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COMPRESSIVE PRINCIPAL STRESSES/STRAINS AND THEIR REGIONAL DISTRIBUTIONS GOVERN EARLY TRABECULAR BONE RESPONSE IN VIVO *Kim, C H; *Takai, E; *Gaing, B M; *Chan, M L; **Zhou, H; ***Von Stechow, D; ***Müller, R; **Dempster, D W; +*Guo, X E +*Bone Bioengineering Laboratory, Department of Biomedical Engineering, Columbia University, New York, NY INTRODUCTION Quantitative relationships between trabecular bone cellular response and mechanical microenvironments in trabecular bone tissue are important in understanding the etiology of osteoporosis and developing optimal designs for joint replacements. Limited data exist regarding the mechanical objectives of trabecular bone adaptation. Many hypotheses have been formulated for the driving mechanical parameters of trabecular bone adaptation, including the strain energy density, or strain energy density gradient [1,2]. An in vivo rat tail model combined with micro computed tomography (µCT) image based finite element (FE) modeling provides a powerful tool to search for the candidates of mechanical parameters to which trabecular bone responds [3]. One unique feature of this animal model is a non-uniform distribution of trabecular bone tissue stress/strain in the tail vertebra when subjected to dynamic uniaxial compression, providing a window to explore regional correlations among trabecular bone response and mechanical parameters. The focus of this study is to identify the primary mechanical parameters, which are responsible for trabecular bone adaptation response. MATERIALS AND METHODS Two hundred and twenty four, male, 9-month-old Sprague-Dawley rats of approximately 500 g in body weight were randomly assigned to 7 treatment groups (1) Control; 2) Vehicle+0N; 3) PTH+0N; 4) Vehicle+50N; 5) PTH+50N; 6) Vehicle+100N; and 7) PTH+100N) at 3 durations (1 week, 2 weeks and 4 weeks) yielding a total of 21 groups (n=10-12 each). Under general anesthesia, threaded K-wires were inserted into the seventh (C7) and ninth (C9) caudal vertebrae of all animals except Control animals [3]. Animals assigned for PTH treatment received s.c. 15 µg/kg/day of ratPTH 1-34. Under general anesthesia, the eighth caudal vertebra (C8) of loaded animals were subjected to 5 minutes of a compressive load of either 50N or 100N using a sinusoidal waveform at 1 Hz. 0N loaded animals were also placed on the loading device for the same period of time as the loaded animals with only the actuator turned off. All treatments were initiated 3 days post -surgery. All animals were sacrificed 24 hours after the final treatment and were double labeled i.p. with 20 mg/kg calcein. Immediately after sacrifice, the C6s (internal control) and C8s from each animal were fixed in formalin then in alcohol. The C8s from loaded animals were scanned using a µCT system at 34 µm resolution, and each image was converted into a specimen-specific voxel-toelement 3D FE model. Boundary conditions simulated either 50N or 100N uniaxial compressive loading, corresponding to the in vivo load level. T he tissue modulus was set as 18 GPa and Poisson’s ratio as 0.3. An element-by-element preconditioned conjugate gradient method was used to extract tissue level strain energy densities (SED) and principal strains (PE1, PE2, PE3, where PE1 =maximal, PE2 =medial, PE3 =minimal) and stresses (PS1, PS2 , PS3 ) for local trabecular regions (proximal, center, distal) of the vertebrae that corresponded to sections analyzed through bone histomorphometry. The C6s and C8s from all animals were embedded undecalcified. 4 µm sections were stained with Goldner’s Trichrome to determine the trabecular bone surface (BS) and 8 µm sections were used to determine the calcein labeled surface (LS) and mineral apposition rate (MAR) in the trabecular bone using a bone histomorphometry software. Labeled surface percentage (LS/BS), MAR, and bone formation rate (BFR) were determined for local trabecular regions (proximal, center, distal). LS/BS and MAR of C8 from each specimen were normalized by LS/BS and MAR of the corresponding C6. The normalized values were then multiplied by the average LS/BS (or MAR) of C6 s from each treatment group. BFR was calculated by multiplying the normalized LS/BS with the normalized MAR. Three sections were analyzed per specimen. The mechanical parameters in the three local trabecular regions were correlated to local LS/BS, MAR, and BFR in corresponding trabecular regions using linear regression. RESULTS The overall trabecular bone responses to PTH and/or mechanical stimulation have been reported previously [4,5]. Only regional correlation data are emphasized. For mechanical loading of 50N or 100N combined with PTH stimulation for 1 week, there are significant correlations between bone tissue minimal (compressive) principal stress/strain as well as SED, with MAR or BFR (Fig. 1, Table 1). A similar correlation between these mechanical parameters and MAR was seen in mechanical loading alone groups. It is striking that the majority of other stress/strain components such as the maximal (tensile; PE1) or medial (PE2 ) principal stress/strain have no correlation with any bone formation indices (Table 1). It is interesting that the loading magnitude (50N or 100N) only has a small influence on trabecular bone response, suggesting that the regional distribution of the mechanical stimuli is more important. For 2 and 4 weeks animals, the correlation dominance of PE3 is no longer observed (data not shown). Figure 1. SED and PE3 vs. MAR for mechanical combined with PTH (left) and mechanical alone (right). Table 1. The correlation coefficients and the p-values for the correlations between various dynamic bone formation indices and trabecular bone tissue mechanical microenvironments at 1 week. The un-shaded fields indicate significant correlations existed. DISCUSSION The analyses of the in vivo data in our rat tail model indicate that the early trabecular bone response follows the regional distribution of the minimal compressive stresses/strains, suggesting that the compressive tissue stresses/strain may be the driving mechanical parameters for trabecular bone response. In early trabecular bone adaptation, increased bone formation is mainly due to increased MAR probably of existing osteoblasts. This suggests that the early responsiveness of these bone cells is tuned to a compressive stress/strain environment, which is the dominant mode of loading in trabecular bone tissue. It is not surprising that SED also correlates well with trabecular bone response, as SED is the sum of the product of principal stress and strain components. It is intriguing that the regional distribution (gradients) is more important in mechanotransduction than the absolute magnitude of trabecular bone tissue stress/strain [2]. The results of 2 and 4 weeks data show that the minimal principal stresses/strains are no longer the sole driving forces at later times. In parallel to this observation, there is a significant increase in LS/BS at 2 and 4 weeks [5], implying the recruitment of newly differentiated osteoblasts. Taking these together, we postulate that these newly recruited osteoblasts may respond not only to minimal, but also other principal stresses/strains. ACKNOWLEDGMENTS The authors thank the NIH (AR45832, AR48287), the Whitaker Foundation (97-0086). REFERENCES 1) Huiskes et al., Nature, 2000; 8; 2) Koontz JT et al. J Biomech. Eng. 2001 3) Guo et al., J Biomech, 2002; 4) Kim et al., Trans of 48th ORS, 2002; 5) Kim et al., Trans of 49 th ORS, 2003. **Regional Bone Center, Helen Hayes Hospital, West Haverstraw, NY. ***Orthopedic Biomechanics Lab, Beth Israel Deaconess Medical Center and Harvard Medical School, Boston, MA. 50th Annual Meeting of the Orthopaedic Research Society Poster No: 0394