How do infant brains fold? Sulcal deepening is linked to development of sulcal span, thickness, curvature, and microstructure

Abstract

Cortical folding begins in utero as sulci emerge and continues postnatally as sulci deepen. However, the timeline and mechanisms of postnatal sulcal development remain poorly understood. Using structural and quantitative magnetic resonance imaging from 79 infant sessions spanning birth to one year, we longitudinally examined macroanatomical parameters and microstructural tissue density (longitudinal relaxation rate, [R₁]) across sulci that emerge in utero between 16-31 gestational weeks. Here we show that early emerging sulci are deeper at birth and deepen more slowly postnatally than later emerging sulci. Across the first year, sulci become wider (42%), thicker (21%), denser with tissue (33%), and less concave (14%). Mean depth is predicted by a weighted combination of sulcal span, thickness, curvature, and microstructure, with differential weights across sulci. Fine-grained analyses of local depth along the sulcus further reveal that sulcal fundi differ from sulcal walls: deeper portions show higher curvature and greater tissue density. These data show that postnatal sulcal deepening is nonuniform and reflect coordinated anatomical and microstructural processes anchored to the timing of sulcal emergence in utero. By establishing normative trajectories of postnatal sulcal development, our findings inform theories of cortical folding and offer a framework for characterizing deviations from typical development.

Introduction

Sulcal folding is a complex process that begins in utero and involves the development of several genetic, macroanatomical, and microstructural features in the brain^{1,2,3,4,5,6,7,8,9}. Early-emerging sulci appear as early as the 14–16th gestational week^1,2,10, and continue to deepen through the first two years of life^11,12. Sulcal depth, a defining morphological property of cortical folds, serves as a predictor of functional specialization^13,14,15,16 and has been implicated in neurological disorders like Down syndrome¹⁷, Autism spectrum disorder¹⁸, and depression¹⁹. Despite its importance, how sulci deepen during the first year of postnatal life, and whether this development is linked with other macro- and microstructural changes, remains poorly understood. Here, we address this gap by using structural and quantitative MRI to characterize the development of 15 sulci from birth to one year of age.

Cortical development during infancy has garnered much attention over the past decade with the advent of large infant data sets. Broadly, it can be described at two complementary levels: macrostructural features that capture the large-scale geometry and anatomy of the brain, and microstructural features that reflect tissue-level composition. Macrostructural features quantify the overall geometry and folding of the cortex, including measures of cortical gyrification²⁰, mean curvature^21,22, cortical thickness^23,24, sulcal depth^25,26, and sulcal fundi and pits^11,12,27 (deepest points along a sulcal fold). Such metrics have been widely used to chart large-scale cortical folding patterns across the brain. While these studies provide valuable insights into global or regional trajectories of cortical development, many analyses have been conducted cross-sectionally and at the group level, limiting our understanding of fine-grained sulcal development over time. Microstructural features, by contrast, capture tissue-level processes, like synaptic growth^28,29, dendritic arborization^30,31, and myelination³², all of which influence cortical tissue density. Advances in quantitative MRI now enable in-vivo measurements of R₁ (tissue relaxation rate)^33,34,35, which is related to tissue density and myelin content, with higher R₁ values reflecting denser tissue^36,37,38. Recent studies discovered that cortical R₁ increases^39,40,41 and exhibits regional developmental gradients during early infancy, with primary visual cortex exhibiting higher R₁ at birth but slower maturation than higher-order visual areas^40,41.

Examining the longitudinal development of individual sulci in infants is important for integrating these two levels of change. First, different sulcal folds emerge at varying gestational stages in utero, raising the question of whether sulci that emerge earlier deepen at different rates than those that emerge later. For example, the calcarine sulcus, which emerges around the 16th gestational week (early in the second trimester), may follow a different developmental trajectory than the occipital-temporal sulcus, which emerges later, around the 28th gestational week (early in the third trimester)^1,2. Second, sulcal deepening does not occur in isolation but alongside broader macrostructural cortical expansion, including increases in cortical thickness, surface area, sulcal length, and volume, as well as decreases in cortical curvature^42,43. Third, sulcal development is likely also shaped by microstructural changes, as tissue-level processes may influence how sulci deepen over time.

Although several theories propose that sulcal deepening is related to cortical expansion via increases in surface area and thickness^4,8,44,45,46, no study has systematically examined the development of multiple macro- and microstructural changes and their relationship to the development of sulcal depth within individual sulci during infancy. Here, we examine the relationship between the development of sulcal depth (SD, Fig. 1a) and four key features (Fig. 1b): (i) sulcal span (SP)—the total sulcal surface area divided by sulcal length (see “Methods” and Supplementary Fig. 1), (ii) cortical thickness (CT), (iii) curvature (CU), and (iv) microstructural tissue density (R₁). For each parameter, we outline predicted patterns of change during the first year of life and the mechanisms that might underlie them. Sulcal depth vs. Sulcal span (SD-SP) (Fig. 1bi, panel one): We predict a positive relationship between SD and SP (Fig. 1bi, panel two), as tangential cortical expansion (parallel to the cortical surface) may stretch sulci laterally, increasing its span and depth by pushing folds deeper into white matter⁴⁷. Alternatively, there may be no relationship between SD and SP (Fig. 1bi, panel three). This could occur if sulcal depth increases without concurrent widening of the sulcus or if sulci widen without deepening. Sulcal depth vs. Cortical thickness (SD-CT) (Fig. 1bii, panel one): We predict a positive relationship between SD and CT, as radial cortical growth (perpendicular to the surface) could push the sulcus deeper into white matter, leading to simultaneous increase in depth and thickness^42,43 (Fig. 1bii, panel two). Alternatively, there may be no relationship, with depth increasing without substantial changes in thickness⁸ (Fig. 1bii, panel three), or there could be a negative correlation, where depth increases as cortex thins, a pattern observed during childhood development⁴⁸. Sulcal depth vs. Curvature (SD-CU) (Fig. 1biii, panel one): We predict a negative relationship between SD and CU (Fig. 1biii, panel two), as expansion and deepening may widen the sulcal base, reducing mean curvature⁴². Alternatively, curvature may remain stable if folds deepen without widening into white matter (Fig. 1biii, panel three), or increase if sulcal deepening makes its base more acutely folded²⁴. Sulcal depth vs. Cortical microstructure (SD-R₁) (Fig. 1biv, panel one): We predict a positive relationship between SD and R₁ (Fig. 1biv, panel two). Prior results suggest that R₁ increases during early infancy^39,40,41, reflecting tissue becomes more dense, perhaps due to myelination. Increases in these features may contribute to sulcal deepening, both directly though tissue accumulation and indirectly by generating mechanical forces, where axonal myelination can exert tension⁴⁹ and increase stiffness⁵⁰. Conversely, as R₁ development is spatially heterogeneous^39,40,41, if R₁ remains stable, there may be no relationship between SD and R₁ (Fig. 1biv, panel three), whereas if R₁ decreases due to pruning, there may be a negative relationship.

Fig. 1: Schematic illustrating possible relationships between sulcal deepening and changes in macrostructural and microstructural parameters during the first year of life.

a Illustration of a cross section of a sulcus (blue) situated between two gyri (orange), with sulcal depth (SD) indicated by a black arrow. b i–iv Each row represents a potential relationship between sulcal deepening and changes in individual macrostructural and microstructural parameters (from birth to 1 year). Panel one shows the parameter, panel two shows parameter changes as the sulcus deepens, and panel three shows how the parameter remains unchanged despite sulcal deepening. (i) Sulcal span (SP). (ii) Cortical thickness (CT). (iii) Cortical curvature (CU). (iv) Microstructural tissue density (R₁). Higher R₁ values correspond to denser cortical tissue (represented by dots).

