Topological turning points across the human lifespan

Topological turning points across the human lifespan | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Topological turning points across the human lifespan Alexa Mousley, Richard Bethlehem, Fang-Cheng Yeh, Duncan Astle This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6120723/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Nov, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Structural topology develops non-linearly across the lifespan and is strongly related to cognitive trajectories. We gathered diffusion imaging from datasets with a collective age range of zero to 90 years old ( N = 4,216). We analysed how 12 graph theory metrics of organization change with age and projected these data into manifold spaces using Uniform Manifold Projection and Approximation. With these manifolds, we identified four major topological turning points across the lifespan – at eight, 32, 62, and 85 years old. These ages defined five major epochs of topological development, each with distinctive age-related changes in topology. These major life epochs each have a distinct direction of topological development and specific changes in the organizational properties driving the age-topology relationship. This study underscores the complex, non-linear nature of human development, with district phases of topological maturation, which can only be illumined with a multivariate, lifespan, population-level perspective. Biological sciences/Neuroscience/Computational neuroscience/Network models Biological sciences/Developmental biology Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 MAIN Trajectories of change in brain structure and function emerge across the lifespan 1 – 4 . Topology, the complex motifs within which neural connections are organized, develops with age and is associated with key cognitive, behavioral, and mental health outcomes 5 – 10 . Topology-outcome relationships have been established within relatively narrow age ranges, such as childhood 6 , 7 , 10 . But what are the underlying principles of organizational change? Are there key points in our lifespans wherein the brain transitions into a different phase of developmental change? Addressing these questions requires comprehensive mapping of lifespan network topology alongside a multidimensional framework capable of establishing the non-linear dynamics of developmental change. Prior research has revealed significant age-related changes in structural topology across the lifespan 4 , 11 . A typically developing infant’s brain network displays adult-like structure with hub distribution, rich clubs, small-worldness, and modularity at birth 12 – 21 . Throughout early development, networks become more integrated with increasing strength and efficiency and decreasing modularity 22 – 24 . In adulthood, many researchers describe an inverted “U” shape of development with a peak occurring around 30 years old where the brain is maximumly efficient and integrated 25 – 27 . This research uses the terms inflection point 1 , 2 , 28 , 29 or peak age 26 , 27 to describe important points of change in organizational metrics – many of which occur in the fourth decade of life and intersect with other developmental and aging milestones. After this point and into late life, aging is associated with reduced connectivity, mainly through pruning of weak connections 11 , 26 , 30 , increased modularity 25 , and more pronounced rich club organization 26 than earlier in life. These established fluctuations of organizational principles underscore the dynamic and complex nature of topology development. Mapping neural systems across the lifespan calls for data-driven methods that can handle complex data and capture high variability without making strong assumptions about the underlying data 31 . Manifold learning is a popular technique to project high-dimensional data into a low-dimensional space by filtering out closely related features likely driven by similar mechanisms 32 , 33 . These projections, created using non-linear dimensionality reduction techniques such as Uniform Manifold Approximation and Projection (UMAP), are easier to interpret while maintaining the intrinsic structure of complex data 32 , 34 . UMAP, in particular, captures both local and global data patterns with faster run times than similar methods (e.g., t-SNE) 34 . The manifold spaces themselves graphically represent the relationships in the original high-dimensional space and, therefore, offer an opportunity to leverage projections to identify points of change. We define these points of change as turning points , indicating significant shifts in the overall trajectory of topology, rather than inflection or peak points, which refer to changes in individual organizational measures. This study takes a data-driven approach to chart structural topological development across the human lifespan. Specifically, we (1) characterize connectivity development; (2) explore topological integration, segregation, and centrality; (3) use UMAP to define topological manifold spaces and identify major turning points across the lifespan therein; and (4) examine how these turning points capture important phases of topological development. RESULTS We gathered diffusion imaging data from nine datasets with a combined age range of zero to 90 years old (Fig. 1 a,b; Extended Data Table 1 ). A large sample ( N = 4,216) including all available images was fiber tracked 35 and harmonized 36 (Fig. 1 c). For analysis, multiple graph theory metrics 37 (Supplementary Table 1) were calculated using normalized weighted networks with a cross-sectional, neurotypical subset ( n = 3,802; female n = 1,994; male n = 1,808). Following topological analysis, we projected age-predicted organizational measures into manifold spaces using UMAP 34 and determined significant turning points in topological development across the lifespan. Connectivity. Before exploring network organization, we first examined general changes in connectivity across the lifespan by preserving the distribution of density through thresholding to 70% of the average raw density per age bin (Fig. 1 c; Supplementary Fig. 1a). Density – the percent of connections present in the network 37 – changed non-linearly across age with high-density networks present around birth and 30 years old and sparse networks observed around 10 and 80 + years old (Fig. 1 e; F density,age = 219.20, estimated df = 8.92, p < 2.00 x 10 − 16 ). In addition, node strength – the sum of edge weights 37 – significantly increased across the lifespan in a linear pattern both in average strength across all nodes and maximum strength across all nodes (Fig. 1 f; F average strength,age = 33.10, estimated df = 5.46, p < 2.00 x 10 − 16 ; F maximum strength,age = 29.15, estimated df = 3.85, p < 2.00 x 10 − 16 ). Overall, these networks displayed the expected pattern of shifting from dense, weak networks in early life to sparse, strong networks in later life 16 , 39 (Fig. 1 d). Full topological analysis with variable density networks is included in the extended data (Extended Data Table 2 ; Extended Data Fig. 1 ). Topology. To remove the confounding factor of network density from the analysis of topological changes, we conducted a density-controlled analysis where each network was constrained to exactly 10% density (Fig. 1 c). This method allows for fair comparison of topological structure across the lifespan without total connectivity biases. Integration metrics. Global efficiency, which measures how well the network is connected by short path lengths 40 , significantly fluctuated across the lifespan, peaking at 29 years old before steadily declining to a minimum at 90 years old (Fig. 2 a; Table 1 ). Other integration metrics include characteristic path length, the average shortest path length of the network 41 , and small-worldness, the ratio of clustering coefficients and characteristic path length 42 . Both showed inverse patterns to global efficiency (Fig. 2 a; Table 1 ). Additionally, average network strength significantly increased in a more linear pattern, reaching its maximum at 90 years old (Fig. 2 a; Table 1 ). These results suggest that while network strength linearly increases with age, topological integration initially decreases in the first decade, peaks at the beginning of the fourth decade, and then declines for the rest of the lifespan. Segregation metrics. Modularity, the division of networks into non-overlapping, highly intra-connected node groups 43 , significantly fluctuated across the lifespan with a minimum at 30 years old and a maximum at 90 years old (Fig. 2 b; Table 1 ). Core/periphery structure, which assesses how well a network separates into a non-overlapping dense core and a sparse periphery 37 , fluctuated more than modularity, peaking at 20 years old and reaching a minimum at 55 years old (Fig. 2 b; Table 1 ). Additionally, networks can be segregated based on a subnetwork with a specific strength (i.e., s-core) or degree (i.e., k-core) 37 . While k-core did not significantly change across age, s-core significantly fluctuated across the lifespan with a minimum at 12 years old followed by a continuous increase to a maximum at 90 years old. Compared to global segregation metrics, average local segregation measures increased more linearly across the lifespan. Local efficiency – the extent to which neighboring nodes are connected by short paths 40 – and clustering coefficient – the extent to which neighboring connected nodes are also connected to each other 41 – both significantly increased to a maximum at 90 years old (Fig. 2 b; Table 1 ). These results emphasize a difference between global segregation, which oscillated across age, and average local segregation, which showed more linear patterns. Beyond differences in fluctuations in mid-life, network segregation peaked in late life. Centrality metrics. Centrality measures nodes’ importance to the network, often based on inclusion in key paths. Betweenness centrality measures the fraction of shortest path lengths that pass through the node 44 , which fluctuated across the lifespan, reaching a minimum at 31 years old and maximum at 90 years old (Fig. 2 c; Table 1 ). Comparatively, subgraph centrality – the weighted sum of all close walks for a node 37 – significantly increased in a more linear pattern (Fig. 2 c; Table 1 ). These results highlight differences in the developmental pattern between individual centrality metrics but indicate a continuous increase in centrality starting around the fifth decade. Generally, network organization displays linear and fluctuating patterns across the lifespan. Various sex effects were found and are in the Extended Data, though these results could be explained by brain size differences that are not considered in this analysis 30 , 45 (Extended Data Fig. 2 ). Overall, average strength, average local efficiency, average clustering coefficient, s-core, and subgraph centrality display linear-like patterns while the other metrics appear to have peaks and valleys throughout the lifespan – many of which appear around 30 years old. Construction of lifespan epochs. Many topological measures are highly correlated and therefore convey redundant and unique topological characteristics (Extended Data Fig. 3 a). Thus, we reduced the dimensionality of this data using manifold learning, resulting in a 3-dimensional topological space capturing crucial patterns in the data. Manifolds were constructed using significant age-predicted metrics (i.e., excluding k-core), which were averaged for each age. Considering the influence of parameter choice on UMAP projections 46 , we created 968 UMAPs with a variety of parameters to capture both local and global-level information (Fig. 3 ). Manifolds were then used to determine major turning points across the lifespan, marking epochs where topological development is occurring along the same trajectory (Fig. 3 c; see “Methods”; “Turning point identification”). Major turning points occur around age eight, 32, 62, and 85 (Fig. 3 c). Sex-stratified projections and turning points are available in the Supplementary Materials (Supplementary Fig. 2). These turning points define five major epochs of life: Epoch One, which lasts from zero to eight years; Epoch Two, which lasts from eight to 32 years; Epoch Three, which lasts from 32 to 62 years; Epoch Four, which lasts from 62 to 85 years; and Epoch Five, which lasts from 85 to 90 years. We explored changes across these epochs using Pearson correlations to assess directional relationships between age and topological measures and LASSO regularized regressions to identify which organizational properties drive the relationship between topology and age. At each turning point, we analyzed significant changes in directionality and key driving topological metrics. Epoch 1: 0–8 years old “infancy into childhood” . The first epoch ranges from zero to eight years ( n = 630), covering the period of infancy through childhood. Significant correlations were found within this epoch in eight organizational measures, characterized by decreasing global integration, increasing local segregation, and stable centrality (Fig. 4 f; Table 2 ). Although many metrics correlate with age, the LASSO regularized regression retained eight measures and identified the clustering coefficient as the strongest topological predictor of age (λ = 0.03; Fig. 4 f; Table 2 ). In contrast, small-worldness is the strongest correlation across this age range (Fig. 4 f; Table 2 ). Thus, while a decrease in small-worldness across this period is the largest directional pattern, the local-level clustering coefficient is the crucial predictor of age (Fig. 4 a). Overall, topological development from zero to eight years old is characterized by decreasing global integration, however, clustering coefficient is a key topological measure across this period. Thus, despite decreasing integration overall, a child's age is most distinct topologically in the extent to which neighboring nodes are interconnected. The first epoch of life ends around 8 years old, which was the most frequently identified turning point, occurring 215 times across all UMAPs (Fig. 3 c). Around eight years old, we observed the factors driving the relationship between topology and age shift from clustering coefficient to betweenness centrality (Fig. 4 a). Directional changes occur as well, with significantly decreasing integration changing to significantly increasing integration after eight years old (Table 2 ; Extended Data Fig. 4 a). Epoch 2: 8–32 years old “Adolescence”. The second epoch occurs from eight to 32 years old ( n = 1,791) and encompasses late childhood through early adulthood. Within this epoch, 10 topological measures were significantly correlated with age, characterized by decreasing network integration and complex segregation and centrality patterns (Fig. 4 e; Table 2 ). Generally, strength-based and local-level segregation increased, but global modularity decreased (Fig. 4 e; Table 2 ). Coinciding with the largest correlation, the LASSO regression reveals that betweenness centrality was the largest driving factor for identifying age (λ = 0.65; Fig. 4 e; Table 2 ). Together, the results highlight a complex pattern of topological change from eight to 32 that can be characterized by increasing integration alongside decreasing global segregation and increasing local-level segregation. Betweenness centrality, which captures nodes’ participation in important paths, is particularly district during this epoch both in terms of the driving factor and largest directional changes. The second epoch of life ends around 32 years old (Fig. 4 c; identified 92 times). At this age, there are many changes in the directionality of topological development. Before 32 years old, global efficiency increased while characteristic path length, small-worldness, modularity, and betweenness centrality significantly decreased – these correlations shift to the opposite direction after 32 years old (Table 2 ; Extended Data Fig. 4 a). This suggests a shift from increasing to decreasing integration as well as changes from decreasing to increasing modularity, and betweenness centrality happens around 32 years old. In addition, the topological metric driving the relationship with age changes from betweenness to small-worldness at 32 years old. Thus, the beginning of the fourth decade of life marks the end of a phase of increasing efficiency and integration and the start of a period of increasing segregation. Epoch 3: 32–62 years old “Adulthood”. The third epoch occurs from 32–62 years old ( n = 1,006), extending across three decades of adulthood. Across this period, 10 topological measures were significantly correlated with age, characterized by decreasing network integration, general increases in segregation, and minimal centrality changes (Fig. 4 d; Table 2 ). While clustering coefficient was most highly correlated with age, the LASSO regression revealed that small-worldness was distinctly associated with age across this period (λ = 0.69; Fig. 4 d; Table 2 ). Thus, as with the first epoch, there was a discrepancy between the largest directional changes and which topological metric was the best age predictor during this period. Together, these results suggest network integration decreased with minimal centrality changes, and while segregation was complex, most segregation metrics increased across this epoch. Despite rapidly increasing clustering, the extent to which the network is highly clustered while also being connected by short path lengths – small-worldness – is the most important factor for predicting age during this adulthood epoch. The third epoch ends around 62 years old and was the least distinct of the four major turning points, as it was only identified 58 times (Fig. 3 c). While there are no significant changes in the directionality of topology at this age (Extended Data Fig. 4 a), we observed the driving topological metric shift from small-worldness to modularity. Though these metrics are correlated, this point marks a change in which the network becomes more segregated into groups, which is the distinct feature of topological development. Epoch 4: 62–85 years old “Early aging”. The fourth epoch ranges from 62–85 years old ( n = 522), spanning the shift from adulthood into early aging. Only six topological metrics significantly correlated with age (Fig. 4 c; Table 2 ). While this period is topologically most distinct in modular changes, decreasing integration and increasing centrality are also present (Fig. 4 c; Table 2 ). The LASSO only retained modularity as a predictor, aligning with the strongest correlation in this period (λ = 1.03; Fig. 4 c; Table 2 ). The last turning point in the lifespan identifies that the end of this epoch is around 85 years old, which was the second most frequently occurring turning point (Fig. 3 c; identified 146 times). There were no significant changes in directionality at