Prediction of cortical bone elastic constants by a two-level micromechanical model using a generalized self-consistent method

A two-level micromechanical model of cortical bone based on a generalized self-consistent method was developed to take into consideration the transversely isotropic elasticity of many microstructural features in cortical bone, including Haversian canals, resorption cavities, and osteonal and interstitial lamellae. In the first level, a single osteon was modeled as a two-phase composite such that Haversian canals were represented by elongated pores while the surrounding osteonal lamellae were considered as matrix. In the second level, osteons and resorption cavities were modeled as multiple inclusions while interstitial lamellae were regarded as matrix. The predictions of cortical bone elasticity from this two-level micromechanical model were mostly in agreement with experimental data for the dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. However, variation in cortical bone elastic constants was greater in experimental data than in model predictions. This could be attributed to variations in the elastic properties of microstructural features in cortical bone. The present micromechanical model of cortical bone will be useful in understanding the contribution of cortical bone porosity to femoral neck fractures.     

Systematic error in mechanical measures of damage during four-point bending fatigue of cortical bone

Accumulation of fatigue microdamage in cortical bone specimens is commonly measured by a modulus or stiffness degradation after normalizing tissue heterogeneity by the initial modulus or stiffness of each specimen measured during a preloading step. In the first experiment, the initial specimen modulus defined using linear elastic beam theory (LEBT) was shown to be nonlinearly dependent on the preload level, which subsequently caused systematic error in the amount and rate of damage accumulation measured by the LEBT modulus degradation. Therefore, the secant modulus is recommended for measurements of the initial specimen modulus during preloading. In the second experiment, different measures of mechanical degradation were directly compared and shown to result in widely varying estimates of damage accumulation during fatigue. After loading to 400,000 cycles, the normalized LEBT modulus decreased by 26% and the creep strain ratio decreased by 58%, but the normalized secant modulus experienced no degradation and histology revealed no significant differences in microcrack density. The LEBT modulus was shown to include the combined effect of both elastic (recovered) and creep (accumulated) strain. Therefore, at minimum, both the secant modulus and creep should be measured throughout a test to most accurately indicate damage accumulation and account for different damage mechanisms. Histology revealed indentation of tissue adjacent to roller supports, with significant sub-surface damage beneath large indentations, accounting for 22% of the creep strain on average. The indentation of roller supports resulted in inflated measures of the LEBT modulus degradation and creep. The results of this study suggest that investigations of fatigue microdamage in cortical bone should avoid the use of four-point bending unless no other option is possible.     

Adaptive changes in micromechanical environments of cancellous and cortical bone in response to in vivo loading and disuse

The skeleton accommodates changes in mechanical environments by increasing bone mass under increased loads and decreasing bone mass under disuse. However, little is known about the adaptive changes in micromechanical behavior of cancellous and cortical tissues resulting from loading or disuse. To address this issue, in vivo tibial loading and hindlimb unloading experiments were conducted on 16-week-old female C57BL/6J mice. Changes in bone mass and tissue-level strains in the metaphyseal cancellous and midshaft cortical bone of the tibiae, resulting from loading or unloading, were determined using microCT and finite element (FE) analysis, respectively. We found that loading- and unloading-induced changes in bone mass were more pronounced in the cancellous than cortical bone. Simulated FE-loading showed that a greater proportion of elements experienced relatively lower longitudinal strains following load-induced bone adaptation, while the opposite was true in the disuse model. While the magnitudes of maximum or minimum principal strains in the metaphyseal cancellous and midshaft cortical bone were not affected by loading, strains oriented with the long axis were reduced in the load-adapted tibia suggesting that loading-induced micromechanical benefits were aligned primarily in the loading direction. Regression analyses demonstrated that bone mass was a good predictor of bone tissue strains for the cortical bone but not for the cancellous bone, which has complex microarchitecture and spatially-variant strain environments. In summary, loading-induced micromechanical benefits for cancellous and cortical tissues are received primarily in the direction of force application and cancellous bone mass may not be related to the micromechanics of cancellous bone.     

Modulation of bone ingrowth of rabbit femur titanium implants by in vivo axial micromechanical loading.

