Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand.
PLoS One. 2012;7(7):e39721. doi: 10.1371/journal.pone.0039721. Epub 2012 Jul 3.
An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent) variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language) to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses) in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form.
多尺度建模的一个重要方面是能够以可以在建模者和工具之间交换的形式表示数学模型。虽然像 CellML 和 SBML 这样的语言的发展为数学模型提供了标准化的声明性交换格式，而与要应用于模型的算法无关，但迄今为止，这些标准尚未提供一种明确的机制来描述参数不确定性。参数不确定性是许多实际系统的固有特征。这种不确定性可能源于多种情况，例如：当测量包含固有误差时；当参数具有未知值并且建模者用概率分布替换它们时；当模型是来自群体的个体时，并且参数对于个体具有未知值，但对于群体的分布是已知的。我们提出并展示了一种通过利用 CellML 中提供的扩展机制在 CellML 模型中声明性地描述不确定性的方法。可以根据单变量连续概率密度函数或一个或多个变量（通常是非独立的）的多个实现来声明性地描述参数不确定性。我们还对 SED-ML（仿真实验描述标记语言）进行了扩展，以描述采样敏感性分析仿真实验。我们通过在不确定性标记语言中对示例模型进行编码，并通过在现有的 CellML 软件库 CellML API 实现中开发不确定性规范的软件实现（包括用于采样敏感分析的 SED-ML 扩展），演示了该方法的可用性。我们使用软件实现对模型进行采样敏感性分析，以证明在这种形式下对具有不确定性的模型进行有用的模拟是可能的。
