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Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

A hydraulically activated bone chamber model was utilized to investigate cellular and microstructural mechanisms of mechanical adaptation during bone repair. Woven trabecular bone and fibrotic granulation tissue filled the initially empty chambers by 8 weeks postimplantation into canine tibial and femoral metaphyses. Without mechanical stimulation, active bone remodeling to lamellar trabecular bone and reconstitution of marrow elements were observed between 8 and 24 weeks. In subsequent loading studies, the hydraulic mechanism was activated on one randomly chosen side of 10 dogs following 8 weeks of undisturbed bone repair. The loading treatment applied an intermittent compressive force (18 N, 1.0 Hz, 1800 cycles/day) for durations of a few days up to 12 weeks. Stereological analysis of three-dimensional microcomputed tomography images revealed an increase in trabecular plate thickness and connectivity associated with the loaded repair tissue microstructure relative to unloaded contralateral controls. These microstructural alterations corresponded to an over 600% increase in the apparent modulus of the loaded bone tissue. A significant increase in the percentage of trabecular surfaces lined by osteoblasts immunopositive for type I procollagen after a few days of loading provided further evidence for mechanical stimulation of bone matrix synthesis. The local principal tissue strains associated with these adaptive changes were estimated to range from approximately −2000 to +3000 μstrain using digital image-based finite element methods. This study demonstrates the sensitivity of bone tissue and cells to a controlled in vivo mechanical stimulus and identifies microstructural mechanisms of mechanical adaptation during bone repair. The hydraulic bone chamber is introduced as an efficient experimental model to study the effects of mechanical and biological factors on bone repair and regeneration.


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

Bone possesses considerable potential to repair and fully regenerate its structure and mechanical properties when damaged.1 Experimental fracture fixation studies have demonstrated that bone repair can be affected by perturbations of the local mechanical environment, correlating accelerated healing with specific ranges of intermittent mechanical stimulation.2–4 Mechanical factors have been theorized and experimentally shown to influence directly the cellular and tissue differentiation patterns and therefore mechanical properties associated with healing bone tissue.5,6 It has, in fact, been argued that mechanically induced alterations of bone mass or structural organization have only been clearly demonstrated under growth or repair conditions.7 Yet little is known about specific cellular and tissue mechanisms of mechanical adaptation during bone repair. An experimental model that allows the in vivo mechanical environment to be controlled and quantified would facilitate investigations of adaptive mechanisms and structure–function relationships in healing bone tissue.

We developed a new in vivo model of bone repair and adaptation called the hydraulic bone chamber (HBC). Implantable chambers of various designs have been used previously to describe the temporal sequence of bone formation at the tissue, cellular, and, most recently, molecular levels.8–13 The hydraulic bone chamber is the first to feature the ability to apply a controlled intermittent force to tissue regenerating within the chamber.

The objectives of this study were three fold. First, the baseline bone repair process was evaluated from 4 to 24 weeks without activating the hydraulic loading mechanism using light microscopy, microcomputed tomography-based stereology, and immunohistochemistry. Second, short-term (2–9 days) and 12-week loading experiments were conducted to quantify cellular and microstructural adaptive responses to a controlled intermittent mechanical stimulus. Finally, digital image-based finite element modeling and homogenization theory were utilized to estimate the microstructural tissue strains associated with the observed adaptive responses.

MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

The HBC implant consisted of a threaded titanium chamber, an internal loading piston, and a hydraulic manifold cap. Two large portals allowed bone to form within the chamber's cylindrical internal volume which measured 7 mm in diameter and length. An internal piston served to apply controlled loads to the tissue forming within the chamber, and a Teflon line, routed subcutaneously from a barbed connector on the manifold cap to an external servohydraulic loading system, delivered pressurized saline to the piston within the assembled implant.

