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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The Royal Society
2021-06-01
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Online Access: | https://royalsocietypublishing.org/doi/10.1098/rsos.202237 |
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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 |
_version_ |
1721375481904758784 |