Description and Characterization of a Novel Method for Partial Volume Simulation in Software Breast Phantoms

A modification to our previous simulation of breast anatomy is proposed to improve the quality of simulated x-ray projections images. The image quality is affected by the voxel size of the simulation. Large voxels can cause notable spatial quantization artifacts; small voxels extend the generation time and increase the memory requirements. An improvement in image quality is achievable without reducing voxel size by the simulation of partial volume averaging in which voxels containing more than one simulated tissue type are allowed. The linear x-ray attenuation coefficient of voxels is, thus, the sum of the linear attenuation coefficients weighted by the voxel subvolume occupied by each tissue type. A local planar approximation of the boundary surface is employed. In the two-material case, the partial volume in each voxel is computed by decomposition into up to four simple geometric shapes. In the three-material case, by application of the Gauss-Ostrogradsky theorem, the 3D partial volume problem is converted into one of a few simpler 2D surface area problems. We illustrate the benefits of the proposed methodology on simulated x-ray projections. An efficient encoding scheme is proposed for the type and proportion of simulated tissues in each voxel. Monte Carlo simulation was used to evaluate the quantitative error of our approximation algorithms.