Researchers have developed a new model to optimize radiation therapy and significantly increase the number of tumour cells killed during treatment.

The new mathematical model, outlined in a recent study led by a University of Waterloo student, can use information about where the majority of the cells in a tumour are located allowing for radiation treatment to be administered to the densest area.

Much consideration is currently usually given to optimal scheduling and dosing when radiation therapy is being prescribed, but the researchers found the treatment could be far more effective at killing brain tumour cells if oncologists also use the information on cell density, and irradiate the densest area of the tumour.

“Typically, cells in a tumour are packed at a higher density in the middle and less as you go further out, but that fact is not fully taken into account in current radiation treatment,” said Cameron Meaney, a PhD candidate in Waterloo’s Department of Applied Mathematics. “If we have a better understanding of tumour cell density, then we could design treatment in a better way to kill more cells.”

In developing their mathematical model to spatially optimize radiation therapy in brain tumours, the researchers set a cap on the total dose a patient could receive throughout their treatment. They then divided the tumour into multiple portions: with the area most densely populated with cells being one portion and the remainder of cells the other. In some instances, they prescribed the dosage of radiation given to each portion, and in other cases, they allowed the model to determine the best ratio.

“It turned out that not necessarily in all cases do you want to distribute the radiation dose evenly between the fractions,” Meaney said. “What our model has shown is that perhaps what’s best is if we take the total radiation dose that we’re allowed to give a patient and administer it over a small area at high strength where the cells are most dense instead of spreading it over a big area with semi-weak strength.”

Given
the
results
of
their
study,
the
researchers
have
proposed
the
following
procedure
for
spatial
optimization
of
radiation:
image
the
tumour
twice,
determine
the
dose
and
treatment
schedule,
ascertain
the
physical
limitations
of
the
radiation
apparatus,
then
optimize
the
first
radiation
fraction
using
their
mathematical
model.

Finally,
using
the
growth
model
deduced
from
the
initial
two
images
to
simulate
the
development
of
the
tumour
cells
between
fractions,
oncologists
can
use
the
derived
cell
density
profile
prior
to
each
instance
of
radiation
application
as
input
to
optimize
the
shape
of
the
radiation
beam.

The
study, *Spatial
Optimization
for
Radiation
Therapy
of
Brain
Tumors*,
authored
by
Waterloo’s
Faculty
of
Mathematics
researchers
Meaney,
Associate
Professor
Mohammad
Kohandel,
Professor
Marek
Stastna
and
Massachusetts
Institute
of
Technology
Professor
Mehran
Kardar,
was
recently
published
in
the
journal
PLOS
One.