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Calibrating models of cancer invasion: parameter estimation using approximate Bayesian computation and gradient

Yunchen Xiao1, Len Thomas1, Mark A J Chaplain1

  • 1School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS UK.

Royal Society Open Science
|June 21, 2021
PubMed
Summary

We developed two computational methods to model cancer invasion. Both approximate Bayesian computation and gradient matching accurately estimated parameters in simulated data, but gradient matching struggled with measurement errors.

Keywords:
Bhattacharyya distanceapproximate Bayesian computationcancer invasiongeneralized additive modelsgradient matchingtumour cells

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Area of Science:

  • Computational biology
  • Mathematical modeling
  • Cancer research

Background:

  • Cancer invasion is a complex spatio-temporal process.
  • Mathematical models, specifically partial differential equations (PDEs), are crucial for understanding cancer invasion dynamics.
  • Accurate parameter estimation is vital for refining these PDE models.

Purpose of the Study:

  • To present and evaluate two distinct computational methods for estimating parameters in a PDE model of cancer invasion.
  • To assess the performance of these methods using simulated data.
  • To investigate the impact of measurement error on parameter estimation accuracy.

Main Methods:

  • Developed a PDE model simulating tumor cell density, extracellular matrix density, and enzyme concentration.
  • Implemented a likelihood-free approach using approximate Bayesian computation (ABC).
  • Applied a two-stage gradient matching method involving generalized additive models (GAMs).

Main Results:

  • Both approximate Bayesian computation and gradient matching methods showed good performance with simulated data.
  • The gradient matching method's parameter estimation ability significantly degraded with increasing simulated measurement error.
  • The study highlights the sensitivity of parameter estimation to data quality.

Conclusions:

  • Two viable computational methods, ABC and gradient matching, can be used for parameter estimation in cancer invasion PDE models.
  • Gradient matching is sensitive to measurement error, suggesting a need for robust data preprocessing or alternative methods when dealing with noisy experimental data.
  • Further research should focus on developing error-resilient parameter estimation techniques for complex biological models.