A neural network to predict the knee adduction moment in patients with osteoarthritis using anatomical landmarks obtainable from 2D video analysis.

OBJECTIVE: The knee adduction moment (KAM) can inform treatment of medial knee osteoarthritis; however, measuring the KAM requires an expensive gait analysis laboratory. We evaluated the feasibility of predicting the peak KAM during natural and modified walking patterns using the positions of anatomical landmarks that could be identified from video analysis. METHOD: Using inverse dynamics, we calculated the KAM for 86 individuals (64 with knee osteoarthritis, 22 without) walking naturally and with foot progression angle modifications. We trained a neural network to predict the peak KAM using the 3-dimensional positions of 13 anatomical landmarks measured with motion capture (3D neural network). We also trained models to predict the peak KAM using 2-dimensional subsets of the dataset to simulate 2-dimensional video analysis (frontal and sagittal plane neural networks). Model performance was evaluated on a held-out, 8-person test set that included steps from all trials. RESULTS: The 3D neural network predicted the peak KAM for all test steps with r2( Murray et al., 2012) 2 = 0.78. This model predicted individuals' average peak KAM during natural walking with r2( Murray et al., 2012) 2 = 0.86 and classified which 15° foot progression angle modifications reduced the peak KAM with accuracy = 0.85. The frontal plane neural network predicted peak KAM with similar accuracy (r2( Murray et al., 2012) 2 = 0.85) to the 3D neural network, but the sagittal plane neural network did not (r2( Murray et al., 2012) 2 = 0.14). CONCLUSION: Using the positions of anatomical landmarks from motion capture, a neural network accurately predicted the peak KAM during natural and modified walking. This study demonstrates the feasibility of measuring the peak KAM using positions obtainable from 2D video analysis.

Prediction of glycosaminoglycan content in human cartilage by age, T1ρ and T2 MRI.

OBJECTIVE: A relationship between T1ρ relaxation time and glycosaminoglycan (GAG) content has been demonstrated in chemically degraded bovine cartilage, but has not been demonstrated with quantitative biochemistry in human cartilage. A relationship has also been established between T2 relaxation time in cartilage and osteoarthritis (OA) severity. We hypothesized that T1ρ relaxation time would be associated with GAG content in human cartilage with normal T2 relaxation times. METHODS: T2 relaxation time, T1ρ relaxation time, and glycosaminoglycan as a percentage of wet weight (sGAG) were measured for top and bottom regions at 7 anatomical locations in 21 human cadaver patellae. For our analysis, T2 relaxation time was classified as normal or elevated based on a threshold defined by the mean plus one standard deviation of the T2 relaxation time for all samples. RESULTS: In the normal T2 relaxation time subset, T1ρ relaxation time correlated with sGAG content in the full-thickness and bottom regions, but only marginally in the top region alone. sGAG content decreased significantly with age in all regions. CONCLUSION: In the subset of cartilage specimens with normal T2 relaxation time, T1ρ relaxation time was inversely associated with sGAG content, as hypothesized. A predictive model, which accounts for T2 relaxation time and the effects of age, might be able to determine longitudinal trends in GAG content in the same person based on T1ρ relaxation time maps.

An approach to quantifying bone overloading and hypertrophy with applications to multiple experimental studies.