Hydraulic bone chambers were implanted bilaterally into canine metaphyseal trabecular bone from a lateral approach in distal femurs and a medial approach in proximal tibias. The periosteal surface was elevated 1 cm posterosuperior to the anterior tibial tubercle and 2 cm posterior to the femoral patellar groove. Implantation sites were prepared by drilling and tapping normal to the bone surface to a depth of 2 cm. Chambers were then screwed into the metaphyses until flush with the cortical surface. For consistency, the tissue infiltration portals were aligned with the long axis of the tibia or femur. The chambers were sealed by matching an asymmetric four-pin configuration on the manifold caps to slots on the chambers, thus compressing an internal o-ring. Following soft tissue closure in layers over the chamber cap, a bump approximately 1 cm in height identified the location of the implants. All surgical procedures and experimental protocols for this study were approved by the University of Michigan committee on the use and care of animals.

To evaluate the repair response within the chambers without mechanical stimulation, six skeletally mature mongrel dogs received two tibial and two femoral chambers each, for a total of 24 implanted chambers. A minimally invasive biopsy procedure that does not require sacrificing the implant host was used to obtain tissue samples. As such, repeated biopsies could be evaluated from the same implantation site on the same animal, providing enhanced experimental control of interanimal variation. Using a sharpened, thin-walled cylinder, tissue cores were extracted from all chambers 4 weeks after the initial implantation surgeries to empty the chambers and provide a consistent time zero starting point for bone formation. Fifty-two cylindrical cores were subsequently biopsied at times ranging from 8 to 24 weeks postsurgery. Differences in cellular and microstructural variables with respect to time and implantation site were statistically tested using a mixed effects analysis of variance (ANOVA) model.

Based on the temporal repair data, mechanical stimulation was initiated following 8 weeks of bone formation without loading in an independent group of 10 dogs. Five dogs with tibial chamber implants received the daily loading treatment on one randomly chosen side for 2–9 days. Five additional dogs were loaded for 12 weeks. Contralateral tibial implants were not activated to provide individually matched control biopsies. Using a trapezoidal waveform and pressure transducer feedback, the hydraulic system was calibrated to apply a compressive 17.8 N load at a rate of 89 N/s and a frequency of 1.0 Hz for 1800 daily loading cycles. These loading parameters were selected based on previous experience using a canine hydraulic endoprosthesis model.14 Population biopsies, normal canine trabecular bone from the proximal tibial metaphyses of cadaveric dogs, were also collected for baseline comparisons. Paired t-tests were used to evaluate differences between loaded and contralateral control biopsies. Comparisons with the population biopsies were made using independent sample t-tests with separate variances.

Each biopsy was fixed in 70% ethanol and then scanned on a microcomputed tomography (microCT) system at an approximate resolution of 25 μm/voxel to stereologically evaluate changes in trabecular microstructure. After thresholding the reconstructed three-dimensional image into bone and nonbone voxels, automated stereological algorithms were used to quantify the morphology and anisotropy of the mineralized trabecular microstructure.15 Independent measures of bone volume fraction, trabecular plate number, and trabecular connectivity were determined as well as mathematically related indices such as trabecular plate thickness, trabecular plate separation, and mean intercept length.15–19 In addition, a trabecular orientation variable was defined as the angle between the maximum principal trabecular direction and the material axis corresponding to the longitudinal direction of the cylindrical biopsies. Complete descriptions of the microCT system and associated stereological analysis algorithms have been published previously.15,20,21

Following microCT scanning, half of each biopsy was decalcified in formic acid sodium citrate, embedded in paraffin, and longitudinally sectioned at 5 μm for histological and immunohistochemical analyses. Osteoblastic expression of type I procollagen was localized as an indicator of matrix synthesis using a monoclonal antibody (IgG1 SP1.D8, Developmental Hybridoma Studies Bank). The potential for nonspecific staining was precluded by including a single negative control tissue section for each analysis which was not exposed to the primary antibody. Paraffin sections of a canine growth plate were also included in each analysis as positive controls of active matrix synthesis. The percentage of trabecular surfaces covered by osteoblasts expressing type I procollagen was estimated using light microscopy by calculating the number of intersections between immunopositive trabecular surfaces and a superimposed Merz grid divided by the total number of grid–bone intersections for each tissue section. Using cellular morphology and proximity to trabecular surfaces as guides, care was taken to distinguish plump, cuboidal-shaped osteoblasts from spindle-shaped fibroblasts.

