Structural magnetic resonance imaging of brain similarity networks

Abstract

Recent advances in structural magnetic resonance imaging (MRI) analytics now allow us to comprehensively map the network organisation of individual brains using the biologically-principled metric of anatomical similarity. Here we offer an overview of the measurement and meaning of structural MRI similarity, especially in relation to two key assumptions that often underlie its interpretation: (i) that MRI similarity can be representative of architectonic similarity between cortical areas; and (ii) that similar areas are more likely to be axonally connected, as predicted by the homophily principle. We first introduce the historical roots and technical foundations of MRI similarity analysis, compared to distinct MRI techniques of structural covariance and tractography analysis. We contextualise these empirical results with two generative models of homophilic networks: an economic model of cost-constrained connectional homophily, and a heterochronic model of ontogenetically phased cortical maturation. We then review: (i) studies of the genetic and transcriptional architecture of MRI similarity in population-averaged and disorder-specific contexts; and (ii) developmental studies of normative cohorts and clinical studies of neurodevelopmental and neurodegenerative disorders. Finally, we prioritise knowledge gaps that must be addressed to consolidate structural MRI similarity as an accessible, valid marker of the architecture and connectivity of an individual brain network.

Introduction

A key goal for neuroscience is to measure the structural network organisation of an individual, living human brain. The principal neuroimaging approaches for mapping single-subject, N=1 structural brain networks have been rooted in the concept of inter-areal connectivity, estimated by white matter tractography of diffusion-weighted magnetic resonance imaging (MRI). Recently, a set of technically and conceptually distinct approaches to structural network mapping have emerged, rooted in the concept of inter-areal similarity, estimated by the correlation (or divergence) between areas in terms of the vector (or distribution) of one or more structural MRI metrics of geometry or tissue composition measured locally in each brain area.

Here we will focus on this growing field of structural MRI similarity network analysis (Seidlitz et al. 2018; Sebenius et al. 2023; Zhou et al. 2011; Homan et al. 2019; Tijms et al. 2012; Kong et al. 2015; Batalle et al. 2013; Paquola et al. 2019). Collectively, these methods differ across several technical dimensions, including the choice of macro-structural and/or microstructural MRI metrics of brain structure to be used as the basis for estimation of morphological or morphometric similarity, and the choice of similarity estimator (Cai et al. 2023; Wang and He 2024). As well as providing a technical introduction to a diverse range of single-subject structural MRI similarity network analysis tools, we will draw attention to their shared historical roots in axonal tract-tracing (Lanciego and Wouterlood 2020; Rubinov et al. 2015), diffusion-weighted imaging tractography (Mori and Zhang 2006; Jbabdi and Johansen-Berg 2011), and group-level structural MRI covariance analysis (Alexander-Bloch et al. et al.,2013). We will also highlight and interrogate two key assumptions that underpin the neuroscientific interpretation of structural MRI similarity in general.

The first key assumption is that structural MRI similarity is convincingly representative of some aspects of architectonic similarity between cortical areas. It is on this basis that we can conceive of an MRI-derived structural similarity network (SSN) as an architectome that represents the whole brain patterning of cortical differentiation, myelination or lamination. Here we will test this assumption, asking how confidently can we “read across” from the structural MRI similarity between two cortical areas to infer their similarity (or dis-similarity) on architectonic, gene transcriptional or other biological dimensions of areal similarity.

The second key assumption is that the structural MRI similarity of two areas is predictive of the number or type of axonal connections between them. It is on this basis that we can further conceive of the same structural MRI similarity matrix as a connectome that represents the whole brain, high-level “wiring diagram” of axonal projections and synaptic connections between cortical areas (Sporns et al. 2005). Drawing on prior theoretical, computational and histological work in support of the homophily principle, we will argue that “like is wired to like”, meaning that architectonically (or transcriptionally) similar regions are more likely to be axonally inter-connected than architectonically dissimilar or differentiated regions (García-Cabezas et al. 2019; Barbas and Rempel-Clower 1997; Barbas 2015). We will also consider how two prior models of human cortical network development, based on economic constraints of wiring cost and heterochronic timing of regional maturation, are consistent with the more general homophily principle that similar areas (which will often mature together and in close spatial proximity) are more often inter-connected with each other (even at the added expense of some long-distance connections).

The discussion of homophilic network development provides a conceptual framework for considering the genetic and transcriptional landscape underlying structural similarity and the emergence of similarity networks across brain development. We will survey the findings relating structural similarity and genomics, which demonstrate alignment between structural similarity and normative gene co-expression between regions, and the concordance between case-control changes in structural similarity networks and cortically patterned transcriptional co-expression of genes enriched for clinical disorders.

Further, we will review studies that have measured structural MRI similarity as a marker of brain network development in normative cohorts, and studies of abnormal structural MRI similarity in patients with neurodevelopmental or neurodegenerative disorders. We will focus on how some of the most notable results of these normative developmental and clinical studies can be interpreted in light of economic and/or heterochronic models of homophilic network development, and on the basis of the two key assumptions underpinning the interpretability of structural MRI similarity analysis.

Finally, we discuss some of the unresolved questions about how to optimise and operationalise structural MRI similarity analysis and the future opportunities for its wider use as a demographically and clinically accessible, diagnostically or prognostically meaningful, measure of the architectome and connectome of a single, living human brain.

Mapping structural networks in the living human brain

Non-invasive neuroimaging methods have developed since the 1990s in an effort to comprehensively and safely measure structural brain network architecture in the living human brain. The principal approach for estimation of axonal connectivity has been tractography of diffusion tensor imaging (DTI) data (Mori and Zhang 2006; Dauguet et al. 2007; Donahue et al. 2016). DTI measures the direction of anisotropic diffusion of water within a voxel of white matter, as a proxy for the direction of bundles of myelinated axons passing through the voxel. By following the direction of intra-voxel diffusion from one voxel to the next it is possible to reconstruct streamlines of diffusion representing large-scale white matter tracts between cortical areas. DTI tractography has the merit of seeking to measure axonal connectivity directly and specifically in a single human brain scan. It has proven to be successful for mapping selected white matter tracts; but there are also several long-standing challenges with this approach which have limited its utility for whole brain mapping of connectomes. The results of DTI tractography are highly sensitive to arbitrary variations in pre-processing or data modelling algorithms (Gajwani et al. 2023; Cieslak et al. 2021), typically include a large number of false positive connections (Maier-Hein et al. 2017; Thomas et al. 2014) but under-estimate the strength of long-distance connections (Donahue et al. 2016), and are potentially confounded by head movement-related effects on diffusion-weighted MRI data, especially in clinical or developmental populations (Donahue et al. 2016; Walker et al. 2012).

Since the early 2000s, the focus on DTI tractography measures of connectivity has been complemented by the development of structural covariance network (SCN) analysis as a measure of areal similarity (Lerch et al. 2006; Alexander-Bloch et al. 2013; Váša et al. 2018; Stauffer et al. 2023; Wright et al. 1999). Structural covariance is typically estimated from a single MRI metric measured at each cortical region in a sample of multiple brain scans. Most commonly, a macro-structural MRI metric like cortical thickness or regional volume has been estimated at each of hundreds of cortical areas in each scan; and then all possible pairwise inter-regional correlations in thickness or volume have been estimated over all scans in the sample. It has been shown that structural covariance estimated “on average” in this way is coupled with other measures of inter-areal similarity, such as co-expression of similar genes in anatomically aligned areas in the Allen Brain Atlas of whole genome transcription (Hawrylycz et al. 2012), as well as both tract-tracing and functional connectivity (Gong et al. 2012; Yee et al. 2018; Valk et al. 2020; Fürtjes et al. 2023; Romero-Garcia et al. 2018). However, it remains a major drawback that the method relies on aggregating multiple scans of a single structural feature and therefore does not provide a direct measure of structural similarity in an individual’s brain scan. The traditional limitation of structural covariance analysis to the consideration of one macro-structural MRI metric has also detracted from its appeal at a time of increasing availability of multiple micro-structural MRI metrics as proxies of intra-cortical myelination (e.g., ratio of T1-weighted/T2-weighted MRI; magnetization transfer or MT), neurite density (neurite orientation dispersion and density imaging or NODDI) and other aspects of cortical tissue composition (Lerch et al. 2017; Weiskopf et al. 2013; Glasser and Van Essen 2011; Zhang et al. 2012).