this age (Extended Data Fig. 4 a); however, the most important factor for identifying age shifts from modularity to core/periphery structure. In other words, from this turning point onwards, the networks start to form distinctly dense core and sparse periphery subnetworks. Epoch 5: 85–90 years old “Late aging”. The last epoch is 85–90 years old ( n = 56), ranging from late aging individuals to the maximum age included in this study. There were no significant correlations between topology and age across this epoch (Fig. 4 b; Table 2 ). In addition, the regularization of the LASSO had to be weakened for any predictors to survive (see “Methods”; “Statistics”). With a less-sparse model, core/periphery structure is the strongest predictor of age, which also aligns with the largest correlation (λ = 0.11; Fig. 4 b; Table 2 ). These results reflect a reduction in the significance of the relationship between topology and age in the latest years of life, though core/periphery structure emerges as the most age-related topological measure. Characterizing all turning points. Beyond detailing changes in topology within each epoch, it is helpful to compare topology differences across epochs. While UMAP provides information about where major turning points occur, we cannot interpret what is topologically changing at these points due to UMAPs having arbitrary dimensions (e.g., no loading scores). Simply put, UMAP informs us where non-linear changes occur but not what those changes are. To explore what topological changes occur around these major turning points, we ran a Principal Components Analysis (PCA) across the 11 topological metrics for the entire lifespan sample, using a parallel analysis to identify three principal components (PCs) that explain 80% of the variance in topological measures (Fig. 5 a). Segregation measures load most heavily onto PC1, while integration metrics load mostly on PC2, and both segregation and centrality metrics load onto PC3 (Fig. 5 a; Extended Data Fig. 3 b-e). PCA scores across epochs had significantly different variance and means in all PCs (Fig. 5 a,c; Table 3 ). We utilized the PCA to compare average PCA scores between consecutive epochs. Significant shifts in PC1 and PC2 occur between epochs one and two (PC1 p = 4.80 x 10 − 04 ; PC2 p = 6.66 x 10 − 08 ) and between epochs two and three (PC1 1 p < 1.00 x 10 − 323 ; PC2 p = 1.39 x 10 − 07 ) (Fig.5a,c; Extended Data Fig. 4 b). Neither epoch comparison had significant differences in PC3 (epochs one and two p = 0.706; epochs two and three p = 0.989) (Extended Data Fig. 4 b). These results suggest that the first two turning points – eight and 32 years old – identify significant shifts occurring in the two primary components, upon which load most segregation and integration metrics (Fig. 5 a; Extended Data Fig. 3 b,c). Epochs three and four – the 62-year-old turning point – is the only point where a significant shift in PCA scores occurs across all PCs (Fig. 5 a,c; Extended Data Fig. 4 b; PC1: p = 6.54 x 10 − 13 ; PC2: p = 1.83 x 10 − 08 ; PC 3: p < 1.00 x 10 − 323 ). These results suggest a distinct shift across all primary components despite no directional changes in topology. Inversely to the first two turning points, the last turning point (85 years old) captures significant changes in PC3 ( p = 0.018) but not PC1 ( p = 0.472) or PC2 ( p = 0.261) (Fig. 5 a,c; Extended Data Fig. 4 b). Together, these results indicate that differences in topology before and after 85 years old appear within segregation and centrality metrics, which load onto PC3 (Fig. 5 a; Extended Data Fig. 3 d). Lastly, we used the trajectories of PCA scores within epochs to examine differences in developmental patterns. Using dynamic time warping, we qualitatively compared the trajectory patterns between each consecutive epoch (Extended Data Fig. 4 c) (see “Methods”; “Dynamic time warping”). The warping distance (Euclidean) conveys how different two trajectories are – larger distances indicate more different trajectory patterns than shorter distances. This analysis showed that epochs one and two have the most similar trajectory patterns, followed by epochs four and five and epochs three and four (Fig. 5 b,c). The two epochs with the most different trajectories are two and three, suggesting that the trajectory pattern is distinctive before and after 32 years old compared to any other turning point (Fig. 5 b,c). When comparing all analyses across all turning points, 32 years old emerges at the largest turning point across the lifespan (Fig. 5 c). The last turning point – 85 years old – appears to be the smallest (Fig. 5 c). The two ‘middle’ turning points – 62 and eight years old – are distinct from each other in that significant directionality changes occur around eight years old but none at 62 years old (Fig. 5 c). Together, these results indicate that the major lifespan turning points signify critical shifts in the trajectory of topological development. DISCUSSION Our results emphasize the complex, non-linear topological changes that occur across the lifespan, with oscillating network integration development between childhood, adolescent, and adult periods. We found that centrality is important during adolescence but minimally for the rest of the life. Additionally, our results show a pattern of increased network segregation but decline of the age-topology relationship in late life. Broadly, the trajectory of topological development can be distinctly separated into multiple phases of development, with four major turning points occurring around eight, 32, 62, and 85 years old. These points indicate where the trajectory of topological development shifts significantly and begins a new projection into a different area of the manifold space. As it is novel to use manifolds to identify topological turning points, we aim to review where these turning points align with important anatomical and contextual milestones. The first turning point indicates that the childhood topological trajectory ends around 8 years old. The first few years of life are marked by consolidation and competitive elimination of synapses 16 and rapid increases in gray and white matter volume 1 . Our results indicated that, topologically, structural networks develop along the same dimensions from birth until about eight years old. This is consistent with a previously identified cortical turning point around 7 years old where there is an efficiency inflection point, cortical thickness peaks, and cortical folding stabilizes and efficiency 47 . This age also aligns with the onset of puberty, which begins from eight to 13 years old for females and nine to 14 years old for males 48 , and marks the initiation of significant alterations in hormone expression 49 and robust neurological changes 50 – 53 . Coinciding with this topological and neurobiological shift, the transition from childhood to adolescence brings with it increased risk of mental health disorders 54 , progression in cognitive capacity 55 , and modifications of socio-emotional and behavioural development 56 , 57 . Thus, the eight-year-old turning point not only signifies a distinct shift in topological development but also aligns with key cognitive, behavioral, and mental health developmental milestones. The second lifespan epoch, ages eight to 32, indicates no significant shift in the trajectory topological development. While adolescence begins with puberty, the end of adolescence is less clear, with older definitions ending before 20 and more recent definitions extending into the mid-20s 58 . The transition to adulthood is influenced by cultural, historical, and social factors, making it context-dependent rather than a purely biological shift 59 , 60 . Our findings suggest that in Western countries (i.e., the United Kingdom and United States of America), adolescent topological development extends to around 32 years old, before brain networks begin a new trajectory of topological development. Additionally, 32 years old is the strongest topological turning point of the lifespan. At this age, the most directional changes and largest shift in trajectory occur compared to the other turning points. These findings are highly consistent with previous work exploring individual topological metrics 25 – 27 that identify significant peak/inflection points at the beginning of the fourth decade. Beyond organizational changes, this turning point aligns with developmental trajectories of white matter. White matter volume and fractional anisotropy peak around 29 years old 1 , 61 , 62 , mean diffusivity arrives at a minimum around 36 years old 61 , 62 , and radial diffusivity reaches a minimum around 31 years old 61 . Together, these results indicate significant changes in white matter integrity and topological development occur around the beginning of the fourth decade of life. After age 32, the longest epoch begins, covering three decades of adulthood until age 62. Compared to rapid maturation in earlier life, changes in network architecture slow during this period 39 , 61 , 62 , which is consistent with our results that the trajectory to topological development is stable. This period of network stability aligns with a plateau in intelligence and personality 39 . Consequently, not only do we observe the alignment of turning points with significant anatomical and cognitive milestones, but also the stable topological epochs of life coincide with periods of anatomical, cognitive, and behaviour consistency. The third turning point, age 62, marks a topological shift without directional changes. Consistent with past work 25 – 27 , we find no directional changes in network organization occurring at this age. However, there were significant differences in PCA scores in all PCs. Therefore, this turning point may reflect protracted or accelerated development. Indeed, accelerated decreases in white matter integrity are known to occur in late life 61 . Additionally, the early 60s marks an important shift in health and cognition in high-income countries, such as the onset of dementia and hypertension 63 , 64 . Hypertension, characterized by chronically elevated blood pressure, is linked to cognitive decline and accelerated brain aging and is also a known risk factor for dementia 65 , 66 . Thus, as with the first two turning points, age 62 also aligns with significant shifts in health and cognition. The last turning point marks a distinct decline in the age-topology. After 85 years old, we found no significant relationships between age and brain organization, and the LASSO regression required weaker regularization than any other epoch for any metrics to survive. It is possible that the lack of significant findings reflects the small sample size ( n = 56). However, when considering the significant correlations from previous epochs, a declining trend appears after middle-age; epoch three had 11 significant correlations, epoch four had six significant correlations, and epoch five had no significant correlations. Therefore, this could reflect a true weakening relationship between age and structural brain topology in late life. The data processing pipeline and manifold construction involve numerous design choices, and while we have attempted to test how these may impact our results, some caveats remain. First, we used four versions of the AAL90 atlas warped to two-year, one-year, and neonatal brain sizes to address early-life brain volume changes 1 , 67 , 68 . This step was crucial for a consistent parcellation necessary for unbiased topological analysis, but atlas alignment differences may exist. Second, we harmonized tracked networks and provided 10 additional analyses exploring various harmonization methods (Supplementary Fig. 3). We chose the approach with the fewest remaining dataset effects. Notably, no turning points coincided with dataset transitions (e.g., BCP ends at five and CALM starts at six), as we would expect if turning points were dataset effects. However, harmonization may have over- or under-corrected for dataset differences. Third, networks were thresholded to a fixed density to ensure unbiased topological analysis, though this may obscure individual differences and small age-related changes variations. Additional analyses to assess the effects of these choices (Supplementary Fig. 1) and variable analysis demonstrate consistent turning points (Supplementary Fig. 4a). Despite this consistency, density-controlled results must be interpreted in the context of thresholding. Finally, we performed sensitivity analyses on turning point identification, which show generally consistent results, though it is important to note that the polynomial fit influences turning points (Supplementary Fig. 4). Additional key limitations are present in the project design. Despite sex effects in individual organizational measures, we did not sex-stratify this data due to sample size considerations. Future work should explore if the four major turning points identified here are sex sensitive. Moreover, the cross-sectional design of this project, due to limited availability of longitudinal lifespan datasets, limits exploration of causality or temporal dynamics within an individual. Additionally, while all participants included were deemed healthy by respective project guidelines, the gap between a healthy older individual and their peers may be larger than that between a healthy middle-aged individual and their peers. It is reasonable to speculate that older individuals in this study are healthier than typical individuals their age, which could bias the older sample. In conclusion, our findings suggest that structural topological development occurs non-linearly across the lifespan, with major turning points occurring around eight, 32, 62, and 85 years old. These ages demarcate periods of complex topological development with distinct age-related changes. This work reinforces the need for multivariate, lifespan, population-level approaches to deepen our understanding of complex topological development. METHODS Datasets and preprocessing. This study includes nine separate datasets that were collected and preprocessed specifically to suit the age range for the sample. Details on dataset samples, imaging procedures and preprocessing are summarized in Extended Data Table 1 . Four datasets were preprocessed in-house using QSIprep 69 , while five datasets were preprocessed by Dr Yeh and made publicly available on DSI studio’s Fiber Data Hub ( https://brain.labsolver.org/ ) (Extended Data Table 1 ). In-house processed datasets. The Baby Connectome Project (BCP) is a multi-site study conducted at the University of North Carolina at Chapel Hill and the University of Minnesota aimed at capturing the typical development of infants 70 . This dataset works as an extension of previous human connectome projects but is optimized for imaging and processing suitable for zero to five-year-olds (Extended Data Table 1 70 ). During harmonization, we utilized all scans from infants 12 months or older; however, for the analysis, we excluded longitudinal and repeat scans by using only the first scan for every infant (Extended Data Table 1 ). Some individuals had two different types of scans within the same session – 6-shell or dir-79 (Extended Data Table 1 ). Due to previous reports that the 6-shell scheme resulted in increased accuracy of local fiber orientation estimates 70 , if both scan types were available, the 6-shell scan was used. The Centre for Attention, Learning and Memory (CALM), Resilience in Education and Development (RED), and Attention and Cognition in Education (ACE) datasets were collected at the MRC Cognition and Brain Sciences Unit at the University of Cambridge. The CALM cohort is a specialized sample of children who are neurodivergent collected at the MRC Cognition and Brain Sciences Unit, University of Cambridge 71 . All scans were included during harmonization; however, only neurotypical controls were included in the analysis (Extended Data Table 1 ). The RED dataset was aimed to sample children from diverse socio-economic (SES) backgrounds 7 . One participant was removed due to missing age data (Extended Data Table 1 ; resulting sample size of n = 75). The ACE dataset aimed to capture a realistic representation of SES across the UK 72 (Extended Data Table 1 ). DSI Studio semi-processed datasets. Dr Yeh has preprocessed and made available many datasets on DSI Studio’s Fiber Data Hub ( https://brain.labsolver.org/ ). The dataset-specific preprocessing methods below are also published on the DSI Studio website. The Developing Human Connectome Project (dHCP) is a collaborative effort between King’s College London, Imperial College London, and Oxford University that collects neuroimaging data from neonates 73 . All longitudinal scans and infants born earlier than 37 weeks gestation (preterm) were excluded from this analysis, resulting in a cross-sectional, term infant sample (Extended Data Table 1 ). The images were denoised and corrected for Gibbs ringing, motion, eddy current, and susceptibility artifact using the diffusion SHARD pipeline 74 . A quality check was conducted using neighboring DWI correction (NDC) 75 . 