College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK.
Living Systems Institute, University of Exeter, Exeter, UK.
PLoS Comput Biol. 2018 Mar 2;14(3):e1006009. doi: 10.1371/journal.pcbi.1006009. eCollection 2018 Mar.
Neural mass models (NMMs) are increasingly used to uncover the large-scale mechanisms of brain rhythms in health and disease. The dynamics of these models is dependent upon the choice of parameters, and therefore it is crucial to be able to understand how dynamics change when parameters are varied. Despite being considered low dimensional in comparison to micro-scale, neuronal network models, with regards to understanding the relationship between parameters and dynamics, NMMs are still prohibitively high dimensional for classical approaches such as numerical continuation. Therefore, we need alternative methods to characterise dynamics of NMMs in high dimensional parameter spaces. Here, we introduce a statistical framework that enables the efficient exploration of the relationship between model parameters and selected features of the simulated, emergent model dynamics of NMMs. We combine the classical machine learning approaches of trees and random forests to enable studying the effect that varying multiple parameters has on the dynamics of a model. The method proceeds by using simulations to transform the mathematical model into a database. This database is then used to partition parameter space with respect to dynamic features of interest, using random forests. This allows us to rapidly explore dynamics in high dimensional parameter space, capture the approximate location of qualitative transitions in dynamics and assess the relative importance of all parameters in the model in all dimensions simultaneously. We apply this method to a commonly used NMM in the context of transitions to seizure dynamics. We find that the inhibitory sub-system is most crucial for the generation of seizure dynamics, confirm and expand previous findings regarding the ratio of excitation and inhibition, and demonstrate that previously overlooked parameters can have a significant impact on model dynamics. We advocate the use of this method in future to constrain high dimensional parameter spaces enabling more efficient, person-specific, model calibration.
神经质量模型（NMM）越来越多地用于揭示健康和疾病中大脑节律的大规模机制。这些模型的动力学取决于参数的选择，因此，能够理解参数变化时动力学如何变化至关重要。尽管与微观尺度的神经元网络模型相比，NMM 在维度上被认为较低，但就理解参数和动力学之间的关系而言，对于经典方法（如数值连续）来说，NMM 仍然过高维。因此，我们需要替代方法来描述高维参数空间中的 NMM 动力学。在这里，我们引入了一个统计框架，使我们能够有效地探索模型参数与 NMM 模拟涌现模型动力学的选定特征之间的关系。我们结合了树和随机森林等经典机器学习方法，以研究多个参数变化对模型动力学的影响。该方法通过使用模拟将数学模型转换为数据库。然后，该数据库用于使用随机森林根据感兴趣的动态特征对参数空间进行分区。这使我们能够快速探索高维参数空间中的动力学，捕获动力学中定性转变的近似位置，并同时评估模型中所有参数在所有维度上的相对重要性。我们将这种方法应用于癫痫发作动力学转变的背景下常用的 NMM。我们发现，抑制子系统对癫痫发作动力学的产生最为关键，证实并扩展了关于兴奋和抑制比例的先前发现，并表明以前被忽视的参数可能对模型动力学产生重大影响。我们提倡在未来使用这种方法来约束高维参数空间，从而实现更高效、特定于个体的模型校准。