Titanium implants commonly used in orthopedics and dentistry integrate into host bone by a complex and coordinated process. Despite increasingly well illustrated molecular healing processes, mechanical modulation of implant bone ingrowth is poorly understood. The objective of the present study was to determine whether micromechanical forces applied axially to titanium implants modulate bone ingrowth surrounding intraosseous titanium implants. We hypothesized that small doses of micromechanical forces delivered daily to the bone-implant interface enhance implant bone ingrowth. Small titanium implants were placed transcortically in the lateral aspect of the proximal femur in 15 New Zealand White rabbits under general anesthesia and allowed to integrate with the surrounding bone for 6 wk. Micromechanical forces at 200 mN and 1 Hz were delivered axially to the right femur implants for 10 min/day over 12 consecutive days, whereas the left femur implants served as controls. The average bone volume 1 mm from mechanically loaded implants (n = 15) was 73 +/- 12%, which was significantly greater than the average bone volume (52 +/- 21%) of the contralateral controls (n = 15) (P < 0.01). The average number of osteoblast-like cells per endocortical bone surface was 55 +/- 8 cells/mm(2) for mechanically loaded implants, which was significantly greater than the contralateral controls (35 +/- 6 cells/mm(2)) (P < 0.01). Dynamic histomorphometry showed a significant increase in mineral apposition rate and bone-formation rate of mechanically stressed implants (3.8 +/- 1.2 microm/day and 2.4 +/- 1.0 microm(3).microm(-2).day(-1), respectively) than contralateral controls (2.2 +/- 0.92 microm/day and 1.2 +/- 0.60 microm(3).microm(-2).day(-1), respectively; P < 0.01). Collectively, these data suggest that micromechanical forces delivered axially on intraosseous titanium implants may have anabolic effects on implant bone ingrowth.     

Thermographic stress analysis in cortical bone.

Under adiabatic (or near adiabatic) conditions a volumetric change in an elastic material will produce a corresponding change in temperature. Based upon this principle, thermographic stress analysis (TSA) measures changes in surface heat flux (which are related to changes in surface temperature) and relates them to a coupled form of strains or stresses. To demonstrate the feasibility of using this technique for biomechanical applications, we thermographically measured heat flux from loaded specimens of cortical bone and correlated the results with strain gage data. Regular parallelepipeds were cut from the cortex of bovine femora and loaded sinusoidally at 20 Hz. At this rate of loading, mechanically induced changes in surface temperature could be sampled (via heat flux) prior to a measureable attenuation of the thermoelastic effect. Correlation coefficients demonstrated a significant linear relationship between TSA and measured and computed mechanical parameters (stress, strain, first strain invariant, and strain energy density). TSA therefore appears to be a promising technology for experimental stress analysis in cortical bone.     

A damage model for nonlinear tensile behavior of cortical bone.

To describe the time-dependent nonlinear tensile behavior observed in experimental studies of cortical bone, a damage model was developed using two internal state variables (ISV's). One ISV is a damage parameter that represents the loss of stiffness. A rule for the evolution of this ISV was defined based on previously observed creep behavior. The second ISV represents the inelastic strain due to viscosity and internal friction. The model was tested by simulating experiments in tensile and bending loading. Using average values from previous creep studies for parameters in the damage evolution rule, the model tended to underestimate the maximum nonlinear strains and to overestimate the nonlinear strain accumulated after load reversal in the tensile test simulations. Varying the parameters for the individual tests produced excellent fits to the experimental data. Similarly, the model simulations of the bending tests could produce excellent fits to the experimental data. The results demonstrate that the 2-ISV model combining damage (stiffness loss) with slip and viscous behavior could capture the nonlinear tensile behavior of cortical bone in axial and bending loading.     

Prediction of bending stiffness and deformed shape of non-axially compressed microtubule by a semi-analytical approach

The bending stiffness of a microtubule is one of the most important parameters needed in the analysis of microtubule deformation. In this study, a semi-analytical approach is developed to predict the bending stiffness and deformed shape of a non-axially compressed microtubule in an explicit closed form. By using the solution presented in this paper and the experimentally observed values given in the literature, both the deformed configuration and bending stiffness of a single microtubule are determined. The proposed method is validated by comparing the obtained results with available data in the literature. The comparison shows that the present semi-analytical formulation provides the same accuracy with reduced numerical effort.     

The osteoclast-endothelium interface during bone resorption in the femurs of young rabbits

Summary The morphological relationship between the osteoclasts at the endosteal surface of two-week-old rabbit femurs and the endothelium of vascular channels of the bone marrow was examined. Light microscopy revealed that 85% of the osteoclasts make direct contact with the endothelial cells. The ultrastructure of this osteoclast-endothelium interface shows that the osteoclast has specialized processes which reach out towards the endothelial cells coming into close proximity with them. On rare occasions, specialized junctions between these processes and the endothelial cells are noted.Study supported by the joint research fund of the Hebrew University-Hadassah School of Dental Medicine founded by the Alpha-Omega Fraternity and the Hadassah Medical OrganizationI would like to thank Mr. Milo Sadownick for his excellent technical assistance     

Evaluation of bone healing in femurs lengthened via the gradual distraction method