To test these hypotheses, we conducted longitudinal and cross-sectional anatomical MRI (T₁- and T₂-weighted) and qMRI in newborns to 1-year-old infants during natural sleep. Here, we focus on the development of 15 long, well-established sulci that emerge in utero between 16 and 31 gestational weeks¹ and are distributed across the four lobes (Fig. 2a, b; see “Methods”): calcarine sulcus (calc), insular sulcus (insula), cingulate sulcus (cing), parieto-occipital sulcus (pos), central sulcus (cent), precentral sulcus (precent), collateral sulcus (cos), superior temporal sulcus (sts), postcentral sulcus (postcent), superior frontal sulcus (sfs), intraparietal sulcus (ips), lateral occipital sulcus (los), inferior frontal sulcus (ifs), occipital temporal sulcus (ots), and inferior temporal sulcus (its). From anatomical MRIs, we estimated sulcal depth [mm], sulcal span [mm], cortical thickness [mm], and curvature [mm⁻¹]; from qMRI, we estimated R₁ [s⁻¹] in cortex (Supplementary Fig. 1 and “Methods”).

Fig. 2: Sulcal folds undergo significant deepening during the first year of postnatal life.

a 15 sulcal folds shown on the cortical surface of an infant. Each color represents a sulcus. b Timeline of sulcal emergence in utero during gestation in weeks based on work by Chi and colleagues¹. c Sulcal depth (SD, in mm) displayed on an inflated cortical surface of a sample infant scanned longitudinally at 26 days (newborn), 94 days (~3 months), 227 days (~6 months), and 368 days (~12 months) (warmer colors: higher SD). d SD increases logarithmically with age in the first year. Superior temporal sulcus (pink arrow, in c) and central sulcus (black arrow, in c) are shallower at 26 days than at 368 days. Each dot: mean SD per infant. Solid line fit: represents the reverse-fit of the log-transformed LMM (Eq. 2), obtained by applying the inverse logarithmic (exponential) function to the model predictions to recover the non-linear relationship. e Estimates of SD at birth (intercept) and (f) rate of SD development (slope), calculated using an LMM relating SD and log₁₀ (age in days) per sulcus. Error bars: standard error of the intercept and slope (N = 43 independent participants). Data shown are from the left hemisphere (LH); Right hemisphere data in Supplementary Fig. 3a–c. Abbreviations of sulcal folds in a): calcarine sulcus (calc), insular sulcus (insula), cingulate sulcus (cing), parieto-occipital sulcus (pos), central sulcus (cent), precentral sulcus (precent), collateral sulcus (cos), superior temporal sulcus (sts), postcentral (postcent), superior frontal sulcus (sfs), intraparietal sulcus (ips), lateral occipital sulcus (los), inferior frontal sulcus (ifs), occipital temporal sulcus (ots), and inferior temporal sulcus (its). Note: the newborn infant in (c) is part of our larger infant data set and is excluded from the remaining analyses due to unusable qMRI data.

Results

Sixty-one full-term infants (N_female = 24) were recruited to participate in the study. We collected usable data in 79 sessions from 43 infants (N_female = 18). Twenty-four (N_female = 11) of the 43 infants were scanned longitudinally (Supplementary Table 1 for demographics; “Methods” for exclusionary criteria). We report data from four timepoints: newborns (N_sessions  = 27, N_female = 10, mean age ± std: 29.14 ± 9.92 days), 3-month-olds (N_sessions  =  20, N_female = 11, 106.35 ± 20.09 days), 6-month-olds (N_sessions  =  22, N_female = 12, 188.45 ± 15.34 days), and 1-year-olds (N_sessions =  10, N_female = 3, 385.80 ± 17.60 days).

To test sulcal development, we identified 15 long-length sulci in each infant (Fig. 2a, b). These sulci were delineated on the surface of the FreeSurfer average adult brain, and projected onto each infant’s surface using cortex-based alignment⁵¹. We tested the reliability of the automated sulcal fold identification by comparing two templates (the FreeSurfer adult template brain and the UNC newborn template brain⁵²) to the manually drawn sulci using dice coefficients⁵³. This analysis revealed a mean dice coefficient of 0.69 ± 0.14 (mean ± standard deviation) across the 15 sulci and both hemispheres, with no significant main effect of age or hemisphere (ps > 0.23) (“Methods” and Supplementary Fig. 2). Our infant dice score is consistent with that measured between manually drawn sulci on adult brains and those projected using adult templates on adult brains (~0.7) in our prior work⁴⁰. This validates that adult-to-infant alignment achieves accuracies comparable to adult-to-adult alignment. Next, per sulcus, we calculated mean sulcal depth, sulcal span, thickness, curvature, and R₁ (see “Methods”).

Sulcal depth development is inverse to order of emergence in utero

Visualizing SD maps of the same infant across four timepoints (newborn, 3 months, 6 months, and 12 months) reveal that sulci deepen from birth to one year (Fig. 2c). For example, the superior temporal sulcus (pink arrow, Fig. 2c) and central sulcus (black arrow, Fig. 2c) are shallower at 26 days than at 368 days.

To quantify this development, we plotted mean SD as a function of age in days and ordered sulci by their time of emergence in utero (Fig. 2d). For conciseness, we report results of the left hemisphere in the main manuscript and those of the right hemisphere in the Supplementary Figs. and tables. SD increases more rapidly between 0 and 6 months than 6–12 months (Fig. 2d and Supplementary Fig. 3a), with an average ~21% increase across the first year of life: 4.51 ±  1.19 mm (mean ± std) at birth, 5.03 ±  1.10 mm at 3 months, 5.2 ±  1.09 mm at 6 months, and 5.45 ±  0.98 mm at 1 year. To model this nonlinear trajectory and account for both cross-sectional and longitudinal data, we applied a linear mixed model (LMM)⁵⁴ across sulcal folds with depth as the dependent measure and log-transformed age (in days) as the continuous independent measure (Eq. 2; “Methods”). Formal model comparisons confirmed better fit for log-transformed versus linear age across the majority of parameters (see “Methods“; we therefore applied this transformation to all analyses for consistency. We found that SD significantly varies across sulci (main effect of sulcus: LH: β = −0.297, SE = 0.027, t₁₁₈₁ = −10.71, p = 1.36 × 10⁻²⁵, 95% CI = [−0.35, −0.24]) and differentially develops across sulci (age by sulcus interaction: LH: β = 0.071, SE = 0.013, t₁₁₈₁ = 5.18, p = 2.62 × 10⁻⁰⁷, 95% CI = [0.04, 0.09]) (full statistics for both hemispheres in Supplementary Table 2).

Because we found a significant interaction between sulcus and age, we used LMMs per sulcus to estimate SD at birth and the rate of SD development (Eq. 3). Rate of SD change revealed an inverse pattern of development relative to the order of emergence in utero, with earlier emerging sulci being deeper at birth (LH: Fig. 2e, RH: Supplementary Fig. 4a) but exhibiting slower rates of postnatal deepening compared to later emerging sulci (LH: Fig. 2f, RH: Supplementary Fig. 4b). For instance, early-emerging calcarine and insula are the deepest at birth (calcarine = 5.92 ± 0.30 mm; insula = 5.78 ± 0.11 mm) while late-emerging OTS and ITS are shallower at birth (OTS = 1.36 ± 0.22 mm; ITS = 1.21 ± 0.17 mm)) (LH: Fig. 2e, RH: Supplementary Fig. 4a, full statistics per sulcus: Supplementary Table 3). At the same time, the calcarine and insula exhibit non-significant or slower deepening postnatally (calcarine: −0.15 ± 0.14 mm/log₁₀ (age in days); mm/insula: 0.26 ± 0.05 mm/log₁₀ (age in days)) than later emerging sulci such as the OTS and ITS, which deepen more rapidly (OTS: 1.23 ± 0.10 mm/log₁₀ (age in days); ITS: 0.75 ± 0.08 mm/log₁₀ (age in days)). Plotting the data by time of emergence on the x-axis illustrates a similar development pattern (Supplementary Fig. 5).

Having established that sulcal deepening is linked to time of emergence in utero, we next examined whether other properties—SP, CT, CU, and R₁—develop with SD, postnatally.

