  Diffuse gliomas are highly infiltrative tumors whose early diagnosis and
follow-up usually rely on magnetic resonance imaging (MRI). However, the
limited sensitivity of this technique makes it impossible to directly assess
the extent of the glioma cell invasion, leading to sub-optimal treatment
planing. Reaction-diffusion growth models have been proposed for decades to
extrapolate glioma cell infiltration beyond margins visible on MRI and predict
its spatial-temporal evolution. These models nevertheless require an initial
condition, that is the tumor cell density values at every location of the brain
at diagnosis time. Several works have proposed to relate the tumor cell density
function to abnormality outlines visible on MRI but the underlying assumptions
have never been verified so far. In this work we propose to verify these
assumptions by stereotactic histological analysis of a non-operated brain with
glioblastoma using a tailored 3D-printed slicer. Cell density maps are computed
from histological slides using a deep learning approach. The density maps are
then registered to a postmortem MR image and related to an MR-derived geodesic
distance map to the tumor core. The relation between the edema outlines visible
on T2 FLAIR MRI and the distance to the core is also investigated. Our results
suggest that (i) the previously suggested exponential decrease of the tumor
cell density with the distance to the tumor core is not unreasonable but (ii)
the edema outlines may in general not correspond to a cell density iso-contour
and (iii) the commonly adopted tumor cell density value at these outlines is
likely overestimated. These findings highlight the limitations of using
conventional MRI to derive glioma cell density maps and point out the need of
validating other methods to initialize reaction-diffusion growth models and
make them usable in clinical practice.