For the 12 week loading experiment only, mechanical testing was performed to measure compressive apparent modulus in the longitudinal direction of loaded and control cylindrical biopsies (Fig. 1). Following 10 preconditioning cycles and the application of a 2.0 N preload, each core was mechanically tested to 1% strain in uniaxial compression. Digital caliper measurements of core diameter and length were used to calculate apparent stress and strain from load and displacement data. Linear regression of the final 25% of the loading phase of the stress-strain curves was used to determine the compressive apparent modulus of each biopsy.

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Figure FIG. 1. Chamber biopsy prepared for prefailure mechanical testing in uniaxial compression.

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A series of homogenization finite element analyses was performed to evaluate the relative influences of canine joint loads and HBC actuator loads on local tissue strains within the chamber. Homogenization theory can be used to estimate and mathematically relate strains and effective stiffnesses at different levels of bone structure.22 In so doing, the influence of globally applied loads (e.g., joint loads) on local strains within microstructured materials (e.g., trabecular bone within the HBC) can be estimated. A three-dimensional global model of a proximal tibia with an implanted HBC was constructed using digital image-based mesh generation (800 μm/voxel).23 The global material properties of the cortical and trabecular bone surrounding the HBC were assumed to be homogenous and isotropic with elastic moduli of 10.0 GPa and 100.0 MPa, respectively. Patellar ligament forces and tibiofemoral contact forces were estimated using a static equilibrium analysis and canine force plate data.24 A three-dimensional local model of the trabecular bone microstructure within the HBC containing over 500,000 hexahedral finite elements was generated directly from the microCT data (50 μm/voxel) of one loaded biopsy. The average tissue modulus for the local model (759.0 MPa) was estimated25 by simulating the in vitro mechanical testing conditions using a combined finite element modeling and mechanical testing method.26,27 The in vivo loading conditions were subsequently modeled to evaluate the local tissue strains associated with cellular and tissue adaptation within the HBC.

RESULTS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

Histologically, the chamber tissue at 4 weeks of repair consisted primarily of highly cellular fibrous tissue, although regions of a finely trabeculated structure were often evident near the infiltration portals (Fig. 2A). By 8 weeks, disorganized, woven trabecular bone was predominant, and the intertrabecular spaces were filled with fibrous tissue and some marrow (Fig. 2B). Von Kossa stained sections of 12-week tissue revealed evidence of bone remodeling in addition to continued appositional bone formation (Fig. 2C). Finally, 16− and 24-week biopsies were composed of bone marrow and a composite woven and lamellar trabecular bone microstructure (Fig. 2D). Cartilage tissue was not evident in chamber biopsies at any time, indicating an intramembranous bone formation pathway.

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Figure FIG. 2. Temporal sequence of repair in the HBC without loading. (A) Four-week H&E stained tissue section at 10×. (B) Eight-week H&E stained tissue section at 10×. (C) Twelve-week Von Kossa stained tissue section at 40×. (D) Twenty-four–week H&E stained tissue section under polarized light to highlight collagen matrix organization.

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Extensive evidence of osteoblastic matrix synthesis as indicated by cellular morphology and expression of type I procollagen was observed at all biopsy times (Fig. 3). However, a significant decrease in the percentage of trabecular surfaces covered by osteoblasts expressing type I procollagen was found as a function of time (Fig. 4). The average trabecular surface expression for 4-week biopsies was 32.5 ± 12.5%, which decreased to 13.6 ± 10.7% for 24-week biopsies (p < 0.05).

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Figure FIG. 3. Expression of type I procollagen in osteoblasts lining trabeculae 8 weeks postsurgery (40×).

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Figure FIG. 4. Influence of short-term and 12-week loading treatments on the percentage of trabecular surfaces covered by osteoblasts expressing type I procollagen relative to a no-load control curve shown as a function of biopsy time.

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The most notable change in trabecular microstructure with respect to biopsy time was a significant increase in the volume fraction of mineralized bone between 4 and 8 weeks (p < 0.05). The average bone volume fraction increased from 3.9 ± 5.3% at 4 weeks to 10.4 ± 10.1% at 8 weeks; however, no additional significant changes were observed to 24 weeks. After 8 weeks, the microstructure of the chamber tissue was, by most stereological measures, similar to that of normal population trabecular bone from the same region with the notable exception of trabecular connectivity. Connectivity was consistently negative (calculated as the negative of the volume normalized Euler number) at all biopsy times, indicating a relatively discontinuous trabecular network.