Sulcal span increases across folds but does not follow prenatal time of emergence

The sulcal span of all 15 sulci increases from birth to one year. This increase in span, like that for SD, is faster between 0 and 6 months than 6–12 months (LH: Fig. 3a, RH: Supplementary Fig. 3b). We observed an average increase of 42% in span from newborns to 1-year-olds. We find that sulcal span significantly varies with age (main effect of age: LH: β = 4.59, SE = 0.76, t₁₁₈₁ = 6.03, p = 2.24 × 10⁻⁹, 95% CI = [3.09, 6.08]) and across sulci (main effect of sulcus: LH: β = −0.37, SE = 0.16, t₁₁₈₁ = −2.24, p = 0.025, 95% CI = [−0.70, −0.04]) (full statistics in Supplementary Table 2). However, sulcal span does not follow a developmental pattern related to time of emergence (LH: Fig. 3b, c, RH: Supplementary Fig. 4c, d, full statistics per sulcus: Supplementary Table 4).

Fig. 3: Sulcal span and cortical thickness increase in sulci during the first year of postnatal life.

a Sulcal span (SP [mm]) increases logarithmically with age across all sulci in the first year of life. Each dot: mean SP per infant. Line: model fit. b, c Estimates of SP at birth (intercept) and rate of development (slope), calculated using a LMM relating mean SP to log₁₀ (participant’s age in days). Error bars: standard error of the intercept and slope (N = 43 independent participants). d–f Same format as (a–c), shown for cortical thickness (CT [mm]). Like SP, CT increases with age. All data shown are from the left hemisphere (LH). RH data in Supplementary Figs. 3 and 4.

Cortical thickening follows sulcus-specific trajectories independent of time of emergence

Like depth and span, CT significantly increases by ~21% from birth to 1 year (LH: Fig. 3d, RH: Supplementary Fig. 3b). Thickness increases with age (main effect of age: LH: β = 0.26, SE = 0.025, t₁₁₈₁ = 10.45, p = 1.62 × 10⁻²⁴, 95% CI = [0.21, 0.31]), varies across sulci (main effect of sulcus: LH: β = −0.017, SE = 5.28 × 10⁻³, t₁₁₈₁ = −3.31, p = 9.68 × 10⁻⁴, 95% CI = [−0.027, −0.007]), and shows sulcus-specific developmental trajectories (age by sulcus interaction: LH: β = 5.92 × 10⁻³, SE = 0.0026, t₁₁₈₁ = 2.25, p = 0.024, 95% CI = [7.67 × 10⁻⁴, 0.011]) (full statistics in Supplementary Table 2). CT significantly increases in all sulci except the calcarine and central sulcus (full statistics per sulcus: Supplementary Table 5). However, cortical thickening does not follow time of emergence (LH: Fig. 3e, f, RH: Supplementary Fig. 4e, f). Instead, sulci that are thicker at birth, such as the calcarine and central sulcus, show minimal thickening, whereas sulci that are thinner at birth, such as the collateral sulcus and insula, exhibit substantial thickening during the first year. Thus, postnatal thickening follows maturational trajectories that are closely tied to thickness at birth than to the timing of sulcal emergence in utero.

Curvature of sulcal folds decreases and becomes less concave

Unlike SD, SP, and CT, which increase with age, CU decreases. On average, CU declines ~14% from birth to one year (LH: Fig. 4a, RH: Supplementary Fig. 3d). Curvature significantly decreases following a logarithmic trajectory (main effect of age: LH: β = −0.013, SE = 0.002, t₁₁₈₁ = −6.68, p = 3.67 × 10⁻¹¹, 95% CI = [−0.017, −0.0096]), varies across sulci (main effect of sulcus: LH: β = 0.003, SE = 4.52 × 10⁻⁴, t₁₁₈₁ = 6.72, p = 2.74 × 10⁻¹¹, 95% CI = [0.0021, 0.0039]) and develops differentially across sulci (age by sulcus interaction: LH: β = 6.13 × 10⁻⁴, SE = 2.25 × 10⁻⁴, t₁₁₈₁ = −2.72, p = 0.0065, 95% CI = [−0.0010, -1.71 × 10⁻⁴]) (full statistics in Supplementary Table 2). Some sulci, such as the calcarine and insula, show minimal curvature change, while others, like the STS and CoS, become markedly less curved (LH: Fig. 4b, c, RH: Supplementary Fig. 4g, h, full statistics per sulcus: Supplementary Table 6). Developmental decreases in mean CU may result from sulcal widening at the fundus, increased cortical expansion along the sulcal walls, or both. Notably, CU changes are not uniform across sulci, suggesting that different sulci undergo distinct developmental trajectories postnatally.

Fig. 4: Curvature and microstructural changes in sulci during the first year of postnatal life.

a Curvature (CU [mm⁻¹]) decreases logarithmically with age across all sulci in the first year of life. Each dot: mean CU per infant. Line: model fit. b, c Estimates of CU at birth (intercept) and rate of development (slope), calculated using a LMM relating mean CU to log₁₀ (participant’s age in days). Error bars: standard error of the intercept and slope (N = 43 independent participants). d–f Same format as (a–c), shown for cortical microstructure (R₁ [s⁻¹]). Unlike CU, R₁ increase with age. All data shown are from the left hemisphere (LH). RH data in Supplementary Figs. 3 and 4.

Sulci undergo extensive microstructural tissue growth in gray matter

We find that R₁ increases (LH: Fig. 4d, RH: Supplementary Fig. 3e) ~33% from birth to 1 year (main effects of age: LH: β = 0.102, SE = 0.0033, t₁₁₈₁ = 30.70, p = 1.25 × 10⁻¹⁵², 95% CI = [0.095, 0.10]). R₁ also varies across sulci (main effect of sulcus: LH: β = −0.0047, SE = 6.77 × 10⁻⁴, t₁₁₈₁ = −7.02, p = 3.61 × 10⁻¹², 95% CI = [−0.0060, -0.0034]) and differentially develops across sulci (age by sulcus interaction: LH: β = 0.0014, SE = 3.37 × 10⁻⁴, t₁₁₈₁ = 4.42, p = 1.10 × 10⁻⁵, 95% CI = [8.27 × 10⁻⁴, 0.0021]) (full statistics for both hemispheres in Supplementary Table 2). R₁ does not follow time of emergence (LH: Fig. 4e, f and RH: Supplementary Fig. 5i, j; full statistics per sulcus: Supplementary Table 7). These results reveal that sulci become microstructurally denser over the first year of life, indicating tissue growth.

Sulcal depth development can be predicted by a linear combination of sulcal span, thickness, curvature, and R₁

Thus far, our data indicate that macrostructural and microstructural parameters undergo distinct age-related changes across sulci. As a sulcus deepens, its span widens, cortex thickens, curvature decreases, and microstructural tissue density increases. However, the magnitude and trajectory of these changes vary across sulci (Figs. 2, 3, and 4). An open question is whether sulcal deepening is systematically related to concurrent macrostructural and microstructural developments.

To visualize how individual parameters vary across sulci, we generated polar plots using normalized metrics across four age groups (0, 3, 6, and 12 months) (LH: Fig. 5b, RH: Supplementary Fig. 6a). Polar plots show distinct developmental fingerprints across sulci. For instance, while both CoS and POS show substantial increases in tissue density (R₁), POS shows proportionally greater expansion in span. These differences suggest that the relationships between depth and other cortical properties may not be uniform across sulci. To quantify these relationships, we used an LMM to test whether the relationship between depth and span, cortical thickness, curvature, and microstructural tissue density varies across sulci. Because all parameters exhibited significant age-related changes, we included age in the model to isolate the independent effects of macrostructural and microstructural properties on sulcal depth (Eq. 4). This model used normalized parameters like that in the polar plots.

