School of Psychology, University of Nottingham, Nottingham, United Kingdom.
Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft, The Netherlands; Brain Center Rudolf Magnus, Department of Psychiatry, University Medical Center Utrecht, Utrecht, The Netherlands.
Neuroimage. 2018 Feb 1;166:371-384. doi: 10.1016/j.neuroimage.2017.11.016. Epub 2017 Nov 11.
There is an increasing awareness of the advantages of multi-modal neuroimaging. Networks obtained from different modalities are usually treated in isolation, which is however contradictory to accumulating evidence that these networks show non-trivial interdependencies. Even networks obtained from a single modality, such as frequency-band specific functional networks measured from magnetoencephalography (MEG) are often treated independently. Here, we discuss how a multilayer network framework allows for integration of multiple networks into a single network description and how graph metrics can be applied to quantify multilayer network organisation for group comparison. We analyse how well-known biases for single layer networks, such as effects of group differences in link density and/or average connectivity, influence multilayer networks, and we compare four schemes that aim to correct for such biases: the minimum spanning tree (MST), effective graph resistance cost minimisation, efficiency cost optimisation (ECO) and a normalisation scheme based on singular value decomposition (SVD). These schemes can be applied to the layers independently or to the multilayer network as a whole. For correction applied to whole multilayer networks, only the SVD showed sufficient bias correction. For correction applied to individual layers, three schemes (ECO, MST, SVD) could correct for biases. By using generative models as well as empirical MEG and functional magnetic resonance imaging (fMRI) data, we further demonstrated that all schemes were sensitive to identify network topology when the original networks were perturbed. In conclusion, uncorrected multilayer network analysis leads to biases. These biases may differ between centres and studies and could consequently lead to unreproducible results in a similar manner as for single layer networks. We therefore recommend using correction schemes prior to multilayer network analysis for group comparisons.
人们越来越意识到多模态神经影像学的优势。来自不同模态的网络通常是孤立处理的，但这与越来越多的证据相矛盾，这些证据表明这些网络存在着非平凡的相互依存关系。即使是来自单一模态的网络，如从脑磁图（MEG）测量得到的特定频带的功能网络，也通常是独立处理的。在这里，我们讨论了多层网络框架如何将多个网络集成到单个网络描述中，以及如何应用图度量来量化多层网络组织以进行组比较。我们分析了单层层网络中众所周知的偏差，例如连接密度和/或平均连通性的组间差异的影响如何影响多层网络，并比较了四种旨在纠正这些偏差的方案：最小生成树（MST）、有效图电阻成本最小化、效率成本优化（ECO）和基于奇异值分解（SVD）的归一化方案。这些方案可以独立应用于各层，也可以应用于整个多层网络。对于应用于整个多层网络的校正，只有 SVD 显示出足够的偏差校正。对于应用于各个层的校正，有三种方案（ECO、MST、SVD）可以纠正偏差。通过使用生成模型以及经验性 MEG 和功能磁共振成像（fMRI）数据，我们进一步证明，所有方案都可以在原始网络受到干扰时识别网络拓扑。总之，未经校正的多层网络分析会产生偏差。这些偏差可能因中心和研究而异，因此可能会以类似于单层层网络的方式导致不可重复的结果。因此，我们建议在进行组比较之前，使用校正方案进行多层网络分析。
