Abstract

The objective of this work was to estimate parameters of a model for diode-laser heating of a culture of cancer cells under the effects of a chemotherapy drug. Two mathematical models were proposed to represent the physical problem during heating: natural convection was considered in the high-fidelity model, while the low-fidelity model was given by a lumped system. The thermal damage caused in the cells by the heating was modeled as a first-order reaction. A Bayesian approach was applied to estimate model parameters with the Markov Chain Monte Carlo (MCMC) method, which was implemented with the Metropolis-Hastings algorithm. The Approximation Error Model (AEM) approach was used to speed up calculations for the inverse problem solution when the high-fidelity model was replaced by the low-fidelity model for the computation of dependent variables. Monte Carlo direct simulations were also performed to compute the transient variation of the number of cells during periods before and after the imposed heating.

摘要

这项工作的目的是估计在化疗药物作用下对癌细胞培养物进行二极管激光加热的模型参数。提出了两种数学模型来表示加热过程中的物理问题：高保真模型中考虑了自然对流，而集总系统给出了低保真模型。由加热在电池中引起的热损伤被建模为一级反应。贝叶斯方法被应用于使用马尔可夫链蒙特卡罗 (MCMC) 方法估计模型参数，该方法是用 Metropolis-Hastings 算法实现的。当高保真模型被低保真模型取代以计算因变量时，近似误差模型 (AEM) 方法用于加速逆问题解的计算。