34 scans (including repeated scans) were excluded due to their low NDC values identified by a median value-based outlier detector. The Human Connectome Project Development (HCPd) aims to capture a diverse but typical developmental sample 76 . This multi-site study includes Harvard University, University of California-Los Angeles, University of Minnesota, and Washington University in St. Louis 76 . Sample and imaging information can be found in Extended Data Table 1 and in further detail Somerville et al. (2018) 76 . The susceptibility and eddy current artifacts were corrected using FSL topup and eddy (FMRIB, Oxford). The correction was conducted through the integrated interface in DSI Studio’s (“Chen” release). The diffusion MRI data were rotated to align with the AC-PC line. The accuracy of b-table orientation was examined by comparing fiber orientations with those of a population-averaged template 77 . The Human Connectome Project Young Adult (HCPya) is a multi-site study collected by the Washington University-University of Minnesota Consortium of the Human Connectome Project (WU-Minn HCP), which aims to capture a large sample of healthy adults 78 . Sample and imaging information can be found in Extended Data Table 1 and in further detail Van Essen et al. (2013) 78 . A group average template was constructed from a total of 930 subjects. The diffusion data were reconstructed in the MNI space using q-space diffeomorphic reconstruction 79 to obtain the spin distribution function 35 . The Human Connectome Project Ageing (HCPa) is a multi-site study aimed at capturing healthy aging from 36 to 100 + years old 80 . The sample used in this analysis excluded participants scanned at 100 + years old ( n = 12), resulting in a cross-sectional sample ranging from 36 to 90 years old (Extended Data Table 1 ; n = 706). Further details on the HCPa sample and imaging methods can be found at Bookheimer et al. (2019) 80 . The susceptibility and eddy current artifacts were corrected using FSL topup and eddy (FMRIB, Oxford). The correction was conducted through the integrated interface in DSI Studio’s (“Chen” release). The diffusion MRI data were rotated to align with the AC-PC line. The Cambridge Centre for Ageing and Neuroscience (CamCAN) project aims to capture age-related changes in neurocognitive systems 81 . This project is conducted at the MRC Cognition and Brain Sciences Unit, University of Cambridge, and focuses on exploring important aspects of health in aging. Sample and imaging information can be found in Extended Data Table 1 and in further detail Shafto et al. (2014) 81 . The b-table was checked by an automatic quality control routine to ensure its accuracy 82 . For dHCP, HCPd, and HCPa, the accuracy of b-table orientation was examined by comparing fiber orientations with those of a population-averaged template 75 . The restricted diffusion was quantified using restricted diffusion imaging 83 . Additionally, with dHCP, HCPd, HCPa and CamCAN, the diffusion data were reconstructed using generalized q-sampling imaging 35 with a diffusion sampling length ratio of 1.25. Alternatively, for HCPya a diffusion sampling length ratio of 2.5 was used, and the output resolution was 1 mm. Connectome construction. Tractography. All networks were tracked using standard GQI plus deterministic tractography in DSI Studio 35 . For participants three years old and older, the QSIprep dsi_studio_gqi workflow 69 was applied with the AAL116 atlas 84 . All other participants were tracked directly in DSI Studio using multiple versions of the AAL atlas. Participants aged 24 to 35 months were tracked with the AAL90 two-year-old atlas 68 , those aged 12 to 23 months with the AAL90 one-year-old atlas 68 , and those younger than 12 months with the AAL90 neonatal atlas 68 . For all networks parcellated with the AAL116 atlas, we removed additional subcortical regions (numbers 91–116), which resulted in the AAL90 atlas. This progressive use of AAL90 atlases with the same regions fit to different brain volumes enables direct comparison between regions across the lifespan while accommodating for drastic brain growth in the first two years of life. All tracking was performed with the same parameters – maximum fiber length of 250mm, minimum fiber length of 30mm, 5 million streamlines, random seeding, 1mm step size, and turning angle 35 ° . We used count-end connectivity, indicating that streamlines were identified between two regions if the streamline ended in both regions. Harmonization. All data, including longitudinal and repeat scans in BCP and neurodivergent group in CALM, were included in harmonization ( N = 4,216). Multiple harmonization methods for variable density and density-controlled networks as well as assessing efficacy of harmonization before and after thresholding and can be found in the supplement (Supplementary Fig. 3). The harmonization methods were evaluated by the total number of FDR-corrected significant effects of study within age-bins across density, modularity, core/periphery structure, global efficiency, average degree, and average strength (see “Methods”; “Graph Theory”), as well as visual inspection of generalized additive models. We determined that our ‘double harmonized’ method before thresholding was the most effective across both variable and density-controlled analyses. Double harmonization was performed using ComBat 36 to harmonize across atlas and then harmonize again across study (Fig. 1 c). For each step, a mask was used to only retain connections that were present before harmonization in addition to setting any negative connections produced by harmonization to zero. Covariates that were preserved during harmonization included participant ID, age, sex, and neurodiversity group to identify children in CALM who are neurodiverse. Thresholding. Before thresholding, 14 participants were identified as outliers (dHCP n = 1; CALM n = 2; RED n = 1; ACE n = 1; HCPya n = 3; HCPa n = 1; CamCAN n = 5) due to having network density above or below three standard deviations for the age bin and were removed. With this reduced sample ( n = 4,202), two thresholding methods were performed – (1) preserve variable density across the lifespan and (2) control density across the lifespan for topological comparison. For the variable density analysis, we performed a generalized additive model (see “Statistics”) on the raw network densities and took 70% of the regression to obtain a ‘target’ density for each age (Supplementary Fig. 1a). Then, for each age group within each study, we applied the absolute threshold that yielded an average density equal to the target density for that age. The resulting networks were thresholded to densities ranging from 21 to 8% with the original relationships between density preserved (Supplementary Fig. 1a). These networks were then used only in the connectivity analysis to explore density, degree, and strength of networks. Additionally, the density-controlled networks were constructed for topological analyses. These networks were thresholded at the individual level so that each individual, regardless of age, had a 10% dense network. 10% was utilized because the sparsest network in the sample was 11%. Thus, 10% was the highest possible density where every network in the sample is thresholded, as well as it being consistent with past lifespan work 38 . Additional densities of 8% and 5% can be found in the supplement (Supplementary Fig. 1B). All networks were converted to normalized weighted networks using weight_conversion() from the Brain Connectivity Toolbox 37 , which rescales all weights to range from 0 to 1. Graph theory. All graph theory metrics were calculated using the Brain Connectivity Toolbox (BCT) in MATLAB 2020b 37 . Global measures included network density, modularity, global efficiency, characteristic path length, core/periphery structure, small-worldness, k-core, and s-core, while local measures utilized were degree, strength, local efficiency, clustering coefficient, betweenness centrality, and subgraph centrality. All local measures were averaged across the network for the topological analysis. Uniform Manifold Approximation and Projection (UMAP). To project topological data into a manifold space, we used the UMAP package in Python version 3.7.3 34 . Before data was put into the UMAP, it was first standardized using Sklearn’s StandardScalar() 85 . UMAP requires four pre-defined parameters – minimum distance and nearest neighbors, number of components, and distance metric. Minimum distance typically ranges between zero to one and determines how closely data points are packed together in the low-dimensional representation (low values result in more clustered representations) 34 . Nearest neighbors defines the size of local neighborhoods when learning the manifold structure 34 . This parameter, therefore, determines the balance between local versus global structure – a low nearest neighbors value pushes the UMAP to capture more local structure and vice versa. Nearest neighbors can be at minimum two or at maximum one less than the length of the data input. The number of components simply determines how many dimensions the projection should be embedded in – we predefined this as three dimensions. Lastly, the distance metric determines how the distance is calculated. We used the Euclidean distance. A limitation of UMAP is that the minimum distance and nearest neighbors parameter choice greatly determines the shape of the projected manifold 46 . While UMAP always captures patterns within the data, the parameter choices alter which patterns are projected, making it challenging to derive meaningful interpretations of the projections. To mitigate this, we derived 968 combinations of UMAP parameters. The nearest neighbour parameter was set to 88 whole numbers that ranged from two to 89, while the minimum distance parameter was 11 values evenly spaced ranging from 0.1 to one. Thus, we conducted our analysis on a complete range of UMAP projections, from manifold representing mostly local patterns through manifolds capturing mainly global patterns. Turning point identification. To determine what constitutes a turning point, we have constructed our own algorithm with multiple parameters. First, we must find a line of best fit through the 3-dimensional manifold. In Python version 3.7.3, we created three polynomial fits – one for each dimension – which requires the choice of the polynomial degree (Fig. 3 a). The equation for each dimension is as follows: $$\:Dimension\left(age\right)={\beta\:}_{0}+{\beta\:}_{1}age+{{\beta\:}_{2}age}^{2}+{{\beta\:}_{3}age}^{3}+{{\beta\:}_{4}age}^{4}+{{\beta\:}_{5}age}^{5}+\:ϵ$$ Polynomials were fit using the polyfit() function from the numpy package, which uses least squares error 86 . Together, these polynomials create the 3D line of best fit through the manifold space. For our main analysis, we fit 5-degree polynomials and have included iterative polynomials ranging from two to 12 in the supplementary materials (Supplementary Fig. 4a). This sensitivity analysis highlights that a degree of five is a middle-ground between visually under fit and overfit lines, with high-degree lines including more middle-age turning points (e.g., between 40–60 years old). Importantly, turning points occurring before 10, around 30, and in the 80s are robust across most degree choices (Supplementary Fig. 4a). Generally, the choice of degree impacts where in the lifespan turning points are identified. We then calculated the gradients of the lines of best fit and identified points in which the gradient changes sign (positive to negative or negative to positive) along each dimension. Small fluctuations were then filtered to remove minor inflections by removing points where the sum of the gradients around the point was relatively small. This filtering process requires two parameters – a gradient window (W) and gradient threshold (T). The gradient window determines the number of years around the inflection point ( i ) that will be the scope of the gradient threshold. The gradient threshold is the cut-off for how large the sum of the absolute value of gradients within this range needs to be to be retained. An inflection point will survive this cutoff if: $$\:T<\:{\sum\:}_{i-W}^{i+W}\left|{G}_{i}\right|$$ G j represents the gradient at i year, W is the gradient window, and T is the gradient threshold. The larger the gradient threshold, the sharper the inflection point (i.e. steep slopes on either side of the point) must be to be kept in the analysis. For our analysis, we defined the gradient window to five years and the gradient threshold to 0.8, though it is important to note that many variations of these parameters result in the same turning points being identified. Sensitivity analysis of varying gradient thresholds can be found in supplement (Supplementary Fig. 4c). This analysis shows that turning points are stable across gradient thresholds 0.1 to 0.8. Turning points around eight and 85 are retained at a gradient threshold of 1.2 but not middle age turning points, indicating that the first and last turning points of the lifespan are the ‘largest’ or ‘sharpest’ in terms of the change in slope through the manifold space (Supplementary Fig. 4c). Thus, this parameter affects the sensitivity to the size of turning points but not where the turning points are located across the lifespan. The second step for identifying turning points in a manifold is to handle instances where multiple points have been detected close together. For example, if age 31 in dimension X and age 33 in dimension Y were identified as inflection points, we interpret these as representing a single turning point rather than two distinct trajectories, given their proximity. This process requires an age window parameter (A) to determine the age range around the inflection point in which a mean will be calculated. This averaging procedure occurs both within and across dimensions. Average turning points are then rounded and considered the ‘final’ turning points. For our analysis, we used an age window parameter of five years and have included a sensitivity analysis to explore how changing the age window affects the turning points identified which can be found in (Supplementary Fig. 4b). Between age windows of one through 10, we see no changes in turning points beyond a single year (Supplementary Fig. 4b). Thus, this parameter effects where a turning point is identified, similar to the degree of the polynomial, though its influence is minimal. Turning points were identified for each of the 968 UMAP projections. Major turning points were defined by the peaks in Gaussian kernel density function of all turning points (Fig. 3 c). Thus, these points are the most frequent ages identified as turning points across all manifolds. We also assessed turning points in variable density networks (Supplementary Fig. 4d) and sex-stratified projections that have been mapped to the combined UMAP space using orthogonal procrustes 87 (Supplementary Fig. 2). This analysis demonstrates that major turning points appear around similar ages for variable density networks and sex-stratified samples as those calculated in density-controlled networks. Thus, our conservative thresholding for easy topological interpretability does not appear to drastically change where in the lifespan major turning points have been identified. Major turning points mark the average age at which topological data begins a new trajectory through the manifold, indicating a distinctly different organisational change across age. Thus, between major turning points, we define age epochs in which topological change is occurring along the same trajectory through the manifold space. Epoch correlations. We applied Pearson correlations within epochs (i.e., age ranges between major turning points) to explore changes in each organisational metrics across age. We also used correlations to examine between epochs simply by identifying when significant correlations in consecutive epochs changed direction (i.e., from a positive correlation to a negative correlation and vice versa) (Extended Data Fig. 4 a) Least Absolute Shrinkage and Selection Operator (LASSO). To explore driving topological factors within epochs, we employed LASSO regularization models 88 in MATLAB 2020b with 10-fold cross-validation (CV) to perform variable selection with multicollinear predictors. The benefit of LASSO models is that they penalize the absolute value of coefficients, which results in some coefficients being pushed to zero, allowing for easy interpretation of important model features 88 . This penalization term is multiplied by a constant, λ, which is determined through the 10-fold CV. 10-fold CV trains the LASSO on nine folds (i.e. subset of the data) and is tested on the 10th fold. To encourage sparsity in the model, we selected the largest lambda where the mean squared error (MSE) is within one standard error of the minimum MSE. For the last epoch, this level of sparsity resulted in no variables selected, and therefore, the LASSO model for epoch five was created by selecting the lambda value with the minimum MSE. Principal Components Analysis (PCA). We conducted a PCA 89 in MATLAB2020b to reduce the dimensionality of graph theory metrics for the purpose of exploring between-epoch changes. After standardizing the data, we ran a PCA with the maximum number of components (11) and conducted a parallel analysis to determine how many components to retain 90 . For the parallel analysis, we created 1,000 iterations of standardized random data and conducted PCAs for each iteration. We then calculated the top 95% confidence interval of eigenvalues produced by the random samples 90 . Components from the original PCA with eigenvalues exceeding the threshold set by 95% confidence interval from the random eigenvalues were retained as this indicates that eigenvalues were larger than expected at chance. This analysis indicated three components be retained (Fig. 5 a). A second PCA was run, this time constrained to three components which convey 80% of variance across the sample (Extended Data Fig. 3 ). To improve loading interpretation, an orthogonal rotation was applied using rotatefactors() with the varimax method 91 . We compared epochs based on their PCA scores, first using Levene's Test for Relative Variation 92 in Python version 3.7.3 to determine if the variance of PCA scores significantly differed across epochs. Since this test was significant, we used Welch’s Analysis of Variance (ANOVA) 93 in Python to assess significant differences in mean PCA scores across epochs. Lastly, we ran post hoc Games-Howell 94 tests in Python to determine which consecutive groups were significantly different (Extended Data Fig. 4 b). The full table of all Games-Howell comparison outcomes can be found in the supplement (Extended Data Table 2 ). In some instances, p-values were set equal to zero due to the truncated precision of Python. In these cases, p-values are reported as less than the minimum printable value, p < 1.00 x 10 − 323 . Dynamic Time Warping (DTW). We also examined differences between epochs using DTW on PCA score series conducted in Python version 3.7.3 95 . DTW warps two time series to their optimal alignment. The algorithm calculates the local Euclidean distances between points in each series, calculating the global alignment between the series as the warping path that minimises the sum of distances between series 95 . DTW distance, defined as the minimum cumulative distance of the warp, quantifies how far points in one series must shift to align with another, providing insight into differences in their shapes. For our analysis, we constructed a series for each epoch across each PC, represented as the average PCA score for each age (Extended Data Fig. 4 c). The DTW distances for optimal warping between consecutive epochs were standardized within each principal component. These distances were then qualitatively compared – with larger distances suggesting more disparity between the shape of those series’ trajectories. Declarations AUTHOR CONTRIBUTIONS A.M. performed fiber tracking, constructed connectomes, conducted the analysis, and drafted the manuscript. F.C. preprocessed, quality controlled, and reconstructed the majority of networks. A.M., D.E.A., and R.B. conceptualized the analysis. D.E.A. and R.B. provided critical manuscript reviews and edits. COMPETING INTERESTS The A.M., D.E.A., and F.C. declare no competing financial or non-financial interests. R.B. declares he is a co-founder of and holds equity in Centile Bioscience Inc. DATA AVAILABILITY The derived data generated in this study are available at https://osf.io/7p4y3/ . CALM data are available at https://portal.camide.cam.ac.uk/overview/1158 . BCP data are available at https://nda.nih.gov/ . The semi-processed data from dHCP, HCPd, HCPya, HCPa, and CamCAN used in this publication are available at https://brain.labsolver.org/ . CODE AVAILABILITY All code is available at https://github.com/alexamousley/lifespan_topological_turning_points . References Bethlehem RAI et al (2022) Brain charts for the human lifespan. 