS/BS, MAR, and BFR/BS. Means are presented with SDs in parentheses. The notation after the parentheses represents comparison between the right and left ulna (Wilcoxon signed rank test). NS, not significant ( p 0.05). FIG. 4. Lamellar bone formation induced by mechanical loading (18.5N) was observed on the periosteal surface of the ulnar diaphysis as outlined by the fluorescent labels (white lines) on the photomicrograph to the right. The labels outline the amount of new bone that was formed in a 7-day period. On average, loading increased bone formation most on the medial and lateral surfaces. tion, had the lowest periosteal strain when loaded. These observations fit the theory of cellular accommodation, (7) which predicts higher strain thresholds in regions of the skeleton where the mechanical strain stimulus is greater. In addition, the results agree with the finding that disuseinduced bone loss is greater in the distal ulna, as opposed to more proximal regions, (5) if we consider bone tissue with a larger strain threshold will be more prone to bone loss with disuse, because of the larger differential between the usual strain magnitude and the disused state. Our observed strain thresholds were larger than that found by Rubin and Lanyon using the isolated avian ulna loading model (2) and by Turner et al. using the rat tibia loading model. (3) The difference in the threshold strain for osteogenesis may be caused by the difference in the orientation of load application for the isolated avian ulna or tibial four-point bending model compared with the ulna axial loading model. It has been suggested that the osteogenic response is elevated when strain distribution in bone tissue is unusual (14) ; thus, one might expect a greater sensitivity to

6 2296 HSIEH ET AL. FIG. 5. Strain thresholds for periosteal bone formation. Triangles represent the proximal ulna, circles represent the ulnar middiaphysis, and the squares represent the distal ulna. Values are means SEM. A quadratic model of the form y a b(x d i ) c(x d i ) 2 was fit to the data (solid lines). For the proximal location, the estimated model is x x 2. The change in threshold value d i was significantly greater than zero for the proximal site versus the distal site (p 0.05) and the midshaft versus the distal site (p 0.05). A segmented regression model was used to estimate the strain thresholds for osteogenesis at different locations along the ulnar diaphysis (dashed lines). Data were fit to the model: y a b(x 1 x c )x 2, where y is periosteal BFR (rbfr/bs), x 1 is peak compressive strain, and x c is the strain threshold. For the proximal ulna, the data were fit best (r 0.60) when a 1, b 0.279, and x c 1343; for the ulnar middiaphysis (r 0.65), a 75, b 0.315, and x c 2284; and for the distal ulna (r 0.69), a 61, b 0.287, and x c FIG. 6. RBFRs (loaded minus unloaded ulnas) varied with location on the periosteal surface (18.5N load). Mechanically induced bone formation was greatest on the medial surface (p 0.05). Although less than that on the medial surface, new bone formation on the lateral surface was enhanced by mechanical loading. There was no consistent loading effect on bone formation at the cranial or caudal surfaces. These results corresponded to the peak strains on the surfaces. Asterisks indicate significant differences from zero (p 0.05). loading for the isolated avian ulna or four-point bending of the tibia, which cause abnormal strain distributions in the bone, compared with axial loading of the ulna that causes a more physiological strain distribution. Mechanically induced bone formation on the periosteal surface was distributed in accordance with strain magnitude. After loading, bone formation was highest on the medial surface the site of compressive strain and the highest strain magnitude; bone formation was next highest on the lateral surface the site of tensile strain. Bone formation on the cranial and caudal surfaces, which had the lowest estimated strain magnitudes with loading, was not affected significantly by loading. These results and previous studies using the rat ulna loading model (4,8) and the rat tibia bending model (3) suggest that maximum bone formation occurs in diaphyseal regions subjected to the highest strain magnitude. Of course, this finding does not contradict previous findings showing that strain rate is key for stimulating osteogenesis, (15 17) because strain rate increased in direct proportion to strain magnitude for the loading regimen used here. The role of loading frequency on osteogenesis in the rat ulna was not tested in this study. In another study, we showed that the periosteal surface of the rat ulna was more responsive to higher loading frequencies (5 Hz and 10 Hz) compared with lower loading frequency (1 Hz), possibly because higher loading frequencies generate larger fluid shear stress on bone cells. (18) In addition, we did not test for the osteogenic effects of strain distribution in the crosssection of the rat ulna; yet, others have shown strain distribution to be important for osteogenesis. (19) There was only a very small osteogenic response to mechanical loading on the endocortical surface of the ulna. We believe the limited endocortical bone response occurred because the endocortical strains induced by applied load were relatively small and perhaps below the osteogenic threshold. The endocortical surface strains depend on the size and geometry of the cortical