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

Yunchen Xiao*, Len Thomas, Mark Andrew Joseph Chaplain

*Corresponding author for this work

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Abstract

We present two different methods to estimate parameters within a partial differential equation model of cancer invasion. The model describes the spatio-temporal evolution of three variables—tumour cell density, extracellular matrix density and matrix degrading enzyme concentration—in a one-dimensional tissue domain. The first method is a likelihood-free approach associated with approximate Bayesian computation; the second is a two-stage gradient matching method based on smoothing the data with a generalized additive model (GAM) and matching gradients from the GAM to those from the model. Both methods performed well on simulated data. To increase realism, additionally we tested the gradient matching scheme with simulated measurement error and found that the ability to estimate some model parameters deteriorated rapidly as measurement error increased.
Original languageEnglish
Article number202237
Number of pages17
JournalRoyal Society Open Science
Volume8
Issue number6
DOIs
Publication statusPublished - 16 Jun 2021

Keywords

  • Tumour cells
  • Cancer invasion
  • Metastasis
  • Approximate Bayesian computation
  • Bhattacharyya distance
  • Gradient matching
  • Generalized additive models

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