No differences in any of the variables were detected for biopsies extracted from the right side versus those from the left side; however, significant differences were detected between femoral and tibial biopsies. Tibial biopsies possessed significantly higher bone volume fraction (p < 0.03), trabecular connectivity (p < 0.02), and trabecular plate thickness (p < 0.001). There was no effect of implantation site on procollagen expression, trabecular plate number, trabecular plate separation, or the anisotropy of the trabecular microstructure.

In the short-term loading study (8 weeks of bone repair followed by 2–9 days of loading), osteoblastic expression of type I procollagen was dramatically influenced by loading (Figs. 4 and 5). The percentage of immunopositive trabecular surfaces ranged from 46.0% after 9 days of loading up to 84.2% after 2 days of loading. Overall, the short-term loaded group averaged 55.9 ± 16.0%, which was significantly higher (p < 0.02) than the mean level of 21.6 ± 4.6% measured for contralateral control biopsies. For the 12-week loading study (8 weeks of bone repair followed by 12 weeks of loading), significant differences in the percentage of trabecular surfaces covered by osteoblasts expressing type I procollagen were found among all groups. The average percentage for loaded biopsies (25.3 ± 10.8%) was significantly higher than that measured for control biopsies (14.0 ± 6.3%). Loaded and control group means were both higher than the population group mean (1.7 ± 1.1%).

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Figure FIG. 5. Type I procollagen expression in tissue loaded for 2 days (10×).

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The contralateral control biopsy from one dog in the 12-week loading study was damaged during extraction. Data from that dog were therefore excluded from the structural analysis of trabecular morphology and anisotropy. Statistical analyses of microstructural changes were performed on data from the four remaining pairs of experimental and control bone chamber biopsies and the four population biopsies.

Adaptation of trabecular microstructure was evaluated for the experimental group loaded for 12 weeks relative to the unloaded control and population groups (Fig. 6). Bone volume fraction averaged 24.4 ± 6.6% for the loaded biopsies, representing an over 75% increase relative to control (13.8 ± 5.0%, p = 0.10) and population (13.6 ± 3.9%, p < 0.05) biopsies (Table 1). Trabecular connectivity was significantly increased in the loaded group with a mean of 7.3 ± 9.5 compared with the control group, which averaged −10.2 ± 15.1 (p < 0.05). There was no significant difference in connectivity between the loaded and population groups (12.3 ± 3.5). In terms of trabecular morphology, no significant differences were detected among any of the groups for trabecular plate number or trabecular plate separation. However, loaded biopsies were composed of significantly thicker trabeculae (119.3 ± 3.8 μm) than control (77.0 ± 17.6 μm) or population biopsies (72.0 ± 4.5).

Table Table 1. Microstructural Adaptation During Trabecular Bone Repair
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Figure FIG. 6. Microcomputed tomography images showing sections of biopsies from the control (left), loaded (middle), and population (right) groups.

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To determine if trabecular orientation was influenced by loading, the angle between the principal trabecular direction and the axis of loading was calculated using the direction cosine matrix of the mean intercept length tensor. The trabeculae within both loaded and control tissue were found to be primarily aligned with the infiltration portals and nearly 90° from the axis of loading (Table 1). Although the trabeculae in the loaded biopsies were aligned 7.1° closer to the axis of loading than control biopsies, this difference was not found to be significant (p = 0.18). Despite minimal trabecular reorientation, however, the mean intercept length of mineralized bone tissue in the direction of loading was significantly increased, indicating specific trabecular thickening in that direction (p < 0.05).

The compressive apparent modulus of bone chamber biopsies receiving 12 weeks of loading averaged 61.8 ± 47.1 MPa. Contralateral control biopsies possessed apparent moduli nearly an order of magnitude lower, averaging 8.2 ± 4.6 MPa (p = 0.09). No significant difference was found between loaded and population biopsies which averaged 95.8 ± 66.1 MPa, while a strong trend toward significance (p = 0.08) was found between control and population biopsies.

