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.

Effects of fluoride treatment on bone strength.

Bone mass and architecture in appendicular and most axial sites is controlled primarily by the tissue-loading history. We introduce a conceptual framework for understanding how fluoride treatment alters this control and can cause systemic increases in bone mass. Due to possible adverse influences of fluoride on the mineralized tissue physical characteristics, however, the increase in bone mass does not necessarily result in an increase in bone strength. Using engineering analyses of bone trabeculae, we calculate the losses in trabecular strength which can be caused by the presence of hypomineralized or hypermineralized fluorotic tissue. Significant increases in bone volume fraction and bone mass may be required to overcome these strength deficits.

Improved method for analysis of whole bone torsion tests.

Structural tests, such as whole bone torsion tests, have become widely accepted methods for assessing average bone material properties. To simplify interpretation of these tests, the nonuniform bone geometry is often analyzed as a tube with a constant cross section (prismatic) and the areal properties of the smallest bone section. This approach may not adequately represent the true torsional behavior of the cross section and does not account for any lengthwise variations in bone geometry. The errors introduced by these approximations are particularly significant when comparing bones of different sizes and geometries. In this paper, we examine the effects of approximating the cross-sectional torsional behavior and of neglecting lengthwise variations in bone geometry. We then present a simple, standardized procedure utilizing a FORTRAN computer program for accurate determination of material properties. We examine first simple idealized bone geometries and then a complex three-dimensional model of the femur from a 26-day-old male Sprague-Dawley rat. For these models, the conventional methods for interpreting torsion tests introduce errors of up to 42% in the shear modulus and up to 48% in the maximum shear stress; a straightforward extension of these methods reduces the errors to within 3%.

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.

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.

Mechanobiologic influences in long bone cross-sectional growth.

We developed a computer model to simulate the interaction of biological and mechanobiological factors in the development of the cross-sectional morphology of long bones. The model incorporated a strong influence of biologically induced bone formation during early development. In addition, an assumed mechanical loading history during growth and development corresponding to age-related changes in body weight and muscle mass was applied. Based on the bone stress stimulus generated by the assumed loads, mechanically induced apposition and resorption rates were calculated at the periosteal and endosteal surfaces using a previously developed bone modeling theory. These methods successfully emulated the growth-related changes seen in long bone diaphyseal structure as well as changes observed in mature bones during aging. The simulations recreated the rapid increase in bone dimensions during development, stabilizing at maturity, and then the gradual, age-related subperiosteal expansion and cortical thinning. Throughout the growth, development, and aging simulations, the values of the bone radii, area, moments of inertia, and apposition rates corresponded well with measurements documented by other researchers.

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.

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.

Mechanical factors in bone growth and development.

Mechanobiologic factors strongly influence skeletal ossification and regulate changes in bone geometry and apparent density during ontogeny. We have developed computer models that implement a simple mathematical rule relating cyclic tissue stresses to bone apposition and resorption. Beginning at the fetal stages of the femoral anlage, these models successfully predict the appositional bone growth and modeling observed in the development of the diaphyseal cross section. The same basic mechanobiologic rule can also predict the architectural construction of the proximal cancellous bone formed in regions of endochondral ossification. Geometry and density changes in adult diaphyseal and cancellous bone as a result of changes in physical activity can be simulated by invoking the same rule used during development. Future clinical and experimental work is needed to provide more quantitative data for mechanobiologic rules and elucidate the interactions between chemical and mechanical factors influencing bone biology.

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.

The role of loading memory in bone adaptation simulations.

The concept that bone responds to a time-averaged value of its current mechanical loading forms the basis for many computational bone adaptation algorithms. Some mathematical formulations have incorporated a quantification of the loading experienced during a single "average" day and thus implicitly assume that bone responds abruptly to changes in its loading history. To better reflect the time delays inherent in bone cell recruitment and activation processes, we included a fading memory of past loading. Implementing an exponentially fading memory with time constants of 5, 20, and 100 days, we simulated bone adaptations to abrupt and gradual changes in mechanical loading. Both an idealized single degree-of-freedom model and a finite element model of the proximal femur were studied. A time constant of 5 days produced time-dependent density changes that were negligibly different from those of the standard approach without memory. Models with higher time constants produced significant transient time lags (up to 8.1% difference) in the predicted short-term (3 months) bone density changes. A time constant of 100 days produced overshoots (by approximately 1%) of the eventual steady-state. All models predicted comparable long-term (after several years) steady-state adaptations. Future experimental analyses will be necessary to better determine appropriate fading memory time constants for bone under various loading conditions.

