Accurate state estimation from uncertain data and models: An application of data assimilation to mathematical models of human brain tumors

Eric Kostelich, Yang Kuang, Joshua M. McDaniel, Nina Z. Moore, Nikolay L. Martirosyan, Mark C. Preul

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

Background: Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.Results: We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.Conclusions: The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.Reviewers: This article was reviewed by Anthony Almudevar, Tomas Radivoyevitch, and Kristin Swanson (nominated by Georg Luebeck).

Original languageEnglish (US)
Article number64
JournalBiology Direct
Volume6
DOIs
StatePublished - Dec 21 2011

Keywords

  • Data assimiliation
  • Glioblastoma multiforme
  • Mathematical models
  • State estimation

ASJC Scopus subject areas

  • Immunology
  • Ecology, Evolution, Behavior and Systematics
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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