BioWorld International Correspondent

LONDON - A mathematical model of tumor growth predicts that adverse conditions such as lack of oxygen and nutrients, and presence of cytotoxic drugs, could cause tumors to become more aggressive and invasive.

One day, researchers suggested, the model could be used to predict how a specific tumor will react to different therapies, helping clinicians tailor treatment according to individual characteristics.

Sandy Anderson, of the division of mathematics at the University of Dundee in Scotland, said, "Our research shows that the microenvironment in which the tumor grows acts like a Darwinian selective force upon how the tumor evolves."

Much current biomedical research into cancer is carried out in isolation from the real environment in which the tumor naturally grows, he pointed out. "These results show, however, that this environment could be the crucial determining factor in the tumor's development," he said.

The work is one of the few purely mathematical papers to ever appear in Cell. Published in the Dec. 1, 2006, issue, the paper is titled "Tumor Morphology and Phenotypic Evolution Driven by Selective Pressure from the Microenvironment."

Vito Quaranta, of the department of cancer biology at Vanderbilt University School of Medicine in Nashville, Tenn., who also is an author of the paper, described the combination of mathematics with laboratory research reported as being "a new era in cancer research."

He said: "Today we can know pretty well that for the next few days we're going to expect good weather or that there's a storm on the way. That's the kind of predictive power we want to generate with our model for cancer invasion."

The mathematical model developed by Anderson, Quaranta and their colleagues encompasses a set of equations for how individual cells grow, divide, move (both randomly or in directed motion), mutate, interact with each other (cell-cell adhesion and in response to crowding) and interact with the microenvironment.

The category of interactions with the microenvironment includes three key variables: the concentration of macromolecules in the extracellular matrix (which varies according to the location of the tumor in, for example, the lung, breast or prostate), the concentration of an enzyme that degrades the matrix and the concentration of oxygen. The researchers deemed the latter category to be representative of any nutrient or nutrients needed for the survival of tumor cells.

One way of thinking about the model is to imagine, the authors suggested, that it represents a slice of tumor lying on a lattice of coordinates. Four equations represent the probability of a single cell, located at a single point on the lattice, moving in any of four directions to another point on the lattice.

Parameters such as motility rates (which might also be influenced by interactions between the cell and the matrix, or by adhesions between cells, or by proliferation) also are taken into account.

At that point, the model assumed that all cells are identical, so to make it more realistic, the researchers introduced a range of phenotypes (with varying cell-cell adhesion characteristics and different proliferation rates, for example). Another layer of complexity involves applying two different patterns of mutation - either with cells becoming gradually more aggressively cancerous over time, or where cells can "jump" to one of 100 predefined phenotypes.

With these, and many more, variations, Anderson and Quaranta and colleagues simulated the growth of different types of tumors.

They predicted that harsh conditions produce tumors that, by their shape, clearly are invasive. Those tumors have "fingers" that project into their surroundings. In make-up, they are dominated by one or a handful of aggressive cell phenotypes.

By contrast, conditions where there was plenty of oxygen and nutrients would lead to the development of tumors that comprise a mixture of aggressive and less aggressive cell phenotypes, with no single type predominating. Those tumors have smooth, non-invasive margins.

Anderson said: "Most of the current treatment strategies are focussed on making the tissue environment as harsh as possible for the tumor in the hope of destroying it. But as my research predicts, this could allow the most aggressive cancer cells to dominate any residual tumor left after treatment and since these more aggressive cells tend to be the most invasive, this could result in an increased chance of metastasis."

Quaranta predicted that mathematics-driven oncology research will in the future allow researchers to determine which drugs will work at which stage of cancer treatment. n

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