Null models in network neuroscience

This introduction will provide a brief overview of the wide range of null models in network neuroscience and motivate their relevance. I will emphasise the spectrum of null models, from liberal models that control few network properties, to conservative models that recapitulate multiple properties of empirical networks. I will also highlight the fact that null models are a method of systematically sampling a larger space of potential networks, and situating the observed brain network in this space. These general ideas are relevant across different types of null models and analysis scenarios, which will be explored in greater detail in subsequent educational presentations.  

I will introduce and demonstrate connectome rewiring algorithms to generate null models. I will begin by describing the key requirements of a rewiring algorithm, including computational efficiency and preservation of basic topological properties, and introduce the Maslov-Sneppen rewiring method. I will then briefly overview advanced rewiring algorithms that are suited to weighted and directed connectivity measures. Examples will be provided to demonstrate the application of various rewiring algorithms to hypothesis testing on the connectome. I will conclude with key recommendations and best practices for the use of rewiring algorithms in network neuroscience and provide a summary of relevant computer codes and packages. My presentation is suited for newcomers to the field and researchers with basic experience. 

Brain networks are high-dimensional (many nodes, many edges) and their topological features summarized succinctly using network and graph-theoretic metrics. It is commonplace to test whether topological feature X could be explained by chance using network-based null models—most often rewiring based models that hold constant low-level features of the network, e.g. density and degree sequence, but otherwise randomize its edges.

Generative models, in contrast, seek to construct synthetic networks based on a set of (simple) mechanistic and generative rules. The synthetic networks can then be compared to the empirical/observed network in terms of their topological features. In general, the aim of generative modeling is to minimize the reconstruction error between the synthetic and observed network. Their wiring rules are variable and typically specified by the user, making it possible to adjudicate between distinct hypotheses of network formation, growth, and evolution.

In this talk I will review several classical generative models in network science—“random graphs”, small-world, preferential attachment, and geometric models. I will focus on a class of generative models that have been applied widely to brain network data. Briefly, these models balance wiring cost minimization and topology to achieve a broad correspondence between synthetic and observed brain networks. I will close by discussing future directions for generative modeling of brain network data. 

Neural activity and functional interactions among neuronal populations are naturally variable from moment to moment, resulting in dynamic configurations of brain activity. Vast and interdisciplinary time-series analysis literature provides computational tools that are used to characterize temporal structure of neural activity, mapping neural dynamics to anatomical and functional brain architecture. Null models of neural time-series are algorithms that generate surrogate time-series, preserving certain temporal characteristics of neural signals while disturbing others. The generated surrogate data can then be used to statistically assess dynamical properties of neural activity and functional brain organization. In this talk, I will introduce commonly used null models of time-series in human neuroimaging, including phase randomization and auto-regressive null models that preserve temporal structure of the signal, and spatiotemporal null models that preserve the inherent spatial autocorrelation of the brain in addition to temporal features of neural activity. I will demonstrate examples of these algorithms and their applications for hypothesis testing in neural time-series analysis. I will conclude by overviewing advantages and disadvantages of using each framework and will provide resources and recommendations for best practices in time-series null model testing in human neuroimaging data analysis. 

Imaging technologies are increasingly used to generate high-resolution maps of brain structure and function. Comparing these brain maps with one another is becoming a popular analysis in neuroscience and facilitates cross-disciplinary scientific discovery. Methods to construct null models that account for spatial autocorrelation - an inherent and fundamental property of the brain - have recently been developed and are quickly being adopted by researchers. In this educational workshop I will present multiple spatial autocorrelation-preserving null models, from spatial permutation tests (“spin test”) to parametrized data models. This workshop will cover the theory underlying these models, including when to use them, why to use them, and their limitations (lecture style), as well as how to generate these nulls in an analysis (hands-on coding demonstration). 

The emergence of brain-wide transcriptional atlases, quantifying the expression of thousands of genes across multiple locations in the brain, opened new opportunities for investigating the molecular correlates of brain network organization. Spatial gene expression data are highly multidimensional, therefore, evaluating associations with neuroimaging measures requires additional considerations across multiple levels of analysis. In this talk I will briefly introduce general concepts of imaging transcriptomics analyses and then will focus on the three main areas for applying different null models: i) dealing with spatial autocorrelation when evaluating the associations between gene expression and neuroimaging data; ii) assessing the specificity of identified associations for the selected sets of genes; and iii) evaluating the functional implications through gene enrichment analyses. I will conclude by outlining the recommendations for best practices and providing an overview of freely available open-source toolboxes implementing current best-practice procedures.