Warping of cross sections in the torsion of long bones with internal fracture fixation plates.

Torsion of noncircular beams results in warping of each cross section. When noncircular cross sections are constrained to remain plane, the resulting shear stress distribution is different from what Saint Venant torsion (with warping) would predict. This has practical implications to the stress analysis of plated long bones subjected to torsional loadings. Analyses in which warping is not allowed predict incorrect stress fields in the plate and bone and overpredict the amount of stress shielding associated with fracture plate fixation.

Stress analysis of a partially slotted intramedullary nail.

A finite element analysis of the Arbeitsgemeinschaft für Osteosynthesefragen/Association for the Study of Internal Fixation (AO/ASIF) intramedullary femoral nail was performed to study the failure of the nail from circumferential cracking near the slot tip. These failures are evidently the result of a stress-concentrating effect owing to the partially slotted nail design. Several finite element models were created of the proximal one-fourth of the nail. One model of the nail incorporated the cloverleaf profile as it is presently manufactured, and one had a circular cross section. An additional three models were created with alternative slot-tip geometries: a narrowed slot, a tapered slot, and a widened slot. Antero-posterior (AP) and medio-lateral (ML) bending loads and torsion loads were applied in two fundamentally different loading modes: (1) loads that were applied on both sides of the slot tip (spanned); and (2) loads that were self-equilibrating distal to the slot tip (non-spanned). For the load cases studied, for all models, the stresses predicted from the finite element models were locally highest at the junction between the open and closed cross sections. Alternative slot-tip shapes had a marked effect on the predicted stresses, in one case reducing maximum stress by 40%. However, no alternative slot tip shape was uniformly superior for all load cases. Therefore, until the in vivo loading modes are known more precisely, an alternative slot-tip shape cannot be proposed.

The influence of fixation peg design on the shear stability of prosthetic implants.

The variety of fixation peg designs existing on prosthetic implants indicates uncertainty regarding the optimum design of fixation pegs for the reduction of stress and relative motion at the bone-implant interface. Fixation pegs have a number of important functions on a prosthesis, one of which is to reduce shear stress and shear displacement at the bone-implant interface. This is a parametric study intended to identify trends in the shear stability of prostheses incorporating a range of fixation peg designs. The parameters varied included the number of fixation pegs on a surface, the size of the pegs, and the aspect ratio (length/diameter) of the pegs. Mechanical tests were performed on urethane foam blocks with mechanical properties comparable to trabecular bone. The results indicated the following: (a) Fixation pegs act independently in resisting shearing force if they are spaced sufficiently far apart. (b) For any given shear displacement, smaller pegs generate a greater resistive shear force per unit of peg projected area in the direction of the applied load than larger pegs having the same aspect ratio. (c) Smaller diameter pegs cause the supporting material to yield at lower displacements. (d) Pegs with a high aspect ratio provide high shear stability with a minimum amount of bone removed, but may bend if the aspect ratio becomes excessive. (e) Smaller, slender pegs generate a greater resistive shear force at a given displacement per unit of peg volume than larger, lower aspect ratio pegs.(ABSTRACT TRUNCATED AT 250 WORDS)

Stresses in plated long-bones: the role of screw tightness and interface slipping.

