Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN 47907, USA.
Bull Math Biol. 2012 Mar;74(3):688-716. doi: 10.1007/s11538-011-9686-9. Epub 2011 Oct 12.
Model-based experiment design specifies the data to be collected that will most effectively characterize the biological system under study. Existing model-based design of experiment algorithms have primarily relied on Fisher Information Matrix-based methods to choose the best experiment in a sequential manner. However, these are largely local methods that require an initial estimate of the parameter values, which are often highly uncertain, particularly when data is limited. In this paper, we provide an approach to specify an informative sequence of multiple design points (parallel design) that will constrain the dynamical uncertainty of the biological system responses to within experimentally detectable limits as specified by the estimated experimental noise. The method is based upon computationally efficient sparse grids and requires only a bounded uncertain parameter space; it does not rely upon initial parameter estimates. The design sequence emerges through the use of scenario trees with experimental design points chosen to minimize the uncertainty in the predicted dynamics of the measurable responses of the system. The algorithm was illustrated herein using a T cell activation model for three problems that ranged in dimension from 2D to 19D. The results demonstrate that it is possible to extract useful information from a mathematical model where traditional model-based design of experiments approaches most certainly fail. The experiments designed via this method fully constrain the model output dynamics to within experimentally resolvable limits. The method is effective for highly uncertain biological systems characterized by deterministic mathematical models with limited data sets. Also, it is highly modular and can be modified to include a variety of methodologies such as input design and model discrimination.
基于模型的实验设计指定了要收集的数据，这些数据将最有效地描述研究中的生物系统。现有的基于模型的实验设计算法主要依赖于 Fisher 信息矩阵方法，以便按顺序选择最佳实验。然而，这些方法在很大程度上是局部方法，需要初始参数值估计，而这些估计通常非常不确定，尤其是在数据有限的情况下。在本文中，我们提供了一种指定多个设计点（并行设计）的信息序列的方法，该方法将约束生物系统响应的动态不确定性，使其处于可通过实验检测到的限制范围内，如估计的实验噪声所指定的。该方法基于计算效率高的稀疏网格，仅需要有界的不确定参数空间；它不依赖于初始参数估计。设计序列通过使用实验设计点的情景树来选择，以最小化系统可测量响应的预测动态中的不确定性。该算法通过使用三种从 2D 到 19D 不等维度的 T 细胞激活模型来说明。结果表明，即使在传统的基于模型的实验设计方法最有可能失败的情况下，也有可能从数学模型中提取有用信息。通过这种方法设计的实验将模型输出动态完全约束在可实验分辨的限制内。该方法对于具有有限数据集的确定性数学模型的高度不确定生物系统非常有效。此外，它具有高度的模块化，可以修改为包括各种方法，如输入设计和模型鉴别。