Fig. 5: SD development can be predicted by a linear combination of SP, CT, CU, and R₁.

a An illustrative representation showing macroanatomical and microstructural changes in a sample infant’s left collateral sulcus (CoS) from birth to one year. b Polar plots representing normalized anatomical and microstructural properties per sulcus. Four solid lines (lighter to darker colors indicate 0-12 months of age) represent 4 age groups. Each concentric circle corresponds to the normalized units to allow the metrics to be plotted together. c Normalized beta values from a linear model relating SD to SP, CT, CU, and R₁. Error bars: standard error of the beta coefficients (N = 43 independent participants). d Scatterplots display predicted mean depth [mm] in left out participants using the model parameters in (c) versus actual mean depth [mm] per sulcus. Each dot is a participant. Mean root mean square error (RMSE [mm]) ± standard deviation [mm] across all leave one-out-subjects is shown above each sulcus. LH: left hemisphere. RH data in Supplementary Fig. 6.

Consistent with the patterns observed in the polar plots, the relationship between depth and macrostructural and microstructural parameters significantly varies across sulci (full statistics for both LH and RH in Supplementary Table 8; LH: significant interaction between SP and sulcus: β = 0.040, SE = 0.0072, t₁₁₇₃ = 5.56, p = 3.36 × 10⁻⁰⁸, 95% CI = [00.02, 0.0]); significant interaction between CT and sulcus: β = −0.061, SE = 0.0082, t₁₁₇₃ = −7.45, p = 1.87 × 10⁻¹³, 95% CI = [−0.077, −0.045]); significant interaction between CU and sulcus: β = −0.05, SE = 0.007, t₁₁₇₃ = −7.45, p = 1.78 × 10⁻¹³, 95% CI = [−0.06, −0.04]; significant interaction between R₁ and sulcus: β = 0.034, SE = 0.009, t₁₁₇₃ = 3.67, p = 2.52 × 10⁻⁴, 95% CI = [0.01 0.05]). These interactions indicate that sulcal deepening is not a single uniform process but emerges from multiple structural factors that differ across folds.

We next examined these relationships within individual sulci. Per sulcus, we ran a separate LMM (Eq. 5) to estimate beta coefficients for each parameter. We found positive beta coefficients for SP and R₁, while CU and CT exhibited both positive and negative values depending on the sulcus (LH: Fig. 5c; RH: Supplementary Fig. 6b; Supplementary Table 9 for beta values per parameter and hemisphere).

To assess the robustness of our model, we tested whether sulcal depth can be predicted in new participants from parameter estimates using a leave-one-out cross-validation approach. Unlike the previous analyses that used normalized parametric values, this model was trained using raw values to preserve interpretability of depth in millimeters. We trained the model on n-1 infants and used it to predict depth in the left-out infant (see “Methods”). Results revealed that mean sulcal depth can be reliably predicted using our model, with an average root mean square error (RMSE) of less than 1 mm (LH: Fig. 5d; RH: Supplementary Fig. 6c). However, prediction accuracy varied across sulci, with the cingulate sulcus yielding the lowest prediction error (RMSE = 0.22 mm), and the calcarine yielding the highest (RMSE = 0.66 mm). Overall, our results highlight that multiple morphological (span, thickness, curvature) and microanatomical (R₁) developments predict depth during the first year of life, even as their weights vary across sulci.

Strong relationship between depth, curvature, and microstructure along a sulcal fold

Our findings thus far suggest that mean sulcal depth is systematically related to macro- and microstructural properties of cortex. However, mean sulcal depth measures inherently average data across different portions of a sulcus (e.g., over the fundus and sulcal walls), which may obscure meaningful fine-grained variation. Prior work has shown that functional properties often vary along the sulcal fold, with stronger functional coupling in the fundus and pit (deepest point along the fundus) versus the walls^{14,15,16,55,56,57,58,59}. Motivated by prior work, we asked whether sulcal depth along the sulcus is spatially coupled with macro- and microstructural properties of cortex during infancy. Specifically, we examined whether depth varies systematically along the long axis of each sulcal fold by quantifying the relationship between local sulcal depth, thickness, curvature, and R₁. Here, we excluded sulcal span because this metric is a single measure per sulcus and does not capture localized variations along the sulcus.

We first visualize how depth, cortical thickness, curvature, and R₁ vary along each sulcus in individual infants. Figure 6a shows the left superior temporal sulcus (STS) in an example one-year-old. Notably, the STS has two distinct deep regions (red peaks in Fig. 6a). Comparing these depth variations to curvature, R₁, and thickness along the sulcus revealed that: (1) curvature follows the depth pattern, with greater curvature in the two deepest regions of the sulcus than in shallower areas, (2) R₁ is higher in deeper regions of the sulcus, and (3) cortical thickness exhibits a weaker relationship with sulcal depth in comparison to R₁ and CU (Fig. 6a, b). We also provide an example for the right CoS in a different one-year-old infant (Supplementary Fig. 7), which illustrates a strong relationship between depth and CU and depth and R₁ along the CoS.

Fig. 6: Strong coupling between depth versus macro- and microstructural properties along the sulcal fold.

a Three-dimensional maps of the left superior temporal sulcus (STS) in a sample one-year-old (418 days), showing depth, curvature, R₁, and CT along the sulcus; warmer colors represent larger values. b Data show the coupling between depth and each parameter. Normalized depth (solid black lines), CT (orange dotted lines), CU (blue dotted lines), and R₁ (green dotted lines) values are plotted as a function of distance along the primary axis of the STS (anterior-posterior). This same principle was applied to all sulci using the axis most aligned with the sulcus’ primary orientation. Mean and standard deviation of the correlation (R) and significance values (p) are provided in each subplot. c Bar plots show normalized beta values from a linear model relating SD to CT, CU, and R₁ along the length of each sulcus. Error bars: standard error of the beta coefficients (N = 43 independent participants). LH left hemisphere. RH data in Supplementary Fig. 7.

To quantify these fine-grained spatial relationships, we applied a similar LMM approach as in our previous analyses (Eq. 4), but instead of using mean parameter values across each sulcus (as in Fig. 5), we modeled parameter values at each point along the long axis of the sulcus (Eq. 6; see “Methods”). Results revealed significant relationships between local sulcal depth and both curvature and R₁, as well as significant interactions between these parameters and sulcus. Specifically, curvature showed the strongest relationship with sulcal depth (β = 0.549, SE = 0.008, t₆₄₉₄₂ = 70.28, p < 0.001, 95% CI = [0.53, 0.56]). R₁ also demonstrated a significant positive relationship with sulcal depth (β = 0.276, SE = 0.012, t₆₄₉₄₂ = 22.81, p = 1.13 × 10⁻¹¹⁴, 95% CI = [0.25, 0.30]). However, cortical thickness did not show a significant main effect on sulcal depth (β = 0.008, SE = 0.012, t₆₄₉₄₂ = 0.63, p = 0.53, 95% CI [−0.016, 0.031]). We observed significant interactions between sulcus and all three parameters: cortical thickness (β = −0.037, SE = 0.001, t₆₄₉₄₂ = −25.29, p = 2.16 × 10⁻¹⁴⁰, 95% CI = [−0.040, −0.035]), curvature (β = 0.012, SE = 0.001, t₆₄₉₄₂ = 13.58, p = 6.05 × 10⁻⁴², 95% CI = [0.010, 0.014]), and R₁ (β = 0.018, SE = 0.002, t₆₄₉₄₂ = 11.61, p = 4.14 × 10⁻³¹, 95% CI = [0.015, 0.021]; statistics for both hemispheres: Supplementary Table 10). Given these interactions, we next estimated the relationship between depth and CT, CU, and R₁ per sulcus using a separate LMM (Eq. 7). We found that deeper points along sulci tended to have higher curvature and R₁, and lower cortical thickness, except for the POS, where the R₁ coefficient was negative (LH: Fig. 6c; RH: Supplementary Fig. 7c; Supplementary Table 11 for beta values per parameter and hemisphere).

