Difference in distribution functions: A new diffusion weighted imaging metric for estimating white matter integrity

Diffusion weighted imaging (DWI) is a widely recognized neuroimaging technique to evaluate the microstructure of brain white matter. The objective of this study is to establish an improved automated DWI marker for estimating white matter integrity and investigating ageing related cognitive decline. The concept of Wasserstein distance was introduced to help establish a new measure: difference in distribution functions (DDF), which captures the difference of reshaping one's mean diffusivity (MD) distribution to a reference MD distribution. This new DWI measure was developed using a population-based cohort (n=19,369) from the UK Biobank. Validation was conducted using the data drawn from two independent cohorts: the Sydney Memory and Ageing Study, a community-dwelling sample (n=402), and the Renji Cerebral Small Vessel Disease Cohort Study (RCCS), which consisted of cerebral small vessel disease (CSVD) patients (n=171) and cognitively normal controls (NC) (n=43). DDF was associated with age across all three samples and better explained the variance of changes than other established DWI measures, such as fractional anisotropy, mean diffusivity and peak width of skeletonized mean diffusivity (PSMD). Significant correlations between DDF and cognition were found in the UK Biobank cohort and the MAS cohort. Binary logistic analysis and receiver operator characteristic curve analysis of RCCS demonstrated that DDF had higher sensitivity in distinguishing CSVD patients from NC than the other DWI measures. To demonstrate the flexibility of DDF, we calculated regional DDF which also showed significant correlation with age and cognition. DDF can be used as a marker for monitoring the white matter microstructural changes and ageing related cognitive decline in the elderly.