# David Pokrajac: Recursive partitioning simulation of breast tissue

Source: Discrete mathematics seminar

**Povzetek.** Three dimensional breast models
represent important tools used in a variety of tasks, from preclinical
evaluation of imaging technique, to dosimetry and computer aided
diagnostic. In collaboration with University of Pennsylvania, we have
developed a breast simulation algorithm that can provide simulation of
various breast structures and control of anthropometric parameters such
as number of fat compartments, thickness of Cooper's ligaments and
percentage of radiologically dense tissue. In this presentation, we
discuss foundations of recursive partitioning algorithm and consider its
experimental performance and asymptotic complexity. Then, we discuss
various improvements of algorithm, aimed to simulate voxels with
multiple materials (partial volume effect), improve control of ligament
thickness and surface smoothness and achieve simulation of milk ducts.
We emphasize solved and open mathematical problems arising from this
application related to non-linear optimization, graph theory,
three-dimensional signal processing and computational geometry.