Technical foundations of single-scan MRI brain similarity networks

It is in this context of growing diversity of (micro-)structural MRI metrics, and technical challenges with existing methods for tractography or structural covariance, that new MRI methods for measuring brain structural similarity in a single brain scan have emerged in the last decade or so.

All structural MRI methods for similarity analysis begin by making comparable measurements of one or more MRI features at each of the constituent regional or areal (spatially coordinated) nodes defined by a parcellation of the brain or cerebral cortex (Figure 1). The inter-areal similarity matrix is then estimated by the pair-wise similarity metrics for each possible pair of regional nodes, and can be analysed topologically as a weighted graph using the same tools from network neuroscience as are applied to other brain connectivity phenotypes, such as functional connectivity (Fornito et al. 2016; Wang and He 2024). Technically, it is much simpler to measure the similarity between two cortical areas than it is to infer the axonal connectivity between them by tracking white matter tracts in diffusion-weighted MRI (Seidlitz et al. 2018; Cieslak et al. 2021). The simplicity and generalizability of similarity analysis in principle has facilitated the emergence of multiple different species of this methodological family, which can be categorised into univariate and multivariate methods.

Figure 1: Structural MRI similarity estimation:

(A) In vivo micro-structural magnetic resonance imaging (MRI) data aims to estimate tissue composition properties including arborization, myelination and diffusion. (B) MRI imaging allows for the analysis of both surface and volumetric features. Standard processing involves the reconstruction of a surface-mesh, which describes surface-features like cortical thickness and curvature using a set of vertices; and volumetric features are estimated by summarising values within voxels. Diffusion tensors quantify properties of water diffusion within tissue and depth-dependent profiling can be used to estimate a micro-structural MRI phenotype at multiple points between the white matter surface and the pial surface. (C) Structural MRI similarity networks can subsequently be estimated from regional feature vectors, to estimate (from top down) (i) SCN: between-subject covariation, based on a single structural feature estimated across subjects at each region, resulting in a single group-level {Regions × Subjects} univariate MRI data matrix; (ii) MSN: between-regional similarity using multiple features estimated at each region for each individual subject, resulting in a subject-specific {Regions × Features} multivariate MRI data matrix; (iii) MPC: between-regional similarity using a single feature estimated at multiple cortical depths for each subject, resulting in a subject-specific {Regions × Depth} spatially organised, univariate MRI data matrix; or (iv) MIND: between-regional similarity using one or many MRI features, estimated at sub-voxel vertex resolution on a cortical surface mesh, resulting in a subject-specific {Regions × Vertices} data matrix. (D) Structural MRI similarity networks are generally estimated as the pairwise association between all possible combinations of regional feature vectors. SCNs are estimated as the inter-subject correlation between the regional values of a single feature estimated for each subject, resulting in a single group-level network. Morphometric similarity is estimated as the pairwise correlation between regional feature vectors comprising multiple features estimated at each region, resulting in a subject-specific MSN. Microstructure profile covariance is estimated as the pairwise correlation between regional feature vectors comprising a single feature estimated at multiple cortical depths, resulting in a subject-specific MPC network. MIND similarity is estimated from the Kullback–Leibler (KL) divergence between univariate (shown here) or multivariate distributions of MRI features, resulting in a subject specific MIND network. (E) In all cases, the resulting {Region × Region} structural similarity matrix can subsequently be analysed as a network using graph theoretical measures.

Univariate similarity networks are based on a single MRI-derived feature (Kong et al. 2015; Homan et al. 2019; Tijms et al. 2012; Zhou et al. 2011; Paquola, Vos De Wael, et al. 2019; Nadig et al. 2021), which may or may not be spatially organised. Microstructural profile covariance (MPC) is an example of a spatially organised univariate approach (Paquola, Bethlehem, et al. 2019). MPC networks can be estimated from the inter-regional, pairwise correlations between cortical depth profiles of a single micro-structural MRI metric, e.g., magnetization transfer, measured repeatedly from the pial surface to the white matter boundary of the cortex. Each cortical depth profile is spatially organised in alignment with the radial lamination of cortex and cytoarchitectonically similar areas of cortex have similar cortical depth profiles, or high MPC (Paquola and Hong 2023). Other univariate methods have characterised the similarity between regions without using information about the spatial organisation of the MRI metric within each region. For example, the Kullback-Leibler divergence between the regional distributions of a single MRI metric measured at many points within each region, e.g., voxels or vertices of a surface mesh, has been used as an estimator of pair-wise similarity to construct a whole-cortex similarity network from a single, spatially unorganised MRI metric in an individual scan (Kong et al. 2015; Homan et al. 2019).

Multivariate similarity networks are based on more than one MRI feature per regional node. For example, morphometric similarity networks (MSNs; Seidlitz et al. 2018) were originally estimated by the pairwise correlations between multimodal feature vectors comprising 10 (or fewer) regional mean MRI features for each node. This approach allowed estimation of inter-areal similarity using a wider range of macro-structural and micro-structural MRI metrics than univariate similarity methods (or structural covariance analysis). However, it is a potential limitation of this method that inter-regional correlations are estimated with relatively few degrees of freedom, dictated by the small number of regionally summarised MRI metrics available (N = number of MRI features, typically <10), compared to the greater degrees of freedom typically available for estimation of structural covariance (N = number of subjects, typically >100). Recent work has generalised Kullback-Leibler divergence to estimate the similarity, i.e., morphometric inverse divergence (MIND; Sebenius et al. 2023), between cortical areas based on multivariate distributions which provide much higher degrees of freedom (N = number of vertices/voxels, typically 1,000 < N < 10,000). The principles of MRI similarity analysis represented by these early studies of brain structure are also potentially generalisable to other brain anatomical systems. For example, sulcal phenotype networks (SPNs) have been proposed to capture the similarity between each pair of sulci on the cortical surface as measured by the correlation between feature vectors comprising multiple metrics of sulcal folding (Snyder et al. 2024).

Key assumptions of structural MRI similarity analysis

It is clear that there are a growing number of ways to measure the structural MRI similarity between brain areas. In using any of these methods to make meaningful neurobiological inferences, however, researchers tend to make the same two key assumptions (illustrated in Figure 2):

Figure 2: Two key assumptions of structural MRI similarity analysis.

The validity of MRI inter-regional similarity as a measure of anatomical connectivity rests on two assumptions: Firstly, (A) that similarity of MRI feature vectors is a meaningful reflection of the similarity of two cortical areas at a cellular scale. In support of this assumption, cortical depth profiles of a micro-structural MRI marker of myelination (magnetization transfer) mirrored histological estimates of cortical myeloarchitectonics, suggesting that the MRI similarity metric of microstructural profile covariance is indicative of the architectonic similarity between a pair of cortical areas (Paquola et al. 2019). Secondly, (B) that MRI similarity is predictive of axonal connectivity between cortical areas. In relation to the second assumption, both MSN and MIND networks have been found to map onto the gold standard connectomes derived from tract tracing in macaque monkeys (Seidlitz et al. 2018; Sebenius et al. 2023). Here, we show group-level matrices (top) and networks (bottom; thresholded at top 15% connections) derived from “ground truth” tract-tracing, MSN and MIND similarity networks derived from MRI data on macaque monkeys (Sebenius et al. 2023). For the data shown, MIND and morphometric similarity were correlated with tract tracing weights at r=0.42 and r=0.27, respectively.

1. Structural MRI similarity at macro scale is representative of cytoarchitectonic and/or myeloarchitectonic similarity between cortical areas at micro scale.

This assumption is necessary for structural MRI similarity to be regarded as a relatively coarse-grained, macro-scale, in vivo proxy of the similarities and dissimilarities between cortical areas, e.g., in terms of their lamination and myelination, identified ex vivo by more fine-grained, micro-scale histological studies. The extent to which MRI-derived similarity represents architectonic similarity is inherently limited by the extent to which MRI features directly relate to measures of the cellular organisation and tissue composition of cortex. On balance, there is strong histological evidence that some individual MRI features map distinctly onto classical metrics of cortical architectonics. For example, magnetization transfer (MT) and the T1w/T2w-ratio have been proposed as proxies for laminated or depth-dependent myelination (Hagiwara et al. 2018); intracellular volume fraction (ICVF) as a proxy of neurite density; and orientation dispersion index (ODI) as a proxy of dendritic arborization (Zhang et al. 2012; Wang et al. 2019; Sato et al. 2017). MRI similarity network metrics, potentially combining information from one or more of multiple MRI features, therefore plausibly provide a proxy for the overall similarity between areas at the microscopic scale of their cellular architecture. There is already some evidence in support of this assumption, e.g., the statistical alignment between cortical depth profiles of MT and histological measurements of cortical myelination (Fig 2A; Paquola et al, 2019). However, it is a priority for the field to build further evidence for this first similarity assumption, using a wider range of MRI metrics, with enhanced spatial resolution, and in translational animal models that allow a systematic comparison between MRI and histological metrics of cortical similarity.

