Download compressive principal stresses/strains and their regional

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