The process of cancer growth is not well understood. While there's plenty of qualitative evidence linking disease progression with parameters such as tumor morphology, histopathology, invasion and associated molecular phenomena, the relative contribution of each factor remains elusive.
To better understand how changes at the molecular and cellular levels influence tumour behaviour, researchers are applying mathematics to the problem, developing computational models to predict, for example, the aggressiveness of tumours or their susceptibility to chemotherapy. Such models could eventually help in the design of targeted treatments for personalized cancer therapy.
Two papers published in the latest issue of Cancer Research detail the development of such mathematical models. First, in a study of gliomas, a research collaboration has developed a model that helps predict how such brain tumours grow and evolve. The model links the behaviour of cancer cells and their surroundings to tumour growth, shape and treatment response (Cancer Res 69 4493).
"This helps us design a treatment," explained lead author Elaine Bearer, professor of pathology and laboratory medicine at Brown University. "By testing potential therapies in the computer, we can get our new drugs much faster to patients."
Bearer and co-workers developed a mathematical formula that incorporates a number of equations describing tumour evolution and growth. The master model was based on formulae that predict how much oxygen tumor cells consume and the rate of oxygen diffusion, as well as quantitative measures of cell growth and metabolic rates. The model is a series of interdependent differential equations, each including variables that can be experimentally manipulated.
Computer-generated depictions of a growing brain tumor show growth at six, eight and 12 months (top, left to right), with development of infiltrative cell front (arrow) at 12 months. Tissue slide (bottom) shows tumour finger (black arrow) advancing in substrate gradient (white arrow). Credit: Bearer lab.
The team validated their model by studying approximately 40 human brain tumor samples, comparing the virtual computational tumour with actual glioma specimens at different stages of tumor evolution.
For different values of the input parameters, the model consistently reproduced the patterns of tumor invasion observed experimentally and in patient tumours, explained co-author Vittorio Cristini, associate professor of health informatics at the University of Texas School of Health Information Sciences (Houston, TX).
The central finding of this work was that tumour growth and invasion are not erratic, or solely explained through genomic and molecular events, but rather are predictable processes that obey biophysical laws.
In the second research paper, Cristini and collaborators used mathematical modelling to successfully predict the effects of doxorubicin on breast-tumor growth. The model incorporated information gleaned from laboratory-grown cancer cells to help determine whether a drug will reach the tumor in sufficient quantities to kill the malignant cells (Cancer Res 69 4484).
"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, lead author of the chemotherapy study and postdoctoral fellow at the UT School of Health Information Sciences.
Ultimately, says Cristini, the model could help design therapies that manipulate the molecular and cellular characteristics of a patient's tumor. This could decrease the spread of the tumor, enabling more effective surgical removal, or increase the tumor's susceptibility to chemotherapy. The model could also enhance efforts to predict a patient's response to a particular drug, by basing the model's input parameters on the individual's data.