Tensor distribution function

Alex D. Leow; Siwei Zhu

doi:10.1117/12.770857

11 March 2008 Tensor distribution function

Alex D. Leow, Siwei Zhu

Proceedings Volume 6914, Medical Imaging 2008: Image Processing; 69142H (2008) https://doi.org/10.1117/12.770857
Event: Medical Imaging, 2008, San Diego, California, United States

Abstract

Diffusion weighted MR imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitizing gradients along a minimum of 6 directions, second-order tensors (represetnted by 3-by-3 positive definiite matrices) can be computed to model dominant diffusion processes. However, it has been shown that conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g. crossing fiber tracts. More recently, High Angular Resolution Diffusion Imaging (HARDI) seeks to address this issue by employing more than 6 gradient directions. To account for fiber crossing when analyzing HARDI data, several methodologies have been introduced. For example, q-ball imaging was proposed to approximate Orientation Diffusion Function (ODF). Similarly, the PAS method seeks to reslove the angular structure of displacement probability functions using the maximum entropy principle. Alternatively, deconvolution methods extract multiple fiber tracts by computing fiber orientations using a pre-specified single fiber response function. In this study, we introduce Tensor Distribution Function (TDF), a probability function defined on the space of symmetric and positive definite matrices. Using calculus of variations, we solve for the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, ODF can easily be computed by analytical integration of the resulting displacement probability function. Moreover, principle fiber directions can also be directly derived from the TDF.

Citation Download Citation

Alex D. Leow and Siwei Zhu "Tensor distribution function", Proc. SPIE 6914, Medical Imaging 2008: Image Processing, 69142H (11 March 2008); https://doi.org/10.1117/12.770857

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