Can mathematical models predict cancer progression?
Mathematicians from Duke University are looking for ways to aid doctors in predicting the way different types of cancers complicate even if the measurements of tumor growth are very difficult to acquire.
In the United States, around one in three people will be diagnosed with cancer at some point. In order to properly treat these patients, accurate predictions of tumor growth are needed in order to assess the type of treatment needed, treatment frequency and dose, and whether a treatment is effective.
According to Duke University Mathematics professor Richard Durrett, who is the lead author of the study, “Mathematical models can help inform a whole host of cancer treatment decisions, but you need an accurate model”.
There have already been multiple mathematical models that were proposed for tumor growth. However, which model is appropriate for which type of cancer is the main concern at present.
Co-author Anne Talkington says that there are some tumors that start to slow down their growth or even stop growing when they reach a certain size, but there are others that still continue to increase in size.
One of the issues of most of these tumor prediction models is that the majority of them are calibrated from tumors growing in mice or in the lab, where conditions such as oxygen supply and nutrients are not the same as compared to that in the human body. Unfortunately, most cancer patients have to undergo treatment or surgery soon after diagnosis, and similar data from humans are hard to acquire.
Models of Tumor Growth
In Durrett and Talkington’s paper published in Bulletin of Mathematical Biology, they discussed on how you can compare common mathematical models of tumor growth with the use of only two time-point measurements of tumor size, which is just usually the data that can be acquired from patients before they begin their treatment.
Because of the fact that they had to work with data from actual patients, they had no choice but to work on the two data points. Although the usual impression is that just two points are not enough, examining trends in growth rates in when the models are fit to tumors of differing sizes allows successful supposition of the best model.
In order to confirm if their method was indeed correct, they searched previous literature for data from cancer patients whose tumors sizes were measured at two points before the start of their treatment, and the measurements came either from mammograms, MRIs or CT scans.
According to their results, breast and liver tumors grow at a very fast rate while the tumors are still small in size. Durrett compares this to “money in a savings account that earns a fixed interest rate”.
In contrast, two types of brain tumors were found to grow the two-thirds power law. This was consistent with the fact that actually only cells on the surface of the tumor are able to proliferate.
Talkington also states that “Some bias has been introduced by the way the data were obtained, but our
results indicate that the method is useful for determining which tumor growth models work best for
different types of cancer”.
To know more about ways on how to predict cancer progression, feel free to browse more articles on this site.
Written by: Yevgeny Aster Dulla, MSc