Many studies have investigated mechanically induced bone formation in mice and rats by applying loads to the long bones, and measuring changes in periosteal cortical bone apposition rates. However, the results are difficult to compare among each other because the loading schemes are generally different. The purpose of the present study was to develop a theoretical framework for evaluating the mechanical stimulus based on the bone daily strain stimulus, which is a function of loading cycles and bone strains. The daily strain stimulus would act as a single unifying parameter for directly comparing data from existing in vivo experiments, and is applied here to twenty previous rat and mouse studies. To calculate the daily strain stimulus, we determined the periosteal daily strain stimulus necessary for bone maintenance (xi(peri,0)) and the strain-cycle weighting exponent (m). In the first approach, we applied data from Rubin and Lanyon's bone maintenance studies. We calculated xi(peri,0) to be 2793 microstrain/day, and m to be 4.5. In the second approach, we used Fritton et al. 's strain gage recordings to calculate xi(peri,0) to be 1496 microstrain/day, and used an m value of 11.88, equal to human bone compressive fatigue properties. Fatigue data provided physiological relevance, and was useful for applying an established remodeling theory to in vivo studies. For both approaches, xi(peri,0) was below the fracture level. We then analyzed the applied strains, cycles, and periosteal bone apposition rates from the previous studies. The range of daily strain stimuli calculated using the first approach was much larger than the range using the second approach (2793-17312 microstrain/day compared to 1496-7681 microstrain/day). None of the studies applied a daily strain stimulus above the complete fatigue failure level, but some studies applied loading that could result in major fatigue microdamage. Bone apposition rates generally increased with increasing daily strain stimulus, which was consistent with previous theoretical models. The results suggest that the daily strain stimulus may be a reasonable first approximation for predicting bone apposition rates in a consistent manner. The use of the daily strain stimulus may be helpful for improving the design of future bone loading studies.

Is cartilage thickness different in young subjects with and without patellofemoral pain?

OBJECTIVE: To determine the differences in load-bearing patellofemoral joint cartilage thickness between genders. To determine the differences in load-bearing cartilage thickness between pain-free controls and individuals with patellofemoral pain. METHODS: The articular cartilage thickness of the patella and anterior femur was estimated from magnetic resonance images in 16 young, pain-free control subjects (eight males, eight females) and 34 young individuals with patellofemoral pain (12 males, 22 females). The average age of all subjects was 28+/-4 years. The cartilage surfaces were divided into regions approximating the location of patellofemoral joint contact during knee flexion. The mean and peak cartilage thicknesses of each region were computed and compared using a repeated-measures Analysis of Variance. RESULTS: On average, males had 22% and 23% thicker cartilage than females in the patella (P < 0.01) and femur (P < 0.05), respectively. Male control subjects had 18% greater peak patellar cartilage thickness than males with patellofemoral pain (P < 0.05); however, we did not detect differences in patellar cartilage thickness between female control subjects and females with patellofemoral pain (P = 0.45). We detected no significant differences in femoral cartilage thickness between the control and pain groups. CONCLUSIONS: Thin cartilage at the patella may be one mechanism of patellofemoral pain in male subjects, but is unlikely to be a dominant factor in the development of pain in the female population.

Mechanobiology of soft skeletal tissue differentiation--a computational approach of a fiber-reinforced poroelastic model based on homogeneous and isotropic simplifications.

The material properties of multipotent mesenchymal tissue change dramatically during the differentiation process associated with skeletal regeneration. Using a mechanobiological tissue differentiation concept, and homogeneous and isotropic simplifications of a fiber-reinforced poroelastic model of soft skeletal tissues, we have developed a mathematical approach for describing time-dependent material property changes during the formation of cartilage, fibrocartilage, and fibrous tissue under various loading histories. In this approach, intermittently imposed fluid pressure and tensile strain regulate proteoglycan synthesis and collagen fibrillogenesis, assembly, cross-linking, and alignment to cause changes in tissue permeability (k), compressive aggregate modulus (H(A)), and tensile elastic modulus (E). In our isotropic model, k represents the permeability in the least permeable direction (perpendicular to the fibers) and E represents the tensile elastic modulus in the stiffest direction (parallel to the fibers). Cyclic fluid pressure causes an increase in proteoglycan synthesis, resulting in a decrease in k and increase in H(A) caused by the hydrophilic nature and large size of the aggregating proteoglycans. It further causes a slight increase in E owing to the stiffness added by newly synthesized type II collagen. Tensile strain increases the density, size, alignment, and cross-linking of collagen fibers thereby increasing E while also decreasing k as a result of an increased flow path length. The Poisson's ratio of the solid matrix, nu(s), is assumed to remain constant (near zero) for all soft tissues. Implementing a computer algorithm based on these concepts, we simulate progressive changes in material properties for differentiating tissues. Beginning with initial values of E=0.05 MPa, H(A)=0 MPa, and k=1 x 10(-13) m(4)/Ns for multipotent mesenchymal tissue, we predict final values of E=11 MPa, H(A)=1 MPa, and k=4.8 x 10(-15) m(4)/Ns for articular cartilage, E=339 MPa, H(A)=1 MPa, and k=9.5 x 10(-16) m(4)/Ns for fibrocartilage, and E=1,000 MPa, H(A)=0 MPa, and k=7.5 x 10(-16) m(4)/Ns for fibrous tissue. These final values are consistent with the values reported by other investigators and the time-dependent acquisition of these values is consistent with current knowledge of the differentiation process.

