An Analysis by Synthesis Approach for Automatic Vertebral Shape Identification in Clinical QCT

Abstract

Quantitative computed tomography (QCT) is a widely used tool for osteoporosis diagnosis and monitoring. The assessment of cortical markers like cortical bone mineral density (BMD) and thickness is a demanding task, mainly because of the limited spatial resolution of QCT. We propose a direct model based method to automatically identify the surface through the center of the cortex of human vertebra. We develop a statistical bone model and analyze its probability distribution after the imaging process. Using an as-rigid-as-possible deformation we find the cortical surface that maximizes the likelihood of our model given the input volume. Using the European Spine Phantom (ESP) and a high resolution µCT scan of a cadaveric vertebra, we show that the proposed method is able to accurately identify the real center of cortex ex-vivo. To demonstrate the in-vivo applicability of our method we use manually obtained surfaces for comparison.

An Analysis by Synthesis Method that Allows Accurate Spatial Modeling of Thickness of Cortical Bone from Clinical QCT

“…This is the key observation that leads to our algorithm. However, in contrast to previous works [19,3,23,24,22], a convenient gaussian approximation for the in-plane PSF is not sufficient anymore. Using a normalized symmetric sum of gaussian in the Fourier domain, the PSF can be approximated with arbitrary precision.…”

“…Several slices of cortical bone were acquired from a non-embedded excised vertebra for detailed analysis in a high-resolution µCT scanner 2 (isotropic resolution 1.73µm). The cortices of the clinical QCT scans were identified using the method of Reinhold et al [19]. The resulting triangle meshes were used to generate a voxel based segmentation and as starting point for the proposed AbS method.…”

“…Bone Model The bone model is an extension of the one used in [19]. Following their notation, the density of the background (e.g.…”

“…Measurement Model As in [19], the imaging process is approximated by a blurring with an in-plane and and out-of-plane PSF. Both PSFs can be combined into a one dimensional, angle dependent PSF g α along a profile.…”

“…Recently, Reinhold et al [19] proposed a method to identify the center of the vertebral cortical bone with sub-voxel accuracy. They used an analysis-bysynthesis (AbS) approach to fit a geometrical model of the cortical shell to the input scan.…”