  MR-based attenuation correction (MRAC) is important for accurate
quantification of the uptake of PET tracers in combined PET/MR scanners.
However, current techniques for MRAC usually require multiple acquisitions or
complex post-processing to discriminate the different tissues. Inspired by the
ancient Greeks, who believed that matter was made of the combination of four
elements (earth, water, air and fire), we formulated a multi-component Magnetic
Resonance (MR) Fingerprinting framework, where every voxel was considered a
weighted combination of four base elements: bone, water, air and fat. We named
our approach Aristotelian MR based attenuation correction (ARISTOMRAC). We used
a 3D radial acquisition scheme at 1.5T, acquiring a transient-state spoiled
acquisition with variable flip angles and echo times (TE), with the shortest
TEs being ultra-short echo times (UTE). We simulated a multi-tissue MR signal
model using the Bloch equations and used dictionary matching to extract tissue
fraction maps for bone water and fat, while air fractions were obtained by
thresholding the UTE parts of our acquisitions at higher spatial resolution.
Compared to previous methods for MR-based Attenuation Correction (MRAC), our
approach used a full multi-component signal model, including multiple tissues
per voxel. For this reason, rather than reconstructing high resolutions images,
MR data can be acquired more efficiently, directly at the resolution needed for
PET attenuation maps. The ARISTOMRAC method allows to accurately estimate the
air, water, bone and fat fractions (Concordance Correlation Coefficient =
0.81/0.91/0.98 for bone, water and fat respectively). Attenuation maps could be
obtained in the head and neck with a single 1-minute acquisition.
