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Publication Detail
A rigorous framework for diffusion tensor calculus
Abstract
In biological tissue, all eigenvalues of the diffusion tensor areassumed to be positive. Calculations in diffusion tensor MRIgenerally do not take into account this positive definitenessproperty of the tensor. Here, the space of positive definitetensors is used to construct a framework for diffusion tensoranalysis. The method defines a distance function between apair of tensors and the associated shortest path (geodesic)joining them. From this distance a method for computing tensormeans, a new measure of anisotropy, and a method for tensorinterpolation are derived. The method is illustrated using simulatedand in vivo data. In biological tissue, all eigenvalues of the diffusion tensor areassumed to be positive. Calculations in diffusion tensor MRIgenerally do not take into account this positive definitenessproperty of the tensor. Here, the space of positive definitetensors is used to construct a framework for diffusion tensoranalysis. The method defines a distance function between apair of tensors and the associated shortest path (geodesic)joining them. From this distance a method for computing tensormeans, a new measure of anisotropy, and a method for tensorinterpolation are derived. The method is illustrated using simulatedand in vivo data.
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