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J Educ Psychol 24:498–520 Horn JL, A RATIONALE AND TEST FOR THE NUMBER (1965) OF FACTORS IN FACTOR ANALYSIS. Psychometrika 30:179–185 Kaiser HF (1958) The varimax criterion for analytic rotation in factor analysis. Psychometrika 23:187–200 Schultz BB (1985) Levene’s Test for Relative Variation. Syst Biol 34:449–456 Welch YBL (1951) On the comparison of several mean values: An alternative approach. Biometrika 38:330–336 Games PA, Howell JF (1976) Pairwise Multiple Comparison Procedures with Unequal N’s and/or Variances: A Monte Carlo Study. J Educ Behav Stat 1:113–125 Giorgino T (2009) Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package. J Stat Softw 31:1–24 Tables Table 1 to 3 are available in the Supplementary Files section. Additional Declarations Yes there is potential Competing Interest. The A.M., D.E.A., and F.C. declare no competing financial or non-financial interests. R.B. declares he is a co-founder of and holds equity in Centile Bioscience Inc. Supplementary Files Table13.docx MousleySupplementaryMaterials.docx ExtendedData.docx Cite Share Download PDF Status: Published Journal Publication published 25 Nov, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6120723","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":432109623,"identity":"61853ff2-9a9a-4948-8aa1-d0228442eaae","order_by":0,"name":"Alexa Mousley","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-9222-5076","institution":"University of Cambridge","correspondingAuthor":true,"prefix":"","firstName":"Alexa","middleName":"","lastName":"Mousley","suffix":""},{"id":432109624,"identity":"7e3a5d7c-7e95-4ccb-a0d0-da9080f607ac","order_by":1,"name":"Richard Bethlehem","email":"","orcid":"","institution":"University of Cambridge","correspondingAuthor":false,"prefix":"","firstName":"Richard","middleName":"","lastName":"Bethlehem","suffix":""},{"id":432109625,"identity":"b70a3ddc-fb00-4342-9ff9-a5fdb72e7636","order_by":2,"name":"Fang-Cheng Yeh","email":"","orcid":"https://orcid.org/0000-0002-7946-2173","institution":"University Of Pittsburgh","correspondingAuthor":false,"prefix":"","firstName":"Fang-Cheng","middleName":"","lastName":"Yeh","suffix":""},{"id":432109626,"identity":"14f59bb4-3907-4d6d-af7d-93985b60fdae","order_by":3,"name":"Duncan Astle","email":"","orcid":"https://orcid.org/0000-0002-7042-5392","institution":"University of Cambridge","correspondingAuthor":false,"prefix":"","firstName":"Duncan","middleName":"","lastName":"Astle","suffix":""}],"badges":[],"createdAt":"2025-02-27 12:00:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6120723/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6120723/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-025-65974-8","type":"published","date":"2025-11-25T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":79259080,"identity":"bbf608d0-4a14-4e03-a9f6-61154cb3c21c","added_by":"auto","created_at":"2025-03-26 09:17:24","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1245580,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDatasets demographics, methods schematic, and network connectivity. (a)\u003c/strong\u003e The distribution of ages (years) across each dataset. \u003cstrong\u003e(b)\u003c/strong\u003e A histogram and density plot of sex distribution across age for the entire sample. \u003cstrong\u003e(c)\u003c/strong\u003e Methods schematic demonstrating that fiber tracking was performed for all participants, each registered to an age-appropriate AAL90 atlas, followed by harmonization using the ComBat algorithm across the atlases and datasets. Next, two thresholding analyses were conducted – variable density and density-controlled. For variable density analysis, networks were thresholded to an age-specific average density (70% of raw density) to preserve variation in network density across the lifespan. For the density-controlled analysis, all networks were thresholded to exactly 10% density\u003csup\u003e38\u003c/sup\u003e to allow for direct topological comparisons, which are not biased by differences in total connectivity. \u003cstrong\u003e(d) \u003c/strong\u003eAverage binarized connectivity matrices and average normalized weighted connectivity matrices. Above each consecutive pair of matrices, the percent change indicates the difference in total connectivity. \u003cstrong\u003e(e) \u003c/strong\u003eDensity (%) significantly fluctuated across the lifespan with a lifetime maximum at birth and minimum around 14 years old (\u003cem\u003ep\u003c/em\u003e \u0026lt; 2.00 x 10\u003csup\u003e-16\u003c/sup\u003e).\u003cstrong\u003e (f)\u003c/strong\u003e The maximum (\u003cem\u003ep\u003c/em\u003e \u0026lt; 2.00 x 10\u003csup\u003e-16\u003c/sup\u003e) and average strength (\u003cem\u003ep\u003c/em\u003e \u0026lt; 2.00 x 10\u003csup\u003e-16\u003c/sup\u003e) significantly and nearly linearly increased across the lifespan with a lifetime minimum at eight years old and maximum at 90 years old. Shaded area around lines of best fit represents 95% confidence intervals. *** indicates \u003cem\u003ep \u003c/em\u003e\u0026lt; 0.001, ** indicates \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.01, * indicates \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.05.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6120723/v1/12fb79739f6e9efd9e77e3c0.png"},{"id":79256714,"identity":"9965580f-57ad-4745-8576-2c1c08b52416","added_by":"auto","created_at":"2025-03-26 09:01:24","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":930299,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTopological changes across the lifespan in density-controlled networks. (a) \u003c/strong\u003eGlobal efficiency peaked while characteristic path length displayed a lifetime minimum around 29 years old. Small-worldness showed a similar developmental pattern to characteristic path length, with all ages demonstrating the presence of small-world structure (i.e., small-worldness \u0026gt; 1). Average network strength, however, significantly increased across the lifespan in a more linear pattern. \u003cstrong\u003e(b) \u003c/strong\u003eModularity significantly fluctuated across the lifespan, peaking in aging individuals. Core/periphery structure had a lifetime peak around 20 years old. S-core (reported as the number of nodes included in the subnetwork) significantly increased across the lifespan in a linear-like pattern. Local efficiency and clustering coefficient both significantly increased linearly across the lifespan. K-core (reported as the number of nodes included in the subnetwork) did not significantly change across the lifespan. \u003cstrong\u003e(c) \u003c/strong\u003eAverage betweenness centrality had a lifetime minimum around 31 years old and significantly increased in late life. Average subgraph centrality significantly increases across the lifespan. Shaded area around lines of best fit represents 95% confidence intervals. *** indicates \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.001, ** indicates \u003cem\u003ep\u003c/em\u003e\u0026lt; 0.01, * indicates \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.05.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6120723/v1/b731cefc0b4e076b5dc0800f.png"},{"id":79258260,"identity":"ee288a26-60a2-4132-ab3f-976630d4d8ac","added_by":"auto","created_at":"2025-03-26 09:09:24","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":498621,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe definition of turning points. (a) \u003c/strong\u003eA manifold space displayed across each dimension (top row) and in a 3-dimensional plot. The scatter plots show the age-average UMAP projection. The polynomial lines of best fit (black) are constructed to fit each. Lines of best fit are found through each of the 968 UMAPs. \u003cstrong\u003e(b) \u003c/strong\u003eSix examples of lines of best fit through manifolds with different UMAP parameters. These lines are used to determine turning points (green points).\u003cstrong\u003e (c) \u003c/strong\u003eAll turning points identified across the 968 UMAP projections are plotted in a histogram and kernel density plot. These plots were used to determine the major turning points, which are ages most frequently identified as turning points across all projections. The major turning points occur at eight, 32, 62, and 85 years old (red ‘x’).\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6120723/v1/43750e2c37e767ca0d03eaf3.png"},{"id":79256721,"identity":"cc0993d8-0b07-42b3-8357-883ea3d819ca","added_by":"auto","created_at":"2025-03-26 09:01:24","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":347349,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTopological changes within the five topological epochs of life. (a) \u003c/strong\u003eSchematic showing the ranges of each epoch across the lifespan. Each tractogram depicts 10 years of aging. To the left of the schematic, per epoch, the metric with the highest LASSO coefficient (β), indicating the strongest predictor of age, is shown. On the right side of the schematic, next to each epoch, the metric with the largest correlation (\u003cem\u003er\u003c/em\u003e) is displayed, highlighting the strongest directional changes across age. For the epochs in which the driving factor and strongest directional change are the same, the metrics are highlighted in grey. The combination plots show all the regularized LASSO coefficients in a bar graph (left y-axis) and the correlations as a scatter plot (right y-axis) for\u003cstrong\u003e (b) \u003c/strong\u003eepoch 5, \u003cstrong\u003e(c)\u003c/strong\u003eepoch 4, \u003cstrong\u003e(d) \u003c/strong\u003eepoch 3, \u003cstrong\u003e(e) \u003c/strong\u003eepoch 2, and \u003cstrong\u003e(f)\u003c/strong\u003e epoch 1. Red scatter points indicate correlations with \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.05. Dotted grey lines highlight zero on the correlation axis.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6120723/v1/65343d497977d9e9b6f0b077.png"},{"id":79258262,"identity":"47c95c73-e286-461c-8b89-e6383672e642","added_by":"auto","created_at":"2025-03-26 09:09:24","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":296044,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCharacterization of turning points using PCA. (a) \u003c/strong\u003eParallel analysis shows three PCs should be retained. The three PCs account for 80% of variance in topological data across the lifespan. On the left, there is a three-dimensional loading plot for the PCA. PC1’s four largest loadings are clustering coefficient, local efficiency, strength, and s-core. PC2’s four largest loadings are global efficiency, characteristic path length, betweenness centrality, and modularity. PC3’s four largest loadings are subgraph centrality, core/periphery structure, small-worldness, and modularity. On the right, average PCA scores for each epoch are plotted in 3-dimensional space. \u003cstrong\u003e(b) \u003c/strong\u003eFrom the DTW analysis, the summed standardized warping distances across all PCs for constructive epochs are plotted in a bar graph. \u003cstrong\u003e(c)\u003c/strong\u003e A turning point summary schematic shows a 3-dimensitonal manifold with turning points (black spheres) and demonstrates the direction of the projection of each epoch. Next to each turning point is a table with the total number of significant changes in correlations of individual topological metrics (‘Direction’), significant shifts across PCs (‘PCA’), and the total standardized warping distance (‘Trajectory’). Together, this schematic characterizes changes that occur at each major turning point. *** indicates \u003cem\u003ep \u003c/em\u003e\u0026lt; 0.001, ** indicates\u003cem\u003ep\u003c/em\u003e \u0026lt; 0.01, * indicates \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.05.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6120723/v1/dece0d988fe4ad6255307007.png"},{"id":96798856,"identity":"6df423e9-84c6-4cf8-adcc-34121e748bc8","added_by":"auto","created_at":"2025-11-26 08:14:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4046830,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6120723/v1/1a35306f-b833-4a5c-aff2-3e6736e6a8e0.pdf"},{"id":79256713,"identity":"a95e2ade-96fa-4bc6-8328-df772ae22109","added_by":"auto","created_at":"2025-03-26 09:01:24","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":24430,"visible":true,"origin":"","legend":"","description":"","filename":"Table13.docx","url":"https://assets-eu.researchsquare.com/files/rs-6120723/v1/bafb8b4f89a1e1a2182dd5b4.docx"},{"id":79256716,"identity":"f51d2707-6f3c-4f17-a834-84ef5fa0c530","added_by":"auto","created_at":"2025-03-26 09:01:24","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":1667893,"visible":true,"origin":"","legend":"","description":"","filename":"MousleySupplementaryMaterials.docx","url":"https://assets-eu.researchsquare.com/files/rs-6120723/v1/7a0397b43bc774b004145ece.docx"},{"id":79256732,"identity":"14d93b34-80b0-4312-8d76-8c072be36424","added_by":"auto","created_at":"2025-03-26 09:01:24","extension":"docx","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":2925274,"visible":true,"origin":"","legend":"","description":"","filename":"ExtendedData.docx","url":"https://assets-eu.researchsquare.com/files/rs-6120723/v1/f1374ba044d6875825767ae0.docx"}],"financialInterests":"\u003cb\u003eYes\u003c/b\u003e there is potential Competing Interest.\nThe A.M., D.E.A., and F.C. declare no competing financial or non-financial interests. R.B. declares he is a co-founder of and holds equity in Centile Bioscience Inc.","formattedTitle":"Topological turning points across the human lifespan","fulltext":[{"header":"MAIN","content":"\u003cp\u003eTrajectories of change in brain structure and function emerge across the lifespan\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Topology, the complex motifs within which neural connections are organized, develops with age and is associated with key cognitive, behavioral, and mental health outcomes\u003csup\u003e\u003cspan additionalcitationids=\"CR6 CR7 CR8 CR9\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. Topology-outcome relationships have been established within relatively narrow age ranges, such as childhood\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. But what are the underlying \u003cem\u003eprinciples\u003c/em\u003e of organizational change? Are there key points in our lifespans wherein the brain transitions into a different phase of developmental change? Addressing these questions requires comprehensive mapping of lifespan network topology alongside a multidimensional framework capable of establishing the non-linear dynamics of developmental change.\u003c/p\u003e \u003cp\u003ePrior research has revealed significant age-related changes in structural topology across the lifespan\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. A typically developing infant\u0026rsquo;s brain network displays adult-like structure with hub distribution, rich clubs, small-worldness, and modularity at birth\u003csup\u003e\u003cspan additionalcitationids=\"CR13 CR14 CR15 CR16 CR17 CR18 CR19 CR20\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Throughout early development, networks become more integrated with increasing strength and efficiency and decreasing modularity\u003csup\u003e\u003cspan additionalcitationids=\"CR23\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. In adulthood, many researchers describe an inverted \u0026ldquo;U\u0026rdquo; shape of development with a peak occurring around 30 years old where the brain is maximumly efficient and integrated\u003csup\u003e\u003cspan additionalcitationids=\"CR26\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. This research uses the terms \u003cem\u003einflection point\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e or \u003cem\u003epeak age\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e to describe important points of change in organizational metrics \u0026ndash; many of which occur in the fourth decade of life and intersect with other developmental and aging milestones. After this point and into late life, aging is associated with reduced connectivity, mainly through pruning of weak connections\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e, increased modularity\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e, and more pronounced rich club organization\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e than earlier in life. These established fluctuations of organizational principles underscore the dynamic and complex nature of topology development.\u003c/p\u003e \u003cp\u003eMapping neural systems across the lifespan calls for data-driven methods that can handle complex data and capture high variability without making strong assumptions about the underlying data\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. Manifold learning is a popular technique to project high-dimensional data into a low-dimensional space by filtering out closely related features likely driven by similar mechanisms\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. These projections, created using non-linear dimensionality reduction techniques such as Uniform Manifold Approximation and Projection (UMAP), are easier to interpret while maintaining the intrinsic structure of complex data\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. UMAP, in particular, captures both local and global data patterns with faster run times than similar methods (e.g., t-SNE)\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. The manifold spaces themselves graphically represent the relationships in the original high-dimensional space and, therefore, offer an opportunity to leverage projections to identify points of change. We define these points of change as \u003cem\u003eturning points\u003c/em\u003e, indicating significant shifts in the overall trajectory of topology, rather than inflection or peak points, which refer to changes in individual organizational measures.\u003c/p\u003e \u003cp\u003eThis study takes a data-driven approach to chart structural topological development across the human lifespan. Specifically, we (1) characterize connectivity development; (2) explore topological integration, segregation, and centrality; (3) use UMAP to define topological manifold spaces and identify major turning points across the lifespan therein; and (4) examine how these turning points capture important phases of topological development.