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Towards uncertainty quantification of a model for cancer-on-chip experiments

Silvia Bertoluzza, Vittoria Bianchi, Gabriella Bretti, Lorenzo Tamellini, Pietro Zanotti

TL;DR

The paper develops and demonstrates a complete uncertainty quantification workflow for a simplified one-dimensional cancer-on-chip model governed by Keller–Segel-type chemotaxis and solved with an HDG method. It uses synthetic data to perform global sensitivity analysis, Bayesian inversion, and forward UQ, all accelerated by sparse-grid surrogates. The study identifies the most influential parameters for the immune cell center of mass and chemoattractant, achieves a data-informed posterior via Gaussian or MCMC approaches, and shows meaningful uncertainty reduction in the quantities of interest, especially over time. The approach lays the groundwork for data-driven digital twins in cancer-on-chip experiments and points to future extensions to higher-dimensional geometries, more complex physics, and real experimental data calibration.

Abstract

This study is a first step towards using data-informed differential models to predict and control the dynamics of cancer-on-chip experiments. We consider a conceptualized one-dimensional device, containing a cancer and a population of white blood cells. The interaction between the cancer and the population of cells is modeled by a chemotaxis model inspired by Keller-Segel-type equations, which is solved by a Hybridized Discontinuous Galerkin method. Our goal is using (synthetic) data to tune the parameters of the governing equations and to assess the uncertainty on the predictions of the dynamics due to the residual uncertainty on the parameters remaining after the tuning procedure. To this end, we apply techniques from uncertainty quantification for parametric differential models. We first perform a global sensitivity analysis using both Sobol and Morris indices to assess how parameter uncertainty impacts model predictions, and fix the value of parameters with negligible impact. Subsequently, we conduct an inverse uncertainty quantification analysis by Bayesian techniques to compute a data-informed probability distribution of the remaining model parameters. Finally, we carry out a forward uncertainty quantification analysis to compute the impact of the updated (residual) parametric uncertainties on the quantities of interest of the model. The whole procedure is sped up by using surrogate models, based on sparse-grids, to approximate the mapping of the uncertain parameters to the quantities of interest.

Towards uncertainty quantification of a model for cancer-on-chip experiments

TL;DR

The paper develops and demonstrates a complete uncertainty quantification workflow for a simplified one-dimensional cancer-on-chip model governed by Keller–Segel-type chemotaxis and solved with an HDG method. It uses synthetic data to perform global sensitivity analysis, Bayesian inversion, and forward UQ, all accelerated by sparse-grid surrogates. The study identifies the most influential parameters for the immune cell center of mass and chemoattractant, achieves a data-informed posterior via Gaussian or MCMC approaches, and shows meaningful uncertainty reduction in the quantities of interest, especially over time. The approach lays the groundwork for data-driven digital twins in cancer-on-chip experiments and points to future extensions to higher-dimensional geometries, more complex physics, and real experimental data calibration.

Abstract

This study is a first step towards using data-informed differential models to predict and control the dynamics of cancer-on-chip experiments. We consider a conceptualized one-dimensional device, containing a cancer and a population of white blood cells. The interaction between the cancer and the population of cells is modeled by a chemotaxis model inspired by Keller-Segel-type equations, which is solved by a Hybridized Discontinuous Galerkin method. Our goal is using (synthetic) data to tune the parameters of the governing equations and to assess the uncertainty on the predictions of the dynamics due to the residual uncertainty on the parameters remaining after the tuning procedure. To this end, we apply techniques from uncertainty quantification for parametric differential models. We first perform a global sensitivity analysis using both Sobol and Morris indices to assess how parameter uncertainty impacts model predictions, and fix the value of parameters with negligible impact. Subsequently, we conduct an inverse uncertainty quantification analysis by Bayesian techniques to compute a data-informed probability distribution of the remaining model parameters. Finally, we carry out a forward uncertainty quantification analysis to compute the impact of the updated (residual) parametric uncertainties on the quantities of interest of the model. The whole procedure is sped up by using surrogate models, based on sparse-grids, to approximate the mapping of the uncertain parameters to the quantities of interest.
Paper Structure (29 sections, 49 equations, 17 figures, 4 tables)

This paper contains 29 sections, 49 equations, 17 figures, 4 tables.

Table of Contents

  1. Keywords
  2. AMS subject classification
  3. Introduction
  4. Contribution and outlook
  5. Organization
  6. Differential model and numerical approximation
  7. CoC experiment
  8. Differential model
  9. HDG solver
  10. Sparse grids surrogates
  11. UQ workflow
  12. General framework
  13. Sensitivity analysis
  14. Sobol indices.
  15. Morris indices.
  16. ...and 14 more sections

Figures (17)

  • Figure 1: Two-dimensional planimetry of the CoC device (left), with blue and red wells initially filled with cancer and immune cells, respectively. The area delimited in green (left) and zoomed in (right) is the monitored part during the laboratory experiment.
  • Figure 2: Schematic representation of the one-dimensional space domain with the initial profile of the chemoattractant source and of the immune cells distribution for a reference parameter combination.
  • Figure 3: Plot of sparse grids on $[-1,1]^N$ for $w=5$. Left: $N=2$, parameters with mutually independent uniform pdf. Center: $N=2$, parameters with mutually independent normal pdf with mean zero and standard deviation $\sigma=0.08$. Right: $N=3$, parameters with mutually independent uniform pdf.
  • Figure 4: Plot of $\mathtt{err}(\mathbf{y}, N_\mathtt{t}, N_\mathtt{s})$ for $12$ random samples $\mathbf{y} \in \Gamma$ (one line per sample). Left: error versus $N_\mathtt{t}$ with fixed $N_\mathtt{s} = 2^8$. Right: error versus $N_\texttt{s}$ with fixed $N_\mathtt{t} = 2^{13}$. The vertical dotted lines indicate the values of $N_\mathtt{t}$ and $N_\mathtt{s}$ fixed in \ref{['eq:HDG-solver-hyperparameters']} for the subsequent analysis.
  • Figure 5: Maximum and root mean square of the relative discrepancy versus the sparse-grid level $w$ for the QoIs $M$ (left) and $I$ (right). The vertical dotted lines indicate the value of $w$ fixed in \ref{['eq:w-fixed']} for the subsequent analysis.
  • ...and 12 more figures

Theorems & Definitions (1)

  • Remark 1