Detailed view of HMPA-segmentation.

<p>(a) An example of an axial slice with proximal femur segmentation; (b) Magnified part of the cortex with profiles: original profiles are in blue/magenta, the green line exemplifies the cortical thickness measurement at a single voxel as a voxel-to-surface distance based on segmentation. Note how direction and length of a profile are related.</p

Relative error of the thickness estimation under two levels of simulated Gaussian noise.

<p>For the range of true thickness values normalized by the full width at half maximum (FWHM) of the Gaussian (), mean value and standard deviation of the corresponding relative error were computed after 250 simulations. These statistical parameters are shown for three methods using three different colors. True reference BMD was used (800 mg/mm), <i>σ</i> = 1.5 mm, <i>c</i> = 150, and <i>b</i> = 0 mg/mm. (a) Noise level = 30 mg/mm; (b) Noise level = 37 mg/mm.</p

Stability of the DM and HMPA methods with respect to changes in BMD_ref on EFP phantom data.

<p>For each scan protocol, method, and VOI of the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187097#pone.0187097.t001" target="_blank">Table 1</a> the difference in 2<i>a</i> computed with the modified BMD_ref (±20%) and with the true BMD_ref is shown.</p

Results of cortical thickness estimation for the EFP phantom based on segmentation with LAT50, DM, and HMPA as deviation from the ground truth.

<p>Applied BMD_ref was measured in the “cortex” of the shaft, the corresponding values are shown in the last row (HU).</p

A new method to determine cortical bone thickness in CT images using a hybrid approach of parametric profile representation and local adaptive thresholds: Accuracy results

<div><p>Motivation</p><p>Cortical bone is an important contributor to bone strength and is pivotal to understand the etiology of osteoporotic fractures and the specific mechanisms of antiosteoporotic treatment regimen. 3D computed tomography (CT) can be used to measure cortical thickness, density, and mass in the proximal femur, lumbar vertebrae, and distal forearm. However, the spatial resolution of clinical whole body CT scanners is limited by radiation exposure; partial volume artefacts severely impair the accurate assessment of cortical parameters, in particular in locations where the cortex is thin such as in the lumbar vertebral bodies or in the femoral neck.</p><p>Method</p><p>Model-based deconvolution approaches recover the cortical thickness by numerically deconvolving the image along 1D profiles using an estimated scanner point spread function (PSF) and a hypothesized uniform cortical bone mineral density (reference density). In this work we provide a new essentially analytical unique solution to the model-based cortex recovery problem using few characteristics of the measured profile and thus eliminate the non-linear optimization step for deconvolution. Also, the proposed approach allows to get rid of the PSF in the model and reduces sensitivity to errors in the reference density. Additionally, run-time and memory effective computation of cortical thickness was achieved with the help of a lookup table.</p><p>Results</p><p>The method accuracy and robustness was validated and compared to that of a deconvolution approach recently proposed for cortical bone and of the 50% relative threshold technique: in a simulated environment with noise and various error levels in the reference density and using CT acquisitions of the European Forearm Phantom (EFP II), a modification of a widely used anthropomorphic standard of cortical and trabecular bone compartments that was scanned with various scan protocols.</p><p>Conclusion</p><p>Results of simulations and of phantom data analysis verified the following properties of the new method: 1) Robustness against errors in the reference density. 2) Excellent accuracy on ground truth data with various noise levels. 3) Very fast computation using a lookup table.</p></div

Validation of the approximate sensitivity estimation (13).

<p>The true relative errors in <i>a</i> with respect to changes in each parameter are shown in blue, corresponding approximations by Taylor expansion are in red (up to the second order term for <i>T</i> and the linear term for <i>R</i> and BMD_ref) and green (the linear term for <i>T</i>). First row is for variation in BMD_ref (left) and <i>T</i> (right) at the level of 0.5 (“thin” cortex), second row is for variation in BMD_ref and <i>T</i> at the thickness level (“thick” cortex). In the third row there are results for <i>T</i> (left, ) and <i>R</i> (right, ). For the very thick cortex, , analytic sensitivity is not shown, as the true sensitivity becomes highly nonlinear due to vicinity of the singular point <i>T</i> = 1 (bottom left and center) and the Taylor expansion with the two first terms does not approximates it well except for a very small neighborhood of the initial value. BMD_ref was set to 1000 mg/mm, , <i>σ</i> was 1.</p

Cortical thickness estimation errors.

<p>There are shown results for DM and HMPA methods, when BMD_ref was measured with errors of ±5% and ±10%, and for LAT50-method which does not depend on BMD_ref (the solid green line). Note how the curve of the hybrid method overlaps the 50%-curve for “large” values of <i>a</i> above a certain “switching point”. (Same parameters were used as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187097#pone.0187097.g003" target="_blank">Fig 3</a>).</p

Segmentation of EFP.

<p>Two CT datasets of the European Forearm Phantom with segmentation contours. Two planar reconstructions are shown, axial and sagittal. (a) Acquired with 120 kV, 20 mAs, sharp convolution kernel B60s; (b) Acquired with 120 kV, 100 mAs, smooth convolution kernel B40s.</p

Relative thickness estimation error with respect to the error in BMD_ref.

<p>The true level of BMD_ref was 800, <i>σ</i> = 1.5, and <i>c</i> = 150 mg/mm, . Note that with true BMD_ref both DM and MPA-methods produce no errors: the corresponding curves coincide with the x-axis.</p