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eWe gathered diffusion imaging data from nine datasets with a combined age range of zero to 90 years old (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea,b; Extended Data Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). A large sample (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4,216) including all available images was fiber tracked\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e and harmonized\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec). For analysis, multiple graph theory metrics\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e (Supplementary Table 1) were calculated using normalized weighted networks with a cross-sectional, neurotypical subset (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3,802; female \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1,994; male \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1,808). Following topological analysis, we projected age-predicted organizational measures into manifold spaces using UMAP\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e and determined significant turning points in topological development across the lifespan.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConnectivity.\u003c/strong\u003e Before exploring network organization, we first examined general changes in connectivity across the lifespan by preserving the distribution of density through thresholding to 70% of the average raw density per age bin (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec; Supplementary Fig.\u0026nbsp;1a). Density \u0026ndash; the percent of connections present in the network\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e \u0026ndash; changed non-linearly across age with high-density networks present around birth and 30 years old and sparse networks observed around 10 and 80\u0026thinsp;+\u0026thinsp;years old (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee; \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003edensity,age\u003c/em\u003e\u003c/sub\u003e = 219.20, estimated df\u0026thinsp;=\u0026thinsp;8.92, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;2.00 x 10\u003csup\u003e\u0026minus;\u0026thinsp;16\u003c/sup\u003e). In addition, node strength \u0026ndash; the sum of edge weights\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e \u0026ndash; significantly increased across the lifespan in a linear pattern both in average strength across all nodes and maximum strength across all nodes (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ef; \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eaverage strength,age\u003c/em\u003e\u003c/sub\u003e = 33.10, estimated df\u0026thinsp;=\u0026thinsp;5.46, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;2.00 x 10\u003csup\u003e\u0026minus;\u0026thinsp;16\u003c/sup\u003e; \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emaximum strength,age\u003c/em\u003e\u003c/sub\u003e = 29.15, estimated df\u0026thinsp;=\u0026thinsp;3.85, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;2.00 x 10\u003csup\u003e\u0026minus;\u0026thinsp;16\u003c/sup\u003e). Overall, these networks displayed the expected pattern of shifting from dense, weak networks in early life to sparse, strong networks in later life\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed). Full topological analysis with variable density networks is included in the extended data (Extended Data Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e; Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTopology.\u003c/strong\u003e To remove the confounding factor of network density from the analysis of topological changes, we conducted a density-controlled analysis where each network was constrained to exactly 10% density (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec). This method allows for fair comparison of topological structure across the lifespan without total connectivity biases.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eIntegration metrics.\u003c/em\u003e Global efficiency, which measures how well the network is connected by short path lengths\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e, significantly fluctuated across the lifespan, peaking at 29 years old before steadily declining to a minimum at 90 years old (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea; Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Other integration metrics include characteristic path length, the average shortest path length of the network\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e, and small-worldness, the ratio of clustering coefficients and characteristic path length\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. Both showed inverse patterns to global efficiency (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea; Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Additionally, average network strength significantly increased in a more linear pattern, reaching its maximum at 90 years old (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea; Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). These results suggest that while network strength linearly increases with age, topological integration initially decreases in the first decade, peaks at the beginning of the fourth decade, and then declines for the rest of the lifespan.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eSegregation metrics.\u003c/em\u003e Modularity, the division of networks into non-overlapping, highly intra-connected node groups\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e, significantly fluctuated across the lifespan with a minimum at 30 years old and a maximum at 90 years old (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb; Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Core/periphery structure, which assesses how well a network separates into a non-overlapping dense core and a sparse periphery\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e, fluctuated more than modularity, peaking at 20 years old and reaching a minimum at 55 years old (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb; Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Additionally, networks can be segregated based on a subnetwork with a specific strength (i.e., s-core) or degree (i.e., k-core)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. While k-core did not significantly change across age, s-core significantly fluctuated across the lifespan with a minimum at 12 years old followed by a continuous increase to a maximum at 90 years old.\u003c/p\u003e\n\u003cp\u003eCompared to global segregation metrics, average local segregation measures increased more linearly across the lifespan. Local efficiency \u0026ndash; the extent to which neighboring nodes are connected by short paths\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e \u0026ndash; and clustering coefficient \u0026ndash; the extent to which neighboring connected nodes are also connected to each other\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e \u0026ndash; both significantly increased to a maximum at 90 years old (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb; Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). These results emphasize a difference between \u003cem\u003eglobal\u003c/em\u003e segregation, which oscillated across age, and average \u003cem\u003elocal\u003c/em\u003e segregation, which showed more linear patterns. Beyond differences in fluctuations in mid-life, network segregation peaked in late life.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eCentrality metrics.\u003c/em\u003e Centrality measures nodes\u0026rsquo; importance to the network, often based on inclusion in key paths. Betweenness centrality measures the fraction of shortest path lengths that pass through the node\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e, which fluctuated across the lifespan, reaching a minimum at 31 years old and maximum at 90 years old (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec; Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Comparatively, subgraph centrality \u0026ndash; the weighted sum of all close walks for a node\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e \u0026ndash; significantly increased in a more linear pattern (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec; Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). These results highlight differences in the developmental pattern between individual centrality metrics but indicate a continuous increase in centrality starting around the fifth decade.\u003c/p\u003e\n\u003cp\u003eGenerally, network organization displays linear and fluctuating patterns across the lifespan. Various sex effects were found and are in the Extended Data, though these results could be explained by brain size differences that are not considered in this analysis\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e (Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). Overall, average strength, average local efficiency, average clustering coefficient, s-core, and subgraph centrality display linear-like patterns while the other metrics appear to have peaks and valleys throughout the lifespan \u0026ndash; many of which appear around 30 years old.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConstruction of lifespan epochs.\u003c/strong\u003e Many topological measures are highly correlated and therefore convey redundant and unique topological characteristics (Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea). Thus, we reduced the dimensionality of this data using manifold learning, resulting in a 3-dimensional topological space capturing crucial patterns in the data. Manifolds were constructed using significant age-predicted metrics (i.e., excluding k-core), which were averaged for each age. Considering the influence of parameter choice on UMAP projections\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e, we created 968 UMAPs with a variety of parameters to capture both local and global-level information (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). Manifolds were then used to determine major turning points across the lifespan, marking epochs where topological development is occurring along the same trajectory (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec; see \u0026ldquo;Methods\u0026rdquo;; \u0026ldquo;Turning point identification\u0026rdquo;). Major turning points occur around age eight, 32, 62, and 85 (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec). Sex-stratified projections and turning points are available in the Supplementary Materials (Supplementary Fig. 2).\u003c/p\u003e\n\u003cp\u003eThese turning points define five major epochs of life: Epoch One, which lasts from zero to eight years; Epoch Two, which lasts from eight to 32 years; Epoch Three, which lasts from 32 to 62 years; Epoch Four, which lasts from 62 to 85 years; and Epoch Five, which lasts from 85 to 90 years.\u003c/p\u003e\n\u003cp\u003eWe explored changes across these epochs using Pearson correlations to assess \u003cem\u003edirectional\u003c/em\u003e relationships between age and topological measures and LASSO regularized regressions to identify which organizational properties \u003cem\u003edrive\u003c/em\u003e the relationship between topology and age. At each turning point, we analyzed significant changes in directionality and key driving topological metrics.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEpoch 1: 0\u0026ndash;8 years old \u0026ldquo;infancy into childhood\u0026rdquo;\u003c/strong\u003e. The first epoch ranges from zero to eight years (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;630), covering the period of infancy through childhood. Significant correlations were found within this epoch in eight organizational measures, characterized by decreasing global integration, increasing local segregation, and stable centrality (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ef; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). Although many metrics correlate with age, the LASSO regularized regression retained eight measures and identified the clustering coefficient as the strongest topological predictor of age (\u0026lambda;\u0026thinsp;=\u0026thinsp;0.03; Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ef; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). In contrast, small-worldness is the strongest correlation across this age range (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ef; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). Thus, while a decrease in small-worldness across this period is the largest \u003cem\u003edirectional\u003c/em\u003e pattern, the local-level clustering coefficient is the crucial predictor of age (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea). Overall, topological development from zero to eight years old is characterized by decreasing global integration, however, clustering coefficient is a key topological measure across this period. Thus, despite decreasing integration overall, a child\u0026apos;s age is most distinct topologically in the extent to which neighboring nodes are interconnected.\u003c/p\u003e\n\u003cp\u003eThe first epoch of life ends around 8 years old, which was the most frequently identified turning point, occurring 215 times across all UMAPs (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec). Around eight years old, we observed the factors driving the relationship between topology and age shift from clustering coefficient to betweenness centrality (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea). Directional changes occur as well, with significantly decreasing integration changing to significantly increasing integration after eight years old (Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e; Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEpoch 2: 8\u0026ndash;32 years old \u0026ldquo;Adolescence\u0026rdquo;.\u003c/strong\u003e The second epoch occurs from eight to 32 years old (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1,791) and encompasses late childhood through early adulthood. Within this epoch, 10 topological measures were significantly correlated with age, characterized by decreasing network integration and complex segregation and centrality patterns (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ee; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). Generally, strength-based and local-level segregation increased, but global modularity decreased (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ee; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). Coinciding with the largest correlation, the LASSO regression reveals that betweenness centrality was the largest driving factor for identifying age (\u0026lambda;\u0026thinsp;=\u0026thinsp;0.65; Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ee; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). Together, the results highlight a complex pattern of topological change from eight to 32 that can be characterized by increasing integration alongside decreasing global segregation and increasing local-level segregation. Betweenness centrality, which captures nodes\u0026rsquo; participation in important paths, is particularly district during this epoch both in terms of the driving factor and largest directional changes.\u003c/p\u003e\n\u003cp\u003eThe second epoch of life ends around 32 years old (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec; identified 92 times). At this age, there are many changes in the directionality of topological development. Before 32 years old, global efficiency increased while characteristic path length, small-worldness, modularity, and betweenness centrality significantly decreased \u0026ndash; these correlations shift to the opposite direction after 32 years old (Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e; Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea). This suggests a shift from increasing to decreasing integration as well as changes from decreasing to increasing modularity, and betweenness centrality happens around 32 years old. In addition, the topological metric driving the relationship with age changes from betweenness to small-worldness at 32 years old. Thus, the beginning of the fourth decade of life marks the end of a phase of increasing efficiency and integration and the start of a period of increasing segregation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEpoch 3: 32\u0026ndash;62 years old \u0026ldquo;Adulthood\u0026rdquo;.\u003c/strong\u003e The third epoch occurs from 32\u0026ndash;62 years old (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1,006), extending across three decades of adulthood. Across this period, 10 topological measures were significantly correlated with age, characterized by decreasing network integration, general increases in segregation, and minimal centrality changes (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ed; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). While clustering coefficient was most highly correlated with age, the LASSO regression revealed that small-worldness was distinctly associated with age across this period (\u0026lambda;\u0026thinsp;=\u0026thinsp;0.69; Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ed; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). Thus, as with the first epoch, there was a discrepancy between the largest \u003cem\u003edirectional\u003c/em\u003e changes and which topological metric was the best age predictor during this period. Together, these results suggest network integration decreased with minimal centrality changes, and while segregation was complex, most segregation metrics increased across this epoch. Despite rapidly increasing clustering, the extent to which the network is highly clustered while also being connected by short path lengths \u0026ndash; small-worldness \u0026ndash; is the most important factor for predicting age during this adulthood epoch.\u003c/p\u003e\n\u003cp\u003eThe third epoch ends around 62 years old and was the least distinct of the four major turning points, as it was only identified 58 times (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec). While there are no significant changes in the directionality of topology at this age (Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea), we observed the driving topological metric shift from small-worldness to modularity. Though these metrics are correlated, this point marks a change in which the network becomes more segregated into groups, which is the distinct feature of topological development.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEpoch 4: 62\u0026ndash;85 years old \u0026ldquo;Early aging\u0026rdquo;.