A theoretical analysis of the relative influences of peak BMD, age-related bone loss and menopause on the development of osteoporosis.

Factors that determine a post-menopausal woman's bone mineral density (BMD) include her mass at the time of skeletal maturity (peak BMD), menopause and the rate of loss she experiences as she ages. Understanding the relative influence of each of these factors may help identify important preventive treatments and provide new ways to identify women at risk for osteoporosis. In this analysis we utilize a computer model of the bone remodeling process to predict the relative influences of peak BMD, menopause and age-related bone loss on the development of osteoporosis. The delay in the onset of osteoporosis (defined as BMD <2.5 SD from the young adult mean) caused by modifying peak BMD, age-related bone loss or the age at menopause is quantified. A 10% increase in peak BMD is predicted to delay the development of osteoporosis by 13 years, while a 10% change in the age at menopause or the rate of non-menopausal bone loss is predicted to delay osteoporosis by approximately 2 years, suggesting that peak BMD may be the single most important factor in the development of osteoporosis.

A theoretical analysis of the changes in basic multicellular unit activity at menopause.

Bone loss at menopause is an important contributor to the development of osteoporosis in women. Although alterations in bone remodeling are the implied process through which bone is lost at menopause, how menopause influences basic multicellular units (BMUs), the teams of cells that perform bone remodeling, is not completely clear. In this analysis we utilize a computer simulation of BMU activity to evaluate the changes that occur at menopause. Transient and maintained changes in both the rate of bone turnover (expressed as the BMU birthrate or origination frequency) and the focal bone balance (differences between the amount of bone formed and resorbed at each remodeling site) are considered. The magnitude of the change in BMU activity is determined parametrically through comparison to lumbar spine bone mineral density data present in the literature. We find that a change in bone turnover that is maintained after menopause, a transient change in focal bone balance at menopause, or a combination of the two is consistent with bone loss patterns seen clinically. Understanding the changes in BMU activity that occur at menopause could lead to improved strategies to treat and prevent postmenopausal osteoporosis.

Long-term predictions of the therapeutic equivalence of daily and less than daily alendronate dosing.

Less than daily alendronate dosing has been identified as an attractive alternative to daily dosing for patients and physicians. A recent 2-year study found bone mineral density (BMD) changes caused by weekly alendronate dosing therapeutically equivalent to that caused by daily dosing. There are no methods that can be used to predict how long therapeutic equivalence will be maintained after the first 2 years of treatment. In addition, it is unclear if dosing less frequently than weekly also might be therapeutically equivalent to daily dosing. In this study we use a computer simulation to develop predictions of the therapeutic equivalence of daily and less than daily dosing over time periods as long as a decade. The computer simulation uses a cell-based computer model of bone remodeling and a quantitative description of alendronate pharmacokinetics/pharmacodynamics (PK/PD). The analyses suggest that less than daily dosing regimens do not increase BMD as much as daily dosing. However, model predictions suggest that dosing as frequent as weekly still may be therapeutically equivalent to daily dosing over periods as long as 10 years. In addition, the simulations predict dosing less frequently than weekly may be therapeutically equivalent to daily dosing within the first year of treatment but may not be therapeutically equivalent after 10 years. Hypotheses based on these simulations may be useful for determining which dosing regimen may be most attractive for clinical trials.