More generally, this similarity assumption can be formulated to predict that structural MRI similarity should be representative of gene transcriptional similarity (or indeed any other measure of biological similarity) between cortical regions. There is also robust and growing evidence for this broader version of the similarity assumption. For example, MSNs and MIND networks (Seidlitz et al. 2018; Sebenius et al. 2023) were both spatially co-located with cortical transcriptional networks derived from whole genome co-expression data in the Allen Human Brain Atlas, with significantly stronger coupling of the more statistically robust MIND networks to transcriptional signatures of inter-areal similarity.

Taken together, it seems reasonable to conclude that structural MRI similarity networks constructed using current methods can be interpreted as architectomes that represent the similarity of cyto- or myelo-architectonic organisation between different cortical regions. However, in order for structural MRI similarity networks to be additionally interpreted as connectomes, that represent the axonal inter-connectivity between cortical regions, a second assumption needs to be assessed.

2. Brain regions that are architectonically similar are more likely to be axonally connected to each other and therefore structural MRI similarity can be regarded as a proxy of connectivity.

Prior evidence from histological and computational studies, synthesised theoretically by the structural model (García-Cabezas et al., 2019), demonstrates that connectivity is typically greater between similar cortical areas. In animal models, tract-tracing techniques are regarded as the gold standard for the connectome because they map precisely the directed monosynaptic connections, from cells of origin, through axonal projections, to synaptic terminals (Markov et al. 2013; Knoblauch et al. et al., 2014). Cross-species, translational neuroimaging studies have shown that multivariate structural MRI similarity (MSN or MIND) between cortical regions was moderately correlated with group-level (anterograde) tract-tracing data in the macaque monkey (Sebenius et al. 2023; Seidlitz et al. 2018). This is probably the most directly supportive evidence to date for the second assumption. MPC metrics have also been validated as a proxy for axonal connectivity, given evidence from histological studies of the BigBrain atlas (Amunts et al. 2013), demonstrating that regions with similar lamination profiles tend to have higher DTI-based connectivity (Wei et al. 2019). Histological studies in primate brains have also found that similarity in cellular composition and lamination is related to axonal connectivity as indexed by retrograde tract-tracing (Hilgetag et al. 2016).

Historical roots of structural MRI similarity networks

These two assumptions defining the relationship between structural MRI similarity and both cortical architectonics and inter-areal axonal connectivity can be placed in an historical context stretching back to the 19th century.

Pioneering post mortem studies of the cerebral cortex established three key concepts of brain architectonics: cortical areas, cortical types, and cortical gradients (see Box 1). This work towards characterising the architectonics of the cortex has been complemented by an equally deep-rooted focus on the connectivity mediated by myelinated axons between cortical areas. Major white matter fibre tracts, like the arcuate fasciculus, were dissected and illustrated with increasing accuracy from the time of Johann Reil (1759-1813). Later in the 19th century, histological methods based on Wallerian axonal degeneration following experimental or clinical lesions enabled mapping of axonal projections from and to specific brain regions, such as those linking the thalamus and neocortex (Hakosalo 2006; Shepherd 2015; Walker, 1938). From about 1890 Paul Flechsig examined hundreds of post-mortem foetal and neonatal human brains and closely described the developmentally phased timing of myelination of different cortical areas. He formulated a “law of myelinogenesis”, a stereotyped sequence of heterochronic myelination of different cortical areas over the course of brain development, from early-myelinating sensory and motor cortex to later-myelinating regions of heteromodal association cortex. On this basis he published a whole brain map of 44 cortical areas defined by myelogenetic timing, rather than by architectonic criteria, as was by then relatively conventional (Flechsig 1920).

Box 1: Cortical areas, types, and gradients.

The cellular composition of cortical areas determines (A) the laminar organisation in terms of cyto- and myelo-architecture (adapted from Vogt and Vogt, 1903). (B) Based on these features, fine-grained cortical areas have been defined (adapted from (Brodmann 1909)), which in turn can be summarised into more coarsely defined (C) cortical types, i.e. groups of regions that share similar laminar organisation (adapted from García-Cabezas et al. et al., 2023). (D) Cortical types are defined by their differentiation into discernible layers , ranging from three-layered allocortex to six-layered eulaminate cortex and koniocortex (adapted from Sancha-Velasco et al. et al., 2023). Agranular and dysgranular cortex comprise the mesocortex, and eulaminate and koniocortical areas make up the isocortex (a.k.a. neocortex) as referenced in Fig 2A. (E) Smooth gradients of laminar differentiation from allocortical origins through adjacent mesocortical and neocortical areas are characteristic of mammalian cortex, e.g., as shown here, the gradient from allocortex of the supracallosal hippocampus (induseum griseum) through mesocortex of the cingulate gyrus to dorsal neocortex in the macaque brain (adapted from García-Cabezas et al., 2019).

Seminal histological studies led to the emergence of three concepts about the architectonics of the cortex: cortical areas, types, and gradients.

Cortical areas were each ideally defined as relatively small patches of cortex uniquely distinguished, by their cytoarchitectonic and/or myeloarchitectonic characteristics, from their spatial neighbours and all other areas of cortex in the brain. The canonical example of arealisation is the famous map published by Korbinian Brodmann in 1909, representing 48 cortical areas in each human cerebral hemisphere, which has become widely known since its adoption, via the stereotactic atlas of Talairach & Tournoux (Talairach and Tournoux 1988), as a descriptive standard for functional localization studies using PET and functional MRI (Zilles 2018). However, several other systems of human cortical arealisation were published before and shortly after Brodmann’s, including the Vogts’ myelo-architectonically defined identification of about 200 areas (Nieuwenhuys et al. 2015), and von Economo and Koskinas’ map of 107 areas (von Economo, Koskinas, and Triarhou 2008; von Economo and Koskinas 1925).

Cortical types subsume or coarse-grain multiple cortical areas, and therefore the number of types has always been much fewer than the proposed numbers of areas. Oskar Vogt (1870-1959) and Cécile Vogt-Mugnier (1875-1962) distinguished two key cortical types by their very different patterns of lamination: allocortex, which has only three layers (including one layer of neurons), and isocortex, which has six layers including a well-defined layer of granule cells (layer IV). Allocortex comprised olfactory cortex and the hippocampal formation, later also sometimes called paleo-cortex and archi-cortex, respectively. These were identified as relatively small and ancestral components of the human brain, which was predominantly composed of more recently evolved isocortex or neocortex. Over time, building on studies by Rose (1929), Filimonoff (1947) and Yakovlev (1959), whose work defined a mesocortical zone of intermediate lamination between allocortex and isocortex, a broad consensus has emerged that there are at least 4 major cortical types, classically named and ranked in order of evolutionary recency: allocortex; mesocortex or paralimbic cortex; isocortex or neocortex; and koniocortex or idiotypic cortex (Mesulam 2000). More recent studies, beginning with those of Sanides (1964; 1962), have divided the mesocortical type - with more than 3 but less than 6 cortical layers - into two sub-types: agranular cortex, which has no visible layer 4 of granule cells, and dysgranular cortex, which has some granular lamination. Likewise the classical type of isocortex has been divided into sub-types of eulaminate cortex (I, II, III), which have progressively denser and deeper granular layers, culminating in primary sensory cortex, e.g., primary visual (V1), calcarine or striate cortex, which has the most clearly differentiated lamination, sometimes described as comprising more than the classical limit of 6 layers.

