Colloquium: “Cubical homology in medical imaging”

Marshall University Math Colloquium
April 22, 2005

Nathan Cantrell
Marshall University

Abstract
Trabecular bone architecture is extremely important in early recognition of estrogen loss and osteoporosis, as loss of bone connectivity is one of the earliest signs of disease. Moreover, intense research is underway to quantify and understand the relationship between trabecular architecture and its mechanical properties for the benefit of both medicine and bio-engineering. Such a complex structure which appears as an evolutionary adaptation to the external forces acting on the bone is extremely difficult to examine quantitatively. Topology, however, may be able to reveal significant characteristics of this network. Is there a correlation between orientation and connectivity of the network and bone strength? The voxelized data produced by μ-MR or μ-CT is ideal for cubical homology, a relatively young homological method. In short, the technique uses the boundaries of cubical building blocks to expose these topological features and simplify certain information into an extremely finite amount of data. Cubical homology and computational abilities are now beginning to coalesce providing enormous implications for the cubical format of computer graphics and medical imaging.