Vittorio Cristini, PhD, uses the example of an airplane to explain what he does in cancer research. "Before calculus," he says, "people couldn't really design a plane that would fly. You can do it by trial and error, but it would probably take centuries." Dr. Cristini has a faster way to try to understand cancer treatment. Like airplane designers today, he uses a mathematical model.
Dr. Cristini is a University of New Mexico Professor of Pathology at the UNM School of Medicine and the Victor and Ruby Hansen Surface Professor in Molecular Modeling of Cancers. He is also a UNM Professor of Chemical Engineering and of Biomedical Engineering. He has developed a detailed mathematical model of cancer that accurately predicts how individuals respond to cancer treatment. His model, based on biology and physics at the cellular, tissue and organ levels, takes over a dozen complex processes into account to give him insight into how drug molecules are transported within cancer tissue and how they interact with cancerous cells. "From the molecular biology point of view, the processes are very complex and very large in number," he says. "So a mathematical framework can help to make sense of it all."
Dr. Cristini and his team gather information from computerized tomography (CT) scans, patient tissue analyses, magnetic resonance imaging (MRI), mammography, and other non-invasive or minimally-invasive procedures that the patient would normally receive. They then translate this patient-specific information into numerical values for a few key variables in the model. These variables include the ratios that describe the volume of blood to tumor cells, the number of drug molecules in the tumor, and the proportion of fast-growing cells in the tumor. The model also includes variables for how drug molecules diffuse between cells, tissue layers and organs; how cells absorb, distribute, metabolize, and excrete drug molecules; and other physical phenomena. A molecule's shape and size can strongly influence its diffusivity in tissues—how well it travels through layer upon layer of tumor cells once the blood vessels expel it.
Using the physical and biological values together, the model's "Master Equations of Cancer,"— as Dr. Cristini calls them — compute how many drug molecules reach the tumor, how far into the tumor they can penetrate, and how many tumor cells they kill. Because the model uses patient-specific values, it can predict the fraction of the tumor that the individual's treatment regimen kills, and even whether the treatment will ultimately be successful and prolong life. So far, the predictions have been astounding.
"We have now demonstrated that the model parameters are significantly correlated with outcome," says Dr. Cristini. "And by outcome, I mean pathologic response. This means that they can be used to predict outcome in a given patient. They even correlate with survival." Dr. Cristini and his clinical collaborators at MD Anderson Cancer Center at the University of Texas in Houston, have submitted the results of one study to Science Translational Medicine. They determined from just a CT scan with contrast—and before any treatment—how pancreatic cancer patients would respond to standard treatments, based on the physical properties of each person's tissue. Another paper, written in collaboration with Elaine Bearer, PhD, UNM Professor of Pathology at the School of Medicine, was recently accepted by the Proceedings of the National Academy of Sciences. In that paper, Dr. Cristini and Dr. Bearer describe how the model accurately predicted chemotherapy response in people with colorectal cancer that invaded the liver and in people with malignant brain tumors.
The model is also useful in making predictions about recurrent tumors. "You can't say that the patient is cancer-free just because you can't see the cells," Dr. Cristini explains. Current imaging technology can't detect very small tumors, which is why periodic screening for certain cancers is recommended. Dr. Cristini's model has shown that because of the physics of diffusion, current cancer treatments should not be expected to kill all the tumor cells; instead, they will leave tumors that are too small to detect. Depending upon the unique biological conditions in the person, those tumor cells may outstrip the immune system's ability to combat them and regrow the tumor at an alarming rate. The model has been very accurate in predicting these recurring tumors.
Dr. Cristini's model also predicts that current nanoparticle technologies can kill 3 times as many cancer cells as conventional chemotherapy drugs—completely kills off tumor cells. The model even predicts which physical attributes will be most important in designing nanoparticles that can target tissues and release their toxic payloads more slowly and precisely.
The next step for Dr. Cristini is to test the model prospectively in a clinical setting. Clinical testing will fully demonstrate how useful the model is in making treatment decisions. With the impressive results so far, he hopes to start that work soon.
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