Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth

Andrea Hawkins-Daarud, Serge Prudhomme, Kristoffer G. van der Zee, J. Tinsley Oden

Research output: Contribution to journalArticlepeer-review

63 Scopus citations

Abstract

The idea that one can possibly develop computational models that predict the emergence, growth, or decline of tumors in living tissue is enormously intriguing as such predictions could revolutionize medicine and bring a new paradigm into the treatment and prevention of a class of the deadliest maladies affecting humankind. But at the heart of this subject is the notion of predictability itself, the ambiguity involved in selecting and implementing effective models, and the acquisition of relevant data, all factors that contribute to the difficulty of predicting such complex events as tumor growth with quantifiable uncertainty. In this work, we attempt to lay out a framework, based on Bayesian probability, for systematically addressing the questions of Validation, the process of investigating the accuracy with which a mathematical model is able to reproduce particular physical events, and Uncertainty quantification, developing measures of the degree of confidence with which a computer model predicts particular quantities of interest. For illustrative purposes, we exercise the process using virtual data for models of tumor growth based on diffuse-interface theories of mixtures utilizing virtual data.

Original languageEnglish (US)
Pages (from-to)1457-1485
Number of pages29
JournalJournal of Mathematical Biology
Volume67
Issue number6-7
DOIs
StatePublished - Dec 1 2013

Keywords

  • Bayesian probability
  • Calibration
  • Tumor growth models
  • Uncertainty quantification
  • Validation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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