Volume-inflation registration (INFREG) for morphometric analysis of human focal cortical dysplasia type II

Summary

Neurodevelopmental expansion of human association cortex increases cortical folding complexity, causing registration inaccuracies that confound detection of subtle pathological signatures like focal cortical dysplasia (FCD) in voxel-based morphometry. We introduce INFREG (volume-inflation registration), integrating surface-based deformation with volumetric alignment to minimize sulcal smoothing. Validated on 80 histologically confirmed FCD cases and 85 controls, INFREG outperformed conventional methods (CAT12/Demons/BrainSuite) by (i) superior template to subject alignment (SSIM = 0.95 ± 0.04; GM/WM Dice = 0.93 ± 0.05 vs. 0.70–0.87, all p < 0.001); (ii) sharper templates with 23%–41% lower intensity SD and finer gyral alignment (3.34 ± 0.13 vs. 3.45 ± 0.15 mm, p < 0.01); (iii) reducing false positive FCD Type II clusters by 70%–88% (p < 0.001) in association cortices; and (iv) halving manual verification time (Observer1:101 ± 67 vs.177 ± 114 s; Observer2:75 ± 48 vs.162 ± 102 s; p < 0.001). In 30 typical cases, 90% localized within top 5 clusters, and all 12 VBM-indeterminate cases resolved. INFREG may enhance clinical workflows for FCD type II evaluation.

Graphical abstract

Highlights

• •INFREG combines surface deformation with volume alignment for sulcal-preserving registration
• •INFREG achieves superior alignment (SSIM = 0.95 ± 0.04) vs. conventional methods (0.70–0.87)
• •INFREG reduces FCD type II false positives by 70%–88% and halves manual verification time
• •INFREG resolves all 12 VBM indeterminate FCD type II cases in a 30 patient cohort

Health sciences; Medicine; Medical specialty; Internal medicine; Neurology

Introduction

Epilepsy, a complex neurological disorder affecting 1% of the global population, carries substantial morbidity, and for those with drug-resistant epilepsy (DRE), resective surgery can be curative if the epileptogenic lesion is accurately identified.^1,2,3 Cortical developmental malformations constitute one of the common etiologies of DRE, accounting for approximately 20% of such cases, with higher rates in pediatric cohorts (40% vs. 12% in adults).⁴ Imaging findings are inconsistent across FCD subtypes.⁵ Focal cortical dysplasia (FCD) type II often exhibits a characteristic triad on MRI—gray matter (GM) thickening (60%), white-gray matter boundary (WGB) blurring (74%), and white matter (WM) T2 hyperintensity (63%).⁶ Conventional visual analysis remains constrained by MRI contrast limitations and inter-reader variability, resulting in undetected cases of up to 80% for type I⁷ and 21%–33% type II FCD.⁶

Lesion identification is particularly critical because complete resection of FCD type II is strongly associated with favorable seizure outcomes.^7,8 Automated detection algorithms can assist presurgical evaluation by highlighting candidate regions that warrant focused radiological review.^9,10,11 Thus, any method that improves lesion detection has the potential to improve surgical candidacy and outcomes.

These limitations of visual diagnosis have driven advancements in computational neuroimaging, particularly voxel-based morphometry (VBM)¹² and surface-based morphometry (SBM),¹³ which enable objective quantification of structural abnormalities using routine clinical MRI protocols. The Morphometric Analysis Program (MAP18),^14,15 a widely used VBM pipeline, computes feature maps highlighting GM and WGB irregularities by comparing individual brains to a normative template.¹⁶ Despite elevated detection sensitivity, MAP18 suffers from low specificity (6%–10%),^9,10 a limitation rooted in its dependence on spatial smoothing to suppress registration-induced false positives—a trade-off that we examine more closely below. When combined with texture analysis, VBM allowed the identification of 9%–15% more epileptogenic foci than visual inspection, although at the cost of reduced interpretability.¹¹ Supervised learning models—including artificial neural network,^17,18,19 deep convolutional neural networks (CNNs),^20,21 and surface-based classifiers^22,23—have recently shown promise for automated FCD detection.²⁴ However, these approaches typically require large, expertly labeled training datasets, can exhibit reduced generalizability, and often function as “black boxes” with limited interpretability for surgical decision making. VBM/SBM retain critical advantages in small-sample reliability and interpretability—essential factors for preoperative planning.²⁵