Cortical gradients emerged later historically, in the work of Constanin von Economo and George Koskinas on human and primate brains (von Economo, Koskinas, and Triarhou 2008; von Economo and Koskinas 1925), and in the phylogenetic studies of Raymond Dart (Dart 1934) and Andrew Abbie (Abbie 1942) on reptile and marsupial brains. It was shown that smooth trends of progressively more laminated architecture emanated from primordial or original zones of the simplest (3 layer) cortex, gradually transitioning through mesocortical then isocortical lamination with increasing distance from the original locus or anlagen. In the brains of reptiles and ancient mammals, two such gradients could be seen originating in two distinct but adjacent allocortical formations (homologous to hippocampus and olfactory cortex in humans). In the 1960s, these ideas were formulated by Friedrich Sanides and others as the dual origin theory of cortex (Sanides 1964; Pandya et al., 2015), which essentially reduced architectonic variation to two gradients of progressively increasing lamination and myelination as a monotonic function of topological and/or topographic distance from one of two original loci: hippocampus or olfactory cortex (Fig 3A). Dual origin theory, although based on the observation of architectonic gradients on the cortical surface, was not simply descriptive but also implied that these visible trends of cortical differentiation were the cumulative record of brain evolution or phylogeny, and likely fundamental to the sequencing of individual brain development or ontogeny (Pandya et al., 2015).

Following the advent of (non-human) tract-tracing methods based on axonal transport of anterograde or retrograde tracers in the 1970s, there have been major advances in mapping the axonal connectivity of mammalian cortex (Lanciego and Wouterlood 2020; Markov et al. 2013), and in understanding how inter-areal axonal projections and terminations are linked to cortical lamination. The structural model, extensively developed by Helen Barbas and colleagues since the 1980s (Barbas, 1986; Barbas and Rempel-Clower 1997; Barbas 2015; García-Cabezas et al. et al., 2019), has linked the probability and lamina-specificity of inter-areal projections to the architectonic similarity (or the ratio of neuronal densities (Beul and Hilgetag, 2019)) between potentially connected areas (Fig 3B). It has been shown that areas belonging to the same architectonic type are more likely to be axonally inter-connected, and at all cortical layers, than areas belonging to different types. Architectonically dis-similar areas are less frequently connected and then by lamina-specific projections: from supragranular layers of higher cortical types to infragranular terminations in lower types; and conversely from infragranular layers of lower cortical types to supragranular layers in higher types (Barbas 1986; Barbas and Rempel-Clower 1997; Beul et al. 2021). Predictions of the structural model have been confirmed experimentally in rat, cat, and macaque tract-tracing datasets; and regression models have been used to predict the probability of inter-areal connection based on the distance and (dis-)similarity between connected areas (Goulas, Majka, et al. 2019). Of course, the experimentally invasive methods of axonal tract-tracing that have provided “gold standard” data on connectivity in animals are ethically precluded in humans, so there is a relative deficit of equally precise data on the connectional anatomy of the human brain. However, post mortem studies in humans have recently highlighted that the trans-synaptic propagation of pathology through the cerebral cortex in three neurodegenerative diseases (Alzheimer’s disease (Uceda-Heras et al. 2024); traumatic encephalopathy (Barbas et al. 2024); and fronto-temporal dementia (Ohm et al. 2024)) appears to be compatible with the laminar patterns of cortico-cortical synaptic connections predicted by the structural model.

Figure 3: Frameworks of cortical evolution, maturation, and organisation:

(A) The dual origin model proposes the emergence of gradients in lamination and myelination anchored in one of two primordial areas of allocortex, either the hippocampus or olfactory cortex (Sanides 1964; Pandya et al. 2015; figure adapted from Goulas, Margulies, et al., 2019). (B) The structural model proposes that the wiring in the brain is defined by columnar connectivity (across all layers) between similar cortical types and by lamina-specific feedforward and feedback connections between dissimilar types (adapted from García-Cabezas et al., 2019). (C) Both classic histological results (adapted from Flechsig (1920)) and recent MRI results (adapted from Grydeland et al., 2019) suggest that cortical areas mature heterochronically (at different times) in development, with primary sensory and motor cortical areas myelinating before or soon after birth, and association cortical areas becoming myelinated in the second decade of life.

Homophily as a principle of brain network organisation

A more general formulation of the structural model, which links lamina-specific connectivity to architectonic differences between cortical types, is the homophily principle, which is simply that similar cortical areas are more likely to be axonally inter-connected than dissimilar areas (Barbas and Rempel-Clower 1997; Akarca et al. 2022). Homophily provides the theoretical link between historical traditions of connectional and architectonic anatomy of the cortex, and it is the most general expression of the principle that structural similarity networks can to a certain extent be interpreted as connectomes, as well as architectomes.

Homophilic principles of nervous system organisation have been demonstrated empirically across a wide range of (i) species (Pathak et al., et al., 2020; Beul et al. et al.,2015; Beul et al. et al., 2017; Goulas et al., 2017); (ii) measures of similarity (Shafiei 2020; Hansen et al. 2023; Bazinet et al. 2023); and (iii) types of brain connectivity (Hansen et al. 2023; Bazinet et al. 2023). While homophilic connectivity is certainly not a universal principle – e.g., koniocortical areas are unlikely to be connected to one another despite their assignment to the same cortical type (Aparicio-Rodríguez and García-Cabezas, 2023) – there is growing evidence for an influential role of homophily on multiple aspects of cortical connectivity. Here, we discuss this evidence, bridging scales and modalities, for biological validation of structural similarity MRI networks as novel markers of the homophilic inter-areal connectivity of individual human (and non-human) brains.

Homophily at the cellular (microscopic) scale

At the micro scale, cross-species work has implicated homophilic wiring as a key principle in the development of neuronal connectivity. For example, the study of the entire C. elegans nervous system has demonstrated preferential connectivity between neurons sharing similar properties (Pathak et al., 2020). Interestingly, this homophilic connectivity in the C. elegans nervous system was observed across a range of independent measures of morphological and developmental similarity, including neural process length and neuron birth time. Homophilic inter-neuronal connectivity has additionally been observed both in vitro and in vivo in the mouse visual system (Cossell et al. 2015; Ko et al. 2013; Harris and Mrsic-Flogel 2013), where neurons with similar response properties show preferential connectivity with each other. Multiple other studies have also converged on a general tendency for cortical mouse neurons with similar morphological properties to share similar connectivity profiles (Liu et al. 2023; Wang et al., 2024). Moreover, topological homophily, where two neurons are more likely to be connected to each other if they are nearest neighbours to a similar set of other neurons, has been shown in multiple lines of human iPSC-derived neurons, as well as human cerebral organoid cultures (Akarca et al. 2022). Of course, homophily is not a hard and fast rule of cellular connectivity - e.g., different signalling molecules can encourage synapses to form according to homophilic, heterophilic, or mixed connectivity patterns (Akarca et al. 2022; Sanes and Zipursky 2020) - but rather a general tendency that appears to remain consistent across organisms and definitions of similarity.

Homophily at the whole brain (macroscopic) scale

At the macro scale, similarity is also a key principle influencing inter-areal connectivity via large-scale axonal tracts in animal models (Beul et al., 2015; Beul et al., 2017; Goulas et al., 2017). For example, histological studies of the macaque cortex have shown that similarity in laminar structure and cellular composition is decisive in determining the strength of axonal connections between brain regions, as measured via gold-standard tract-tracing (Hilgetag et al. 2016, 2019). In the macaque cortex, cytoarchitectural similarity was a better predictor of connectivity than either i) relative cortical thickness or ii) Euclidean distance; and these results have been replicated in the cat cortex (Beul et al., 2015; Beul et al., 2018). There have also been concordant findings from recent work on assortativity in brain networks, which has identified a high level of topological homophily in macaque cortical networks constructed from tract-tracing measures of neuronal projection density and from an MRI-derived proxy of myelination, the T1w/T2w ratio, but not cortical thickness (Bazinet et al. 2023).

Multimodal homophily of human brain networks

Similarity between cortical areas in humans has been defined using a diverse array of normative biological measures, including neurotransmitter receptor distributions and glucose metabolic rates from positron emission tomography (PET), gene expression and histological profiles from post mortem atlases, and neurophysiological time series from functional MRI (fMRI) and electrophysiological data (Hansen et al. 2022; Horwitz et al., 1984; Wang et al. 2020; Zhang et al. 2021; Wei et al. 2019).

