MATHEMATICS HELPS PREDICT CANCER'S GROWTH
Mathematicians at Duke
University are developing ways to help doctors predict how different cancers
are likely to progress when actual measurements of tumor growth are hard to
come by.
More than one in three people in the
United States will be diagnosed with cancer at some point in their lives.
Accurate predictions of tumor growth are key to determining the right dose of
radiation and chemotherapy, how often patients should undergo screening, and
whether a treatment is effective.
"Mathematical models can help inform a whole host of
cancer treatment decisions, but you need an accurate model," said Duke
mathematics professor Richard Durrett, who is leading the research.
Numerous mathematical models of tumor growth have been
proposed, but which ones are most appropriate for different types of cancer
remains an open question.
"Some tumors stop or slow down once they reach a
certain size, while others continue to grow," said co-author and Duke
undergraduate Anne Talkington.
Part of the difficulty comes from the fact that most tumor
growth models are calibrated using serial measurements of tumors growing in
mice or in the lab, where the supply of oxygen and nutrients isn't the same as
tumors growing in a person. But because most cancer patients begin treatment --
including surgery -- as soon as possible after diagnosis, similar growth data
for tumors in humans are hard to come by.
In a study published online in the Bulletin
of Mathematical Biology, Durrett and Talkington describe a way to
compare common mathematical models of tumor growth, using only two time-point
measurements of tumor size -- often the maximum number of size measurements
available before patients begin treatment.
"Working with data from actual patients forces us to
work with only two time points," Durrett said. "At first it may seem
that two points is not enough, since any model can be made to go through two
data points. However, by examining trends in the growth rates when the models
are fit to tumors of different sizes, we are able to figure out what the best
model is."
To test their method, the authors scoured the literature for
previously published data from cancer patients whose tumors were measured at
two time points before treatment via repeat mammograms, CT scans or MRIs.
The results suggest that breast and liver tumors grow
exponentially, at least when the tumors are still small.
"Like money in a savings account that earns a fixed
interest rate," Durrett said.
Two types of neurological tumors, on the other hand, grew
according to the two-thirds power law, consistent with the idea that only cells
on the surface of the tumor can divide.
"Some bias has been introduced by the way the data were
obtained, but our results indicate that the method is useful for determining
which tumor growth models work best for different types of cancer,"
Talkington said.
Comments
Post a Comment