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Tumor Growth and Chemo Response Could Be Predicted By Mathematical Model

May 18, 2009

The aggressiveness of tumors and their susceptibility to chemotherapy may become easier to predict based on a mathematical model developed at The University of Texas Health Science Center at Houston.

In spite of extensive experimental and clinical studies, the process of cancer growth is not well understood. Tumors are complex systems, with changes at the molecular and cellular levels influencing shape and behavior in sometimes unpredictable ways. New research by a scientist in mathematical oncology at the UT Health Science Center at Houston suggests that mathematical modeling based on data from the molecular and cellular levels could shed light on tumor development and lead to better treatments.

Cancer is the second most common cause of death in the United States, exceeded only by heart disease, according to the American Cancer Society.

At the 100th annual meeting of the American Association for Cancer Research in Denver this spring, Vittorio Cristini, Ph.D., an associate professor of health informatics at The University of Texas School of Health Information Sciences at Houston, demonstrated the predictability of tumor growth in brain cancer and chemotherapy response in breast cancer. Findings appear in two different papers in the May 15 print issue of the association’s peer-reviewed journal Cancer Research.

The mathematical model developed by Cristini’s lab works by defining tumor biologic and molecular properties relating to laboratory and clinical observations of cancers. In this model, the behavior of cancer cells and their surroundings is linked to tumor growth, shape and treatment response.

“The central finding of this work is that tumor growth and invasion are not erratic or unpredictable, or solely explained through genomic and molecular events, but rather are predictable processes obeying biophysical laws,” the authors wrote in the paper addressing predictability of tumor growth in brain cancer.

Tumors obtain nutrients and oxygen by harnessing the surrounding blood vessels and making new vessels. Since there typically aren’t enough nutrients and oxygen to support tumor cells, an uneven distribution of these substances is created inside and around the tumor mass, Cristini said.

The research of Cristini and colleagues, who worked in collaboration with Elaine L. Bearer, M.D., Ph.D., professor at the Brown School of Medicine, suggests that tumor growth and invasion could be predicted by using biophysical laws that link the effects of the uneven distribution of cell nutrients and oxygen to overall tumor behavior.

For different values of the input parameters, the model consistently reproduced the patterns of tumor invasion observed in experiments and in patient tumors, Cristini said. The patterns were regulated by changes in cellular characteristics, causing more aggressive tumor cells to invade the healthy tissue. As cancer cells invade and replicate themselves, they make the tumor shape unstable and more invasive. The model correctly predicted the different types of invasion under a variety of conditions.

Human brain tumor represented in three dimensions by the mathematical model. Using the model, the variation in oxygen and nutrients that the cells experience may be predictably linked to the overall tumor shape, invasiveness and response to drug treatment.

The model further predicted that the different forms of cancer invasion correspond to different stages of tumor progression, Cristini said. In regions of low oxygen, these changes may include a slowdown in cell replication and heightened cell migration, which can result in a “single-cell file” invasion pattern. As cells aggregate in regions that have better access to nutrients and oxygen, migration is lessened and cell replication is resumed. This leads to the formation of wave-like patterns of cell rearrangements at the tumor boundary and the formation of round infiltrative “fingers” that can detach from the tumor as clusters of cells.

In the second paper, working in collaboration with Mary Edgerton, M.D., Ph.D., associate professor of pathology at The University of Texas M. D. Anderson Cancer Center, the researchers used the mathematical model to successfully predict the effects of doxorubicin on breast tumor growth. The model incorporates information gleaned from cancer cells grown in the laboratory to determine whether a prescribed drug will reach the tumor in sufficient quantities to kill the malignant cells. “We seek to improve the precision of prescribing chemotherapeutic drugs, since it is sometimes hard to tell which will work and which will not, and what the optimal dose is for a particular patient,” said Hermann Frieboes, Ph.D., lead author of the chemotherapy study and a post doctoral fellow at the UT School of Health Information Sciences.
In the not-too-distant future, the mathematical model could help design therapies in which the molecular and cellular characteristics of a patient’s tumor are manipulated, Cristini said. This could decrease the spread of the tumor and help surgeons remove growths more effectively. This manipulation could also increase the susceptibility of tumors to chemotherapy, he added. The model could augment efforts to predict drug response, which currently include removing a tiny sample of cancer tissue and testing the response of its cells to cancer drugs in a laboratory situation before the patient starts treatment. By basing the model input parameters on specific patient data, the treatment outcomes could be predicted better.

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