bone cross-section and are proportional to the periosteal surface strains. Although endocortical strains cannot be determined exactly, they can be estimated from the periosteal strains and the ratios of the endocortical to periosteal radii under the assumption that the ulna is loaded mainly in bending. The ratios of endocortical radius to periosteal radius ranged from 0.15 to 0.2 for the adult rat ulna. Thus, the average endocortical surface strain should be no more than 20% of the periosteal surface strain in response to dynamic loading. Our results show that the rat ulnar loading model is useful for studying bone adaptation in adult rats. A potential concern was the loading-induced fracture of the ulnas we observed in 21% of the rats in group 4 (18.5N) and 100% of the rats in group 5 (22.5N). Exclusion of the results from these rats would not be expected to affect the major results presented in this article. However, the results indicate that one must load the rat ulna close to the fracture threshold to achieve osteogenesis. In this study, fractures occurred in group 4 (18.5N) in the distal ulna, where peak strains were about 5610 strain, after a total of 3000 cycles (ninth day of loading) and in group 5 (22.5N), where peak strains reached about 6790 strain, after about 180 cycles (first day of loading). Bentolila et al. reported that bone matrix microdamage was observed in all ulnar diaphyses of adult rats exposed to fatigue loading with a peak strain of 4000 strain for approximately 9000 cycles. (20) Comparison of Bentolila et al. s loading regimen with ours suggests that

7 BONE FORMATION IN THE ADULT RAT ULNA microdamage may have been present in the distal ulna for our loading groups 4 and 5. At this point, it is unclear whether that microdamage affected bone formation on either the periosteal or endocortical surfaces. In conclusion, bone formation on the periosteal surface of the ulna increases in a dose-response manner with mechanical strain when a threshold is surpassed. Periosteal bone formation in response to dynamic loading varies with diaphyseal location, with the strain threshold increasing in magnitude from proximal to distal locations. The highest strain threshold was found in the distal ulna, which typically is subjected to higher strains, and the lowest strain threshold was found in the proximal ulna, which typically receives lower strains. ACKNOWLEDGMENTS This work was supported in part by the National Institutes of Health (NIH) grant AR REFERENCES 1. Chow JWM, Jagger CJ, Chambers TJ 1993 Characterization of osteogenic response to mechanical stimulation in cancellous bone of rat caudal vertebrae. Am J Physiol 265:E340 E Rubin CT, Lanyon LE 1985 Regulation of bone mass by mechanical strain magnitude. Calcif Tissue Int 37: Turner CH, Forwood MR, Rho J-Y, Yoshikawa T 1994 Mechanical loading thresholds for lamellar and woven bone formation. J Bone Miner Res 9: Mosley JR, March BM, Lynch J, Lanyon LE 1997 Strain magnitude related changes in whole bone architecture in growing rats. Bone 20: Jaworski ZFG, Liskova-Kiar M, Uhthoff HK 1980 Effect of long-term immobilization on the pattern of bone loss in older dogs. J Bone Joint Surg Br 62B: Turner CH 1999 Site-specific skeletal effects of exercise: Importance of interstitial fluid pressure. Bone 24: Turner CH 1999 Toward a mathematical description of bone biology: The principle of cellular accommodation. Calcif Tissue Int 65: Torrance AG, Mosley JR, Suswillo RFL, Lanyon LE 1994 Noninvasive loading of the rat ulna in vivo induces a strainrelated modeling response uncomplicated by trauma or periosteal pressure. Calcif Tissue Int 54: Forwood MR, Bennett MB, Blowers AR, Nadorfi RL 1993 Modification of the in vivo four-point loading model for studying mechanically induced bone adaptation. Bone 23: Hsieh Y-F, Wang T, Turner CH 1999 Viscoelastic response of the rat loading models: Implications for studies of strainadaptive bone formation. Bone 25: Rubin CT, Lanyon LE 1982 Limb mechanics as a function of speed and gait: A study of functional strains in the radius and tibia of horse and dog. J Exp Biol 101: Bertram JEA, Biewener AA 1988 Bone curvature: Sacrificing strength for load predictability? J Theor Biol 131: SAS Institute, Inc SAS/STAT User s Guide, Version 8, Cary, SAS Institute, Inc., NC, USA. 14. Lanyon LE 1992 Control of bone architecture by functional load bearing. J Bone Miner Res 7:S369 S Mosley JR, Lanyon LE 1998 Strain rate as a controlling influence on adaptive modeling in response to dynamic loading of the ulna in growing male rats. Bone 23: O Connor JA, Lanyon LE, MacFie J 1982 The influence of strain rate on adaptive bone remodelling. J Biomech 15: Turner CH, Owan I, Takano Y 1995 Mechanotransduction in bone: Role of strain rate. Am J Physiol 269:E438 E Hsieh, Y-F, Turner CH 2001 Effects of loading frequency on mechanically induced bone formation. J Bone Miner Res 16: Judex S, Gross TS, Bray RC, Zernicke RF 1997 Adaptation of bone to physiological stimuli. J Biomech 30: Bentolila V, Boyce TM, Fyhrie DP, Drumb R, Skerry TM, Schaffler MB 1998 Intracortical remodeling in adult rat long bones after fatigue loading. Bone 23: Address reprint requests to: Charles H. Turner, Ph.D. Director of Orthopedic Research Indiana University School of Medicine 541 Clinical Drive, Room 600 Indianapolis, IN 46202, USA Received in original form February 9, 2001; in revised form May 2, 2001; accepted May 18, 2001.