  Mathematical models are becoming increasingly important in magnetic resonance
imaging (MRI), as they provide a mechanistic approach for making a link between
tissue microstructure and signals acquired using the medical imaging
instrument. The Bloch equations, which describes spin and relaxation in a
magnetic field, is a set of integer order differential equations with a
solution exhibiting mono-exponential behaviour in time. Parameters of the model
may be estimated using a non-linear solver, or by creating a dictionary of
model parameters from which MRI signals are simulated and then matched with
experiment. We have previously shown the potential efficacy of a magnetic
resonance fingerprinting (MRF) approach, i.e. dictionary matching based on the
classical Bloch equations, for parcellating the human cerebral cortex. However,
this classical model is unable to describe in full the mm-scale MRI signal
generated based on an heterogenous and complex tissue micro-environment. The
time-fractional order Bloch equations has been shown to provide, as a function
of time, a good fit of brain MRI signals. We replaced the integer order Bloch
equations with the previously reported time-fractional counterpart within the
MRF framework and performed experiments to parcellate human gray matter, which
is cortical brain tissue with different cyto-architecture at different spatial
locations. Our findings suggest that the time-fractional order parameters,
{\alpha} and {\beta}, potentially associate with the effect of interareal
architectonic variability, hypothetically leading to more accurate cortical
parcellation.
