Robert T. Whalen

Calcaneal loading during walking and running

PURPOSE This study of the foot uses experimentally measured kinematic and kinetic data with a numerical model to evaluate in vivo calcaneal stresses during walking and running. METHODS External ground reaction forces (GRF) and kinematic data were measured during walking and running using cineradiography and force plate measurements. A contact-coupled finite element model of the foot was developed to assess the forces acting on the calcaneus during gait. RESULTS We found that the calculated force-time profiles of the joint contact, ligament, and Achilles tendon forces varied with the time-history curve of the moment about the ankle joint. The model predicted peak talocalcaneal and calcaneocuboid joint loads of 5.4 and 4.2 body weights (BW) during walking and 11.1 and 7.9 BW during running. The maximum predicted Achilles tendon forces were 3.9 and 7.7 BW for walking and running. CONCLUSIONS Large magnitude forces and calcaneal stresses are generated late in the stance phase, with maximum loads occurring at approximately 70% of the stance phase during walking and at approximately 60% of the stance phase during running, for the gait velocities analyzed. The trajectories of the principal stresses, during both walking and running, corresponded to each other and qualitatively to the calcaneal trabecular architecture.

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. The authors have compared their algorithm to three commonly used single-energy correction techniques. Experimental results show that their algorithm is much more robust and accurate. The authors have also shown that QCT measurements obtained using their 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. The authors have tested the dual-energy setup to obtain an accurate estimate for the attenuation coefficient function of K/sub 2/HPO/sub 4/ solution.

Prediction of human gait parameters from temporal measures of foot-ground contact

Investigation of the influence of human physical activity on bone functional adaptation requires long-term histories of gait-related ground reaction force (GRF). Towards a simpler portable GRF measurement, we hypothesized that: 1) the reciprocal of foot-ground contact time (1/tc); or 2) the reciprocal of stride-period-normalized contact time (T/tc) predict peak vertical and horizontal GRF, loading rates, and horizontal speed during gait. GRF data were collected from 24 subjects while they walked and ran at a variety of speeds. Linear regression and ANCOVA determined the dependence of gait parameters on 1/tc and T/tc, and prediction SE. All parameters were significantly correlated to 1/tc and T/tc. The closest pooled relationship existed between peak running vertical GRF and T/tc (r2 = 0.896; SE = 3.6%) and improved with subject-specific regression (r2 = 0.970; SE = 2.2%). We conclude that temporal measures can predict force parameters of gait and may represent an alternative to direct GRF measurements for determining daily histories of habitual lower limb loading quantities necessary to quantify a bone remodeling stimulus.

Factors in Daily Physical Activity Related to Calcaneal Mineral Density in Men

To determine the factors in daily physical activity that influence the mineral density of the calcaneus, we recorded walking steps and the type and duration of exercise in 43 healthy 26-to 51-yr-old men. Areal (g.cm-2) calcaneal bone mineral density (CBMD) was measured by single energy x-ray densitometry (SXA, Osteon, Inc., Wahiawa, HI). Subjects walked a mean (+/- SD) of 7902 (+/- 2534) steps per day or approximately 3.9 (+/- 1.2) miles daily. Eight subjects reported no exercise activities. The remaining 35 subjects spent 143 (2-772) (median and range) min.wk-1 exercising. Twenty-eight men engaged in exercise activities that generate single leg peak vertical ground reaction forces (GRFz) of 2 or more body weights (high loaders, HL), and 15 reported exercise or daily activities that typically generate GRFz less than 1.5 body weights (low loaders, LL). CBMD was 12% higher in HL than LL (0.668 +/- 0.074 g.cm-2 vs 0.597 +/- 0.062 g.cm-2, P < 0.004). In the HL group, CBMD correlated to reported minutes of high load exercise (r = 0.41, P < 0.03). CBMD was not related to the number of daily walking steps (N = 43, r = 0.03, NS). The results of this study support the concept that the dominant factor in daily physical activity relating to bone mineral density is the participation in site specific high loading activities, i.e., for the calcaneus, high calcaneal loads.