Homogenization analyses indicated that removal of tibiofemoral and patellar ligament joint forces did not appreciably alter the distribution or magnitude of tissue strain energy density (SED) within the chamber. Upon removal of joint loads, the average predicted tissue SED decreased by only 1.6%, indicating that the hydraulic actuator is the primary source of mechanical stimulation within the HBC. Local maximum and minimum principal strains imposed by the 17.8 N actuator load are shown in Fig. 7. After 12 weeks of structural adaptation, local strains ranged from approximately −2000 to +3000 μstrain. Regional evaluation of local strains indicated that higher tensile and compressive strains were concentrated closer to the hydraulic actuator and near the periphery of the cylindrical biopsies.

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Figure FIG. 7. Superimposed histogram of local maximum and minimum principal tissue strains after 12 weeks of structural adaptation.

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DISCUSSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

The objectives of this study were to characterize the baseline repair response within the HBC out to 24 weeks, identify adaptive mechanisms at the cellular and tissue levels during bone repair, and quantify the associated local mechanical environment. The hydraulic bone chamber implant was introduced as a simple in vivo experimental model with the unique capability to deliver a controlled compressive force to a mechanically isolated core of regenerating bone tissue. This feature was utilized to test whether type I procollagen expression, parameters of trabecular microstructure, or apparent mechanical properties are altered by daily intermittent mechanical loading. In addition, local tissue strains imposed by the HBC actuator were estimated after 12 weeks of structural adaptation using digital image-based finite element modeling and homogenization theory.

Bone formation in the hydraulic bone chamber occurred exclusively via a primary repair sequence without a cartilaginous intermediary. This observation is consistent with previous bone chamber and defect studies and is presumably a consequence of the stable mechanical environment within the chamber and the highly vascular metaphyseal site of implantation.10,27 The commencement of bone formation was captured best in 4-week tissue, which showed groups of plump cells coalescing within fibrous tissue and depositing islands of matrix near the infiltration portals. Both the spindle-shaped cells within fibrous tissue and the cuboidal cells producing bone matrix were strongly positive for type I procollagen, supporting a possible differentiation link between these cells. Osteoblast cells in biopsies beyond 8 weeks began to take on a more flattened morphology coincident with the significant decrease in percentage of trabecular surfaces covered by osteoblasts expressing type I procollagen.

Tibial chamber implantation sites were associated with a significantly greater amount of bone formation than femoral sites. Increased bone formation at tibial sites may be a consequence of their closer proximity to the periosteal surface, which is an initial site of bone regeneration in long bone fractures and a source of osteoprogenitor cells.1 Based on the temporal histological and microstructural data from the preliminary study, the subsequent loading experiments were conducted in tibial chambers only, and the hydraulic loading piston was activated following 8 weeks of initial bone formation without loading.

Trabecular connectivity was the most sensitive structural parameter to mechanical stimulation during bone repair. Without loading, the average trabecular connectivity at biopsy times ranging from 4 to 24 weeks was found to be consistently negative. A low or negative connectivity is indicative of a structure with fewer redundant connections and possibly islands of unattached mineralization. The introduction of a mechanical stimulus to 8-week bone chamber tissue was associated with a dramatic increase in the connectivity of the trabecular microstructure. Increased connectivity intuitively increases the ability of the structure to resist mechanical deformations and may therefore represent an important adaptive mechanism during trabecular bone repair.

The 77% increase in bone volume fraction associated with 12 weeks of daily compressive mechanical loading was primarily a consequence of trabecular plate thickening rather than an increase in the number of trabeculae. These results directly support a hypothesis of Goulet and coworkers as well as results from immobilization and ovariectomy studies suggesting that mechanical factors modulate trabecular thickness while hormonal or biochemical influences more directly affect trabecular number.15,29–31 Interestingly, the bone volume fraction and trabecular plate thickness were also increased in loaded biopsies relative to population tissue from the same region. These results may indicate that additional matrix was initially deposited to compensate for the presumably inferior mechanical properties of the newly formed woven bone tissue.