The X-ray attenuation characteristics and density of human calcaneal marrow do not change significantly during adulthood.

Changes in the material characteristics of bone marrow with aging can be a significant source of error in measurements of bone density when using X-ray and ultrasound imaging modalities. In the context of computed tomography, dual-energy computed techniques have been used to correct for changes in marrow composition. However, dual-energy quantitative computed tomography (DE-QCT) protocols, while increasing the accuracy of the measurement, reduce the precision and increase the radiation dose to the patient in comparison to single-energy quantitative computed tomography (SE-QCT) protocols. If the attenuation properties of the marrow for a particular bone can be shown to be relatively constant with age, it should be possible to use single-energy techniques without experiencing errors caused by unknown marrow composition. Marrow was extracted by centrifugation from 10 mm thick frontal sections of 34 adult cadaver calcanei (28 males, 6 females, ages 17-65 years). The density and energy-dependent linear X-ray attenuation coefficient of each marrow sample were determined. For purposes of comparing our results, we then computed an effective CT number at two GE CT/i scan voltages (80 and 120 kVp) for each specimen. The coefficients of variation for the density, CT number at 80 kVp and CT number at 120 kVp were each less than 1%, and the parameters did not change significantly with age (p > 0.2, r2 < 0.02, power > 0.8 where the minimum acceptable r2 = 0.216). We could demonstrate no significant gender-associated differences in these relationships. These data suggest that calcaneal bone marrow X-ray attenuation properties and marrow density are essentially constant from the third through sixth decades of life.

A theoretical analysis of the contributions of remodeling space, mineralization, and bone balance to changes in bone mineral density during alendronate treatment.

In patients with osteoporosis, alendronate treatment causes an increase in bone mineral density (BMD) and a decrease in fracture incidence. Alendronate acts by changing the bone remodeling process. Changes in bone remodeling resulting in decreased remodeling space, increased bone balance per remodeling cycle, and increased mineralization (ash mass/bone mass) have all been associated with alendronate treatment. Understanding the relative contributions of these parameters to BMD increases could help predict the utility of long-term (>10 years) or intermittent treatment strategies, as well as treatment strategies in which another pharmaceutical is administered concurrently. We have developed a computer simulation of bone remodeling to compare the contributions of focal bone balance and mineralization on BMD by simulating alendronate treatment using a bone balance method (decreased remodeling space, increased focal bone balance, uniform bone mineralization) and a mineralization method (decreased remodeling space, neutral focal bone balance, varying bone mineralization). Although both methods are able to predict BMD increases caused by alendronate over short periods, our findings suggest that the mineralization method may be more descriptive of long-term alendronate treatment. This implies that mineralization may be a larger contributor to BMD changes caused by alendronate than the focal bone balance. Based on this finding we offer a hypothesis to describe how remodeling space, focal bone balance, and mineralization each contribute to alendronate-induced BMD changes. Future analyses with this method could be used to identify improved dosing regimens and to predict which osteoporosis treatments would best complement each other.

The influence of bone volume fraction and ash fraction on bone strength and modulus.

