Multivariate Approaches to Modeling and Analysis

Normative modelling (NM) is an emerging method for parsing heterogeneity of brain imaging phenotypes[1–4]. Until now, however, NM has focused on the estimation centiles derived from cross-sectional data ('distance centiles'). While distance centiles quantify individual's deviation from the median, they cannot quantify longitudinal change, and of movements across centiles across time. To estimate the significance of such centile crossings, velocity centiles are needed. These map the rate of change and require a fundamentally different approach. They can also only be estimated from longitudinal data.
Further, 'thrive lines'[5] can be derived from estimates of the correlation between two successive measurements.[6] These are defined as a +/- 1.96 SD rate of change. Translated to neuroimaging, a change outside of a projected thrive line ('failure to thrive') would signify a change more extreme than 97.5% of the population between those two measurements.
Here, we present three fundamental novelties: we update our large scale pre-trained normative models[7] using an advanced non-Gaussian model[8], we augment our previous cross sectional data set[7] with 23264 longitudinally processed scans from 10812 subjects and we estimate velocity centiles and thrive lines for 148 cortical[9] and 37 subcortical[10] regions of interest (ROIs). To our knowledge, this provides the first method that enables statistical quantification of change in brain imaging derived features at the level of the individual. 

Major depressive disorder (MDD) is a heterogeneous disorder with onset spanning early adolescence to older adulthood (Malhi & Mann, 2018), closely linked to abnormal brain lifespan development (Schmaal et al., 2017). Previous studies have established brain age prediction models, showing that MDD patients generally have an older brain age than HCs (Dunlop et al., 2021; Han et al., 2021). However, heterogeneity in brain age deviations among MDD patients and its links to divergent developmental trajectories of functional networks, clinical profiles, and gene expression patterns remain unclear. Addressing these issues could provide deeper insights into MDD neurodevelopmental heterogeneity. 

Machine Learning (ML) in neuroscientific research offers opportunities to understand neuronal underpinnings of behaviour in health and disease. While ML applications often aim to advance neuroscientific understanding, they are frequently judged solely based on accuracy, fueling a "performance race" in model development. Problematically, such high accuracies, especially in neuroscience, are often achieved by relying on confounder information. This reliance can exacerbate challenges, including unreliable predictions, non-reproducibility, limited generalizability, and non-interpretability of ML results.
In clinical settings, randomized control trials (RCT) are a well-established tool to mitigate confounding influences to obtain cause-effect insights. In contrast, ML solutions are typically applied to observational data, which require post-hoc statistical confounder control, treating confounding as a purely associative phenomenon. However, distinguishing confounding effects from mediators, colliders or proxies, requires understanding of the directionality of effects, i.e. causal reasoning, to prevent faulty adjustments that may introduce spurious correlations (Hamdan, 2023). Additionally, integrating causal reasoning into neuroscientific ML workflows can facilitate investigation of brain-behavioural cause-effect relationships, akin to RCTs in clinical studies.
Here, using a brain-behavioural predictive example, we illustrate how to leverage domain knowledge to build a Directed Acyclic Graph (DAG) of causal relations and how this DAG can serve as a basis for confounder adjustment in ML analysis, enabling provisional causal insights (Pearl & Mackenzie, 2018). 

Neuroscientists have long attempted to subdivide the human brain into a mesh of anatomically and functionally distinct, contiguous regions (Huang, 2005, Yeo, 2011). This challenge become particularly complex in the neonatal brain, where functional organization differs markedly from that of adults (Peng, 2020). During the third trimester, the neonatal brain undergoes a critical phase of enhanced functional segregation, primarily driven by the rapid development of functional connectivity and the formation of hubs in primary regions (Cao, 2017). However, achieving accurate and reliable parcellation of specific functional networks (FNs) in newborns presents unique challenges. The combined effects of rapid functional segregation, low imaging quality, and the absence of established functional atlases complicate this process. In this study, we developed a four-stage bottom-up approach to parcellate neonatal brain FNs, providing a foundational neonatal functional brain atlas. This approach integrates a transformer-based autoencoder architecture for extracting novel features, coupled with innovative regularized NMF clustering algorithm. 

Anaesthetics act on molecular signalling to suppress behaviour. Combined with neuroimaging, they provide a unique opportunity to investigate how local neural dynamics mediate the link between microscale chemoarchitecture and the organism's functional repertoire. However, most studies focus on single species, single anaesthetics, and hand-picked properties of neural activity (e.g. entropy, power spectrum), providing a fundamentally incomplete picture.

To overcome these challenges, we systematically characterise how diverse anaesthetics perturb the entire dynamical profile of the invertebrate, murine and primate brain cross thousands of time-series features (Fig.1). 

Understanding the organizational principles that shape the network architecture of the brain remains a fundamental challenge in neuroscience. The prevailing view is that the brain is a discrete network of intricately connected neurons and neuronal populations (Bullmore and Sporns 2009). From this framework, several generative network models have been proposed to identify the wiring rules that might shape connectome architecture (Betzel 2017). These models are generally able to capture topological properties of empirical data, but fail to capture topographical (i.e., spatial) properties (Oldham 2023).
 
An alternative view, informed by neural field theory (NFT)(Robinson 1997), involves treating brain structures, particularly the cortex, as continuous. Spatiotemporally patterned neocortical dynamics are then viewed as emerging from waves of excitation travelling through the continuous cortical sheet (Robinson 1997). Critically, it can be shown that these waves arise from a superposition of a fundamental basis set of resonant standing wave patterns that correspond to the eigenmodes of cortical geometry, an equivalence given by the well-known Helmholtz equation used in diverse diverse areas of physics and engineering (Robinson et al., 1997 ;Pang et al., 2023). These eigenmodes thus correspond to preferred, resonant modes of cortical excitation.
 
A corollary of this view is that anatomical connections in the brain may preferentially link different areas to support resonance of the geometric modes, under a Hebbian-like plasticity mechanism (i.e., cells that fire together wire together). Here, we test this hypothesis by using a simple model that preferentially connects distinct cortical areas according to their profiles of geometric resonance. The model is simple and highly scalable, yielding, to our knowledge, the first generative model of weighted conectome architecture at the vertex level. Our model out-performs traditional models assuming discretized graph-like structures, highlighting the utility of continuous approaches that prioritize the physical and spatial properties of the brain.