Institute for Mechanics of Materials and Structures, (TU Wien) Vienna University of Technology, Karlsplatz 13/202, 1040, Vienna, Austria.
Institute for Mechanics of Materials and Structures, (TU Wien) Vienna University of Technology, Karlsplatz 13/202, 1040, Vienna, Austria.
Comput Biol Med. 2021 Sep;136:104717. doi: 10.1016/j.compbiomed.2021.104717. Epub 2021 Aug 4.
When striving for reconstructing and predicting bone remodeling processes by means of mathematical models, cell population models have become a popular option. From a conceptual point of view, these models are able to take into account an arbitrary amount of regulatory mechanisms driving the development of bone cells and their activities. However, in most cases, the models include a large number of parameters; and most of those parameters cannot be measured, which certainly compromises the credibility of cell population models. Here, new insights are presented as to the potential improvement of this unsatisfactory situation. In particular, a previously published bone remodeling model was considered, and based on combination and merging of the original parameters, the total number of parameters could be reduced from 28 to 18, without impairing the model's versatility and significance. Furthermore, a comprehensive number of one- and two-variable sensitivity studies were performed, pointing out which parameters (alone and in combination with other parameters) influence the model predictions significantly - for that purpose, the mean squared relative error (MSRE) between simulations based on the original parameters and based on varied parameters was considered as failure measure. It has turned out that the model is significantly more sensitive to parameters which can be considered as phenomenological (such as differentiation, proliferation, and apoptosis rates) than to parameters which are directly related to specific processes (such as dissociation rate constants, and maximum concentrations of the involved factors). Using common correlation measures (such as Pearson, Spearman, and partial ranked correlation coefficients), correlation studies revealed that the correlations between most parameters and the MSRE are weak, while a few parameters exhibited moderate correlations. In conclusion, the results shown in this paper provide valuable insights concerning the design of new experiments allowing for measurement of the parameters which are most influential in the context of bone remodeling simulation.
当通过数学模型努力重建和预测骨重塑过程时，细胞群体模型已成为一种流行的选择。从概念上讲，这些模型能够考虑到驱动骨细胞及其活动的任意数量的调节机制。然而，在大多数情况下，模型包含大量的参数；而且大多数参数都无法测量，这无疑会影响细胞群体模型的可信度。本文提供了一些新的见解，旨在改善这种不理想的情况。特别是，考虑了之前发表的骨重塑模型，并基于原始参数的组合和合并，将参数总数从 28 减少到 18，而不会损害模型的通用性和重要性。此外，还进行了全面的单变量和双变量敏感性研究，指出了哪些参数（单独和组合）对模型预测有显著影响——为此，将基于原始参数和基于变化参数的模拟之间的均方相对误差（MSRE）作为失败衡量标准。结果表明，该模型对可视为现象学的参数（如分化、增殖和凋亡率）比与特定过程直接相关的参数（如解离速率常数和涉及因素的最大浓度）更敏感。使用常见的相关度量（如 Pearson、Spearman 和部分排序相关系数）进行相关研究，结果表明大多数参数与 MSRE 之间的相关性较弱，而少数参数则具有中等相关性。总之，本文的结果提供了有关设计新实验的有价值的见解，这些实验允许测量在骨重塑模拟中最具影响力的参数。
