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

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-dimension...

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Main Authors: Yunchen Xiao, Len Thomas, Mark A. J. Chaplain
Format: Article
Language:English
Published: The Royal Society 2021-06-01
Series:Royal Society Open Science
Subjects:
Online Access:https://royalsocietypublishing.org/doi/10.1098/rsos.202237
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spelling doaj-414db3ef018d43f68a3198388c70596d2021-06-16T07:05:52ZengThe Royal SocietyRoyal Society Open Science2054-57032021-06-018610.1098/rsos.202237Calibrating models of cancer invasion: parameter estimation using approximate Bayesian computation and gradient matchingYunchen Xiao0Len Thomas1Mark A. J. Chaplain2School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS UKSchool of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS UKSchool of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS UKWe 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.https://royalsocietypublishing.org/doi/10.1098/rsos.202237tumour cellscancer invasionapproximate Bayesian computationBhattacharyya distancegradient matchinggeneralized additive models
collection DOAJ
language English
format Article
sources DOAJ
author Yunchen Xiao
Len Thomas
Mark A. J. Chaplain
spellingShingle Yunchen Xiao
Len Thomas
Mark A. J. Chaplain
Calibrating models of cancer invasion: parameter estimation using approximate Bayesian computation and gradient matching
Royal Society Open Science
tumour cells
cancer invasion
approximate Bayesian computation
Bhattacharyya distance
gradient matching
generalized additive models
author_facet Yunchen Xiao
Len Thomas
Mark A. J. Chaplain
author_sort Yunchen Xiao
title Calibrating models of cancer invasion: parameter estimation using approximate Bayesian computation and gradient matching
title_short Calibrating models of cancer invasion: parameter estimation using approximate Bayesian computation and gradient matching
title_full Calibrating models of cancer invasion: parameter estimation using approximate Bayesian computation and gradient matching
title_fullStr Calibrating models of cancer invasion: parameter estimation using approximate Bayesian computation and gradient matching
title_full_unstemmed Calibrating models of cancer invasion: parameter estimation using approximate Bayesian computation and gradient matching
title_sort calibrating models of cancer invasion: parameter estimation using approximate bayesian computation and gradient matching
publisher The Royal Society
series Royal Society Open Science
issn 2054-5703
publishDate 2021-06-01
description 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.
topic tumour cells
cancer invasion
approximate Bayesian computation
Bhattacharyya distance
gradient matching
generalized additive models
url https://royalsocietypublishing.org/doi/10.1098/rsos.202237
work_keys_str_mv AT yunchenxiao calibratingmodelsofcancerinvasionparameterestimationusingapproximatebayesiancomputationandgradientmatching
AT lenthomas calibratingmodelsofcancerinvasionparameterestimationusingapproximatebayesiancomputationandgradientmatching
AT markajchaplain calibratingmodelsofcancerinvasionparameterestimationusingapproximatebayesiancomputationandgradientmatching
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