\u003c/strong\u003e The fourth epoch ranges from 62\u0026ndash;85 years old (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;522), spanning the shift from adulthood into early aging. Only six topological metrics significantly correlated with age (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). While this period is topologically most distinct in modular changes, decreasing integration and increasing centrality are also present (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). The LASSO only retained modularity as a predictor, aligning with the strongest correlation in this period (\u0026lambda;\u0026thinsp;=\u0026thinsp;1.03; Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). The last turning point in the lifespan identifies that the end of this epoch is around 85 years old, which was the second most frequently occurring turning point (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec; identified 146 times). There were no significant changes in directionality at this age (Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea); however, the most important factor for identifying age shifts from modularity to core/periphery structure. In other words, from this turning point onwards, the networks start to form distinctly dense core and sparse periphery subnetworks.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEpoch 5: 85\u0026ndash;90 years old \u0026ldquo;Late aging\u0026rdquo;.\u003c/strong\u003e The last epoch is 85\u0026ndash;90 years old (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;56), ranging from late aging individuals to the maximum age included in this study. There were no significant correlations between topology and age across this epoch (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). In addition, the regularization of the LASSO had to be weakened for any predictors to survive (see \u0026ldquo;Methods\u0026rdquo;; \u0026ldquo;Statistics\u0026rdquo;). With a less-sparse model, core/periphery structure is the strongest predictor of age, which also aligns with the largest correlation (\u0026lambda;\u0026thinsp;=\u0026thinsp;0.11; Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb; Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). These results reflect a reduction in the significance of the relationship between topology and age in the latest years of life, though core/periphery structure emerges as the most age-related topological measure.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCharacterizing all turning points.\u003c/strong\u003e Beyond detailing changes in topology \u003cem\u003ewithin\u003c/em\u003e each epoch, it is helpful to compare topology differences \u003cem\u003eacross\u003c/em\u003e epochs. While UMAP provides information about where major turning points occur, we cannot interpret what is topologically changing at these points due to UMAPs having arbitrary dimensions (e.g., no loading scores). Simply put, UMAP informs us \u003cem\u003ewhere\u003c/em\u003e non-linear changes occur but not what those changes are. To explore \u003cem\u003ewhat\u003c/em\u003e topological changes occur around these major turning points, we ran a Principal Components Analysis (PCA) across the 11 topological metrics for the entire lifespan sample, using a parallel analysis to identify three principal components (PCs) that explain 80% of the variance in topological measures (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea). Segregation measures load most heavily onto PC1, while integration metrics load mostly on PC2, and both segregation and centrality metrics load onto PC3 (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea; Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb-e). PCA scores across epochs had significantly different variance and means in all PCs (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea,c; Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eWe utilized the PCA to compare average PCA scores between consecutive epochs. Significant shifts in PC1 and PC2 occur between epochs one and two (PC1 \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4.80 x 10\u003csup\u003e\u0026minus;\u0026thinsp;04\u003c/sup\u003e; PC2 \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;6.66 x 10\u003csup\u003e\u0026minus;\u0026thinsp;08\u003c/sup\u003e) and between epochs two and three (PC1 1 \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;1.00 x 10\u003csup\u003e\u0026minus;\u0026thinsp;323\u003c/sup\u003e; PC2 \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.39 x 10\u003csup\u003e\u0026minus;\u0026thinsp;07\u003c/sup\u003e) (Fig.5a,c; Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb). Neither epoch comparison had significant differences in PC3 (epochs one and two \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.706; epochs two and three \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.989) (Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb). These results suggest that the first two turning points \u0026ndash; eight and 32 years old \u0026ndash; identify significant shifts occurring in the two primary components, upon which load most segregation and integration metrics (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea; Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb,c). Epochs three and four \u0026ndash; the 62-year-old turning point \u0026ndash; is the only point where a significant shift in PCA scores occurs across all PCs (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea,c; Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb; PC1: \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;6.54 x 10\u003csup\u003e\u0026minus;\u0026thinsp;13\u003c/sup\u003e; PC2: \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.83 x 10\u003csup\u003e\u0026minus;\u0026thinsp;08\u003c/sup\u003e; PC 3: \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;1.00 x 10\u003csup\u003e\u0026minus;\u0026thinsp;323\u003c/sup\u003e). These results suggest a distinct shift across all primary components despite no directional changes in topology. Inversely to the first two turning points, the last turning point (85 years old) captures significant changes in PC3 (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.018) but not PC1 (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.472) or PC2 (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.261) (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea,c; Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb). Together, these results indicate that differences in topology before and after 85 years old appear within segregation and centrality metrics, which load onto PC3 (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea; Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ed).\u003c/p\u003e\n\u003cp\u003eLastly, we used the trajectories of PCA scores within epochs to examine differences in developmental patterns. Using dynamic time warping, we qualitatively compared the trajectory patterns between each consecutive epoch (Extended Data Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec) (see \u0026ldquo;Methods\u0026rdquo;; \u0026ldquo;Dynamic time warping\u0026rdquo;). The warping distance (Euclidean) conveys how different two trajectories are \u0026ndash; larger distances indicate more different trajectory patterns than shorter distances. This analysis showed that epochs one and two have the most similar trajectory patterns, followed by epochs four and five and epochs three and four (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb,c). The two epochs with the most different trajectories are two and three, suggesting that the trajectory pattern is distinctive before and after 32 years old compared to any other turning point (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb,c).\u003c/p\u003e\n\u003cp\u003eWhen comparing all analyses across all turning points, 32 years old emerges at the largest turning point across the lifespan (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec). The last turning point \u0026ndash; 85 years old \u0026ndash; appears to be the smallest (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec). The two \u0026lsquo;middle\u0026rsquo; turning points \u0026ndash; 62 and eight years old \u0026ndash; are distinct from each other in that significant directionality changes occur around eight years old but none at 62 years old (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec). Together, these results indicate that the major lifespan turning points signify critical shifts in the trajectory of topological development.\u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eOur results emphasize the complex, non-linear topological changes that occur across the lifespan, with oscillating network integration development between childhood, adolescent, and adult periods. We found that centrality is important during adolescence but minimally for the rest of the life. Additionally, our results show a pattern of increased network segregation but decline of the age-topology relationship in late life. Broadly, the trajectory of topological development can be distinctly separated into multiple phases of development, with four major turning points occurring around eight, 32, 62, and 85 years old. These points indicate where the trajectory of topological development shifts significantly and begins a new projection into a different area of the manifold space. As it is novel to use manifolds to identify topological turning points, we aim to review where these turning points align with important anatomical and contextual milestones.\u003c/p\u003e \u003cp\u003eThe first turning point indicates that the childhood topological trajectory ends around 8 years old. The first few years of life are marked by consolidation and competitive elimination of synapses\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e and rapid increases in gray and white matter volume\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Our results indicated that, topologically, structural networks develop along the same dimensions from birth until about eight years old. This is consistent with a previously identified cortical turning point around 7 years old where there is an efficiency inflection point, cortical thickness peaks, and cortical folding stabilizes and efficiency\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. This age also aligns with the onset of puberty, which begins from eight to 13 years old for females and nine to 14 years old for males\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e, and marks the initiation of significant alterations in hormone expression\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e and robust neurological changes\u003csup\u003e\u003cspan additionalcitationids=\"CR51 CR52\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e. Coinciding with this topological and neurobiological shift, the transition from childhood to adolescence brings with it increased risk of mental health disorders\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e, progression in cognitive capacity\u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e, and modifications of socio-emotional and behavioural development\u003csup\u003e\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e,\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e. Thus, the eight-year-old turning point not only signifies a distinct shift in topological development but also aligns with key cognitive, behavioral, and mental health developmental milestones.\u003c/p\u003e \u003cp\u003eThe second lifespan epoch, ages eight to 32, indicates no significant shift in the trajectory topological development. While adolescence begins with puberty, the end of adolescence is less clear, with older definitions ending before 20 and more recent definitions extending into the mid-20s\u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e. The transition to adulthood is influenced by cultural, historical, and social factors, making it context-dependent rather than a purely biological shift\u003csup\u003e\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e,\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e\u003c/sup\u003e. Our findings suggest that in Western countries (i.e., the United Kingdom and United States of America), adolescent topological development extends to around 32 years old, before brain networks begin a new trajectory of topological development.\u003c/p\u003e \u003cp\u003eAdditionally, 32 years old is the strongest topological turning point of the lifespan. At this age, the most directional changes and largest shift in trajectory occur compared to the other turning points. These findings are highly consistent with previous work exploring individual topological metrics\u003csup\u003e\u003cspan additionalcitationids=\"CR26\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e that identify significant peak/inflection points at the beginning of the fourth decade. Beyond organizational changes, this turning point aligns with developmental trajectories of white matter. White matter volume and fractional anisotropy peak around 29 years old\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e,\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e\u003c/sup\u003e, mean diffusivity arrives at a minimum around 36 years old\u003csup\u003e\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e,\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e\u003c/sup\u003e, and radial diffusivity reaches a minimum around 31 years old\u003csup\u003e\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e\u003c/sup\u003e. Together, these results indicate significant changes in white matter integrity and topological development occur around the beginning of the fourth decade of life.\u003c/p\u003e \u003cp\u003eAfter age 32, the longest epoch begins, covering three decades of adulthood until age 62. Compared to rapid maturation in earlier life, changes in network architecture slow during this period\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e,\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e,\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e\u003c/sup\u003e, which is consistent with our results that the trajectory to topological development is stable. This period of network stability aligns with a plateau in intelligence and personality\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. Consequently, not only do we observe the alignment of turning points with significant anatomical and cognitive milestones, but also the stable topological epochs of life coincide with periods of anatomical, cognitive, and behaviour consistency.\u003c/p\u003e \u003cp\u003eThe third turning point, age 62, marks a topological shift without directional changes. Consistent with past work\u003csup\u003e\u003cspan additionalcitationids=\"CR26\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e, we find no directional changes in network organization occurring at this age. However, there were significant differences in PCA scores in all PCs. Therefore, this turning point may reflect protracted or accelerated development. Indeed, accelerated decreases in white matter integrity are known to occur in late life\u003csup\u003e\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e\u003c/sup\u003e. Additionally, the early 60s marks an important shift in health and cognition in high-income countries, such as the onset of dementia and hypertension\u003csup\u003e\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e,\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e\u003c/sup\u003e. Hypertension, characterized by chronically elevated blood pressure, is linked to cognitive decline and accelerated brain aging and is also a known risk factor for dementia\u003csup\u003e\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e,\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e\u003c/sup\u003e. Thus, as with the first two turning points, age 62 also aligns with significant shifts in health and cognition.\u003c/p\u003e \u003cp\u003eThe last turning point marks a distinct decline in the age-topology. After 85 years old, we found no significant relationships between age and brain organization, and the LASSO regression required weaker regularization than any other epoch for any metrics to survive. It is possible that the lack of significant findings reflects the small sample size (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;56). However, when considering the significant correlations from previous epochs, a declining trend appears after middle-age; epoch three had 11 significant correlations, epoch four had six significant correlations, and epoch five had no significant correlations. Therefore, this could reflect a true weakening relationship between age and structural brain topology in late life.\u003c/p\u003e \u003cp\u003eThe data processing pipeline and manifold construction involve numerous design choices, and while we have attempted to test how these may impact our results, some caveats remain. First, we used four versions of the AAL90 atlas warped to two-year, one-year, and neonatal brain sizes to address early-life brain volume changes\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e,\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e\u003c/sup\u003e. This step was crucial for a consistent parcellation necessary for unbiased topological analysis, but atlas alignment differences may exist. Second, we harmonized tracked networks and provided 10 additional analyses exploring various harmonization methods (Supplementary Fig.\u0026nbsp;3). We chose the approach with the fewest remaining dataset effects. Notably, no turning points coincided with dataset transitions (e.g., BCP ends at five and CALM starts at six), as we would expect if turning points were dataset effects. However, harmonization may have over- or under-corrected for dataset differences. Third, networks were thresholded to a fixed density to ensure unbiased topological analysis, though this may obscure individual differences and small age-related changes variations. Additional analyses to assess the effects of these choices (Supplementary Fig.\u0026nbsp;1) and variable analysis demonstrate consistent turning points (Supplementary Fig.\u0026nbsp;4a). Despite this consistency, density-controlled results must be interpreted in the context of thresholding. Finally, we performed sensitivity analyses on turning point identification, which show generally consistent results, though it is important to note that the polynomial fit influences turning points (Supplementary Fig.\u0026nbsp;4).\u003c/p\u003e \u003cp\u003eAdditional key limitations are present in the project design. Despite sex effects in individual organizational measures, we did not sex-stratify this data due to sample size considerations. Future work should explore if the four major turning points identified here are sex sensitive. Moreover, the cross-sectional design of this project, due to limited availability of longitudinal lifespan datasets, limits exploration of causality or temporal dynamics within an individual. Additionally, while all participants included were deemed healthy by respective project guidelines, the gap between a healthy older individual and their peers may be larger than that between a healthy middle-aged individual and their peers. It is reasonable to speculate that older individuals in this study are healthier than typical individuals their age, which could bias the older sample.