Flexible proton density (PD) mapping using multi-contrast variable flip angle (VFA) data

Quantitative proton density (PD) maps measure the amount of free water, which is important for non-invasive tissue characterization in pathology and across lifespan. PD mapping requires the estimation and subsequent removal of factors influencing the signal intensity other than PD. These factors include the T1, T2* relaxation effects, transmit field inhomogeneities, receiver coil sensitivity profile (RP) and the spatially invariant factor that is required to scale the data. While the transmit field can be reliably measured, the RP estimation is usually based on image post-processing techniques due to limitations of its measurement at magnetic fields higher than 1.5 T. The post-processing methods are based on unified bias-field/tissue segmentation, fitting the sensitivity profile from images obtained with different coils, or on the linear relationship between T1 and PD. The scaling factor is derived from the signal within a specific tissue compartment or reference object. However, these approaches for calculating the RP and scaling factor have limitations particularly in severe pathology or over a wide age range, restricting their application. We propose a new approach for PD mapping based on a multi-contrast variable flip angle acquisition protocol and a data-driven estimation method for the RP correction and map scaling. By combining all the multi-contrast data acquired at different echo times, we are able to fully correct the MRI signal for T2* relaxation effects and to decrease the variance and the entropy of PD values within tissue class of the final map. The RP is determined from the corrected data applying a non-parametric bias estimation, and the scaling factor is based on the median intensity of an external calibration object. Finally, we compare the signal intensity and homogeneity of the multi-contrast PD map with the well-established effective PD (PD*) mapping, for which the RP is based on concurrent bias field estimation and tissue classification, and the scaling factor is estimated from the mean white matter signal. The multi-contrast PD values homogeneity and accuracy within the cerebrospinal fluid (CSF) and deep brain structures are increased beyond that obtained using PD* maps. We demonstrate that the multi-contrast RP approach is insensitive to anatomical or a priori tissue information by applying it in a patient with extensive brain abnormalities and for whole body PD mapping in post-mortem foetal imaging.