Extracting a biomarker for the mean cross-sectional area from the ODF

Finding new biomarkers related to the microstructure of white matter (WM) is an active area of research in theMRI community [1]. As opposed to the usual MRI markers such as fractional anisotropy (FA), thesebiomarkers provide a closer insight on the tissue structure. We introduce a new microstructure basedbiomarker that is related to the axon diameter distribution (ADD) and can be obtained with a q-space imaging[2] technique like DSI [3] or MAP [4]. This feature is related with the nature and purpose of WM paths in bothnormal and pathological conditions [5], and is obtained from the Orientation Distribution Function (ODF) [6] astwice its maximum value. We show that this value is related with the mean cross-sectional area (MCSA) of anensemble of parallel axons. The same geometric feature was proposed in [4] as a scalar index ofmicrostructure, but was not related to the ODF. In this work we give the formal relation between thismicrostructure feature and the ODF, and validate it using state-of-the-art numerical simulations.