\u003c/p\u003e \u003cp\u003eIn conclusion, our findings suggest that structural topological development occurs non-linearly across the lifespan, with major turning points occurring around eight, 32, 62, and 85 years old. These ages demarcate periods of complex topological development with distinct age-related changes. This work reinforces the need for multivariate, lifespan, population-level approaches to deepen our understanding of complex topological development.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cp\u003e \u003cb\u003eDatasets and preprocessing.\u003c/b\u003e This study includes nine separate datasets that were collected and preprocessed specifically to suit the age range for the sample. Details on dataset samples, imaging procedures and preprocessing are summarized in Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Four datasets were preprocessed in-house using QSIprep\u003csup\u003e\u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e69\u003c/span\u003e\u003c/sup\u003e, while five datasets were preprocessed by Dr Yeh and made publicly available on DSI studio\u0026rsquo;s Fiber Data Hub (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://brain.labsolver.org/\u003c/span\u003e\u003cspan address=\"https://brain.labsolver.org/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) (Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cem\u003eIn-house processed datasets.\u003c/em\u003e The Baby Connectome Project (BCP) is a multi-site study conducted at the University of North Carolina at Chapel Hill and the University of Minnesota aimed at capturing the typical development of infants\u003csup\u003e\u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e\u003c/sup\u003e. This dataset works as an extension of previous human connectome projects but is optimized for imaging and processing suitable for zero to five-year-olds (Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003csup\u003e70\u003c/sup\u003e). During harmonization, we utilized all scans from infants 12 months or older; however, for the analysis, we excluded longitudinal and repeat scans by using only the first scan for every infant (Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Some individuals had two different types of scans within the same session \u0026ndash; 6-shell or dir-79 (Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Due to previous reports that the 6-shell scheme resulted in increased accuracy of local fiber orientation estimates\u003csup\u003e\u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e\u003c/sup\u003e, if both scan types were available, the 6-shell scan was used.\u003c/p\u003e \u003cp\u003eThe Centre for Attention, Learning and Memory (CALM), Resilience in Education and Development (RED), and Attention and Cognition in Education (ACE) datasets were collected at the MRC Cognition and Brain Sciences Unit at the University of Cambridge. The CALM cohort is a specialized sample of children who are neurodivergent collected at the MRC Cognition and Brain Sciences Unit, University of Cambridge\u003csup\u003e\u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e\u003c/sup\u003e. All scans were included during harmonization; however, only neurotypical controls were included in the analysis (Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The RED dataset was aimed to sample children from diverse socio-economic (SES) backgrounds\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. One participant was removed due to missing age data (Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e; resulting sample size of \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;75). The ACE dataset aimed to capture a realistic representation of SES across the UK\u003csup\u003e\u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e72\u003c/span\u003e\u003c/sup\u003e (Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cem\u003eDSI Studio semi-processed datasets.\u003c/em\u003e Dr Yeh has preprocessed and made available many datasets on DSI Studio\u0026rsquo;s Fiber Data Hub (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://brain.labsolver.org/\u003c/span\u003e\u003cspan address=\"https://brain.labsolver.org/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). The dataset-specific preprocessing methods below are also published on the DSI Studio website.\u003c/p\u003e \u003cp\u003eThe Developing Human Connectome Project (dHCP) is a collaborative effort between King\u0026rsquo;s College London, Imperial College London, and Oxford University that collects neuroimaging data from neonates\u003csup\u003e\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e\u003c/sup\u003e. All longitudinal scans and infants born earlier than 37 weeks gestation (preterm) were excluded from this analysis, resulting in a cross-sectional, term infant sample (Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The images were denoised and corrected for Gibbs ringing, motion, eddy current, and susceptibility artifact using the diffusion SHARD pipeline\u003csup\u003e\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e\u003c/sup\u003e. A quality check was conducted using neighboring DWI correction (NDC)\u003csup\u003e\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e\u003c/sup\u003e. 34 scans (including repeated scans) were excluded due to their low NDC values identified by a median value-based outlier detector.\u003c/p\u003e \u003cp\u003eThe Human Connectome Project Development (HCPd) aims to capture a diverse but typical developmental sample\u003csup\u003e\u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e\u003c/sup\u003e. This multi-site study includes Harvard University, University of California-Los Angeles, University of Minnesota, and Washington University in St. Louis\u003csup\u003e\u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e\u003c/sup\u003e. Sample and imaging information can be found in Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and in further detail Somerville et al. (2018)\u003csup\u003e\u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e\u003c/sup\u003e. The susceptibility and eddy current artifacts were corrected using\u003c/p\u003e \u003cp\u003eFSL topup and eddy (FMRIB, Oxford). The correction was conducted through the integrated interface in DSI Studio\u0026rsquo;s (\u0026ldquo;Chen\u0026rdquo; release). The diffusion MRI data were rotated to align with the AC-PC line. The accuracy of b-table orientation was examined by comparing fiber orientations with those of a population-averaged template\u003csup\u003e\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe Human Connectome Project Young Adult (HCPya) is a multi-site study collected by the Washington University-University of Minnesota Consortium of the Human Connectome Project (WU-Minn HCP), which aims to capture a large sample of healthy adults\u003csup\u003e\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e\u003c/sup\u003e. Sample and imaging information can be found in Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and in further detail Van Essen et al. (2013)\u003csup\u003e\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e\u003c/sup\u003e. A group average template was constructed from a total of 930 subjects. The diffusion data were reconstructed in the MNI space using q-space diffeomorphic reconstruction\u003csup\u003e\u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e\u003c/sup\u003e to obtain the spin distribution function\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe Human Connectome Project Ageing (HCPa) is a multi-site study aimed at capturing healthy aging from 36 to 100\u003csup\u003e+\u003c/sup\u003e years old\u003csup\u003e\u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e80\u003c/span\u003e\u003c/sup\u003e. The sample used in this analysis excluded participants scanned at 100\u003csup\u003e+\u003c/sup\u003e years old (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;12), resulting in a cross-sectional sample ranging from 36 to 90 years old (Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e; \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;706). Further details on the HCPa sample and imaging methods can be found at Bookheimer et al. (2019)\u003csup\u003e\u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e80\u003c/span\u003e\u003c/sup\u003e. The susceptibility and eddy current artifacts were corrected using FSL topup and eddy (FMRIB, Oxford). The correction was conducted through the integrated interface in DSI Studio\u0026rsquo;s (\u0026ldquo;Chen\u0026rdquo; release). The diffusion MRI data were rotated to align with the AC-PC line.\u003c/p\u003e \u003cp\u003eThe Cambridge Centre for Ageing and Neuroscience (CamCAN) project aims to capture age-related changes in neurocognitive systems\u003csup\u003e\u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e81\u003c/span\u003e\u003c/sup\u003e. This project is conducted at the MRC Cognition and Brain Sciences Unit, University of Cambridge, and focuses on exploring important aspects of health in aging. Sample and imaging information can be found in Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and in further detail Shafto et al. (2014)\u003csup\u003e\u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e81\u003c/span\u003e\u003c/sup\u003e. The b-table was checked by an automatic quality control routine to ensure its accuracy\u003csup\u003e\u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e82\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFor dHCP, HCPd, and HCPa, the accuracy of b-table orientation was examined by comparing fiber orientations with those of a population-averaged template\u003csup\u003e\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e\u003c/sup\u003e. The restricted diffusion was quantified using restricted diffusion imaging\u003csup\u003e\u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e83\u003c/span\u003e\u003c/sup\u003e. Additionally, with dHCP, HCPd, HCPa and CamCAN, the diffusion data were reconstructed using generalized q-sampling imaging\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e with a diffusion sampling length ratio of 1.25. Alternatively, for HCPya a diffusion sampling length ratio of 2.5 was used, and the output resolution was 1 mm.\u003c/p\u003e \u003cp\u003e \u003cb\u003eConnectome construction.\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eTractography.\u003c/em\u003e All networks were tracked using standard GQI plus deterministic tractography in DSI Studio\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. For participants three years old and older, the QSIprep dsi_studio_gqi workflow\u003csup\u003e\u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e69\u003c/span\u003e\u003c/sup\u003e was applied with the AAL116 atlas\u003csup\u003e\u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e84\u003c/span\u003e\u003c/sup\u003e. All other participants were tracked directly in DSI Studio using multiple versions of the AAL atlas. Participants aged 24 to 35 months were tracked with the AAL90 two-year-old atlas\u003csup\u003e\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e\u003c/sup\u003e, those aged 12 to 23 months with the AAL90 one-year-old atlas\u003csup\u003e\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e\u003c/sup\u003e, and those younger than 12 months with the AAL90 neonatal atlas\u003csup\u003e\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e\u003c/sup\u003e. For all networks parcellated with the AAL116 atlas, we removed additional subcortical regions (numbers 91\u0026ndash;116), which resulted in the AAL90 atlas. This progressive use of AAL90 atlases with the same regions fit to different brain volumes enables direct comparison between regions across the lifespan while accommodating for drastic brain growth in the first two years of life. All tracking was performed with the same parameters \u0026ndash; maximum fiber length of 250mm, minimum fiber length of 30mm, 5\u0026nbsp;million streamlines, random seeding, 1mm step size, and turning angle 35\u003csup\u003e\u0026deg;\u003c/sup\u003e. We used count-end connectivity, indicating that streamlines were identified between two regions if the streamline ended in both regions.\u003c/p\u003e \u003cp\u003e \u003cem\u003eHarmonization.\u003c/em\u003e All data, including longitudinal and repeat scans in BCP and neurodivergent group in CALM, were included in harmonization (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4,216). Multiple harmonization methods for variable density and density-controlled networks as well as assessing efficacy of harmonization before and after thresholding and can be found in the supplement (Supplementary Fig.\u0026nbsp;3). The harmonization methods were evaluated by the total number of FDR-corrected significant effects of study within age-bins across density, modularity, core/periphery structure, global efficiency, average degree, and average strength (see \u0026ldquo;Methods\u0026rdquo;; \u0026ldquo;Graph Theory\u0026rdquo;), as well as visual inspection of generalized additive models. We determined that our \u0026lsquo;double harmonized\u0026rsquo; method before thresholding was the most effective across both variable and density-controlled analyses. Double harmonization was performed using ComBat\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e to harmonize across atlas and then harmonize again across study (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec). For each step, a mask was used to only retain connections that were present before harmonization in addition to setting any negative connections produced by harmonization to zero. Covariates that were preserved during harmonization included participant ID, age, sex, and neurodiversity group to identify children in CALM who are neurodiverse.\u003c/p\u003e \u003cp\u003e \u003cem\u003eThresholding.\u003c/em\u003e Before thresholding, 14 participants were identified as outliers (dHCP \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1; CALM \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2; RED \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1; ACE \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1; HCPya \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3; HCPa \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1; CamCAN \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5) due to having network density above or below three standard deviations for the age bin and were removed. With this reduced sample (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4,202), two thresholding methods were performed \u0026ndash; (1) preserve variable density across the lifespan and (2) control density across the lifespan for topological comparison.\u003c/p\u003e \u003cp\u003eFor the variable density analysis, we performed a generalized additive model (see \u0026ldquo;Statistics\u0026rdquo;) on the raw network densities and took 70% of the regression to obtain a \u0026lsquo;target\u0026rsquo; density for each age (Supplementary Fig.\u0026nbsp;1a). Then, for each age group within each study, we applied the absolute threshold that yielded an average density equal to the target density for that age. The resulting networks were thresholded to densities ranging from 21 to 8% with the original relationships between density preserved (Supplementary Fig.\u0026nbsp;1a). These networks were then used only in the connectivity analysis to explore density, degree, and strength of networks.\u003c/p\u003e \u003cp\u003eAdditionally, the density-controlled networks were constructed for topological analyses. These networks were thresholded at the individual level so that each individual, regardless of age, had a 10% dense network. 10% was utilized because the sparsest network in the sample was 11%. Thus, 10% was the highest possible density where every network in the sample is thresholded, as well as it being consistent with past lifespan work\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. Additional densities of 8% and 5% can be found in the supplement (Supplementary Fig.\u0026nbsp;1B). All networks were converted to normalized weighted networks using weight_conversion() from the Brain Connectivity Toolbox\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e, which rescales all weights to range from 0 to 1.\u003c/p\u003e \u003cp\u003e \u003cb\u003eGraph theory.\u003c/b\u003e All graph theory metrics were calculated using the Brain Connectivity Toolbox (BCT) in MATLAB 2020b\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. Global measures included network density, modularity, global efficiency, characteristic path length, core/periphery structure, small-worldness, k-core, and s-core, while local measures utilized were degree, strength, local efficiency, clustering coefficient, betweenness centrality, and subgraph centrality. All local measures were averaged across the network for the topological analysis.\u003c/p\u003e \u003cp\u003e \u003cb\u003eUniform Manifold Approximation and Projection (UMAP).\u003c/b\u003e To project topological data into a manifold space, we used the UMAP package in Python version 3.7.3\u003csup\u003e34\u003c/sup\u003e. Before data was put into the UMAP, it was first standardized using Sklearn\u0026rsquo;s StandardScalar()\u003csup\u003e\u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e85\u003c/span\u003e\u003c/sup\u003e. UMAP requires four pre-defined parameters \u0026ndash; minimum distance and nearest neighbors, number of components, and distance metric. Minimum distance typically ranges between zero to one and determines how closely data points are packed together in the low-dimensional representation (low values result in more clustered representations)\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. Nearest neighbors defines the size of local neighborhoods when learning the manifold structure\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. This parameter, therefore, determines the balance between local versus global structure \u0026ndash; a low nearest neighbors value pushes the UMAP to capture more local structure and vice versa. Nearest neighbors can be at minimum two or at maximum one less than the length of the data input. The number of components simply determines how many dimensions the projection should be embedded in \u0026ndash; we predefined this as three dimensions. Lastly, the distance metric determines how the distance is calculated. We used the Euclidean distance.