These results underscore the critical importance of within-sulcus analyses in understanding cortical folding. Our fine-grained approach reveals local relationships between depth and other cortical properties that differ from the relationships observed when examining mean values across entire sulci. Specifically, the analysis of mean values indicated a negative relationship between sulcal depth and curvature (Fig. 5c; Supplementary Table 9), whereas the within-sulcus analysis demonstrated a positive local relationship between these properties (Fig. 6c). Similarly, the relationship between depth and cortical thickness was positive in the mean-value analysis but predominantly negative in the within-sulcus analysis, with variations observed across different sulci. These differences are not due to model variations, as mean sulcal depth is negatively related to mean curvature and positively related to mean thickness even when sulcal span is excluded from the model. Rather, these shifts in direction likely reflect the spatial scale of our analyses. While mean curvature and thickness average across the entire sulcus—including both the fundus and sulcal walls—local, within-sulcus analyses preserve anatomically meaningful variations along the fold.

Overall, our findings show that deeper points along sulci have higher curvature, higher microstructural density tissue, and lower thickness. Higher microstructural tissue density and higher curvature in deeper portions of sulci (fundi) suggest that sulcal fundi may undergo distinct tissue development compared to sulcal walls. Moreover, the negative relationship between depth and thickness is consistent with prior work showing that thickness declines linearly with depth⁴⁸.

Discussion

Our findings reveal a dynamic interplay between sulcal macroanatomy and microstructural tissue density during infant development. Using cross-sectional and longitudinal data, we provide a systematic analysis of anatomical and microstructural changes in individual sulcal folds during the first year of postnatal life. First, our work reveals a sulcus-specific developmental pattern whereby early-emerging sulci are deeper at birth but deepen more slowly postnatally compared to later-emerging sulci. Second, concurrent with sulcal deepening, we observe increases in sulcal span, thickness, and microstructural tissue density, accompanied by reductions in curvature. Third, our results reveal distinct yet strong relationships between depth, curvature, thickness, and microstructural tissue density along the length of sulci, highlighting local structural coupling within sulcal folds. Finally, by modeling sulcal depth as a weighted combination of macroanatomical and microstructural parameters, we find that sulcal deepening is not a result of a single mechanism but instead reflects an interplay of multiple interacting processes.

Early-emerging sulci are deeper at birth but show minimal postnatal deepening, while later-emerging sulci are shallower at birth but deepen more rapidly postnatally. This developmental pattern supports recent work proposing that sulci may be classified into two distinct categories based on their fetal emergence timing: “linear” sulci, which emerge early, are simpler, more genetically determined, and remain relatively stable, versus “complex” sulci, which emerge later and continue to change significantly after birth⁹. This pattern also aligns with prenatal imaging studies^60,61 that describe a sequential wave of sulcal maturation from central to more lateral and anterior regions. This progression may reflect early fetal cytoarchitectonic patterning governed by a genetically encoded proto-map established early in fetal development^27,61,62.

Alongside sulcal deepening, we found that sulcal span, cortical thickness, and R₁ significantly increase during the first year of life, while curvature decreases. However, in contrast to sulcal depth, the development of other features does not systematically vary with gestational emergence. This dissociation suggests that depth may be more directly shaped by early prenatal influences, while other macrostructural and microstructural properties undergo differential developments during infancy. Our findings also align with hypothesized mechanisms of sulcal deepening proposed in Fig. 1. The simultaneous increases in sulcal span and depth are consistent with cortical expansion in the tangential direction⁴⁷ (parallel to the cortical surface), which may stretch folds laterally and drive them deeper into white matter due to spatial constraints imposed by the skull¹³. The increase in sulcal depth and cortical thickness aligns with radial expansion⁵ (perpendicular to the cortical surface). The observed decrease in curvature suggests that sulci may become less concave during this time of development, possibly due to widening at the fundus and/or lengthening or stretching along sulcal walls. Finally, increasing cortical R₁ values point to extensive tissue growth, which may further expand cortex, thereby contributing to differential growth that push sulci deeper into white matter. Our finding that sulcal depth is positively correlated with R₁—both on average and locally—suggests that changing tissue density, perhaps related to increased myelination, can alter mechanical properties, such as stiffness, and may contribute to sulcal deepening^63,64,65. Additionally, maturation of superficial white matter⁴¹, white matter fiber tracts^66,67,68, and differential tangential growth of gray and white matter^4,6,49,69,70 may also impact sulcal deepening during infancy. Future work using diffusion imaging and fiber tracking along with cortical measures can examine this interplay.

Cortical folding is often modeled as the mechanical outcome of differential expansion and structural constraints, incorporating metrics like cortical thickness, surface area, and gray-white matter elasticity^4,23,44,71. These models have successfully demonstrated how large-scale folding patterns can emerge from physical forces acting on an elastic, largely homogeneous cortical sheet. However, general folding mechanisms alone are insufficient to explain the sulcus-specific developmental variability that we observe across spatial location and gestational timing. Our findings, along with insights from large-scale developmental datasets^72,73,74, highlight the need for biomechanical models to incorporate the heterogeneity across sulci. These empirical patterns offer critical constraints for building nuanced, data-driven models of cortical folding. Additionally, most existing simulations—including gel-based physical models—do not account for fine-grained anatomical variation within sulci, which limits the ability to fully explain how folding develops. Our finding that the deeper portions of sulci consistently exhibit higher microstructural density (R₁) and curvature suggests that localized tissue maturation and mechanical forces may differentially influence the development of sulcal fundi compared to their surrounding walls. Future models that implement localized variation in tissue density (e.g., modeling higher R₁ as increased stiffness or reduced elasticity) can provide insight into how mechanical forces within the gray matter contribute to cortical folding.

While our study focused on structural development, our findings offer insights into how sulcal maturation may relate to the emergence of function during infancy⁷⁵. Sulcus-specific developmental trajectories suggest that the timing of sulcal emergence may influence when and how cognitive functions mature. For instance, the superior temporal sulcus, which houses functional regions involved in social communication and language, continues to develop during childhood with changes in depth, curvature, thickness, span, and microstructure. In contrast, sulci like the calcarine, which contains the primary visual cortex (V1) associated with processing simple visual features such as edges and contrast⁷⁶, appears to be more mature at birth. These observations raise the possibility that anatomical and functional development unfold in tandem. Although this idea aligns with findings from animal models⁷⁷, structural developments have yet to be incorporated into computational models of human brain development, which typically model functional development^{78,79,80,81,82,83}.

Our results also suggest that the fundus, or deepest part of a sulcus, may serve as a meaningful biomarker in early development. First, fundi exhibit higher curvature and R₁ than sulcal walls, suggesting distinct maturational trajectories between these regions at both the macro- and microstructural levels. Second, larger R₁ increases in fundi suggest that fundi may be localized zones of denser microstructure. R₁ increases may be coupled with increased myelination^32,38,40, synapse formation^29,77, and dendritic growth³¹, which in turn may affect cortical function. Indeed, previous studies have shown that functional selectivity is higher in fundi. For example, our prior work showed that place-selectivity is higher in the fundus of the collateral sulcus in children and adults, and this functional-structural coupling strengthens with age¹⁵. Likewise, deeper regions in the superior temporal sulcus have been linked to language and social processing^14,57,59, and deeper portions of the central sulcus are associated with motor representations of the hand^56,58. Future work should examine fine-grained relationships between anatomical and functional development during infancy^84,85,86,87, as it has implications on atypical sulcal development^19,59.

Deviations from typical folding patterns and sulcal depth irregularities have been associated as biomarkers of Autism Spectrum Disorder^18,88, Down syndrome¹⁷, and schizophrenia⁸⁹. By establishing normative trajectories of postnatal sulcal development, our findings serve as a benchmark for identifying early deviations. The strong coupling observed between sulcal depth and macro- and microstructural tissue properties suggests that concurrent disruptions of various measures may be more precise indicators of atypical development than any measure alone.

In conclusion, our findings demonstrate that postnatal sulcal development is governed by sulcus-specific, locally coupled macroanatomical and microstructural processes. Sulcal depth shows a systematic relationship with prenatal emergence timing, while span, thickness, curvature, and tissue density follow distinct postnatal trajectories. Together, these results show that cortical folding is not driven by a single global mechanism, but instead emerges from the interaction of multiple, heterogenous processes operating at different spatial and developmental scales. By providing quantitative benchmarks of typical sulcal development, this work advances a biologically grounded framework for understanding cortical folding and identifying early deviations associated with neurodevelopmental disorders.

