Mathematical modeling predicts tumor growth
Mathematical modeling is a description of a system or a process through mathematical language, usually equations. When we have a mathematical model that has been validated adequately, we can use it to understand why things happen the way they happen, and, perhaps more importantly, to predict how a system will behave in the future. This is done routinely in weather forecasts, which are based on mathematical models and computer simulations.
In modeling prostate tumor growth, we encounter obstacles at two levels. First, we do not know with certainty what the fundamental principles governing tumor growth are. Second, we do not have access to a lot of high-quality data that can be used to refine the models.
We believe high-quality imaging data can help us build models for tumor forecasting, ultimately providing insights on cancer diagnosis, prognosis and treatments. The idea was conceived by a group of people, including myself; Thomas J.R. Hughes, a collaborator at University of Texas at Austin; and Guillermo Lorenzo, a former student of mine. We thought a process like tumor growth could be modeled by applying some knowledge of the fundamental governing mechanisms, as well as by acquiring sufficient data (by using high-resolution medical images). We built tools to incorporate that data into mathematical models.
Our team has used different types of medical images, including ultrasound and several modalities of magnetic resonances. We developed algorithms to build a faithful representation of the three-dimensional geometry of the prostate and the tumor, along with efficient algorithms to solve the equations we established.
An interesting thing about mathematical modeling is that the models contain huge amounts of information that is encoded into very complex equations. To access that wealth of information, you need to find approximate solutions to the equations using large-scale computations. By solving the equations, you reveal the secrets that they hide.
In a breakthrough discovery, based on the results of our computational method, we hypothesized that prostate enlargement due to benign prostatic hyperplasia mechanically impedes prostate cancer growth. Benign prostatic hyperplasia is a common disease in aging men that causes the prostate to enlarge progressively. Before our research, it was known that men with larger prostates tend to harbor prostatic tumors that grow more slowly.
However, the underlying mechanisms that explain this interaction between benign prostatic hyperplasia and prostate cancer are largely unknown. Our model indicated that benign prostatic hyperplasia may mechanically hinder prostate cancer growth by producing increasingly intense mechanical stresses in the prostate over time, which are known to slow down tumor dynamics.
This discovery suggests that reducing the prostate, through surgery or drugs, may be a bad idea because doing so could promote tumor growth. Science is an iterative, self-correcting process, and so is modeling. Our models will need to be refined and improved as we can obtain more and higher-quality data due to the ever-increasing quality of medical images. The biggest challenge involves collecting more information from medical images and incorporating that data into the model.
In an optimal outcome, medical doctors will have access to a database with a detailed description of our individual anatomy and physiology. We envision a future in which that database is updated frequently, and connected to algorithms that predict the onset or evolution of disease.
Hector Gomez, PhD
Professor, School of Mechanical Engineering
Professor, Weldon School of Biomedical Engineering (by courtesy)
College of Engineering, Purdue University
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