VBM primarily utilizes registration,²⁶ feature representation, and group-level comparative techniques, whereby iterative coregistration mapping to Montreal Neurological Institute (MNI)²⁷ space allows regional outliers in constructed mean templates²⁸ to indicate pathological features. However, the accuracy of this comparison depends critically on the fidelity of the underlying registration. When registration fails—as it often does in anatomically complex regions—the resulting misalignment introduces spurious residuals that mimic true pathology. A fundamental source of false positives in template-based VBM lies in registration errors concentrated in regions of high cortical folding variability. Human association cortices—including lateral temporal, lateral parietal, and dorsomedial prefrontal regions—undergo disproportionate developmental expansion (up to 4-fold),²⁹ developing complex, individually variable folding patterns. This variability in sulcal anatomy causes conventional volumetric registration to systematically fail: deformation fields constrained by continuity requirements cannot independently align opposing sulcal banks, introducing signal residuals at mismatched sulci. Spatial smoothing (typically 6–15 mm FWHM) is widely applied to mitigate these residuals, at the cost of reducing sensitivity to small lesions and blurring fine anatomical detail.³⁰ The cortical folding paradox—the tension between individual gyral fingerprints and population-based registration—remains a fundamental neuroimaging challenge.

In contrast to VBM’s volumetric approach, SBM circumvents the cortical folding paradox by inflating the cortex to align sulcal patterns before performing statistical comparisons, consistently outperforming volumetric methods in spatial normalization accuracy³¹ and FCD detection.²³ However, SBM faces significant barriers to routine clinical adoption: surface reconstruction requires computationally intensive mesh optimization and topological correction; surface-based metrics (e.g., local gyrification index) lack validated diagnostic thresholds; and results must be visualized on inflated surfaces, which is incompatible with the slice-based review paradigm used by radiologists. Consequently, VBM remains dominant in clinical settings, despite its registration limitations.

To overcome this limitation, enhanced registration techniques that preserve sulcal structures are essential, benefiting from group-level feature mean templates that facilitate precise quantification of epileptic malformations. However, despite these advances, no existing suitable method fully bridges the gap between surface-based anatomical precision and voxel-based clinical operability. To address this, we introduce volume inflation registration (INFREG). INFREG extends the cortical surface unfolding principle into the volumetric domain: the cortex is computationally inflated to flatten sulci, registration is performed in this unfolded space where folding variability is eliminated, and the result is deflated back to native voxel space. This enables sulcus discontinuous deformation fields while preserving direct voxel level correspondence with the original 3D MRI—combining SBM’s anatomical fidelity with VBM’s clinical operability. We validate INFREG exclusively on FCD type II, the subtype most commonly associated with MRI visible gray-white junction blurring, and comprehensively benchmark its registration accuracy, template quality, and lesion detection performance against multiple conventional pipelines. In this study, as shown in Figure 1, we (i) detail the INFREG framework, including surface reconstruction, cortical surface registration, volume inflation/deflation, and template-based feature computation; (ii) quantitatively evaluate its registration accuracy against six conventional methods at both voxel and geometric levels; (iii) assess the sharpness and anatomical precision of population mean templates constructed in the inflated domain; and (iv) validate the clinical potential of INFREG-based feature maps for FCD type II detection in 80 patients and 85 controls, including a reading time experiment with two neurologists.

Figure 1.

Overview of the pipeline in this research

(A) Flow chart of surface registration. After the individual brain is globally aligned with the WM surface (maximum curvature coloring) of the MNI template, the conformal mapping is performed to the ball space and then deformed to align.

(B) Sketch map of surface expansion and volume inflation. The gyri folds of the original image are opened and flattened after the action of the inflation deformation field. Left, 2D representation of WM surfaces expanding outward/inward (dilate/erode), maintaining equal thickness and no crossing; right, 3D representation of WM surfaces expanding between the original surface (left column) and the inflated surface (right column). All the vertices of the two series of surface clusters form a one-to-one corresponding point set (V_m, V_f), and the deformation field of volume inflation can be obtained by interpolating the original spatial position corresponding to any position of the inflation space (interp[V_m, V_f, v]).