Methods

Participants

Sixty-one full-term and healthy infants (N_female= 24) were recruited to participate in the study. Forty-three out of sixty-one infants provided usable data. We excluded data from infants that could not fall asleep inside the MRI scanner, which led to excessive motion and unusable data (see additional exclusion criteria in section titled “Expectant parent and infant screening procedure”). Hence, we report longitudinal and cross-sectional data from 43 infants (N_female = 18) gathered over 79 scanning sessions, across 4 timepoints: newborns (N_sessions  = 27; 10 females; M_age ± std: 29.14 ± 9.92 days), 3-month-olds (N_sessions  =  20; 11 females; 106.35 ± 20.09 days), 6-months-old (N_sessions  =  22; 12 females; 188.45 ± 15.34 days), and 1-year-old (N_sessions =  10; 3 females; 385.80 ± 17.60 days). 24 out of the 43 infants participated in 2 or more timepoints (Supplementary Table 1). Our sample included participants from the following racial and ethnic backgrounds: 1 Hispanic, 5 Asian, 20 Caucasian, and 17 multiracial participants (Supplementary Table 1).

Expectant parent and infant screening procedure

Expectant parents and their infants in our study were recruited from the San Francisco Bay Area using social media platforms. We performed a two-step screening process. First, parents were screened over the phone for eligibility based on exclusionary criteria designed to recruit a sample of typically developing infants. Second, eligible expectant mothers were screened once again after giving birth. Exclusionary criteria were as follows: recreational drug use during pregnancy, significant alcohol use during pregnancy (more than three instances of alcohol consumption per trimester; more than 1 drink per occasion), lifetime diagnosis of Autism spectrum disorder or a disorder involving psychosis or mania, taking prescription medications for any of these disorders during pregnancy, insufficient written and spoken English ability to understand the instructions of the study, or learning disabilities that would preclude participation. Exclusionary criteria for infants were birth prior to 36 gestational weeks, low birthweight (<2.5 kg), small height (< 46 cm), any congenital, genetic, and neurological disorders, visual problems, complications during birth that involved the infant (e.g., NICU stay), history of head trauma, and contraindications for MRI (e.g., metal implants). Participants were compensated with 25 dollars per hour for their participation. Study protocols were approved by the Stanford University Internal Review Board on Human Subjects Research. All ethical regulations relevant to human research participants were followed.

Data acquisition

All included infants completed multiple scanning protocols to obtain anatomical and quantitative MRI data in a 3T GE UHP MRI scanner at the Center for Cognitive and Neurobiological Imaging at Stanford University. Data were reconstructed using GE’s online reconstruction software (version RX28.0). Scanning was done with first level SAR to ensure infants’ safety. Of the 79 scanning sessions, 68 were collected using a Nova 32-channel head coil, and the remaining 11 used a custom 32-channel infant head coil⁹⁰.

Scanning sessions were scheduled in the evenings around the infants’ typical bedtime. Each session lasted between 2.5 and 5 h, including time to prepare the infant and waiting time for them to fall asleep. Upon arrival, caregivers provided written informed consent for themselves and their infant to participate in the study. Before entering the MRI suite, both caregiver and infant were checked to ensure that they were metal-free, and caregivers changed the infant into MR-safe cotton onesies and footed pants provided by the researchers. The infant was swaddled with a blanket with their hands to their sides to avoid their hands creating a loop. Then, the researchers inserted soft wax earplugs into the infant’s ears. During sessions involving newborn infants, an MR-safe plastic immobilizer (MedVac, www.supertechx-ray.com) was used to stabilize the infant and their head position. Once the infant was ready for scanning, the caregiver and infant entered the MR suite. The caregiver was instructed to follow their child’s regular sleep routine. When the infant was asleep, the caregiver placed the infant on the scanner bed. Weighted bags were placed at the edges of the bed to prevent any side-to-side movement. Additional pads were also placed around the infant’s head and body to stabilize head position. MRI compatible neonatal noise attenuators (https://newborncare.natus.com/products-services/newborn-care-products/nursery-essentials/minimuffs-neonatal-noise-attenuators) and headphones (https://www.alpinehearingprotection.com/products/muffy-baby) were placed on the infant’s ears, to lower sound transmission. An experimenter stayed inside the MR suite with the infant during the entire scan.

For additional monitoring of the infant’s safety and tracking of the infant’s head motion, an infrared camera was affixed to the head coil and positioned for viewing the infant’s face in the scanner. The researcher operating the scanner monitored the infant via the camera feed, which allowed for the scan to be stopped immediately if the infant showed signs of waking or distress. This setup also allowed us to track the infant’s motion; scans were stopped and repeated if there was excessive head motion. To ensure scan data quality, in addition to real-time monitoring of the infant’s motion via an infrared camera, MR brain image quality was also assessed immediately after acquisition of each sequence and sequences were repeated if necessary.

Data acquisition parameters and preprocessing

Anatomical MRI

T1-weighted and T2-weighted images were acquired and used for tissue segmentation. T1-weighted image acquisition used GE’s BRAVO sequence with TE = 2.7 ms, TR = 6.7 ms, echo train length = 1; voxel size = 1 mm³; Scan time: ~3 min. T2-weighted image acquisition used GE’s CUBE sequence with TE = 122 ms, TR  =  3650 ms; echo train length = 120; voxel size = 1 mm³; FOV  =  20.5 cm; Scan time: ~4 min.

Quantitative MRI

An inversion-recovery EPI (IR-EPI) sequence with multiple inversions times (TI) was used to estimate quantitative relaxation time R₁ (R₁  =  1/T₁) in each voxel. The IR-EPI used a slice-shuffling technique to acquire 20 TIs with the first TI  =  50 ms and TI interval = 150 ms. A second IR-EPI with reverse-phase encoding direction was also acquired. Other acquisition parameters were voxel size = 2 mm³; number of slices = 60; FOV  =  20 cm; in-plane/through-plane acceleration = 1/3; Scan time: 1 min and 45 s. To obtain R₁ maps, we first performed susceptibility-induced distortion correction on the IR-EPI images using FSL’s top-up⁹¹ and the IR-EPI acquisition with reverse-phase encoding direction. We then used the distortion corrected images to fit the T₁ relaxation signal model using a multi-dimensional Levenberg–Marquardt algorithm. In an inversion-recovery sequence, the signal S(t) has an exponential decay over time (t) with a decay constant T₁:

$$S\left(t\right)=a\left(1-{{be}}^{\left(-\frac{t}{{T}_{1}}\right)}\right)$$

(1)

In Eq. 1, a is a constant that is proportional to the initial magnetization of the voxel and b is the effective inversion coefficient of the voxel (for perfect inversion b  =  2). We applied an absolute value operation on both sides of the equation and used the resulting equation as the fitting model because the magnitude images were used to fit the model. The magnitude images only keep the information about the strength of the signal but not the phase or the sign of the signal. The output of the algorithm is the estimated quantitative T₁ value per voxel. From the T₁ estimate, we calculate R₁ (R₁  =  1/T₁) as R₁ is directly proportional to macromolecular tissue volume. QMRI data fitting is performed using the brain mask and not the whole head.

Since we collect the qMRI data around the infant’s typical bedtime, and only when the infant is asleep inside the scanner, we do not perform any additional motion correction on the qMRI scan as all scans are collected with sleeping infants. However, if we notice any ringing in and around the scans due to any motion, we exclude the infant’s data from further analysis.