Interestingly, all such measures of similarity tend to be correlated with each other, despite being measured in diverse data modalities that represent biologically distinct signals (Hansen et al. 2023). For example, brain regions with similar distributions of neurotransmitter receptors, gene expression profiles, or rates of glucose metabolism are more likely to be connected through white-matter tracts (Hansen et al. 2023; Fulcher and Fornito 2016). Likewise, inter-regional similarity in cortical thickness, myelination, and gene expression imply stronger normative functional connectivity (Richiardi et al. 2015; Bazinet et al. 2023; Shafiei 2020). Of course, not all measures of similarity are homophilic to the same extent, and heterophilic connections will be important for the anatomical and functional integration of dissimilar cortical areas (Bazinet et al. 2023; Shafiei 2020). However, there is broad and growing support for the concept that the cortex and/or the whole brain is homophilic across multiple domains; regions that are similar in one phenotypic domain (transcriptional, cellular, functional etc) tend to be similar in others (Bazinet et al. 2023; Shafiei 2020), and similar regions are more likely to be inter-connected axonally.

Generative models of homophilic brain network development

The observation of the brain as a homophilic system raises the question of how such a system develops in the first place, and what the implications might be for using structural MRI similarity to study typical and atypical neurodevelopmental processes in humans.

Here we will focus on two linked models for brain network development that have emerged to account for homophily (and many other topological and geometric properties) of brain networks (Figure 4): an economic model rooted in distance-related wiring costs and their offsetting by the topological value of homophily (Vértes et al. 2012; Betzel et al. 2016); and a heterochronic model that shows how homophilic adult brain networks can be generated by the known and distinctively human neurodevelopmental process of phased, staged or heterochronic maturation (Huttenlocher and Dabholkar 1997; Goulas et al., 2019).

Figure 4: Two theories of homophilic network development.

(A) A visualisation of economic network development. According to cost-constrained homophily, the likelihood of a connection forming between two nodes can be parameterised by two terms: the similarity between two nodes (with higher inter-node similarity increasing the likelihood of connection) and the cost of forming a connection (with higher cost decreasing the likelihood of connection). Here, cortical areal similarity is indicated by colour and connection cost is proportional to the distance between connected areas. (B) An illustration of normative and disordered heterochronic development. Cortical areas or nodes that develop at the same time will tend to share similar attributes, and will also tend to make connections with other concurrently developing nodes – thereby leading to a homophilic network. Conversely abnormal sequencing or synchronisation of heterochronic cortical development will lead to the formation of adult networks with atypical homophily.

The economic model of homophilic brain development

Economic thinking about brain networks originated early in the history of neuroscience. Santiago Ramón y Cajal explained diverse histological features in terms of conservation laws stating that all nervous systems were organised to: i) maximise conductivity speed, or conserve time; ii) minimise the cellular material needed to form individual neurons, and iii) minimise intracranial volume requirements, in other words, conserve space (Garcia-Lopez et al. 2010; Cajal and Azoulay 1995). Cajal’s conservation laws for material (ii) and volume (iii) are commonly now conflated in the more general concept that minimization of wiring cost is a crucial factor in the formation of brain networks, as it is more generally for all spatially embedded networks (Bassett et al. 2010). However, minimization of wiring cost, e.g., the total length of axonal projections in a nervous system, does not entirely account for the observed topological properties of brain networks at micro and macro scales. For example, the wiring costs of axonal tract-tracing networks from the macaque monkey and the mouse (Rubinov et al. 2015), and that of the neuronal network estimated from electron microscopy in C. elegans, are not minimal (Kaiser and Hilgetag 2006). Nervous systems include more long-distance connections than would be allowed by strict minimisation of cellular material in space, probably because of the sometimes competitive pressure to conserve conduction time. The conservation of conduction time will favour the minimal number of synaptic connections intervening between any pair of neurons - i.e., topologically speaking, the shortest path length between neuronal nodes in a graph - even if the time-efficiently connected neurons are spatially distanced from each other. Competitive conservation principles of wiring cost and conduction efficiency have recently been demonstrated as a consistent feature of mammalian connectomes reconstructed from DTI tractography in 123 different species (Assaf et al. 2020).

Economic ideas of brain network organisation (Bullmore and Sporns 2012) have been computationally formalised in terms of the probability of a connection between two regions (neurons) being defined by a trade-off between the wiring cost and the topological value of each new connection or edge added to the network (Vértes et al. 2012; Betzel et al. 2016). Cost is typically approximated by an exponential function of the distance between the two nodes, D{i,j}, and higher cost reduces connection probability; value can be expressed by a range of topological properties, T{i,j}, of the connected nodes and/or the connecting edge, and higher value increases connection probability. In general, a simple two-parameter economic model can be formalised as follows: P{i,j} ~ D{i,j}^η + γ T{i,j}, where η penalises cost and γ weights value.

Multiple recent studies on generative models of human foetal and adult connectomes have explored a wide range of variations on this general theme, investigating many possible topological value metrics, cost functions of distance, and parameter values for η and γ. Results have converged on cost-constrained homophily as the most parsimonious (2 parameter) rule for simulation of human brain network statistics (Oldham et al. 2022; Akarca et al. 2022), and for networks defined by their topological similarity (e.g., Akarca et al., 2022) or by other biological features such as correlated gene expression (Oldham et al., 2022). The relative success of cost-constrained homophily models in accounting for human brain network organisation implies that connectivity is more likely between nodes that are already similar even if they are physically distant from each other. However, it is not straightforward to translate the parameters η and γ to well-defined neurodevelopmental processes. A positive bias in favour of homophilic connections (γ > 0) has been linked to Hebbian principles of synaptic plasticity (Lynn et al., 2024; Vértes et al., 2014); and the distance penalty (η < 0) could be represented by spatial gradients of axonal growth factors or other morphogens known to be important for planar differentiation of mammalian cortex (Puelles et al. 2019).

The heterochronic model of homophilic brain development

A complementary model for homophilic brain network generation is based on the known neurodevelopmental process of spatially organised, heterochronic maturation of the human cortex (Goulas et al., 2019). The idea that different areas of cortex mature at different times (heterochronically) over development was well-articulated by Flechsig’s law of myelinogenesis (Flechsig 1920), which stated that primary sensory and motor cortical areas were myelinated before or soon after birth, whereas association cortical areas did not become fully myelinated until the second decade. This observation has been substantiated by MRI studies of age-related changes in proxies of intra-cortical myelination (e.g., T1w/T2w ratio; MT), which are consistent with anatomically organised waves of myelinogenesis in postnatal life (Grydeland et al. 2019; Whitaker et al. 2016). The concept of heterochronic cortical development has also been generalised from myeloarchitectonics to histogenetics more broadly. Significant timing differences in neurogenesis have been observed, with mesocortical areas terminating neurogenetic programs earlier than eulaminate areas, and the koniocortex having the longest period of neurogenesis (Rakic 2002). Prior work has also shown that different areas have different timing or rates of synaptic formation and elimination or pruning (Bayer and Altman 1987; Huttenlocher and Dabholkar 1997). It is noteworthy that there are limitations to this theory of heterochronic development. For example, there are striking differences in the timing of prenatal development of the thalamus and the cerebral cortex (Kahle 1951, Ruiz-Cabrera et al. 2023); yet the two are strongly, monosynaptically and reciprocally connected. Thus, further evidence is required before this theory can be confidently extended beyond the scope of postnatal cortical development to account for subcortical and whole brain network development.

Several computational simulation studies have supported the general homophilic principle that regions which have similar developmental trajectories will be similar also in terms of other properties (Goulas et al., 2019; Beul et al., 2018; Barbas and Hilgetag 2023), hypothetically due to shared genetic and/or convergent environmental effects. Indeed, it has been demonstrated that modelling brain network development as the outcome of spatially-ordered, heterochronic phases of maturation (without any other constraints) was sufficient to recreate the majority of the network topology of both normative fly and human connectomes (Goulas et al., 2019). In complementary work, it was found that simulations of the joint development of both cytoarchitecture and axonal growth, under simple biological assumptions in a heterochronic paradigm, leads to the expected alignment between cell composition and connectivity observed in histological studies of model organisms (Beul et al. 2018). The importance of heterochronicity is further underlined by the study of the complete C. elegans nervous system, in which neurons are more likely to connect with each other if they emerge at a similar developmental time (Pathak et al., 2020; Nicosia et al. 2013). Finally, the feasibility of using structural similarity analysis to study heterochronic network development is anticipated by the finding that structurally similar and/or covarying brain regions tend to follow similar developmental trajectories (Alexander-Bloch et al. 2013; Wu et al. 2023).

