Identifiability and sensitivity analysis of heterogeneous cell population models
Identifiability and sensitivity analysis of heterogeneous cell population models
复制标题
异质细胞群模型的可识别性和敏感性分析
DOI：
10.18419/opus-4562
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Shen Zeng
中科院分区：
文献类型：
--
作者：
Shen Zeng
在这篇论文中，我们引入了新的概念，异质细胞群体的建模和分析。异质细胞群体可以解释为具有异质参数和初始条件的结构相同的细胞的大群体。它们出现在生物系统中，如高等生物的组织或微生物的菌落。
用于对异质细胞群体进行建模的公知方法是所谓的基于密度的方法，其中异质细胞群体的状态由细胞状态的概率密度给出。在这种方法中，概率密度的演化是以偏微分方程的形式给出的。我们扩展这种方法通过测量理论的考虑，它利用了问题的概率性质。这一新的分析的结果是一个框架，其中密度的演变是由运营商描述。
异质细胞群体模型分析的关键任务之一是参数估计。对于异质细胞群体，我们希望估计参数和初始条件的概率密度。然而，为了能够执行参数估计，总是需要系统的特定可识别性属性。本文首次提出了异质细胞群体模型的结构可识别性概念。研究表明，这一概念与相应单细胞模型的可观测性密切相关。这两个概念之间的联系进行了研究，并在一个具体的例子说明。
本文的第二个重点是对一类异质细胞群体模型进行灵敏度分析。在这里，我们研究相对于参数和初始条件的概率密度的变化或误指定的灵敏度。
In this thesis, we introduce novel concepts to the modeling and analysis of heterogeneous cell populations. Heterogeneous cell populations can be interpreted as large populations of structurally identical cells with heterogeneous parameters and initial conditions. They appear in biological systems such as tissues of higher organisms or colonies of microorganisms.
A well-known approach for the modeling of heterogeneous cell populations is the so called density-based approach, in which the state of a heterogeneous cell population is given by the probability density of the cell states. The evolution of the probability densities is in this approach given in terms of a partial differential equation. We extend this approach via a measure theoretical consideration, which exploits the probabilistic nature of the problem. The result of this novel ansatz is a framework in which the evolution of densities is described by operators.
One of the key tasks in the analysis of heterogeneous cell population models is parameter estimation. For heterogeneous cell populations we want to estimate the probability density of parameters and initial conditions. However, to be able to perform parameter estimation, one always needs specific identifiability properties of a system. We formulate for the first time the concept of structural identifiability of a heterogeneous cell population model. It is revealed that this concept is closely related to observability of the corresponding single cell model. The connection between both concepts is studied and illuminated in a concrete example.
The second emphasis of this thesis is the implementation of sensitivity analysis to the class of heterogeneous cell population models. Here we study sensitivity with respect to variations or misspecifications in the probability density of parameters and initial conditions.
影响因子：
3
作者：
Hasenauer J;Waldherr S;Doszczak M;Radde N;Scheurich P;Allgöwer F
通讯作者：
Allgöwer F