BACKGROUND: Treatment of leg length inequality via lengthening of the shorter extremity is an infrequent orthopedic procedure due to the requirement of special distraction devices and possible serious complications. Essential qualitative changes in operative technique development are associated with the name of G. A. Ilizarov, who paved the way for the autoregenerate gradual distraction method in the 1950s. MATERIAL AND METHODS: In the years 1990 through 2006 a total of 57 patients underwent femur lengthening via gradual distraction using various types of external fixators at the Department of Pediatric Surgery, Orthopedics, and Traumatology, Faculty Hospital in Brno. The quality of bone healing was monitored and a number of parameters followed and statistically evaluated using regularly scheduled X-ray examinations. RESULTS: In 11 cases we had to remove the external fixator following the distraction phase, perform an osteosynthesis via a splint and fill the distraction gap via spongioplasty. The bone healing was satisfactory in the remaining 46 patients and the lengthened bone required no other fixation method. The analysis showed statistically significant deceleration in bone healing following distraction in female patients over 12 years of age, and in boys over 14 years of age. Lack of periosteal callus five weeks after surgery always signified serious problems in further healing. Severe complications were recorded in 11 cases during the distraction phase, and in 9 cases after the removal of the distraction apparatus. CONCLUSIONS: The aim of this report was to present the results of our study of distraction gap bone healing using the gradual lengthening approach.     

Conservation of Na+ vs. K+ by the rat cortical collecting duct

Regulation of transport by principal cells of the distal nephron contributes to maintenance of Na(+) and K(+) homeostasis. To assess which of these ions is given a higher priority by these cells, we investigated the upregulation of epithelial Na(+) channels (ENaC) in the rat cortical collecting duct (CCD) during Na depletion with and without simultaneous K depletion. ENaC activity, assessed as whole cell amiloride-sensitive current in split-open tubules, was 260 ± 40 pA/cell in K-repleted but virtually undetectable (3 ± 1 pA/cell) in K-depleted animals. This difference was confirmed biochemically by the reduced amounts of the cleaved forms of both the α-ENaC and γ-ENaC subunits measured in immunoblots. In contrast, in K-depleted rats, simultaneously reducing Na intake did not affect the activity of ROMK channels, assessed as tertiapin-Q-sensitive whole cell currents, in the CCDs. The lack of Na current in K-depleted animals was the result of reduced levels of aldosterone in plasma, rather than a reduced sensitivity to the hormone. However, rats on a low-Na, low-K diet for 1 wk did not excrete more Na than those on a low-Na, control-K diet for the same period of time. Immunoblot analysis indicated increased levels of the thiazide-sensitive NaCl cotransporter and the apical Na-H exchanger NHE3. This suggests that with reduced K intake, Na balance is maintained despite reduced aldosterone and Na(+) channel activity by upregulation of Na(+) transport in upstream segments. Under these conditions, Na(+) transport by the aldosterone-sensitive distal nephron is reduced, despite the low-Na intake to minimize K(+) secretion and urinary K losses.     

A biomechanical comparison of composite femurs and cadaver femurs used in experiments on operated hip fractures

Fourth generation composite femurs (4GCFs, models #3406 and #3403) simulate femurs of males <80 years with good bone quality. Since most hip fractures occur in old women with fragile bones, concern is raised regarding the use of standard 4GCFs in biomechanical experiments. In this study the stability of hip fracture fixations in 4GCFs was compared to human cadaver femurs (HCFs) selected to represent patients with hip fractures.Ten 4GCFs (Sawbones, Pacific Research Laboratories, Inc., Vashon, WA, USA) were compared to 24 HCFs from seven females and five males >60 years. Proximal femur anthropometric measurements were noted. Strain gauge rosettes were attached and femurs were mounted in a hip simulator applying a combined subject-specific axial load and torque. Baseline measurements of resistance to deformation were recorded. Standardized femoral neck fractures were surgically stabilized before the constructs were subjected to 20,000 load-cycles. An optical motion tracking system measured relative movements.Median (95% CI) head fragment migration was 0.8 mm (0.4 to 1.1) in the 4GCF group versus 2.2 mm (1.5 to 4.6) in the cadaver group (p=0.001). This difference in fracture stability could not be explained by observed differences in femoral anthropometry or potential overloading of 4GCFs. 4GCFs failed with fracture-patterns different from those observed in cadavers.To conclude, standard 4GCFs provide unrealistically stable bone-implant constructs and fail with fractures not observed in cadavers. Until a validated osteopenic or osteoporotic composite femur model is provided, standard 4GCFs should only be used when representing the biomechanical properties of young healthy femurs.     

Collagenase-released non-collagenous proteins of cortical bone matrix.

