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Estimating intratumoral heterogeneity from spatiotemporal data

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Abstract

Glioblastoma multiforme (GBM) is a malignant brain cancer with a tendency to both migrate and proliferate. We propose modeling GBM with heterogeneity in cell phenotypes using a random differential equation version of the reaction–diffusion equation, where the parameters describing diffusion (D) and proliferation (\(\rho \)) are random variables. We investigate the ability to perform the inverse problem to recover the probability distributions of D and \(\rho \) using the Prohorov metric, for a variety of probability distribution functions. We test the ability to perform the inverse problem for noisy synthetic data. We then examine the predicted effect of treatment, specifically, chemotherapy, when assuming such a heterogeneous population and compare with predictions from a homogeneous cell population model.

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Authors and Affiliations

  1. Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University, Raleigh, USA

    E. M. Rutter, H. T. Banks & K. B. Flores

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  1. E. M. Rutter
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  2. H. T. Banks
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  3. K. B. Flores
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Correspondence to K. B. Flores.

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In memory of Karl Hadeler, for his inspiring research and teaching, and dedication to mentoring.

This research was supported in part by the Air Force Office of Scientific Research under Grant Number AFOSR FA9550-15-1-0298 and in part by the National Science Foundation under NSF Grant Number DMS-0946431.

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Rutter, E.M., Banks, H.T. & Flores, K.B. Estimating intratumoral heterogeneity from spatiotemporal data. J. Math. Biol. 77, 1999–2022 (2018). https://doi.org/10.1007/s00285-018-1238-6

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  • DOI: https://doi.org/10.1007/s00285-018-1238-6

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