Generation of cortical surfaces

We generated gray and white matter tissue segmentations using the T1- and T2-weighted images. Multiple steps were applied to generate an accurate segmentation of each infant’s brain at each timepoint (Supplementary Fig. 1): (1) An initial segmentation of gray and white matter was generated from the T1-weighted brain volume using infant FreeSurfer’s automatic segmentation code ((infant-recon-all; version freesurfer-linux-centos7_x86_64-infant-dev-4a14499-20210109; https://surfer.nmr.mgh.harvard.edu/fswiki/infantFS⁴⁵). (2) A second segmentation was done using both the T1- and T2-weighted anatomical images and the brain extraction toolbox (Brain Extraction and Analysis Toolbox, iBEAT, v-2.0 cloud processing, https://ibeat.wildapricot.org/). iBEAT V2.0 was specifically designed for processing infant brain MRI data (0–2 years), using contrasts properties of both T1w and T2w images, and employs deep learning techniques trained on infant data to handle the unique challenges of low contrast between gray and white matter in developing brains. Through visual inspection, we determined that iBEAT provided a more accurate segmentation of the gray-white matter boundaries in our low-contrast infant images compared to the infant FreeSurfer approach. (3) The iBEAT segmentation was further manually corrected to fix segmentation errors in the white and gray matter (such as mislabeled white matter voxels or holes) using ITK-SNAP (http://www.itksnap.org/). (4) The iBEAT corrected segmentation was reinstalled into FreeSurfer. The reinstalling process allows us to obtain clean surface maps, and more accurate macroanatomical features required for our analysis. The resulting segmentation in FreeSurfer format is used for all further analyses. A mesh of each infant’s cortical surface was then generated from the boundary of the white and gray matter. This mesh was inflated for visualization of the morphological and macrostructural tissue properties. All FreeSurfer commands were executed through MATLAB R2023a.

Selecting sulcal folds of interest

To study the morphological development of sulcal folds in the first year of human life, we selected 15 long-length sulcal folds that emerge in utero between 16 and 31 gestational weeks¹ (Fig. 2a, b) to cover the full range of sulcal emergence from the second to third trimester^9,61. Furthermore, we chose folds appearing before 32 gestational weeks as folds that appear beyond this time are less stable across individuals and are shallower, hence difficult to accurately delineate during early days of human life. To that extent, we examined: calcarine sulcus (calc), insular sulcus (insula), cingulate sulcus (cing), parieto-occipital sulcus (pos), central sulcus (central), precentral sulcus (precent), collateral sulcus (cos), superior temporal sulcus (sts), postcentral (postcent), superior frontal sulcus (sfs), intraparietal sulcus (ips), lateral occipital sulcus (los), inferior frontal sulcus (ifs), occipital temporal sulcus (ots), and inferior temporal sulcus (its). We selected these specific sulcal folds because of: (i) their spatial location and wide distribution across the four lobes of the brain, (ii) their time of emergence in utero – from 16 gestational weeks to 31 gestational weeks, which covers the full range of sulcal emergence from the second to third trimester during fetal development, (iii) their consistency across fetuses and infants at birth and minimal inter-subject variability at time of emergence^1,61, and (iv) their functional relevance. We chose (i) early-emerging sulci (appearing before 20 gestational weeks e.g., calcarine), (ii) sulci emerging between 21st and 25th gestational weeks, which coincide with a critical phase of cortical expansion and gyrification^1,60,61 (e.g., central sulcus), and (iii) late-emerging sulci, between 26 and 31 weeks, which exhibit relatively larger variability in their time of emergence and morphology^9,61 and unique geometric and folding properties that distinguish them from earlier-developing counterparts (e.g., superior frontal sulcus).

Labeling sulci of interest

To delineate the 15 sulci on each infant brain, we manually defined sulcal boundaries on the FreeSurfer average adult surface generated from 39 adults⁵¹. For sulci well-defined in the Destrieux atlas, we used the existing labels (aparc.a2009s)⁹² with manual adjustments informed by the curvature information. For sulci that have multiple partitions, such as the insula, we used the inferior circular sulcus as defined in the Destrieux altas⁹², as it tends to be the deepest sulcus in the brain¹⁵. For delineating the OTS, we used the fusiform gyrus as the medial boundary and the inferior temporal gyrus as the lateral boundary, and in cases of fragmentation⁹³, we labeled all identifiable portions of the sulcus by relying on the curvature information of the FreeSurfer average adult’s inflated surface. Next, using cortex-based alignment⁵¹ and FreeSurfer function “mri_label2label”, we projected the individual sulci onto each infant’s brain (Fig. 2a, example infant). Finally, we used the FreeSurfer function “mri_label2vol” to convert labels into nifti volumes.

Quality check on the delineation of sulci

To examine the quality and accuracy of the anatomical placement of the projected sulci from the FreeSurfer average adult brain onto an individual infant’s brain, we conducted two quality checks (Supplementary Fig. 2). First, we tested if cortex-based alignment of the 15 sulci varied with age by comparing the correspondence between the 15 automatically projected sulci to their 15 manually delineated counterparts in individual infant brains. To account for the large number of infants in our dataset and match the smaller number of 12-month-old infants (N = 12), we randomly selected 10 infants per age group: newborns, 3-month-olds, 6-month-olds, 12-months-old (N_total=40). We then manually drew 1200 sulci (15 sulcus folds per infant per hemisphere, 15 × 2 × 40) in the native brain space as the ground truth. Next, we measured the overlap between the manually drawn and automatically aligned sulcal labels using dice coefficients⁵³. Using a 3-way analysis of variance (ANOVA) with factors: age group (newborns, 3-month-olds, 6-month-olds, 12-month-olds), hemisphere (left/right), and sulcus (N = 15), and dice coefficients as the dependent measure, we found no significant main effect of age and hemisphere (ps > 0.23) but a main effect of sulcus (p < 0.05). This analysis suggests that cortex-based alignment, when applied to infant brains using FreeSurfer’s average adult brain, maintains a consistent level of accuracy across the first year of life, despite significant brain volume changes during infancy (Supplementary Fig. 2a).

Next, we conducted an additional analysis to compare the sulci projected from an infant template brain versus those projected using the FreeSurfer adult template in the prior analysis. To do this, we downloaded the UNC newborn template brain⁵² to match our 10 newborn samples from the prior analysis. We then delineated the 15 sulcal folds on the UNC template (30 sulcal folds, across left and right hemispheres) and projected UNC infant template sulci onto 10 individual newborn surfaces. We calculated the dice coefficients per infant, per sulcus, comparing the UNC projected versus manually drawn sulcal fold. Finally, a 3-way ANOVA with factors (1) template (N = 2, UNC versus FreeSurfer), (2) hemisphere (left/right), and (3) sulcus (N = 15) and dice coefficients as the dependent measure, showed no significant main effect of template or hemisphere (ps > 0.05) (Supplementary Fig. 2b) but a main effect of sulcus (p < 0.05). Overall, our analyses indicated that it is practical and reliable to project adult templates and adult atlases on infant brains with the critical caveat that thorough preprocessing, cortical segmentation, alignment quality checks are performed prior to any analysis.

Generation of macrostructural/morphological maps: sulcal depth (SD), cortical thickness (CT), curvature (CU), and sulcal span (SP)

To examine the development of various morphological properties in the 15 sulcal folds, we used FreeSurfer’s automated algorithm to obtain (i) sulcal depth (in mm), (ii) cortical thickness (in mm), (iii) cortical curvature (mm⁻¹), and (iv) sulcal span (in mm) for each infant (Supplementary Fig. 1). All morphological measurements are generated within each infant’s native brain space and each infant contributed to a single value, per metric, per sulcus.

To obtain the mean depth measures per sulcus and infant, we used the SD maps (lh.sulc/rh.sulc) generated using the FreeSurfer’s auto-segmentation algorithm. Sulcal depth is measured as the signed dot product of the movement vector and the outward pointing surface normal of the white matter surface during inflation. For a sulcus, the movement vector points outward (toward the pial surface) and therefore is presented by positive values in the lh.sulc and rh.sulc files. In contrast, for a gyral crown, the movement vector points inward and is represented by negative values. Here, we only focused on the sulcal folds. Mean SD (in mm) per sulcus was calculated as the average depth of all voxels in a sulcus. Cortical thickness is measured as the average of the closest distance from each vertex on the white matter surface to the pial surface and from the pial surface back to the white matter surface, as defined by FreeSurfer⁹⁴. These vertex-wise thickness values (in mm) are stored in the lh.thickness and rh.thickness files. Mean cortical thickness for each sulcus was obtained by averaging the thickness values of all vertices within that sulcus. Curvature is defined as the average of the two principal curvatures, which represent the directions in the normal plane where the curvature takes its maximum and minimum values. It is measured in mm⁻¹ as 1/r, where r is the radius of the best-fitting circle. This value indicates whether the vertex is concave or convex and is stored in the lh.curv and rh.curv files.