Twelve weeks of daily compressive loading was associated with a greater than 600% increase in apparent modulus relative to contralateral controls which did not receive loading from the chamber piston. Statistical analysis revealed this difference to be a strong trend (p = 0.09) due to large variability in the loaded group data. The variability associated with the loaded group apparent modulus can be attributed to the presence of pockets of fibrous tissue in some of the loaded biopsies which substantially reduced their resistance to deformation. The fibrous tissue pockets were located on the peripheral edge toward the ends of the cylindrical biopsies. These areas were in close proximity to the edges of the chamber infiltration portals and therefore likely experienced relatively high shear stresses upon activation of the hydraulic loading mechanism. This observation is consistent with the theories of Carter and coworkers proposing that high shear or tensile hydrostatic stresses stimulate fibrous tissue formation.5 Histological analysis of tissue which did not receive loading indicated that fibrous tissue is generally absent from the chamber tissue after 8 weeks of repair. Since the loaded specimens were biopsied 20 weeks postsurgery, this observation provides additional evidence to support a mechanical role for the presence of localized fibrous tissue regions.

The dramatic and consistent increase in the percentage of trabecular surfaces lined by osteoblasts expressing type I procollagen for both the short-term and 12-week loading groups indicates a response to mechanical loading above the baseline activity level due to repair. The current study does not specifically address whether the mechanical stimulus accelerated the recruitment and differentiation of pluripotential cells to matrix-producing osteoblasts or whether the imposed loads “turned on” pre-existing osteoblasts, osteoprogenitor cells, or bone-lining cells. However, the observed type I procollagen response after only 2–3 days of loading provides preliminary evidence for direct in vivo stimulation of pre-existing cells. Finally, the observation that osteoblastic activity was still elevated relative to contralateral controls after 12 weeks of loading indicates that an adaptive equilibrium of trabecular microstructure may not have been reached in this study.

The results of this study suggest that bone repair can be influenced by a controlled in vivo mechanical stimulus and support the hypothesis that newly formed bone is deposited in mechanically appropriate locations. Several adaptive responses and mechanisms have been identified. First, a marked increase in the percentage of trabecular surfaces covered by procollagen-positive osteoblasts was evident within a few days of commencing the daily loading regimen and persisted out of 12 weeks of loading. Second, 12 weeks of loading was associated with a thickening and connecting of the trabecular microstructure but not an increase in the number of trabeculae. Loading the de novo bone within the chamber initiated the reconstitution of a well-connected trabecular microstructure possessing mechanical properties similar to that of normal trabecular bone. Finally, the mean intercept length of mineralized tissue in the direction of loading was increased in the loaded specimens via a preferential trabecular thickening mechanism and not a significant reorientation or drift of trabeculae toward the axis of loading.

The observed microstructural changes resulted in a principal tissue strain distribution ranging from about −2000 to +3000 μstrain. The local principal strains after 12 weeks of adaptation were similar to estimates of physiological canine trabecular bone strains32 supporting the belief that limitation of strain magnitude is an important objective of tissue adaptation. Tissue strains within the HBC implant were found to be 98.4% isolated from canine joint loads. It is therefore reasonable to estimate in vivo tissue strains by direct analysis of microstructural finite element models using the known HBC actuator loads as boundary conditions and avoiding the need to model multiple levels of bone structure. Using these computational methods and the hydraulic bone chamber model, hypotheses may be tested relating microstructural stress or strain distribution to spatial variations in tissue formation, cell differentiation, and protein or gene expression.

Acknowledgements

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

This study was supported by NIH grants AR-31793 and AR-20557. The authors also thank the following individuals for their support on this study: J. Baker, M. Moalli, M. Stock, K. Sweet, and R. Taylor. Type I procollagen antibody (IgG1, SP1.D8) provided by the Developmental Studies Hybridoma Bank maintained by the Department of Pharmacology and Molecular Sciences, Johns Hopkins University School of Medicine and the Department of Biological Sciences, University of Iowa. Finite element analysis software provided by Psiphics, Inc., Ann Arbor, Michigan.

REFERENCES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES
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