Data Assimilation in Brain Tumor Models
Data Assimilation in Brain Tumor Models
复制标题
脑肿瘤模型中的数据同化
DOI：
10.1007/978-1-4614-4178-6_9
复制
发表时间：
2013
影响因子：
1.4
通讯作者：
Nikolay L. Matirosyan
中科院分区：
文献类型：
--
作者：
Joshua M McDaniel;E. Kostelich;Y. Kuang;J. Nagy;M. Preul;N. Moore;Nikolay L. Matirosyan
应用数学和科学中的一个典型问题是在给定动力系统当前状态的情况下估计其未来状态。一种旨在理解决定系统行为的一个或多个方面的方法是数学建模。这种方法经常需要表述一组方程，通常是偏微分方程或常微分方程的系统。然后根据实验数据测量模型参数，或通过计算机模拟或其他方法估计模型参数，例如在[26]中完成的卡方参数优化或在神经科学[33]中经常使用的遗传算法。然后通过数学分析和数值模拟来研究模型的解，通常是为了对感兴趣的动力系统和任何可用的相关时间序列数据进行定性拟合。虽然数学建模可以提供有意义的见解，但由于模型的理想化假设，实验数据和参数的测量误差以及系统中的混沌行为，它的预测价值可能有限。在本章中，我们探索了一种不同的方法，专注于给定生物过程的模型和观测数据的最优状态估计，同时考虑了两者的相对不确定性。本病例探讨的是多形性胶质母细胞瘤（GBM）的生长和扩散，这是一种非常具有侵袭性的胶质瘤脑肿瘤，临床治疗仍然非常困难。所采用的方法不同于生物学中使用的其他方法，因为它不依赖于数学模型，而是寻求最佳初始条件。这与[21]中讨论的其他技术形成对比，这些技术依赖于模型，并寻求在给定观测值和感兴趣系统中的不确定性的情况下找到最佳模型参数化。
A typical problem in applied mathematics and science is to estimate the future state of a dynamical system given its current state. One approach aimed at understanding one or more aspects determining the behavior of the system is mathematical modeling. This method frequently entails formulation of a set of equations, usually a system of partial or ordinary differential equations. Model parameters are then measured from experimental data or estimated from computer simulation or other methods, for example chi-squared parameter optimization as done in[26] or genetic algorithms which are frequently used in neuroscience [33]. Solutions to the model are then studied through mathematical analysis and numerical simulation usually for qualitative fit to the dynamical system of interest and any relative time-series data that is available. While mathematical modeling can provide meaningful insight, it may have limited predictive value due to idealized assumptions underlying the model, measurement error in experimental data and parameters, and chaotic behavior in the system. In this chapter we explore a different approach focused on optimal state estimation given a model and observational data of a biological process, while accounting for the relative uncertainty in both. The case explored here is the growth and spread of glioblastoma multiforme (GBM), a very aggressive form of glioma brain tumor which remains extremely difficult to manage clinically. The method employed is different from other approaches used in biology in that it is independent of the mathematical model and seeks an optimal initial condition. This is in contrast to other techniques such as those discussed in [21], which are model dependent and seek to find an optimal model parameterization given the observations and uncertainties in the system of interest.