Patient-specific parameter estimates of glioblastoma multiforme growth dynamics from a model with explicit birth and death rates

Lifeng Han, Steffen Eikenberry, Changhan He, Lauren Johnson, Mark C. Preul, Eric J. Kostelich, Yang Kuang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Glioblastoma multiforme (GBM) is an aggressive primary brain cancer with a grim prognosis. Its morphology is heterogeneous, but prototypically consists of an inner, largely necrotic core surrounded by an outer, contrast-enhancing rim, and often extensive tumor-associated edema beyond. This structure is usually demonstrated by magnetic resonance imaging (MRI). To help relate the three highly idealized components of GBMs (i.e., necrotic core, enhancing rim, and maximum edema extent) to the underlying growth “laws,” a mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. This model generates a traveling-wave solution that mimics tumor progression. We develop several novel methods to approximate key characteristics of the wave profile, which can be compared with MRI data. Several simplified forms of growth and death terms and their parameter identifiability are studied. We use several test cases of MRI data of GBM patients to yield personalized parameterizations of the model, and the biological and clinical implications are discussed.

Original languageEnglish (US)
Pages (from-to)5307-5323
Number of pages17
JournalMathematical Biosciences and Engineering
Volume16
Issue number5
DOIs
StatePublished - 2019

Keywords

  • Glioblastoma multiforme
  • Parameter estimation
  • Patient-specific models
  • Reaction-diffusion models

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

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