Although bone strength and modulus are known to be influenced by both volume fraction and mineral content (ash fraction), the relative influence of these two parameters remains unknown. Single-parameter power law functions are used widely to relate bone volume or ash fraction to bone strength and elastic modulus. In this study we evaluate the potential for predicting bone mechanical properties with two-parameter power law functions of bone volume fraction (BV/TV) and ash fraction (alpha) of the form y = a(BV/TV)(b) alpha(c) (where y is either ultimate strength or elastic modulus). We derived an expression for bone volume fraction as a function of apparent density and ash fraction to perform a new analysis of data presented by Keller in 1994. Exponents b and c for the prediction of bone strength were found to be 1.92 +/- 0.02 and 2.79 +/- 0.09 (mean +/- SE), respectively, with r(2) = 0.97. The value of b was found to be consistent with that found previously, whereas the value of c was lower than values previously reported. For the prediction of elastic modulus we found b and c to be 2.58 +/- 0.02 and 2.74 +/- 0.13, respectively, with r(2) = 0.97. The exponent related to ash fraction was typically larger than that associated with bone volume fraction, suggesting that a change in mineral content will, in general, generate a larger change in bone strength and stiffness than a similar change in bone volume fraction. These findings are important for interpreting the results of antiresorptive drug treatments that can cause changes in both ash and bone volume fraction.

Influence of bone mineral density, age, and strain rate on the failure mode of human Achilles tendons.

OBJECTIVE: To examine the influence of strain rate, bone mineral density, and age in determining the mode by which human Achilles tendons fail. DESIGN: Dual-energy X-ray absorptiometry and mechanical testing of excised Achilles tendon-calcaneus specimens. BACKGROUND: The Achilles tendon can fail by tendon rupture or bony avulsion. These injuries are caused by similar loading mechanisms and can present similar symptoms. It is important to understand when each mode of injury is likely to occur so that accurate diagnoses can be made and appropriate treatments selected. METHODS: Excised human Achilles tendons were loaded to failure at strain rates of 1% s(-1) and 10% s(-1) following dual-energy X-ray absorptiometry examination to determine bone mineral density near the tendon insertion. Calcaneal bone mineral density, donor age, and strain rate were compared between specimens that failed by avulsion and those that failed by tendon rupture. RESULTS: While strain rate was not observed to affect failure mode, the calcaneal bone mineral density of specimens that failed by avulsion was significantly lower than the bone mineral density of specimens that failed by tendon rupture (P=0.004). There was a significant decrease in bone mineral density with age (P=0.004), and the difference in age between the avulsed and ruptured specimens was close to statistical significance (P=0.058). For the avulsed specimens, there was a significant linear relationship between failure load and bone mineral density squared (P=0.002). Logistic regression indicated that the effect of age on failure mode is secondary to the primary effect of bone mineral density. CONCLUSIONS: The avulsions were primarily "premature" failures associated with low bone mineral density. Since bone mineral density decreases with age, older individuals are more likely to experience avulsions while younger individuals are more likely to experience tendon ruptures.

Mechanical properties of the human achilles tendon.

OBJECTIVE: To determine whether the human Achilles tendon has higher material properties than other tendons and to test for strain rate sensitivity of the tendon. DESIGN: Mechanical testing of excised tendons. BACKGROUND: While the human Achilles tendon appears to experience higher in vivo stresses than other tendons, it is not known how the Achilles tendon's material properties compare with the properties of other tendons. METHODS: Modulus, failure stress, and failure strain were measured for excised human Achilles tendons loaded at strain rates of 1% s(-1) and 10% s(-1). Paired t-tests were used to examine strain rate effects, and average properties from grouped data were used to compare the Achilles tendon's properties with properties reported in the literature for other tendons. RESULTS: Failure stress and failure strain were higher at the faster strain rate, but no significant difference in modulus was observed. At the 1% s(-1)rate, the mean modulus and failure stress were 816 MPa (SD, 218) and 71 MPa (SD, 17), respectively. The failure strain was 12.8% (SD, 1.7) for the bone-tendon complex and 7.5% (SD, 1.1) for the tendon substance. At the 10% s(-1) rate, the mean modulus and failure stress were 822 MPa (SD, 211) and 86 MPa (SD, 24), respectively. The mean failure strain was 16.1% (SD, 3.6) for the bone-tendon complex and 9.9% (SD, 1.9) for the tendon substance. These properties fall within the range of properties reported in the literature for other tendons. CONCLUSIONS: The material properties of the human Achilles tendon measured in this study are similar to the properties of other tendons reported in the literature despite higher stresses imposed on the Achilles tendon in vivo.

