NONLINEAR TUBE-FITTING FOR THE ANALYSIS OF ANATOMICAL AND FUNCTIONAL STRUCTURES

Jeff Goldsmith, Johns Hopkins Bloomberg School of Public Health, Department of Biostatistics
Brian S. Caffo, Johns Hopkins Bloomberg School of Public Health, Department of Biostatistics
Ciprian Crainiceanu, Johns Hopkins Bloomberg School of Public Health, Department of Biostatistics
Daniel Reich, Johns Hopkins Hospital, School of Medicine, Radiology and Radiological Science
Yong Du, Johns Hopkins University, School of Medicine, Radiology-Medical Imaging Physics
Craig Hendrix, Johns Hopkins University, Clinical Pharmacology

Abstract

We are concerned with the estimation of the exterior surface of tube-shaped anatomical structures. This interest is motivated by two distinct scientific goals, one dealing with the distribution of HIV microbicide in the colon and the other with measuring degradation in white-matter tracts in the brain. Our problem is posed as the estimation of the support of a distribution in three dimensions from a sample from that distribution, possibly measured with error. We propose a novel tube-fitting algorithm to construct such estimators. Further, we conduct a simulation study to aid in the choice of a key parameter of the algorithm, and we test our algorithm with validation study tailored to the motivating data sets. Finally, we apply the tube-fitting algorithm to a colon image produced by single photon emission computed tomography (SPECT)and to a white-matter tract image produced using diffusion tensor `imaging (DTI).