(C) Mean template schematic constructed by different registration methods. The red and blue boxes show the mean template of the prefrontal gray-white border (WGB) with T1, respectively. In the traditional method, the feature map is mapped to the MNI space by the low-degree-of-freedom (Elastix) and high-degree-of-freedom (CAT12) registration methods, and the average value is calculated. The results show that the latter can show more secondary furrows, but still has blur. INFREG computes the mean template by deforming the feature map into the inflated domain, and the results show clear gyri.

(D) Evaluation of three methods (Demons, CAT12, INFREG) registered the template to the patient’s brain. SSIM: structural similarity. The areas highlighted in red on the 1-SSIM map indicate that the patient’s brain is significantly different from the template. The residual feature is the value of the patient’s brain feature minus the template. A bright spot indicates a potential lesion, while a bright spot outside the red dashed box (real lesion) is a false positive.

Results

Implementation and characteristics of the volume-inflating method

Cortical surface-based registration improves alignment precision by leveraging a deformable framework for sulcal-gyral matching. We extend this principle through voxel-level expansion of the surface inflation paradigm, enabling direct volumetric registration. We focus more on the WM surface than the GM surface because it is more associated with FCD lesions. Here, we detail implementation strategies, methodological advancements, and computational outcomes.

Cortical surface reconstruction, optimization, and registration

Precise cortical surface reconstruction serves as the foundation for subsequent registration processes. To expedite this computationally intensive step for brain datasets, Vox2Cortex, an open-source deep learning tool, was employed. It achieved reconstruction times of less than 1 min per subject on a single GPU (for each mesh of a hemisphere with 42,016 vertices <8 GB), representing a speedup exceeding 100-fold compared to FreeSurfer and CAT12. However, the initial reconstruction of the WM surface exhibited partial misalignment with the centreline of WGB (the border of WM). As shown in Figure 2, the mean WGB probability of each vertex was adopted to measure the alignment accuracy, and the original extracted surface exhibited an average error of 0.4 (compared to the expected highest probability value of 1). To address this issue, as shown in Figures 2A and S2, we implemented an iterative optimization protocol that appended vertices to the WGB following its gradient, resulting in a reduction of surface fit error by 81.2 ± 2.3% (before vs. after optimization; p < 0.001) across 40 test cases. Similar optimizations have been applied to the GM surface. This strategy, combined with deep-learning-based reconstruction and interpretable correction, improves the efficiency of batch data analysis while preserving anatomical accuracy. The surface registration of directly aligned sulci can be used as the initial boundary of voxel registration. Therefore, we performed surface registration using a surface mean curvature map of the hemispherical GM inner surface extended to a rectangle, similar to the SVreg pipeline of BrainSuite, but with a higher initial alignment and smaller local flattening deformation, as shown in Figures 3 and S2.

Figure 2.

Characteristics of volume in inflation space

(A) The WM surface extracted by Vox2cortex is optimized and attached to the WGB. The attached error is defined as the average of the WGB gradients at all vertices, see also Figure S2.

(B) HCPex map and its inflated color volume rendering, using MRIcroGL software. a, b, and c are three different adjacent brain regions in the original space, which remain adjacent after inflation. c is buried below the cortex and is not visible in the original GM volume rendering, but is visible after inflation (pink area).

(C) Evaluation of the thickness retention of WM surfaces in outward/inward expansion.

(D) Visualization of the characteristics of the inflation deformation field MNI template. Top: deformation field grid and color-coded displacement; bottom: Jacobian of deformation field, where blue indicates folded region and red indicates large deformation region.

(E) Intensity-normalized T1 images (GM: 1, WM: 2) were subjected to Gaussian blur in the original and inflated spaces, respectively. The blue curve is the intensity sampled in a straight line across the sulci, and the red and yellow spots on the right are the shapes of the actual blur kernel here.

Figure 3.

Visualization of surface registration

(A) Sketch map of the original surface, sphere mapping, and unfolded texture for cortex registration, using maximum curvature coloring.

(B) Cortical surfaces of three individuals and results of registration to the template. 6 landmarks are delineated to aid in the reading of the figure: a, superior frontal gyrus; b, central sulcus; c, parieto-occipital junction area; d, dorsal middle frontal gyrus; e, lateral fissure; f, middle temporal gyrus.