Mechanobiology of initial pseudarthrosis formation with oblique fractures.

Mechanical stresses play an important role in regulating tissue differentiation in a variety of contexts during skeletal development and regeneration. It has been shown that some intermittent loading at a fracture site can accelerate secondary fracture healing. However, it has not been shown how the stress and strain histories resulting from mechanical loading of a fracture might, in some cases, inhibit normal fracture healing and induce pseudarthrosis formation. In this study, finite element analysis is used to calculate hydrostatic stress and maximum principal tensile strain patterns in regenerating tissue around the site of an oblique fracture. Using a mechanobiologic view on tissue differentiation, we compared calculated stress and strain patterns within the fracture callus to the histomorphology of a typical oblique pseudarthrosis. Tissue differentiation predictions were consistent with the characteristic histomorphology of oblique pseudarthrosis: in the interfragmentary gap. tensile strains led to "cleavage" of the callus; at the ends of both fracture fragments, hydrostatic pressure and tensile strain caused fibrocartilage formation, and, at discrete locations of the periosteum at the oblique fracture ends, mild hydrostatic tension caused bone formation. We also found that discrete regions of high hydrostatic pressure correlated with locations of periosteal bone resorption. When previous findings with distraction osteogenesis are considered with these observations, it appears that low levels of hydrostatic pressure may be conducive to periosteal cartilage formation but high hydrostatic pressure may induce periosteal bone resorption during bone healing. We concluded that tissue differentiation in pseudarthrosis formation is consistent with concepts previously presented for understanding fracture healing, distraction osteogenesis, and joint formation.

Interpretation of calcaneus dual-energy X-ray absorptiometry measurements in the assessment of osteopenia and fracture risk.

Dual-energy X-ray absorptiometry (DXA) of the calcaneus is useful in assessing bone mass and fracture risk at other skeletal sites. However, DXA yields an areal bone mineral density (BMD) that depends on both bone apparent density and bone size, potentially complicating interpretation of the DXA results. Information that is more complete may be obtained from DXA exams by using a volumetric density in addition to BMD in clinical applications. In this paper, we develop a simple methodology for determining a volumetric bone mineral apparent density (BMAD) of the calcaneus. For the whole calcaneus, BMAD = (BMC)/ADXA3/2, where BMC and ADXA are, respectively, the bone mineral content and projected area measured by DXA. We found that ADXA3/2 was proportional to the calcaneus volume with a proportionality constant of 1.82 +/- 0.02 (mean +/- SE). Consequently, consistent with theoretical predictions, BMAD was proportional to the true volumetric apparent density (rho) of the bone according to the relationship rho = 1.82 BMAD. Also consistent with theoretical predictions, we found that BMD varied in proportion to rho V1/3, where V is the bone volume. We propose that the volumetric apparent density, estimated at the calcaneus, provides additional information that may aid in the diagnosis of osteopenia. Areal BMD or BMD2 may allow estimation of the load required to fracture a bone. Fracture risk depends on the loading applied to a bone in relation to the bone's failure load. When DXA is used to assess osteopenia and fracture risk in patients, it may be useful to recognize the separate and combined effects of applied loading, bone apparent density, and bone size.

Mechanobiology of tendon adaptation to compressive loading through fibrocartilaginous metaplasia.

Tendons that wrap around bones often undergo fibrocartilaginous metaplasia. In this paper, we examine the biomechanical causes and consequences of this metaplasia. We propose an adaptation rule in which tissue permeability changes in response to local cyclic hydrostatic pressures associated with physical activity. The proposed rule predicts the development of a low-permeability region corresponding to the fibrocartilaginous region in a representative wrap-around tendon. A poroelastic finite element model is used to examine the time-dependent fluid pressures and compressive stresses and strains in the solid constituents of the tendon's extrafibrillar matrix. The low permeability in the adapted fibrocartilaginous region maintains fluid pressures, protecting the solid constituents of the tendon's extracellular matrix from high compressive stresses and strains that could disrupt the matrix organization. Adaptation through fibrocartilaginous metaplasia therefore allows wrap-around tendons to function effectively over a lifetime without sustaining excessive mechanical damage due to cyclic compressive loading.