Two distinct groups of non-collagenous components were isolated from rat cortical bone gelatin which had previously been digested with purified bacterial collagenase. One component was disulfide-bonded, strongly acidic, trypsin-labile glycoprotein aggregate with a molecular mass of more than 100,000 daltons. When reduced with beta-mercaptoethanol this protein disaggregated into subunits with a molecular mass of about 60,000 daltons. The other components consisted of a group of polypeptides with a molecular mass of about 5,000 daltons. The latter group was present in collagenase digests prepared from normal bone gelatin but was hardly detectable or absent in digests of gelatin prepared from either autolyzed, trypsinized or lathyritic bone, or from the residue of neutral salt extracted rat tail tendon.     

Micromechanics modeling of Haversian cortical bone properties.

A finite-element micromechanics model for Haversian cortical bone tissue has been developed and studied. The model is an extension of two-dimensional micromechanics techniques for fiber-reinforced composite materials. Haversian systems, or secondary osteons, are considered to be the fiber component, and interstitial lamellar bone the matrix material. The cement line is included as an 'interphase' component along the fiber/matrix interface. The model assumes a regular repeatable spacing of the longitudinally aligned continuous fibers and is, therefore, restricted to approximating Haversian cortical bone in its present form. Haversian porosity is modeled explicitly by incorporating a hollow fiber to represent the Haversian canal. Solutions have been obtained by applying uniform macroscopic stresses to the boundaries of the repeating unit cell model. Macroscopic mechanical property predictions correspond reasonably well with the experimental data for cortical bone, but are necessarily dependent on the input properties for each constituent, which are not well established. The predicted variation in the elastic modulus with porosity is not as sensitive as that observed experimentally. Stresses within the constituents can also be modeled with this method and are demonstrated to deviate from the macroscopic applied stress levels.     

A comparison of methods for measuring cortical bone thickness

Repeated measures of periosteal and endosteal widths of the left second metacarpal from two samples of radiographs were made independently with either a dial caliper or an electronic digitizer connected to a microcomputer. In addition, periosteal and endosteal bone widths of a common sample of radiographs were measured with dial calipers and the electronic digitizer. Dial calipers and an electronic digitizer are both very reliable, but intraobserver errors produced with the use of the digitizer are significantly less than those produced with the use of dial calipers. However, measurements made with the electronic digitizer are systematically larger than corresponding widths measured with dial calipers, but this difference is very small.     

Cement line staining in undecalcified thin sections of cortical bone.

A technique for demonstrating cement lines in thin, undecalcified transverse sections of cortical bone has been developed. Cortical bone samples are processed and embedded undecalcified in methyl methacrylate plastic. After sectioning at 3-5 microns, cross-sections are transferred to a glass slide and flattened for 10 min. Sections of cortical bone are stained for 20 sec free-floating in a fresh solution of 1% toluidine blue dissolved in 0.1% formic acid. The section is dehydrated in t-butyl alcohol, cleared in xylene, and mounted with Eukitt's medium. Reversal lines appear as thin, scalloped, dark blue lines against a light blue matrix, whereas bone formation arrest lines are thicker with a smooth contour. With this technique cellular detail, osteoid differentiation, and fluorochrome labels are retained. Results demonstrate the applicability of a one-step staining method for cement lines which will facilitate the assessment of bone remodeling activity in thin sections of undecalcified cortical bone.     

Effects of physical training on cortical bone at midtibia assessed by peripheral QCT.

Effects of long-term exercise on volumetric bone mineral density (vBMD), bone mineral content, bone geometric properties, and the strength indexes of bone were examined in a cross-sectional study of athletes and controls. Tibias of 25 jumpers (13 women), 30 swimmers (15 women), and 25 controls (15 women), aged 18-23 yr, were scanned at midsite by using peripheral quantitative computed tomography. The cortical vBMD of female athletes was lower than that of the controls (2.00 +/- 0.05, 1.90 +/- 0.08, and 1.92 +/- 0.12 g/cm3, respectively, for controls, swimmers, and jumpers). On the other hand, periosteal areas of male jumpers and female athletes were greater than that of controls (460 +/- 50, 483 +/- 46, and 512 +/- 55 mm2, respectively, for male controls, swimmers, and jumpers, and 283 +/- 52, 341 +/- 73, and 378 +/- 75 mm2, respectively, for female controls, swimmers, and jumpers). The endocortical area of female swimmers was greater than that of controls (103 +/- 29, 148 +/- 52, and 135 +/- 54 mm2, respectively, for controls, swimmers, and jumpers). The polar moment of inertia and strength strain index of male jumpers and female athletes were significantly greater than those of controls, except for the difference in strength strain index between male jumpers and controls. We conclude that the improvement of mechanical properties of young adult bone in response to long-term exercise is related to geometric adaptation and not to vBMD.