Physics applies to everything. So when the University of New Mexico's Dr. Vittorio Cristini started researching cancer, he applied physics. The result he got was a set of mathematical equations that describe, for each person, how many of their tumor cells a cancer treatment could kill. Cristini and his collaborators have applied these equations to pancreatic cancer – an application that could soon help oncologists use the mathematical model to develop treatment plans for all cancer patients.
Cristini, a UNM Professor in the Department of Pathology at the UNM School of Medicine and the Victor and Ruby Hansen Surface Professor in Molecular Modeling of Cancers, has previously published papers in “The Proceedings of the National Academy of Sciences” and “ACS Nano” describing a mathematical model for all tumors. In their most recent paper, published in the “Journal of Clinical Investigation,” Cristini and his collaborators at the University of Texas MD Anderson Cancer Center – Dr. Eugene Koay, Dr. Christopher H. Crane and Dr. Jason B. Fleming – write about ipovascular tumors, which are tumors that don’t have a good blood supply. Many pancreatic cancers are ipovascular.
The lack of a good blood supply hampers the blood’s ability to reach all cells.
“Actually, one of the first results of this investigation demonstrated how profoundly different transport is in the tumor region within the pancreas with respect to the normal pancreas surrounding it," Cristini explains. "Transport impairment is really a signature of cancer.”
Cristini’s equations use information from a person’s initial, minimally- or non-invasive cancer tests. In this study, the researchers used pre-treatment CT scans with contrast from 176 people at the MD Anderson Cancer Center who then underwent chemo-radiation treatment. Using the CT scan information, they calculated a number called the “blood volume fraction.” This number is smaller than one, and describes how good — or not — a tumor’s blood supply is. Blood volume fraction is 2 to 10 times smaller in a tumor than in normal tissue.
Cristini and his collaborators showed previously that liver tumors with high blood volume fraction responded better to chemotherapy drugs than liver tumors with low blood volume fraction. But the relationship was non-linear. As the model equations predicted, high blood volume fraction tumors die far more extensively than low blood volume tumors.
In their most recent paper, the researchers show that ipovascular tumors respond directly to the amount of chemo-radiation treatment; it’s a simpler, linear response. “So, the linear regime of the general model equations works well for ipovascular tumors,” says Cristini. Their paper showed that the model’s calculations based on the individual’s pre-treatment CT scans accurately predicted how well the tumor absorbed the chemotherapy drugs, how well the chemo-radiation treatment worked and even correlated significantly with patient survival.
The equations can use the results from pre-treatment computerized tomography (CT) scans, tissue analyses and magnetic resonance imaging (MRI). Because oncologists already use these test results to develop a treatment plan, they can use Cristini’s equations to adjust their plan to each person. Cristini now has clinical trials in development at several institutions, including the UNM Cancer Center, to test this idea.
“We want to test the model prospectively and also test it in different types of disease,” he says. “But we want to do more. We want to see if we can actually use these mathematics to improve the outcome for people with cancer.”