Clustering method for estimating principal diffusion directions

Abstract

Diffusion tensor magnetic resonance imaging (DTMRI) is a non-invasive tool for the investigation of white matter structure within the brain. However, the traditional tensor model is unable to characterize anisotropies of orders higher than two in heterogeneous areas containing more than one fiber population. To resolve this issue, high angular resolution diffusion imaging (HARDI) with a large number of diffusion encoding gradients is used along with reconstruction methods such as Q-ball. Using HARDI data, the fiber orientation distribution function (ODF) on the unit sphere is calculated and used to extract the principal diffusion directions (PDDs). Fast and accurate estimation of PDDs is a prerequisite for tracking algorithms that deal with fiber crossings. In this paper, the PDDs are defined as the directions around which the ODF data is concentrated. Estimates of the PDDs based on this definition are less sensitive to noise in comparison with the previous approaches. A clustering approach to estimate the PDDs is proposed which is an extension of fuzzy c-means clustering developed for orientation of points on a sphere. MDL (Minimum description length) principle is proposed to estimate the number of PDDs. Using both simulated and real diffusion data, the proposed method has been evaluated and compared with some previous protocols. Experimental results show that the proposed clustering algorithm is more accurate, more resistant to noise, and faster than some of techniques currently being utilized.