向癌症芯片实验模型的不确定性量化迈进
Towards uncertainty quantification of a model for cancer-on-chip experiments
AI总结：
本文提出利用数据驱动方法对癌症芯片实验模型进行不确定性量化，通过敏感性分析、贝叶斯技术及代理模型减少参数不确定性影响。
摘要：
本文是使用数据驱动的微分模型预测和控制癌症芯片实验动态的第一步。我们考虑了一个一维装置，包含癌细胞和白血细胞群体。癌细胞与白血细胞群体的相互作用通过受Keller-Segel型方程启发的趋化模型进行建模，该模型通过混合不连续伽辽金方法求解。我们的目标是利用（合成）数据来调整主导方程的参数，并评估由于参数调整后仍存在的残余不确定性对动态预测的不确定性影响。为此，我们应用了参数微分模型的不确定性量化技术。首先，我们使用Sobol和Morris指数进行全局敏感性分析，以评估参数不确定性对模型预测的影响，并固定对预测影响微乎其微的参数值。随后，我们通过贝叶斯技术进行逆不确定性量化分析，以计算剩余模型参数的数据驱动概率分布。最后，我们进行正向不确定性量化分析，以计算更新（残余）参数不确定性对模型感兴趣的量的影响。整个过程通过使用基于稀疏网格的代理模型来加速，以近似不确定参数到感兴趣量的映射。
英文摘要：
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.
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