CT Image Electron Density Quantification in Regions with Metal Implants: Implications for Radiotherapy Treatment Planning

In radiotherapy planning, computed tomography (CT) images are used to quantify the electron density of tissues and provide spatial anatomical information. Treatment planning systems use these data to calculate the expected spatial distribution of absorbed dose in a patient. CT imaging is complicated by the presence of metal implants which cause increased image noise, produce artifacts throughout the image and can exceed the available range of CT number values within the implant, perturbing electron density estimates in the image. Furthermore, current dose calculation algorithms do not accurately model radiation transport at metal-tissue interfaces. Combined, these issues adversely affect the accuracy of dose calculations in the vicinity of metal implants. As the number of patients with orthopedic and dental implants grows, so does the need to deliver safe and effective radiotherapy treatments in the presence of implants. The Medical Physics group at the Cancer Centre of Southeastern Ontario and Queen's University has developed a Cobalt-60 CT system that is relatively insensitive to metal artifacts due to the high energy, nearly monoenergetic Cobalt-60 photon beam. Kilovoltage CT (kVCT) images, including images corrected using a commercial metal artifact reduction tool, were compared to Cobalt-60 CT images throughout the treatment planning process, from initial imaging through to dose calculation. An effective metal artifact reduction algorithm was also implemented for the Cobalt-60 CT system. Electron density maps derived from the same kVCT and Cobalt-60 CT images indicated the impact of image artifacts on estimates of photon attenuation for treatment planning applications. Measurements showed that truncation of CT number data in kVCT images produced significant mischaracterization of the electron density of metals. Dose measurements downstream of metal inserts in a water phantom were compared to dose data calculated using CT images from kVCT and Cobalt-60 systems with and without artifact correction. The superior accuracy of electron density data derived from Cobalt-60 images compared to kVCT images produced calculated dose with far better agreement with measured results. These results indicated that dose calculation errors from metal image artifacts are primarily due to misrepresentation of electron density within metals rather than artifacts surrounding the implants.

On The Dirichlet Distribution

The Dirichlet distribution is a multivariate generalization of the Beta distribution. It is an important multivariate continuous distribution in probability and statistics. In this report, we review the Dirichlet distribution and study its properties, including statistical and information-theoretic quantities involving this distribution. Also, relationships between the Dirichlet distribution and other distributions are discussed. There are some different ways to think about generating random variables with a Dirichlet distribution. The stick-breaking approach and the Pólya urn method are discussed. In Bayesian statistics, the Dirichlet distribution and the generalized Dirichlet distribution can both be a conjugate prior for the Multinomial distribution. The Dirichlet distribution has many applications in different fields. We focus on the unsupervised learning of a finite mixture model based on the Dirichlet distribution. The Initialization Algorithm and Dirichlet Mixture Estimation Algorithm are both reviewed for estimating the parameters of a Dirichlet mixture. Three experimental results are shown for the estimation of artificial histograms, summarization of image databases and human skin detection.