Finally, we added a new measure, sulcal span, to study how the expansion of sulcal walls impacts folding and depth during development. Traditional sulcal width⁹⁵ measures quantify the linear distance in the brain volume between opposing banks (the facing walls on either side of a sulcal fold), but they do not capture how the cortical surface within the sulcus stretches or enlarges as the brain grows. In other words, width provides a straight-line volumetric distance, whereas sulcal span approximates the expansion of the folded surface itself. We defined sulcal span (SP) as the average wall-to-wall distance within a sulcus, operationalized as the total surface area of the sulcus divided by its length. Surface area was measured as the sum of the areas of all triangles composing the sulcus on the tessellated cortical surface (lh.area/rh.area). Sulcal length was estimated as the distance between the anterior-most and posterior-most points of the sulcus along its long axis. To obtain these endpoints, each sulcal label was converted to its volume NIFTI, and length was measured as the Euclidean distance between the most anterior and posterior z coordinates (see Supplementary Fig. 1b for the STS). We note two limitations of our definition of sulcal span using the Euclidean distance: (i) it may underestimate the length of the sulcal fold if they curve or zigzag along the cortical surface and (ii) this measurement may be sensitive to the selection of sulcal edges.

Calculation of mean microstructural tissue density (R₁) in gray matter

To examine the development of microstructural properties, we used the R₁ maps per infant and calculated mean R₁ in the gray matter of each sulcus. Mean R₁ was calculated as the average R₁ of all voxels within a sulcus from the gray-white matter boundary to the pial surface. Like morphological parameters, the microstructural properties were also generated from each infant’s native brain space, and each infant contributed a single value per sulcus.

Statistics and reproducibility

To quantify developmental effects of sulcal depth, sulcal span, thickness, curvature and R₁, we used linear mixed models (LMMs)⁹⁶ with the ‘fitlme’ function in MATLAB R2023a (MathWorks, Inc.). All analyses were done separately for the left and right hemispheres. LMMs allow for explicit modeling of both within-subject effects (e.g., longitudinal measurements) and between-subject effects (e.g., cross-sectional data) with an unequal number of points per participant, as well as examination of main and interactive effects of both continuous (age) and categorical (e.g., sulcus) variables. This framework is particularly advantageous for our dataset because it accommodates complex interactions (e.g., parameter × sulcus) and enables us to test developmental effects at multiple levels of specificity from global age-related trends across all sulci to specific interactions and localized effects within individual sulci.

To determine the optimal model for relating each parameter to age, we followed a two-step model selection process. First, because developmental effects are larger in the first 6 months than the second 6 months of life, we formally tested which model better accounted for this non-linear trajectory. We used log-likelihood tests (via the ‘compare’ function in MATLAB v2023a) to compare two models across all parameters and hemispheres: (1) an LMM with a linear age term (parameter ~ age * sulcus + (1|infant)), and (2) an LMM with a log-transformed age term (parameter ~ log10(age) * sulcus + (1|infant)). We found that the log-transformed age model better predicted the data in 7 out of the 10 comparisons (likelihood test: ps  <  0.05). That is, for all parameters, except for sulcal span bilaterally and R₁ in the right hemisphere, the log model was a better fit. Therefore, to maintain a consistent analytical approach, we selected the log-transformed age for all subsequent analyses.

Second, we used LMMs to model within and between participant effects. In all our LMMs (eqs. 2-7), each infant was modeled with a random intercept.

Based on this selection process, the final model below was used to test the development in sulcal depth, sulcal span, cortical thickness, curvature, and R₁:

$$parameter \;(SD/SP/CT/CU/R1) \sim log10(age\,of\,infant(days)) * sulcus+(1|infant)$$

(2)

Parameters SD/SP/CT/CU/R₁ are the dependent variables, age of infant is a continuous predictor, sulcus is a categorical variable (N = 15), and the term: 1|infant indicates a random effect of infant. As we found a significant interaction between age and sulcus, we conducted additional LMMs for each sulcus to quantify its developmental trajectory.

$$parameter (SD/SP/CT/CU/R1) \sim log10(age\,of\,infant(days))+(1|infant)$$

(3)

Prediction of sulcal depth with respect to span, thickness, curvature, and R₁

First, to visualize how the individual parameters develop and vary with respect to each other across the sulci, we generated polar plots using RStudio (Version 2023.12.0 + 369) and normalized parameters of the 15 sulci across four age groups (0, 3, 6, and 12 months). To test whether SP, CT, CU, R_1, and age predict sulcal depth, we conducted an LMM relating SD to all these parameters. As parameters have different units and ranges, we used normalized values in the models below. Normalization of each parameter (x) was as follows: $\frac{x-\min (x)}{\max \left(x\right)-\min (x)}$, hence the values of model parameters range between 0 and 1.

$$SD\sim 1+(Age+SP+CT+R1+CU) * sulcus+(1|infant)\,$$

(4)

Since we found significant interactions between sulcus and SP, CT, R1, and CU, we conducted an additional analysis per sulcus to quantify the beta weights of these parameters per sulcus:

$$SD\sim 1+(SP+CT+R1+CU)+(1|infant)$$

(5)

We also conducted a leave-one-out cross-validation using Eq. 5 across all subjects. Here, we predict the sulcal depth for each sulcus, per subject, then calculate the RMSE between the predicted and actual depth. Finally, across all subjects (and their errors), we calculate the mean RMSE and the standard deviation of these errors. Hence, we report these as: mean RMSE ± standard deviation of errors in Fig. 5d.

Generation of sulcal depth, thickness, curvature, and R₁ profiles

For each sulcus, we generated depth, thickness, curvature, and R₁ profiles along the long axis of each sulcus. To do this, we first transformed each infant’s SD/CT/CU/R₁ maps into FreeSurfer’s average cortical space. This allowed us to compare the profile relationships between each parameter and depth per subject in a common space per sulcus, maintaining consistency in the number of points along the long axis of each sulcus. Next, we divided each sulcus into N points based on its primary orientation: for sulci oriented primarily along the posterior-anterior axis (calcarine, insula, cingulate, collateral, superior temporal, superior frontal, inferior frontal, occipital temporal, and inferior temporal sulcus), we used z-coordinates; for sulci oriented primarily along the superior-inferior axis (parietal occipital sulcus), we used y-coordinates; and for sulci oriented primarily along the lateral-medial axis (central, precentral, postcentral, intraparietal, and lateral occipital sulcus), we used x-coordinates. For each point along the primary axis, we averaged the depth, CT, CU, and R₁ values separately along the two orthogonal planes to obtain profiles per micro- and macro-level parameter along the sulcus. For instance, in the STS, per z-coordinate, we averaged all points in the x-y plane to obtain a profile per parameter along the anterior-posterior axis (Fig. 6b). This provides fine-grained information along the length of the sulcus. Next, to quantitatively test the strength of relationships across sulcal folds and infants and for visualization purposes, we normalized the profiles of SD, CU, R₁, and CT along the entire length of each sulcus, and calculated the correlations (using Pearson’s correlation coefficient (R)) between SD versus CU/R₁/CT profiles separately for the left superior temporal sulcus and right collateral sulcus for visualization purposes. To test whether CT, CU, R₁ predict sulcal depth along a sulcal fold, we first conducted an LMM relating SD to all these parameters:

$$SD\sim 1+(CT+CU+R1) * sulcus+(1|infant)\,$$

(6)

Since we found a significant interaction between all parameters and sulcus, we conducted an analysis per sulcus to quantify the beta weights of these parameters per sulcus:

$$SD\sim 1+(CT+CU+R1)+(1|infant)$$

(7)

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.