Diffusion-Limited Diffusion MRI & a Universal Optimum B-Value

Van Wedeen¹, Guangping Dai¹

If we model q-space MRI as an imaging micro-structure, its effective resolution is the sum of two terms: camera resolution proportional to q-1=(γGt)-1, and blurring by the diffusion kernel, which if Gaussian has width (2Dt)-1/2. Defining effective resolution as the root-mean-square, setting t=δ=∆ and minimizing, the best-possible diffusion-limited structural resolution is Rmin=√3(D/γG)1/3, achieved with encoding time topt=D-1/3(γG)-2/3 and bopt=(π2/6)D-1. In vivo, if observed max(D-1)≈5Dwater-1 then bopt≈20,000s/mm-2. Thus, an optimal b-value of q-space MRI depends only on diffusivity and is gradient-independent; stronger gradients improve structural resolution insofar as they reduce diffusion encoding time at optimal b.