“Symmetry of the gradient profile as second dimension in Mitra’s short time diffusion expansion“

Abstract:

Measuring the diffusion coefficient with NMR at different diffusion times offers unique opportunities to unveil information about cellular structures. At short diffusion time, a universal expansion exists that relates the diffusion coefficient to properties of the cellular structure like surface-to-volume ratio or membrane permeability. This expansion is often referred to as Mitra’s expansion. In this talk, the influence of the temporal profile of diffusion weighting gradients on the Mitra expansion is elucidated. It is shown that flow compensated diffusion gradients, i.e. temporal gradient profiles whose first moment equals zero, are blind to the term that is linear in diffusion time, which is the term that is proportional to mean curvature and membrane permeability. A gradient profile that smoothly interpolates between flow compensated and classical bipolar gradients is proposed. This gradient profile is parameterized by a parameter ?, which varies between ?=0 (equals bipolar gradients) and ?=½ (equals flow compensated gradients). It is proposed to use such interpolating gradient profiles to obtain information related to the sample microstructure by regarding this parameter ? as a second experimental dimension. This allows one to perform two dimensional experiments, sampling the plane spanned by the diffusion time and symmetry parameters such as ?. This two dimensional Ansatz is shown to yield an improved precision in simulations and experiments performed with capillary phantoms of 100 µm radius. 

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