\u003c/p\u003e \u003cp\u003eA limitation of UMAP is that the minimum distance and nearest neighbors parameter choice greatly determines the shape of the projected manifold\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e. While UMAP always captures patterns within the data, the parameter choices alter which patterns are projected, making it challenging to derive meaningful interpretations of the projections. To mitigate this, we derived 968 combinations of UMAP parameters. The nearest neighbour parameter was set to 88 whole numbers that ranged from two to 89, while the minimum distance parameter was 11 values evenly spaced ranging from 0.1 to one. Thus, we conducted our analysis on a complete range of UMAP projections, from manifold representing mostly local patterns through manifolds capturing mainly global patterns.\u003c/p\u003e \u003cp\u003e \u003cb\u003eTurning point identification.\u003c/b\u003e To determine what constitutes a turning point, we have constructed our own algorithm with multiple parameters. First, we must find a line of best fit through the 3-dimensional manifold. In Python version 3.7.3, we created three polynomial fits \u0026ndash; one for each dimension \u0026ndash; which requires the choice of the polynomial degree (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea). The equation for each dimension is as follows:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:Dimension\\left(age\\right)={\\beta\\:}_{0}+{\\beta\\:}_{1}age+{{\\beta\\:}_{2}age}^{2}+{{\\beta\\:}_{3}age}^{3}+{{\\beta\\:}_{4}age}^{4}+{{\\beta\\:}_{5}age}^{5}+\\:ϵ$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ePolynomials were fit using the polyfit() function from the \u003cem\u003enumpy\u003c/em\u003e package, which uses least squares error\u003csup\u003e\u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e86\u003c/span\u003e\u003c/sup\u003e. Together, these polynomials create the 3D line of best fit through the manifold space. For our main analysis, we fit 5-degree polynomials and have included iterative polynomials ranging from two to 12 in the supplementary materials (Supplementary Fig.\u0026nbsp;4a). This sensitivity analysis highlights that a degree of five is a middle-ground between visually under fit and overfit lines, with high-degree lines including more middle-age turning points (e.g., between 40\u0026ndash;60 years old). Importantly, turning points occurring before 10, around 30, and in the 80s are robust across most degree choices (Supplementary Fig.\u0026nbsp;4a). Generally, the choice of degree impacts \u003cem\u003ewhere\u003c/em\u003e in the lifespan turning points are identified.\u003c/p\u003e \u003cp\u003eWe then calculated the gradients of the lines of best fit and identified points in which the gradient changes sign (positive to negative or negative to positive) along each dimension. Small fluctuations were then filtered to remove minor inflections by removing points where the sum of the gradients around the point was relatively small. This filtering process requires two parameters \u0026ndash; a gradient window (W) and gradient threshold (T). The gradient window determines the number of years around the inflection point (\u003cem\u003ei\u003c/em\u003e) that will be the scope of the gradient threshold. The gradient threshold is the cut-off for how large the sum of the absolute value of gradients within this range needs to be to be retained. An inflection point will survive this cutoff if:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:T\u0026lt;\\:{\\sum\\:}_{i-W}^{i+W}\\left|{G}_{i}\\right|$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eG\u003csub\u003ej\u003c/sub\u003e represents the gradient at \u003cem\u003ei\u003c/em\u003e year, W is the gradient window, and T is the gradient threshold. The larger the gradient threshold, the sharper the inflection point (i.e. steep slopes on either side of the point) must be to be kept in the analysis. For our analysis, we defined the gradient window to five years and the gradient threshold to 0.8, though it is important to note that many variations of these parameters result in the same turning points being identified. Sensitivity analysis of varying gradient thresholds can be found in supplement (Supplementary Fig.\u0026nbsp;4c). This analysis shows that turning points are stable across gradient thresholds 0.1 to 0.8. Turning points around eight and 85 are retained at a gradient threshold of 1.2 but not middle age turning points, indicating that the first and last turning points of the lifespan are the \u0026lsquo;largest\u0026rsquo; or \u0026lsquo;sharpest\u0026rsquo; in terms of the change in slope through the manifold space (Supplementary Fig.\u0026nbsp;4c). Thus, this parameter affects the sensitivity to the \u003cem\u003esize\u003c/em\u003e of turning points but not where the turning points are located across the lifespan.\u003c/p\u003e \u003cp\u003eThe second step for identifying turning points in a manifold is to handle instances where multiple points have been detected close together. For example, if age 31 in dimension X and age 33 in dimension Y were identified as inflection points, we interpret these as representing a single turning point rather than two distinct trajectories, given their proximity. This process requires an age window parameter (A) to determine the age range around the inflection point in which a mean will be calculated. This averaging procedure occurs both within and across dimensions. Average turning points are then rounded and considered the \u0026lsquo;final\u0026rsquo; turning points. For our analysis, we used an age window parameter of five years and have included a sensitivity analysis to explore how changing the age window affects the turning points identified which can be found in (Supplementary Fig.\u0026nbsp;4b). Between age windows of one through 10, we see no changes in turning points beyond a single year (Supplementary Fig.\u0026nbsp;4b). Thus, this parameter effects \u003cem\u003ewhere\u003c/em\u003e a turning point is identified, similar to the degree of the polynomial, though its influence is minimal.\u003c/p\u003e \u003cp\u003eTurning points were identified for each of the 968 UMAP projections. \u003cem\u003eMajor\u003c/em\u003e turning points were defined by the peaks in Gaussian kernel density function of all turning points (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec). Thus, these points are the most frequent ages identified as turning points across all manifolds. We also assessed turning points in variable density networks (Supplementary Fig.\u0026nbsp;4d) and sex-stratified projections that have been mapped to the combined UMAP space using orthogonal procrustes\u003csup\u003e\u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e87\u003c/span\u003e\u003c/sup\u003e (Supplementary Fig.\u0026nbsp;2). This analysis demonstrates that major turning points appear around similar ages for variable density networks and sex-stratified samples as those calculated in density-controlled networks. Thus, our conservative thresholding for easy topological interpretability does not appear to drastically change where in the lifespan major turning points have been identified. Major turning points mark the average age at which topological data begins a new trajectory through the manifold, indicating a distinctly different organisational change across age. Thus, between major turning points, we define age epochs in which topological change is occurring along the same trajectory through the manifold space.\u003c/p\u003e \u003cp\u003e \u003cb\u003eEpoch correlations.\u003c/b\u003e We applied Pearson correlations within epochs (i.e., age ranges between major turning points) to explore changes in each organisational metrics across age. We also used correlations to examine \u003cem\u003ebetween\u003c/em\u003e epochs simply by identifying when significant correlations in consecutive epochs changed direction (i.e., from a positive correlation to a negative correlation and vice versa) (Extended Data Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea)\u003c/p\u003e \u003cp\u003e \u003cb\u003eLeast Absolute Shrinkage and Selection Operator (LASSO).\u003c/b\u003e To explore driving topological factors within epochs, we employed LASSO regularization models\u003csup\u003e\u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e88\u003c/span\u003e\u003c/sup\u003e in MATLAB 2020b with 10-fold cross-validation (CV) to perform variable selection with multicollinear predictors. The benefit of LASSO models is that they penalize the absolute value of coefficients, which results in some coefficients being pushed to zero, allowing for easy interpretation of important model features\u003csup\u003e\u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e88\u003c/span\u003e\u003c/sup\u003e. This penalization term is multiplied by a constant, λ, which is determined through the 10-fold CV. 10-fold CV trains the LASSO on nine folds (i.e. subset of the data) and is tested on the 10th fold. To encourage sparsity in the model, we selected the largest lambda where the mean squared error (MSE) is within one standard error of the minimum MSE. For the last epoch, this level of sparsity resulted in no variables selected, and therefore, the LASSO model for epoch five was created by selecting the lambda value with the minimum MSE.\u003c/p\u003e \u003cp\u003e \u003cb\u003ePrincipal Components Analysis (PCA).\u003c/b\u003e We conducted a PCA\u003csup\u003e\u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e89\u003c/span\u003e\u003c/sup\u003e in MATLAB2020b to reduce the dimensionality of graph theory metrics for the purpose of exploring between-epoch changes. After standardizing the data, we ran a PCA with the maximum number of components (11) and conducted a parallel analysis to determine how many components to retain\u003csup\u003e\u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e90\u003c/span\u003e\u003c/sup\u003e. For the parallel analysis, we created 1,000 iterations of standardized random data and conducted PCAs for each iteration. We then calculated the top 95% confidence interval of eigenvalues produced by the random samples\u003csup\u003e\u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e90\u003c/span\u003e\u003c/sup\u003e. Components from the original PCA with eigenvalues exceeding the threshold set by 95% confidence interval from the random eigenvalues were retained as this indicates that eigenvalues were larger than expected at chance. This analysis indicated three components be retained (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea). A second PCA was run, this time constrained to three components which convey 80% of variance across the sample (Extended Data Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). To improve loading interpretation, an orthogonal rotation was applied using rotatefactors() with the varimax method\u003csup\u003e\u003cspan citationid=\"CR91\" class=\"CitationRef\"\u003e91\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eWe compared epochs based on their PCA scores, first using Levene's Test for Relative Variation\u003csup\u003e\u003cspan citationid=\"CR92\" class=\"CitationRef\"\u003e92\u003c/span\u003e\u003c/sup\u003e in Python version 3.7.3 to determine if the variance of PCA scores significantly differed across epochs. Since this test was significant, we used Welch\u0026rsquo;s Analysis of Variance (ANOVA)\u003csup\u003e\u003cspan citationid=\"CR93\" class=\"CitationRef\"\u003e93\u003c/span\u003e\u003c/sup\u003e in Python to assess significant differences in mean PCA scores across epochs. Lastly, we ran post hoc Games-Howell\u003csup\u003e\u003cspan citationid=\"CR94\" class=\"CitationRef\"\u003e94\u003c/span\u003e\u003c/sup\u003e tests in Python to determine which consecutive groups were significantly different (Extended Data Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). The full table of all Games-Howell comparison outcomes can be found in the supplement (Extended Data Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). In some instances, p-values were set equal to zero due to the truncated precision of Python. In these cases, p-values are reported as less than the minimum printable value, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;1.00 x 10\u003csup\u003e\u0026minus;\u0026thinsp;323\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003cb\u003eDynamic Time Warping (DTW).\u003c/b\u003e We also examined differences between epochs using DTW on PCA score series conducted in Python version 3.7.3\u003csup\u003e95\u003c/sup\u003e. DTW warps two time series to their optimal alignment. The algorithm calculates the local Euclidean distances between points in each series, calculating the global alignment between the series as the warping path that minimises the sum of distances between series\u003csup\u003e\u003cspan citationid=\"CR95\" class=\"CitationRef\"\u003e95\u003c/span\u003e\u003c/sup\u003e. DTW distance, defined as the minimum cumulative distance of the warp, quantifies how far points in one series must shift to align with another, providing insight into differences in their shapes. For our analysis, we constructed a series for each epoch across each PC, represented as the average PCA score for each age (Extended Data Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). The DTW distances for optimal warping between consecutive epochs were standardized within each principal component. These distances were then qualitatively compared \u0026ndash; with larger distances suggesting more disparity between the \u003cem\u003eshape\u003c/em\u003e of those series\u0026rsquo; trajectories.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch3\u003eAUTHOR CONTRIBUTIONS\u003c/strong\u003e\u003c/h3\u003e\n\u003cp\u003eA.M. performed fiber tracking, constructed connectomes, conducted the analysis, and drafted the manuscript. F.C. preprocessed, quality controlled, and reconstructed the majority of networks. A.M., D.E.A., and R.B. conceptualized the analysis. D.E.A. and R.B. provided critical manuscript reviews and edits.\u0026nbsp;\u003c/p\u003e\n\u003ch3\u003eCOMPETING INTERESTS\u003c/strong\u003e\u003c/h3\u003e\n\u003cp\u003eThe A.M., D.E.A., and F.C. declare no competing financial or non-financial interests. R.B. declares he is a co-founder of and holds equity in Centile Bioscience Inc.\u003c/p\u003e\n\u003ch3\u003eDATA AVAILABILITY\u003c/h3\u003e\n\u003cp\u003eThe derived data generated in this study are available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://osf.io/7p4y3/\u003c/span\u003e\u003cspan address=\"https://osf.io/7p4y3/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. CALM data are available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://portal.camide.cam.ac.uk/overview/1158\u003c/span\u003e\u003cspan address=\"https://portal.camide.cam.ac.uk/overview/1158\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. BCP data are available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://nda.nih.gov/\u003c/span\u003e\u003cspan address=\"https://nda.nih.gov/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. The semi-processed data from dHCP, HCPd, HCPya, HCPa, and CamCAN used in this publication are available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://brain.labsolver.org/\u003c/span\u003e\u003cspan address=\"https://brain.labsolver.org/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003ch3\u003eCODE AVAILABILITY\u003c/h3\u003e\n\u003cp\u003eAll code is available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/alexamousley/lifespan_topological_turning_points\u003c/span\u003e\u003cspan address=\"https://github.com/alexamousley/lifespan_topological_turning_points\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBethlehem RAI et al (2022) Brain charts for the human lifespan. 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J R Stat Soc Ser B Stat Methodol 58:267\u0026ndash;288\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHotelling H (1933) Analysis of a complex of statistical variables into principal components. J Educ Psychol 24:498\u0026ndash;520\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHorn JL, A RATIONALE AND TEST FOR THE NUMBER (1965) OF FACTORS IN FACTOR ANALYSIS. Psychometrika 30:179\u0026ndash;185\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKaiser HF (1958) The varimax criterion for analytic rotation in factor analysis. Psychometrika 23:187\u0026ndash;200\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSchultz BB (1985) Levene\u0026rsquo;s Test for Relative Variation. Syst Biol 34:449\u0026ndash;456\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWelch YBL (1951) On the comparison of several mean values: An alternative approach. 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J Stat Softw 31:1\u0026ndash;24\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTable 1 to 3 are available in the Supplementary Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6120723/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6120723/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eStructural topology develops non-linearly across the lifespan and is strongly related to cognitive trajectories. We gathered diffusion imaging from datasets with a collective age range of zero to 90 years old (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4,216). We analysed how 12 graph theory metrics of organization change with age and projected these data into manifold spaces using Uniform Manifold Projection and Approximation. With these manifolds, we identified four major topological turning points across the lifespan \u0026ndash; at eight, 32, 62, and 85 years old. These ages defined five major epochs of topological development, each with distinctive age-related changes in topology. These major life epochs each have a distinct direction of topological development and specific changes in the organizational properties driving the age-topology relationship. This study underscores the complex, non-linear nature of human development, with district phases of topological maturation, which can only be illumined with a multivariate, lifespan, population-level perspective.\u003c/p\u003e","manuscriptTitle":"Topological turning points across the human lifespan","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-26 09:01:19","doi":"10.21203/rs.3.rs-6120723/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"38b3ae09-ee16-4062-af70-15b41800eed3","owner":[],"postedDate":"March 26th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":46027127,"name":"Biological sciences/Neuroscience/Computational neuroscience/Network models"},{"id":46027128,"name":"Biological sciences/Developmental biology"}],"tags":[],"updatedAt":"2025-11-26T08:14:27+00:00","versionOfRecord":{"articleIdentity":"rs-6120723","link":"https://doi.org/10.1038/s41467-025-65974-8","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2025-11-25 05:00:00","publishedOnDateReadable":"November 25th, 2025"},"versionCreatedAt":"2025-03-26 09:01:19","video":"","vorDoi":"10.1038/s41467-025-65974-8","vorDoiUrl":"https://doi.org/10.1038/s41467-025-65974-8","workflowStages":[]},"version":"v1","identity":"rs-6120723","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6120723","identity":"rs-6120723","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}