Scientists Develop Mathematical Model to Predict Cancer Cells’ Resistance to Therapy

Key Points

  • Although targeted chemotherapeutics can provide remissions, they are often short-lived because cancer cells become resistant to the therapies, usually within a few months.
  • A small number of cells resistant to any targeted therapy are always present in large solid tumors at the start of therapy, and these cells clonally expand once therapy is administered.
  • Simultaneous use of two or more drugs is more effective in treating cancer than the use of sequential therapy.

New research using mathematical models of different types of cancer—including melanoma, pancreatic, and colorectal—to determine the evolutionary dynamics of lesions in response to treatment is revealing why and how cancer cells resist targeted therapies. The study by Ivana Bozic, PhD, from the Department of Mathematics at Harvard University, and colleagues was published online in eLife.

Study Details

The investigators, a team of mathematicians and oncologists from a variety of academic centers, designed a mathematical model to predict the effects of combination targeted therapies on tumors based on data obtained from 20 melanoma patients receiving vemurafenib (Zelboraf). They then applied their model to an independent set of pancreatic, colorectal, and melanoma cancer patients with metastatic disease. Their findings showed that when dual therapy is used, most patients experience longer-term disease control as long as there were no single cell mutations that caused cross-resistance to both drugs. In patients with large disease burden, triple therapy is needed. They also found that when two drugs are used simultaneously rather than sequentially, they were much more effective.

“As medicine becomes increasingly personalized, more and more emphasis is being placed on the development of therapies that target specific cancer-causing mutations. But while many of these drugs are effective in the short-term, and do extend patient lives, tumors tend to evolve resistance to them within a few months,” the researchers wrote.

The reason drugs often fail is because large tumors are genetically diverse and there is likely to be a small population of cells within the tumor that is resistant to the effects of the drugs, said the authors.

Mathematical Model Used

The model used by the researchers is based on a multitype birth-death cell branching process and includes two phases: pretreatment and treatment. Using this method, the researchers found that even if there is just one genetic alteration within any of the 6.6 billion base pairs present in a human diploid cell that can confer resistance to two targeted drugs, the treatment will not have sustaining benefit for most patients with advanced disease. The same is true for triple therapy.

“If there is a possibility of a mutation conferring cross-resistance to three drugs, lesions of the size commonly observed in patients with advanced cancers will always recur,” said the researchers.

Their results provide realistic expectations for the effectiveness of new drug combinations and information that can be used in the design of clinical trials for new cancer therapeutics, said the researchers.

The content in this post has not been reviewed by the American Society of Clinical Oncology, Inc. (ASCO®) and does not necessarily reflect the ideas and opinions of ASCO®.




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