Using a three-dimensional finite element model of a plated long bone, we studied the influence of screw tightness, sliding frictional interfaces, and loading magnitude on the stresses within the plated bone. The model incorporated frictional interface elements that allowed stress-free separation under tensile loading to occur between the plate and bone and between the screw heads and the plate. The applied loading stimulated both static preloads created by tightening the screws that secure the plate to the bone and physiologic loads created by activity. Initial screw tightening with plate application created regions of bone hydrostatic compressive stress that may be partly responsible for ischemia under the plate. The inclusion of frictional interfaces resulted in a nonlinear relationship between physiologic loan and bone strain that was dependent on screw tightness. This nonlinear response correlated well with the results of previous in vitro studies showing that slippage between the plate and the bone can occur at physiologic load levels. The results showed that the effect of such slippage can be at least as important as plate material, rigidity, and placement in determining the degree of stress shielding. The results also indicated that previous plated bone models that assumed tight interfaces may have overestimated the extent of mechanical stress shielding.

Correlations between mechanical stress history and tissue differentiation in initial fracture healing.

A general theory for the role of intermittently imposed stresses in the differentiation of mesenchymal tissue is presented and then applied to the process of fracture healing. Two-dimensional finite element models of a healing osteotomy in a long bone were generated and the stress distributions were calculated throughout the early callus tissue under various loading conditions. These calculations were used in formulating theoretical predictions of tissue differentiation that were consistent with the biochemical and morphological observations of previous investigators. The results suggest that intermittent hydrostatic (dilatational) stresses may play an important role in influencing revascularization and tissue differentiation and determining the morphological patterns of initial fracture healing.

Cellular shape and pressure may mediate mechanical control of tissue composition in tendons.

In vivo studies have suggested that mechanical factors are involved in the regulation of the morphology and biochemical composition of tendons that wrap around bones. In these tendons, fibrocartilage is found in the segment wrapped around the bone, and tendon far from the bone displays normal tendon histomorphology. Recent in vitro studies have shown that intermittently loaded connective tissue cells are sensitive to changes in cellular shape and hydrostatic pressure: stretching and distortion of the cells enhances production of fibrous matrix and hydrostatic pressure enhances production of cartilaginous matrix. We used finite-element analysis to determine whether the regions of increased development of cartilaginous matrix in tendons that wrap around bones correspond to regions in which tendon cells are subjected to higher pressures, and whether the maintenance and rearrangement of fibrous extracellular matrix in these tendons is associated with regions of stretching and distortion of cells. We found that regions of cartilaginous matrix and fibrous matrix formation and turnover correlate well with patterns of hydrostatic compressive stress and distortional strain in the tendon. Although further experiments clearly are needed to establish the predictive value of our approach, hydrostatic stress and distortional strain history--parameters intimately related to changes in cellular pressure and shape, respectively--appear to be important tissue-level mechanical stimuli that regulate cartilaginous and fibrous matrix composition of connective tissues.

Role of mechanical loading in the progressive ossification of a fracture callus.

The progressive ossification pattern in a fracture callus was predicted based on a theory that relates the local stimulus for ossification to the tissue mechanical loading history. Two-dimensional finite element analyses of a fracture callus were considered at three different stages of ossification. The sites of callus ossification represented in the initial model were predicted by previous analyses relating mechanical stress and vascularity to the differentiation of mesenchymal tissue in the early callus. The zones of further ossification, bone bridging, and bone consolidation predicted in the present study were found to be similar to the ossification patterns that have been documented by other researchers. The approach used to predict fracture healing is identical to that of previous studies predicting joint morphogenesis, with the exception that fracture healing requires continuous, attached skeletal elements, whereas joint morphogenesis requires discontinuous, articulating skeletal elements.

An approach for time-dependent bone modeling and remodeling--theoretical development.

A time-dependent approach for emulating bone modeling and remodeling in response to the daily loading history is presented. We postulate that genotype, systemic metabolic conditions, and local tissue interactions establish the level of local tissue mechanical stimulation (attractor state) appropriate for the maintenance of bone tissue. The net daily rate of apposition or resorption on a bone surface is determined by the difference between the actual stimulus and the tissue attractor state and can be modulated by other biologic factors. In calculating the net change in local bone apparent density, the technique takes into account the bone surface area available for osteoblastic and osteoclastic activity. Endosteal, periosteal, haversian, and cancellous bone modeling and remodeling are thereby treated in a consistent, unified fashion.