Modeling of polychromatic attenuation using computed tomography reconstructed images

This paper presents a procedure for estimating an accurate model of the CT imaging process including spectral effects. As raw projection data are typically unavailable to the end-user, we adopt a post-processing approach that utilizes the reconstructed images themselves. This approach includes errors from x-ray scatter and the nonidealities of the built-in soft tissue correction into the beam characteristics, which is crucial to beam hardening correction algorithms that are designed to be applied directly to CT reconstructed images. We formulate this approach as a quadratic programming problem and propose two different methods, dimension reduction and regularization, to overcome ill conditioning in the model. For the regularization method we use a statistical procedure, Cross Validation, to select the regularization parameter. We have constructed step-wedge phantoms to estimate the effective beam spectrum of a GE CT-I scanner. Using the derived spectrum, we computed the attenuation ratios for the wedge phantoms and found that the worst case modeling error is less than 3% of the corresponding attenuation ratio. We have also built two test (hybrid) phantoms to evaluate the effective spectrum. Based on these test phantoms, we have shown that the effective beam spectrum provides an accurate model for the CT imaging process. Last, we used a simple beam hardening correction experiment to demonstrate the effectiveness of the estimated beam profile for removing beam hardening artifacts. We hope that this estimation procedure will encourage more independent research on beam hardening corrections and will lead to the development of application-specific beam hardening correction algorithms.

A new frame‐based registration algorithm

This paper presents a new algorithm for frame registration. Our algorithm requires only that the frame be comprised of straight rods, as opposed to the N structures or an accurate frame model required by existing algorithms. The algorithm utilizes the full 3D information in the frame as well as a least squares weighting scheme to achieve highly accurate registration. We use simulated CT data to assess the accuracy of our algorithm. We compare the performance of the proposed algorithm to two commonly used algorithms. Simulation results show that the proposed algorithm is comparable to the best existing techniques with knowledge of the exact mathematical frame model. For CT data corrupted with an unknown in-plane rotation or translation, the proposed technique is also comparable to the best existing techniques. However, in situations where there is a discrepancy of more than 2 mm (0.7% of the frame dimension) between the frame and the mathematical model, the proposed technique is significantly better (p < or = 0.05) than the existing techniques. The proposed algorithm can be applied to any existing frame without modification. It provides better registration accuracy and is robust against model mis-match. It allows greater flexibility on the frame structure. Lastly, it reduces the frame construction cost as adherence to a concise model is not required.

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.

Cross-sectional structural parameters from densitometry

Bone densitometry has previously been used to obtain cross-sectional properties of bone from a single X-ray projection across the bone width. Using three unique projections, we have extended the method to obtain the principal area moments of inertia and orientations of the principal axes at each scan cross-section along the length of the scan. Various aluminum phantoms were used to examine scanner characteristics to develop the highest accuracy possible for in vitro non-invasive analysis of cross-sectional properties. Factors considered included X-ray photon energy, initial scan orientation, the angle spanned by the three scans (included angle), and I(min)/I(max) ratios. Principal moments of inertia were accurate to within +/-3.1% and principal angles were within +/-1 degrees of the expected value for phantoms scanned with included angles of 60 degrees and 90 degrees at the higher X-ray photon energy (140 kVp). Low standard deviations in the error (0.68-1.84%) also indicate high precision of calculated measurements with these included angles. Accuracy and precision decreased slightly when the included angle was reduced to 30 degrees. The method was then successfully applied to a pair of excised cadaveric tibiae. The accuracy and insensitivity of the algorithms to cross-sectional shape and changing isotropy (I(min)/I(max)) values when various included angles are used make this technique viable for future in vivo studies.

Assessment of Long Bone Flexural Properties from Bone Densitometry

While bone densitometry is the accepted non-invasive method of quantifying bone mineral content in bones, its assessment of bone structural properties is less well understood. The objective of our current work is to compare cross-section shape or areal properties of long bones computed from densitometry data with cross-section flexural properties obtained from surface strain measurements.