Mechanobiology in the development, maintenance, and degeneration of articular cartilage.

During skeletal development, the establishment of a layer of cartilage at the ends of long bones is intimately linked to the process of endochondral ossification. Previous in vivo studies and computer models suggest that mechanobiological factors can play a key role in modulating cartilage growth and ossification. Specifically, intermittent hydrostatic pressure is thought to maintain cartilage, and shear stresses encourage cartilage destruction and ossification. In the present investigation we examined the combined effects of hydrostatic pressure and shear stress--in the form of an osteogenic index--on the development of a layer of articular cartilage, using an idealized finite element computer model. The results of our analyses provide further support for the view that mechanobiological factors play a key role in regulating the distribution of cartilage thickness and in maintaining a stable cartilage layer at maturity. The model predicts that joints that experience higher contact pressures will have thicker cartilage layers. These predictions are consistent with observations of cartilage thickness in both humans and animals. Variations in articular mechanical load are predicted to modulate cartilage thickness. These results are consistent with the view that the mechanobiological factors responsible for the development of diarthrodial joints eventually lead to cartilage degeneration and osteoarthritis (OA) with aging.

Tendon and ligament adaptation to exercise, immobilization, and remobilization.

This study provides a theoretical and computational basis for understanding and predicting how tendons and ligaments adapt to exercise, immobilization, and remobilization. In a previous study, we introduced a model that described the growth and development of tendons and ligaments. In this study, we use the same model to predict changes in the cross-sectional area, modulus, and strength of tendons and ligaments due to increased or decreased loading. The model predictions are consistent with the results of experimental exercise and immobilization studies performed by other investigators. These results suggest that the same fundamental principles guide both development and adaptation. A basic understanding of these principles can contribute both to prevention of tendon and ligament injuries and to more effective rehabilitation when injury does occur.

A model of mechanobiologic and metabolic influences on bone adaptation.

Bone adaptation, the process through which bone mass is modified in the body, plays a key role in the development of osteoporosis. Bone adaptation is known to be influenced by both mechanical and metabolic stimuli. Previous studies have concentrated on changes in bone adaptation caused by mechanical stimuli (mechanobiologic influences), yet current treatments for osteoporosis depend significantly on metabolic influences. We develop a theoretical model of bone adaptation that accounts for both mechanobiologic and metabolic influences. We demonstrate the utility of this model using a simulation of the cellular processes of bone adaptation on a representative volume of cancellous bone. Our long-term objective is the development of a more comprehensive computational model that will aid in the study of osteoporosis and other bone diseases.

Reconstruction algorithm for polychromatic CT imaging: application to beam hardening correction.

This paper presents a new reconstruction algorithm for both single- and dual-energy computed tomography (CT) imaging. By incorporating the polychromatic characteristics of the X-ray beam into the reconstruction process, the algorithm is capable of eliminating beam hardening artifacts. The single energy version of the algorithm assumes that each voxel in the scan field can be expressed as a mixture of two known substances, for example, a mixture of trabecular bone and marrow, or a mixture of fat and flesh. These assumptions are easily satisfied in a quantitative computed tomography (QCT) setting. We have compared our algorithm to three commonly used single-energy correction techniques. Experimental results show that our algorithm is much more robust and accurate. We have also shown that QCT measurements obtained using our algorithm are five times more accurate than that from current QCT systems (using calibration). The dual-energy mode does not require any prior knowledge of the object in the scan field, and can be used to estimate the attenuation coefficient function of unknown materials. We have tested the dual-energy setup to obtain an accurate estimate for the attenuation coefficient function of K2 HPO4 solution.