Weather forecasting models could predict brain tumor growth

Ever wondered how meteorologists can accurately predict the weather? They use complex spatiotemporal weather models – mathematical equations that track the motions of the atmosphere through time and space and combine them with incoming data streams from weather stations and satellites. Now, a new study published in the open access journal Biology Direct has determined that the mathematical methodology used to assimilate data for weather forecasting could be used to predict the spread of brain tumors.

The authors from Arizona State University and the Barrow Neurological Institute in Phoenix, Arizona, wanted to prove that mathematical methods used in weather prediction could be useful in clinical situations – not just in brain cancer, but also in other cancers and diseases. They chose to study glioblastoma multiforme, a malignant brain cancer.

Glioblastoma multiforme is the most common and most aggressive of the brain cancers. It is largely resistant to chemotherapy and radiotherapy and can quickly invade large, sensitive regions of the brain, which makes it almost impossible to remove via surgery and almost certain to recur afterwards. An average patient’s survival is less than 15 months from initial diagnosis. Because little progress has been made in its treatment and its dynamics involve complex geometry, the glioblastoma is a particularly good cancer with which to test a mathematical model.

In addition to setting out to prove that good quantitative predictions of the glioblastoma’s growth and spread are possible, the lead authors, Eric Kostelich, a professor in the School of Mathematical and Statistical Sciences in ASU’s College of Liberal Arts and Sciences, and Mark Preul with Barrow Neurological Institute, wanted to provide uncertainty estimates. An algorithm previously developed for numerical weather prediction – a modern state estimation algorithm known as a Local Ensemble Transform Kalman Filter (LETKF) – was applied to two different mathematical models of the growth and spread of glioblastoma. Synthetic magnetic resonance images of a hypothetical tumor were used for this purpose.

Data assimilation techniques were then used to update the state vector – the initial condition of the glioblastoma growth model – combining new observations with one or more prior forecasts. The team then measured the feasibility of the model in individual patient cases for making short-term (60-day) forecasts of the cancer’s spread and growth.

Despite this being a preliminary study, the authors were successful in demonstrating the feasibility of LETKF for short-term, clinically relevant predictions of the growth and spread of malignant brain tumors. This type of forecasting and data assimilation provides an accurate and computationally efficient way of updating the initial condition (state vector) of a complex spatiotemporal model with new quantitative measurements. The intelligent model can also take into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging.

Preul believes that the algorithm should be considered for future efforts that use mathematical models for clinical purposes in individual patient cases.

"Though work remains before our approach can be seriously considered in clinical settings, an accurate forecast system for glioblastoma may prove useful for treatment planning and patient counseling," he said.

“This work with Dr. Preul and his group combines the strengths of ASU's School of Mathematical and Statistical Science's faculty in nonlinear dynamics, atmospheric science and mathematical biology with the world-class clinical and laboratory capabilities of the Barrow Neurological Institute," Kostelich said.

"It's exciting that interdisciplinary investigations can lead to novel research directions, and I am grateful that ASU encourages these kinds of collaborations."