Genetic architecture of homophilic structural MRI brain networks

Observed alignment between gene expression and structural similarity

Prenatal developmental programs of brain gene expression are essential to the proper differentiation of migrating neurons (Telley et al. 2016; Klingler 2023) and the arealisation of the developing cortex (Pagliaro et al. 2023; Cadwell et al. 2019). Further, brain gene expression continues to program key neurodevelopmental trends, like synaptic pruning or cortical myelination, occurring heterochronically throughout the course of childhood, adolescence and adult life (Li et al. 2018).

In light of the transcriptional influences on cortical differentiation (Cadwell et al. 2019), the homophily principle predicts that structurally similar brain regions should not only develop at similar time points and be anatomically connected, but should also share similar genomic influences. In accordance with this prediction, structural similarity has been empirically shown to closely mirror genomic similarity (Figure 5A). Specifically, structural similarity between regions measured by MSN/MIND network analysis was strongly coupled to transcriptional similarity between regions (e.g., normative gene co-expression profiles; Sebenius et al. 2023; Seidlitz et al. 2018). The coupling between MSN/MIND and transcriptional similarity networks was notably stronger than the relationship between DTI-derived connectivity and regional gene co-expression, suggesting that genomic processes are more strongly linked to MRI similarity phenotypes of cortical architecture than to DTI-derived estimates of cortical connectivity.

Figure 5: The genetic and transcriptional basis of structural similarity.

(A) A visualisation of the empirically strong coupling between the transcriptional similarity between cortical areas, as defined by whole genome co-expression, and the structural MRI-derived similarity between areas. The right panel was adapted from Sebenius et al. (2023), where structural similarity between each possible pair of cortical areas measured by MIND was highly correlated (r=0.76) with normative gene co-expression profiles from anatomically aligned areas of the Allen Human Brain Atlas (Hawrylycz et al. 2012). (B) Schematic of potential effects of genetic sequence variation on cortical similarity, including variants in noncoding regions, which may cause changes in transcriptional programs that normally control development of cortical lamination and thickness. Thus variation in DNA, although common to all cells in the brain, is expected to have spatially patterned effects on gene expression across the cortex, represented phenotypically by node-level and edge-level effects on structural MRI similarity networks.

The strong observed relationship between structural MRI similarity of individual brain networks and transcriptional similarity is consistent with prior findings of strong coupling between group-level structural covariance and whole genome co-expression (Stauffer et al. 2023; Fürtjes et al. 2023; Romero-Garcia et al. 2018; Yee et al. 2018). Further analysis of twin and genetic data has confirmed that MIND networks, MPC networks, and MSNs are heritable phenotypes (Sebenius et al. 2023; Valk et al. 2022; Wu et al. 2023), with heritabilities comparable to more conventional, localised MRI phenotypes, e.g., cortical thickness, suggesting that individual differences in structural similarity networks are genetically driven to some considerable extent.

Aligning atypical structural similarity with changes in gene expression

Since structural similarity is both heritable and closely coupled to spatio-temporally patterned cortical gene expression, changes in structural similarity networks associated with normal development or brain-related disorders will plausibly reflect underlying genomic processes (as conceptually illustrated in Figure 5B) such as early developmental events of cortical specification that have been well-described in mammals (Puelles 2013; Ruiz-Cabrera et al. 2023; Puelles et al. 2019; Puelles et al. 2024). Many empirical studies have shown that changes of structural similarity may be a consequence of expected patterns of altered gene expression. For example, the spatial patterns of morphometric similarity changes related to ageing (Niu et al. 2024), neurodegenerative disorders (Zhang et al. 2021; Tranfa et al. 2024; Qu et al. 2024; Wang et al. 2024), multiple neuropsychiatric disorders (Morgan et al. 2019; Xue et al. 2023; Zong et al. 2023), and subtypes of disorders (Yao et al. 2023) have all been shown to closely align with the normative cortical patterning of the expression of genes specifically related to the (heritable) disorder or trait in question.

One prior study examined the patterning of altered MSN degree in patients with one of six different chromosomal copy number variation (CNV) disorders, an experimental paradigm with the advantage of studying MRI phenotypes in patients with clear (causal) genetic aetiology. The cortical patterning of altered MSN degree was specifically and consistently aligned with the normative expression of genes from the affected chromosome in each of the 6 neurogenetic disorders. Moreover, altered peripheral (blood) gene expression predicted disease-related changes in morphometric similarity, thus linking subject-specific changes in blood gene expression to changes in brain MRI similarity networks (Seidlitz et al. 2020).

These studies linking disorder-related changes in structural similarity to the spatial patterning of normative gene expression share a key neurodevelopmental assumption: namely, that changes in cortical transcription occurring early in life, e.g. during prenatal phases of brain development, will manifest as structural similarity changes that collocate with the spatial patterning of disorder-related gene expression measured in healthy, adult cortex (Hawrylycz et al. 2012). The fact that empirical results have generally supported this assumption suggests that structural similarity may plausibly represent genomically-mediated changes that occurred early brain network development. However, their shared reliance on a normative dataset of adult gene expression (Hawrylycz et al. 2012) makes it difficult to pinpoint the exact mechanism linking early changes in transcription to structural similarity changes later in life. As such, validation and extension of this approach using additional transcriptomic datasets from larger, more demographically and/or developmentally diverse cohorts would be highly valuable (Wang et al. 2018; Miller et al. 2014). Another shared limitation of this approach is that it relies on spatial colocation analysis with regional gene expression, so only structural similarity phenotypes measured at regional level, e.g., weighted degree, are analyzable, thus precluding transcriptional alignment with structural similarity networks at their most fundamental and interpretable unit, the edge.

Future research using genome-wide association studies (GWAS) will be essential to elucidate how these transcriptional results relate to the expected pleiotropic relationships of common genetic variation associated with both MRI similarity phenotypes and genetic risk for brain-related disorders. Emerging biobank-scale data has enabled important work demonstrating the role of common variants to other MRI-derived measures of brain structure (Eliott et al. 2018; Smith et al. 2021) and their relationship to the genetics of both normative development (Brouwer et al. 2022) and neurodevelopmental conditions (Brouwer et al. 2022; Warrier et al. 2023). To date, some GWAS studies have analysed the genetics of structural similarity network phenotypes (Wu et al. 2023), but this work remains limited and underpowered. More powerful GWAS of structural MRI similarity phenotypes would add important validation and mechanistic context to the evidently strong coupling between MRI similarity and gene co-expression phenotypes, and it would enable the genetic study of edge-level network phenotypes. In any future GWAS, the use of trans-ancestral genetic cohorts will be important to ensure generalizability of findings to populations of non-European descent (Fu et al. 2024).

Typical and atypical human structural brain network development

Previous work on structural brain network development has been limited by the difficulty of obtaining high quality DTI connectomes, especially in younger populations (Dauguet et al. 2007; Donahue et al. 2016; Yendiki et al. 2014), and the fact that structural covariance networks are only estimated at the group-level. Despite potential limits to the extent to which similarity can explain earlier developmental processes, e.g., in the presence of multiple overlapping covariance-generating processes (Hallgrímsson and Hall 2011; Hallgrímsson et al. 2009), single-subject structural similarity networks represent a step forward in this area by making it straightforward to track group mean and individual trajectories of brain network development in health and disease. This newfound ability to track longitudinal change is necessary for understanding the emergence of structural similarity networks through the dynamics of the complex relationships between network-based phenotypes and the underlying (constituent) morphometric features (Hallgrímsson and Hall 2011; Hallgrímsson et al. 2009).

Recent work using both cross-sectional and longitudinal data has highlighted coordinated normative changes in similarity network topology throughout development, from infancy (Zhao et al. 2023; Fenchel et al. 2020; Batalle et al. 2013; Wang et al. 2024) to preadolescence (Wu et al. 2023), adolescence (Dorfschmidt et al. 2024), through adulthood (Niu et al. 2024; Janssen et al. 2024; Jingming Li et al. 2024), and across the lifespan more generally (Jiao Li et al. 2024; Jingming Li et al. 2024). It appears that a small-world network organisation can be observed in structural similarity networks as early as 22 weeks post conception (Zhao et al. 2023), adult-like cortical modules are present at birth (Fenchel et al. 2020), and even an individual signature of connectivity, or a connectome fingerprint, is observable prior to full-term gestation (Wang et al. 2024). Recent work has further highlighted the contrasting extremes of the lifespan, early development and late-life, as periods of greatest developmental change in structural similarity (Li et al. 2024).

