A continuum of components: Flexible fast fraction mapping in sodium MRI

Parameter mapping in sodium MRI data is challenging due to inherently low SNR and spatial resolution, prompting the need to employ robust models and estimation techniques. This work aims to develop a continuum model of sodium $$ -decay to overcome the limitations of the commonly employed bi-exponential models. Estimates of mean $$ -decay and fast component fraction in tissue are emergent from the inferred continuum model.

A closed-form continuum model was derived assuming a gamma distribution of $$ components. Sodium MRI was performed on four healthy human subjects and a phantom consisting of closely packed vials filled with an aqueous solution of varying sodium and agarose concentrations. The continuum model was applied to the phantom and in vivo human multi-echo 7T data. Parameter maps by voxelwise model-fitting were obtained.

The continuum model demonstrated comparable estimation performance to the bi-exponential model. The parameter maps provided improved contrast between tissue structures. The fast component fraction, an indicator of the heterogeneity of localised sodium motion regimes in tissue, was zero in CSF and high in WM structures.

The continuum distribution model provides high quality, high contrast parameter maps, and informative voxelwise estimates of the relative weighting between fast and slow decay components.