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.

翻译：本研究是首次尝试利用数据驱动的微分模型来预测和控制癌症芯片实验的动力学行为。我们考虑一个概念化的一维装置，其中包含一个癌组织和一个白细胞群体。癌细胞与细胞群体之间的相互作用通过受Keller-Segel型方程启发的趋化模型进行建模，并采用杂交间断伽辽金方法求解。我们的目标是通过（合成）数据来调整控制方程的参数，并评估由于参数调整后残留的不确定性对动力学预测造成的影响。为此，我们应用了参数微分模型的不确定性量化技术。首先，我们同时使用Sobol指数和Morris指数进行全局敏感性分析，以评估参数不确定性如何影响模型预测，并固定影响可忽略的参数值。随后，我们通过贝叶斯技术进行逆向不确定性量化分析，计算剩余模型参数的数据驱动概率分布。最后，我们执行前向不确定性量化分析，以计算更新后的（残留）参数不确定性对模型关注量的影响。整个流程通过基于稀疏网格的代理模型来加速，该模型用于近似不确定参数到关注量的映射关系。