Relatedly, structural similarity networks constructed in adults using morphometric measures of sulcal phenotypes, i.e., sulcal phenotype networks (SPNs), have been shown to closely reflect the heterochronic timing of sulcus formation in foetal brain development during the second half of gestation (Snyder et al. 2024). SPNs comprised two modules of sulci with distinctly linear or complex (fractal) morphometrics (Snyder et al. 2024), corresponding to historical concepts of two (or three) classes of sulci (Chi et al. 1977): primary sulci, which began to form by folding of the initially smooth cortical surface from about 20 weeks, were represented by the linear module; and secondary (or tertiary) sulci, which formed in later gestation, were represented by the complex module of the SPN.

Multiple studies have suggested a developmentally-relevant role of decreased structural similarity, or increased dis-similarity, hypothetically representing increased architectonic differentiation, between paralimbic and isocortical areas. Specifically, one study of a normative longitudinal adolescent cohort found that nodal degree of structural similarity increases in paralimbic cortex, and decreases in isocortical areas, over the age range 14-24 years (Dorfschmidt et al. 2024). A separate study of pre-adolescents linked higher dis-similarity between paralimbic and isocortical areas with higher cognitive abilities, in terms of both fluid and crystallised intelligence (Wu et al. 2023). Collectively, these results highlight distinct developmental trends in MRI (dis-)similarity between distinct cortical types. This sensitivity of structural similarity network phenotypes to age-related changes in brain organisation is also reflected in their accurate prediction of an individual’s age from a single MRI scan, which out-performed age prediction by DTI tractography in the same sample (Galdi et al. 2018; Sebenius et al. 2023).

Case-control studies of atypical brain structural networks in neurodevelopmental and neurodegenerative disorders

The links between cortical similarity and development provide a potential mechanism by which variation in disease can occur: changes that occur during gestation or early development, due to genomic or environmental factors, could alter the typical spatiotemporal programming of similarity network formation (Barbas and Hilgetag 2023), as illustrated in Figure 4B. Indeed, variation in normative development of structural similarity has been linked to individual differences in cognitive skills and sub-clinical psychopathology (Wu et al. 2023; Fenchel et al. 2022; Jiao Li et al. 2024); for example, the degree of frontal and temporal cortical hubs in MSNs was correlated with verbal IQ scores in young adults (Seidlitz et al 2018). In a clinical context, similarity networks have shed light on case-control differences in multiple neuropsychiatric disorders, including schizophrenia (Janssen et al. 2024; Zong et al. 2023; Morgan et al. 2019; Yao et al. 2023, 2024; Park et al. 2023), and mood disorders like major depressive disorder and bipolar disorder (Lei et al. 2022; Xue et al. 2023; Li et al. 2021), which are commonly considered to arise in part due to atypical neurodevelopmental trajectories (Sowell et al. 2003). Many of these case-control differences in MRI similarity network phenotypes have been related to disorder-related changes in gene expression during foetal or early postnatal life. Considering the other end of the lifespan, multiple studies have reported abnormal structural MRI similarity in neurodegenerative disorders (Zhang et al. 2021; Yajie Wang et al. 2024; Jenkins et al. 2024). Lastly, while many studies have focused on discrete case-control differences, at least two studies have linked individual differences in continuous symptom severity to structural similarity network metrics estimated in an individual brain scan (Zhang et al. 2021; Zong et al. 2023). For comprehensive reviews of recent studies reporting case-control differences and/or normative brain development and ageing trends in MRI similarity network phenotypes, see Wang and He (2024) and Cai et al. (2023).

An interesting point of consistency with normative developmental studies can be observed in multiple case-control studies that observe pathological effects of disorders on MRI similarity within or between paralimbic versus neocortical areas (Royer et al. 2023; Martins et al. 2022). These findings align with prior work suggesting that different cortical types are associated with differential predisposition to pathogenic changes (García-Cabezas et al. 2019; Haroutunian et al. 2009), e.g., links have been made between the high synaptic plasticity and increased vulnerability to neuropsychiatric disorder-related changes of paralimbic areas compared to neocortical areas (García-Cabezas et al., 2019; Barbas et al., 1995).

In developmental and clinical research using fMRI, a key methodological question is how head motion affects functional connectivity. The same question likely impacts structural similarity as well, but has not yet been so well-studied. Head motion is more common in younger subjects and clinical populations (Dosenbach et al. 2017) and it is known to have spatially varied effects on regional morphometric phenotypes (Reuter et al. 2015; Alexander-Bloch et al. 2016), increasing their variance and affecting their structural covariance (Pardoe and Martin 2022). Future research will need to investigate more extensively how head motion influences structural similarity network phenotypes and their constituent MRI features.

Open Questions

As structural MRI similarity analysis continues to grow in popularity, more work is needed to elucidate both fundamental properties of MRI similarity networks and their potential for translational use. We conclude by highlighting three key open questions:

What is the optimal (set of) MRI feature(s) to measure brain similarity?

Researchers studying structural MRI similarity are faced with the decision of choosing a set of structural MRI features to include in network construction, prompting the question: which set of features is “best”? There is no clear-cut answer. Prior work on multivariate similarity networks using leave-one-feature-out analysis has demonstrated robustness of inter-areal similarity to the choice of specific features (Fenchel et al. 2020; Seidlitz et al. 2018). However no formal feature-selection protocol has yet been established. It seems likely that similarity between different MRI features may reflect different aspects of the architectural or connectional organisation of the brain. For example, while similarity in cortical thickness predicted neither axonal connectivity in the macaque (Hilgetag et al. 2016) nor human DTI-based axonal connections, it did predict functional connectivity in humans (Bazinet et al. 2023). Moreover, increasing the number of macrostructural features used to construct MSN or MIND networks resulted in closer resemblance to tract tracing networks (Sebenius et al. 2023). Relatedly, combining multiple group-level similarity networks (laminar, gene expression, etc.) resulted in a stronger correlation with group-level (DTI-based) structural connectivity (Hansen et al., 2023). This suggests that it may be advantageous to take a multivariate approach to measuring cortical similarity “in general”, across multiple modalities of MRI, as expected to some degree by the homophily principle; but retain the option to use univariate approaches to measuring more specifically interpretable similarity networks. For example, MRI similarity analysis based solely on a micro-structural marker of cortical myelination, e.g., MT or T1/T2 ratio, is more straightforward to interpret specifically as a proxy of myeloarchitectonic similarity between two cortical areas than a multivariate similarity analysis potentially combining both micro- and macro-structural MRI metrics, as well as fMRI connectivity, in the construction of a general homophily map of the cortex.

Future work using both human imaging and translational animal models will be essential to learn more about which (combinations of) MRI sequences or parameters are most clearly representative of which underlying architectural and connectional phenotypes, and to understand in a more nuanced way how the many diverse aspects of brain similarity that have recently become measurable are related to each other and to organisational principles. One particularly valuable extension of this work would be to disambiguate which measures of structural MRI similarity are most reflective of other inter-areal relationships in the brain, including functional connectivity derived from fMRI or MEG, metabolic or neurotransmitter similarity derived from PET imaging, and complementary aspects of anatomical connectivity including presence/absence, number and strength of tractographic axonal streamlines. This will be important in more clearly defining the organisational principles that underlie the observed relationships between multiscale, multimodal MRI perspectives on cortical similarity. This deeper knowledge would also be very helpful to investigators wanting to optimise MRI feature selection for structural similarity network analysis designed to address their specific research questions (see Box 2 for a User Guide).

Box 2: User Guide: contexts for usage of various structural MRI similarity methods.

Researchers planning to measure MRI similarity must decide which method for similarity estimation should be used. The choice of method will likely depend on the specific research questions at hand, the interpretability of results, and the data modalities available. Some illustrative contexts for the usage of different methods are summarised here:

• Structural covariance networks: SCNs may be particularly suitable for studies of a single MRI feature, e.g., cortical thickness, and its covariance patterns at the group level of patients with a shared diagnosis, e.g., schizophrenia. Structural covariance is closely coupled to genetic correlation between cortical areas, since phenotypic correlation generally approximates genetic correlation (Cheverud 1988; Valk et al. 2020; Stauffer et al. 2023). Therefore, a comparison of group-level SCNs between clinical cohorts may plausibly be interpreted as an indication of altered genomic organisation underlying any disorder-related changes in structural covariance. SCNs are less appropriate when subject-level data are desired or essential, for example, in longitudinal studies of brain development.

