Data Assimilation in Brain Tumor Models - Mathematical Methods and Models in Biomedicine - page 226

Fig. 2 A representative contrast enhanced magnetic resonance image of a GBM patient at initial
diagnosis. The right panel shows the edema outlined in a closed curve and the enhancement region
below the edema. See text for additional details
tumor cells are poorly understood and stochastic in nature. Typically tumors exhibit
genetic abnormalities leading to heterogeneous compositions of cells, metabolism,
and vasculature. Brain anatomy varies on an individual basis, and tumors deform
the brain geometry depending on their size and location (known as the mass effect).
The second problem arises from interpretation of MR imaging studies. Due
to the risks associated with surgical treatment and the problem of accessing
the tumor through the skull, noninvasive MR scans are the primary method for
assessing the progression of gliomas, including GBM. MR scans are usually taken
at intervals from weeks to months depending on the treatment regime. Patients are
administered a contrast agent that highlights visibility of the tumor vasculature from
the surrounding brain tissue. GBM tumors are highly vascular; thus, strength of
contrast is typically interpreted as a measure of glioma cell density. The region
of highest intensity is called the enhancing region and corresponds to area of
highest blood vessel density, and most likely blood plasma that has leaked into
surrounding brain tissue. This area along with the nearby necrotic regions of less
contrast is sometimes called the tumor core. The region of lower contrast, usually
near the enhancing region, is called the edema , which is interpreted to be swelling
of noncancerous brain tissue due to leaky and abnormal tumor vasculature and
infiltration of “healthy” tissue by the tumor [ 10 ]. Figure 2 shows a contrast enhanced
MR image of a patient tumor. The red and yellow boundaries mark the enhancing
and edema, respectively. The image also shows the mass effect of the tumor in the
right hemisphere.
It is difficult to infer quantitative information about the underlying cell density
from MRI data for many reasons. First the relationship (if any exists) between a
pixel intensity at a given a point and the cell density there is unknown. Quantitative
comparison of patient MRI data to a simulated tumor requires a common geometry.
Thus a second problem, known as registration error, arises from inaccuracies in