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A Bayesian sequential learning framework to parameterise continuum models of melanoma invasion into human skin

Alexander P Browning, Parvathi Haridas, View ORCID ProfileMatthew J Simpson
doi: https://doi.org/10.1101/284612
Alexander P Browning
1School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia
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Parvathi Haridas
2Institute of Health and Biomedical Innovation, QUT, Kelvin Grove, Australia
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Matthew J Simpson
3School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia
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Abstract

We present a novel framework to parameterise a mathematical model of cell invasion that describes how a population of melanoma cells invades into human skin tissue. Using simple experimental data extracted from complex experimental images, we estimate three model parameters: (i) the melanoma cell proliferation rate, λ; (ii) the melanoma cell diffusivity, D; and (iii) δ, a constant that determines the rate that melanoma cells degrade the skin tissue. The Bayesian sequential learning framework involves a sequence of increasingly-sophisticated experimental data from: (i) a spatially uniform cell proliferation assay; (ii) a two-dimensional circular barrier assay; and, (iii) a three-dimensional invasion assay. The Bayesian sequential learning approach leads to well-defined parameter estimates. In contrast, taking a naive approach that attempts to estimate all parameters from a single set of images from the same experiment fails to produce meaningful results. Overall our approach to inference is simple-to-implement, computationally efficient, and well-suited for many cell biology phenomena that can be described by low dimensional continuum models using ordinary differential equations and partial differential equations. We anticipate that this Bayesian sequential learning framework will be relevant in other biological contexts where it is challenging to extract detailed, quantitative biological measurements from experimental images and so we must rely on using relatively simple measurements from complex images.

Footnotes

  • E-mail: matthew.simpson{at}qut.edu.au

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Posted August 07, 2018.
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A Bayesian sequential learning framework to parameterise continuum models of melanoma invasion into human skin
Alexander P Browning, Parvathi Haridas, Matthew J Simpson
bioRxiv 284612; doi: https://doi.org/10.1101/284612
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A Bayesian sequential learning framework to parameterise continuum models of melanoma invasion into human skin
Alexander P Browning, Parvathi Haridas, Matthew J Simpson
bioRxiv 284612; doi: https://doi.org/10.1101/284612

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