• Morphometric similarity networks: MSNs have the benefit of a large body of literature supporting their validity, including evidence that the degree or hubness of cortical areas in MSNs is spatially aligned with relevant cognitive and transcriptional phenotypes. Applications seeking to build on or refer to this literature may consider the use of MSNs. MSNs can be especially useful to study similarity networks that include macrostructural MRI phenotypes, e.g. cortical surface area, that are not well-defined at the vertex or voxel level and so are more suitable for correlation analysis of a regional mean feature vector.

• Microstructural profile covariance networks: MPCs model layer-specific, spatially-resolved brain structural features. They are therefore particularly well-suited to studies hypothetically motivated by lamina-specific aspects of cortical architectonics and connectivity, e.g., the structural model. Given their validation against histological benchmarks from the BigBrain atlas (Amunts et al. 2013), MPCs are a suitable methodological choice to study MRI similarity networks that are aligned with classical, microscopic measures or cortical cyto- and myeloarchitectonics. MPCs are less appropriate for studying similarity based on macrostructural MRI features. They are not currently developed for multivariate MRI similarity analysis.

• Morphometric inverse divergence networks: MIND networks may be most appropriate when researchers are interested in studying the similarity between any number of features measured at the individual level. Given the strong observed relationship of MIND phenotypes to normative gene co-expression, and their increased heritability compared to MSNs, MIND may be plausibly used to investigate genetic and/or transcriptomic underpinnings of structural network alterations. The flexibility of using one or more of multiple MRI features to make MIND networks also enables tailoring the method based on specific research goals. For example, if a researcher is interested in using MIND similarity as a proxy for connectivity, they may decide to optimise feature selection for MIND network construction by focusing on the subset of available MRI features that are most strongly validated as markers of cortical myelination or neurite density.

Where are the data gaps in our understanding of homophilic network development?

Multiple gaps exist in our understanding of structural brain network development and the (homophilic) principles that guide it, which could be addressed by future work. First, building on recent developmental studies of MRI similarity network phenotypes (Dorfschmidt et al. 2024), it will be essential to study longitudinal changes in cortical similarity from foetal life and early childhood through adolescence and into old age, in order to gain a comprehensive understanding of normative development of human cortical similarity networks. This research will be greatly facilitated by the use and creation of open resources for human network science which equitably represent the whole human population (Bethlehem et al. 2022). Such observational studies will be powerfully complemented by comparable MRI similarity studies of animal models, which can add mechanistic understanding through highly controlled experimental settings and invasive neurobiological measurement of benchmark data, e.g., tract-tracing measures of connectivity. Additionally, large-scale imaging-genetic datasets will increasingly enable the mechanistic and causal analysis of normative developmental processes and neurodevelopmental disorders of cortical similarity network organisation.

Most work to date has focused on similarity between cortical areas. While initial studies show relevant changes in structural similarity between cortex and subcortex during development (Wu et al. 2023), it is currently unclear whether the assumptions underpinning MRI similarity of cortical areas are also applicable to MRI similarity between subcortical structures, or between subcortical and cortical areas. For example, evidence is currently lacking for homophilic cortico-thalamic connectivity, and cortico-thalamic projections do not support the heterochronic model of homophilic network development that currently pertains only to the cortex (Ruiz-Cabrera et al. 2023; Kahle 1951). In contrast, the architectonics of cortical areas appear to determine cortico-striatal connectivity, such that cortical areas of similar type connect to adjacent striatal sectors (Yeterian and Pandya 1991; Del Rey and García-Cabezas 2023). Future work will be needed to interpret MRI similarity more securely as a proxy for architectonic similarity and axonal connectivity between subcortical nuclei and between cortex and subcortex in a whole brain MRI similarity network.

What are the prospects and challenges of translating structural MRI similarity research to clinical applications?

Despite growing success as tools for scientific discovery, quantitative multimodal structural MRI, functional MRI and diffusion weighted imaging have not yet achieved widespread clinical application. A translational barrier for brain network measures is their reliance on specific and often time-consuming MR sequences that lack a realistic path to clinical implementation. In contrast, MRI similarity analysis pipelines are technically robust and can generate an individual brain network from a single standard structural (T1-weighted) MRI scan, as is routinely acquired in research and clinical settings. Indeed prior work has specifically tested the feasibility of clinical translation of these networks by demonstrating reasonable correspondence between MSNs derived from only a single T1-weighted MRI scan and MSNs derived from a wider range of multimodal MRI features (King and Wood 2020), and a number of studies have found relevant effects of clinical disorders on T1-weighted-only morphometric similarity networks (Morgan et al. 2019; Xue et al. 2023; Martins et al. 2022). The combination of algorithmic robustness and generalizability of similarity network analysis to many extant MRI datasets is potentially a leap forward to real world applications, compared to other fMRI- or DTI-based network methods, which require clinically non-standard data to be specially collected and expertly analysed. This direction of travel towards greater democratisation of brain network analysis is further accelerated by advances in deep learning-based segmentation that can be used to parcellate anatomical regions from lower resolution scans, like computed tomography data (Billot et al. 2023), or low-field (Sarracanie et al. 2015) and quick-scan MRI protocols (Váša et al. 2022), which could also be used in the future to provide input features for similarity analysis of clinically accessible data that have not previously been analysable from a network perspective.

Ongoing efforts to widen the geographical and demographic inclusivity of MRI data, including international research quality (Prado et al. 2024) and low-field scanning consortia (Abate et al. 2024), as well as increasing use of mobile MRI scanning units (Deoni et al. 2022), are expected to generate larger and more representative MRI datasets that will also be amenable to similarity network analysis. As the scale and diversity of data used for similarity network analysis grows, future work will need to attend closely to the effects of data quality, including effects of head motion on structural MRI features and similarity, and the impact of variation in data pre-processing and similarity analysis pipelines on network phenotypes. It will also be important to use normative benchmarking to control for site or scanner differences in data acquisition and to precisely measure clinically meaningful differences in cortical similarity in individual patients. The dissemination and adoption of reproducible MRI similarity data acquisition and analysis pipelines, consistent with open science principles, will be important to accelerate realisation of these translational opportunities.

Glossary

Similarity

is estimated as the association, usually correlation or divergence, between two areas in terms of the vector or distribution of one or more structural MRI metrics of geometry or tissue composition measured locally in each area.

Architectome

is a representation of the cortical patterning of differentiation, myelination or lamination in terms of inter-areal similarity.

Mesocortex

including the insular and cingulate gyrus, has been further subdivided into more primitive (peri-allocortical, agranular) and more evolved (pro-isocortical, dysgranular) zones of cortex (Mesulam and Mufson 1982).

Isocortex

has been subdivided into 3 cyto-architectonically distinct zones of eulaminate cortex, or into functionally differentiated zones of unimodal or heteromodal association cortex.

Structural model

links cytoarchitectonic class with connectivity which posits that the probability and type of connection between two cortical areas depends on their cortical type, with within-layer connections expected between areas of the same type and specific cross-layer connections expected between areas of different types.

Wiring cost

refers to the biological cost of forming and maintaining axonal connections between cortical areas, which is often approximated by the physical distance of the connection.

Anlagen

are initial clusters of embryonic cells, or more generally the foundation of future tissue types that will differentiate with development.

Cytoarchitectonics

is the study of the cellular composition, clustering and layering of neuronal tissue, including but not limited to the proportion of different cell types and their orientation in space; historically rooted in microscopic histology.

Myeloarchitectonics

is often used to refer to the layering and density of myelinated axonal fibres in microscopic histological studies of the cortex but can also be used to refer to the macroscopic organization of white matter tracts interconnecting cortical areas.

Heterochronicity (or heterochrony)

refers to differences in timing or duration of developmental or evolutionary processes in different brain regions.

Connectivity

in the context of cortical anatomy refers primarily to monosynaptic axonal connections between areas, such as demonstrated by tract-tracing studies in animal models and approximated by structural MRI similarity and DTI-based tractography.

Homophily

means that structurally similar cortical areas are more likely to be connected than dis-similar areas, and that structurally similar areas are also likely to be similar to each other in terms of functional connectivity, gene co-expression and other aspects of similarity. Homophily has several near-synonyms, including assortativity, clustering and local efficiency in the language of graph theory. Heterophily is the opposite of homophily, meaning that structurally dis-similar cortical areas are more likely to be axonally connected.