title: Accurate state estimation from uncertain data and models: an application of data assimilation to mathematical models of human brain tumors.
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.
  
  
  METHODS
  This article was reviewed by Anthony Almudevar, Tomas Radivoyevitch, and Kristin Swanson (nominated by Georg Luebeck).
authors.affiliation: School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, USA. kostelich@asu.edu
authors.forename: Eric J
authors.initials: EJ
authors.lastname: Kostelich
authors.forename: Yang
authors.initials: Y
authors.lastname: Kuang
authors.forename: Joshua M
authors.initials: JM
authors.lastname: McDaniel
authors.forename: Nina Z
authors.initials: NZ
authors.lastname: Moore
authors.forename: Nikolay L
authors.initials: NL
authors.lastname: Martirosyan
authors.forename: Mark C
authors.initials: MC
authors.lastname: Preul
mesh_terms: D000465:Algorithms; D001932:Brain Neoplasms / Q000000981:diagnostic imaging / Q000473:pathology*; D003198:Computer Simulation; D005544:Forecasting / Q000379:methods*; D005909:Glioblastoma / Q000000981:diagnostic imaging / Q000473:pathology*; D006801:Humans; D008279:Magnetic Resonance Imaging; D008495:Medical Oncology / Q000379:methods*; D008954:Models, Biological; D013997:Time Factors; D014463:Ultrasonography; D035501:Uncertainty