Optimized Measurement of Anomalous Diffusion

INTRODUCTION Several groups have recently proposed the use of the Kohlrausch-Williams-Watts (KWW) stretched-exponential function to model the diffusion attenuation curves observed in biological tissues [1-4]. The KWW function is given by Mo exp[-(bD) α], where the free parameters of the model are the anomalous exponent α, the apparent diffusion coefficient D, and the unweighted signal intensity Mo. The KWW model has the flexibility to accurately model multi-exponential decays, and the anomalous exponent offers a novel source of contrast associated with the structural complexity of the diffusion environment. Noise contamination is a significant limitation of high b-value diffusion weighted (DW) imaging experiments, and is of particular concern when estimating parameters of complicated functions like the KWW model. We propose to address the noise issue using two techniques. First, we optimize the choice of experimental b-values using the Cramér-Rao bound (CRB) [5]. Second, we mitigate the effects of noise by using a previously proposed statistical joint-reconstruction algorithm [6,7].