Parameter sensitivity investigation of a mathematical model of glioma tumorigenesis mediated by platelet-derived growth factor
by
Susan Christine Massey
University of Washington
Coauthors: Peter Canoll, MD, PhD, Columbia University; Kristin Swanson, PhD, University of Washington

Gliomas are the most prevalent form of primary brain tumor in adults. Despite all possible treatment attempts, including aggressive surgical resection, these tumors are uniformly fatal. Dr. Peter Canoll at Columbia University has demonstrated that rats develop brain tumors closely resembling human gliomas when their glial progenitor cells are injected with a retrovirus expressing platelet-derived growth factor (PDGF). Most notably, at 17 days post infection only 30% of the tumor cells are infected progenitor cells—the other 70% are malignant uninfected progenitor cells, presumably recruited to the tumor by interactions with PDGF. Using the empirical data collected by his lab, we have developed a mathematical model to describe the observed tumor growth in this rat experiment. We used a sensitivity analysis technique incorporating latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCC) to vary parameters against each other and determine which parameters in the model are most influential upon the ratio of uninfected progenitor cells to total (infected and uninfected progenitors) in the tumor at day 17. Our investigation revealed that the two most influential parameters affecting the observed tumor growth pattern are the max proliferation rate of infected progenitors (and thus the amount of extra cellular PDGF available) and the max rate of consumption of PDGF by nearby uninfected progenitors. Specifically, even when controlling for variability in the other unknown model parameters, an increase in the max proliferation rate of the infected cell population results in an increase in the percentage of the cells at the core of the tumor that are recruited (rather than infected). This may suggest that more aggressive (highly proliferative) gliomas would have the most recruited cells within the tumor and may benefit most from PDGF targeted therapies (e.g., Gleevec). This is a novel insight that may help in patient selection for such targeted therapies. We are exploring the potential impact of PDGF targeted therapies on tumors with differing affinities for PDGF within the context of the current model and parallel experimentation. Our initial results suggest that this model may lead to a better understanding of what drugs may help glioma patients, by quantifying the relative importance of PDGF. Future work will also focus more on analyzing the model to look for PDGF influenced spatial migration patterns of the respective cells in the growing tumor to compare with observational studies tracking the migration of individual cells over several hours.

Date received: May 19, 2008