Journal of Mathematical Biology

, Volume 67, Issue 6–7, pp 1457–1485 | Cite as

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


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.


Bayesian probability Calibration Validation  Uncertainty quantification Tumor growth models 

Mathematics Subject Classification

03B42 35R60 35Q92 62F15 



The authors gratefully recognize the support by the Department of Energy under Award Number DE-FC52-08NA28615 and by the National Science Foundation under Grant No. 1115865. K.v.d.Z. also acknowledges the support of the Netherlands Organisation for Scientific Research (NWO) via the Innovational Research Incentives Scheme (IRIS), Veni grant 639.031.033. The authors also acknowledge useful discussions with Ivo Babuška, Hector Gomez, Luca Dede, and Jesse Windle.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andrea Hawkins-Daarud
    • 1
  • Serge Prudhomme
    • 2
  • Kristoffer G. van der Zee
    • 3
  • J. Tinsley Oden
    • 2
  1. 1.Northwestern UniversityChicagoUSA
  2. 2.The University of Texas at AustinAustinUSA
  3. 3.Eindhoven University of TechnologyEindhovenThe Netherlands

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