C, D, and F, marked in red, indicate regions of high anatomical variability.

(C) Flattened texture maps and registration results for three individuals, see also Figure S1.

(D) Mean and standard deviation (S.D.) of 9 iterative Demons co-registration of flattened texture maps of 80 normal individuals. c, d, and f markers with high s.

(D and E) Surface co-registration results for BrainSuite as baseline contrast.

Cortical volume-inflation

Then, expand the surface registration to cover the voxels of the entire cortex. Unlike traditional techniques, such as the harmonious expansion algorithm implemented in the BrainSuite, our proposed voxel inflation technique represents a volume deformation-based on cortical expansion and interpolation with intrinsic reversibility. Considering the complex folding pattern of the cortex, it is crucial to maintain local consistency and homotypic integrity throughout the process. As shown in Figure 2, the WM surface expands outward along a gradient of the distance field of WGB while maintaining its local structure and topology. The expanded GM maintained a nearly uniform thickness except near the spinal cord gyrus (thickness ratio over 1.2). Adjacent brain regions retain their inter-regional information (e.g., adjacent regions A, B, and C keep their boundaries intact) while eliminating wrinkles. Swelling of deep WM may cause slight topological distortions (characterized by Jacobi determinants below zero) and thicken WM deep within the clefts and sulci. However, except for the “transmantle sign,” for imaging studies of diseases such as epilepsy or cortical malformations, difficulties are mainly focused on cortical GM proximity, and thus, defects in deep WM conversion have minimal impact on the analysis. Therefore, subcortical structures were not considered in the subsequent processing and analysis in this study.

Computation characteristics in the inflated-volume domain

To elucidate the properties of cortical voxel inflation, Figure 2F demonstrates the application of data smoothing. Volume smoothing reduces mismatches and improves the signal-to-noise ratio of functional signals, such as fMRI imaging signals. However, it risks contaminating folded gyral regions, leading to erroneous activation. Previous studies have shown that sensitivity increases when smoothing occurs in cortical surface domains.³² Trying isotropic 3D Gauss smoothing directly in the voxel expansion space and then reverting to the original fold configuration, we observed preserved sulci morphology next to the intermingled GM with adjacent regions. Switching to folded space, the Gauss kernel morphs into a flattened, anisotropic shape along the gyrus surface, significantly mitigating cross-folding GM crosstalk. After artificial local scribed measurement, and the overall voxel comparison, the gray-white matter contrast loss in the dilated volume domain (normalized gray level difference: 1.4 vs. 0.6 in this case) can be significantly reduced compared to the original voxel domain after filtering with a blur kernel of the same size.

Evaluation of inflate-registration in the voxel domain

Our voxel inflation registration (INFREG) technique demonstrates exceptional accuracy in regular cortical territories and avoids overfitting in aberrant gyral zones, thereby providing an insightful benchmark for scrutinizing anomalous lesions within neuroimaging contexts. Through multifaceted evaluations, juxtaposed with respected volume registration benchmarks including Elastix, Demons, ANTs, BrainSuite, and CAT12, our methodology exhibits superiority across numerous metrics. To avoid losing abnormal features of the patient’s brain, we tested the effect of registering the average template to the patient’s brain and assessed the registration ability of cortical regions outside the lesion zone by image similarity. The evaluation results are shown below by quantitative comparison and intuitive visualization.

Quantitative voxel-level evaluation

Our registration results are visualized in Figures 4, S3, and S5 show multiple slices of detailed examples. At the voxel level (remove voxels subcortical and within lesion labels), outcomes were contrasted with the aforementioned competitors, with assessments hinging on the structural similarity index measurement (SSIM) and Dice coefficients for GM and WM. Our methodology achieved SSIM = 0.95 ± 0.04 and GM/WM Dice = 0.93 ± 0.05, significantly surpassing rivals (SSIM: 0.70–0.82, Dice: 0.72–0.87, p < 0.001 with all competitors in pairwise t tests, N = 40, as shown in Table 1).

Figure 4.

Evaluation of several classical registration methods with INFREG at the voxel level

(A) Performance comparison of MNI templates registered to 40 FCD patient brains using different methods, with the patient brain serving as the gold standard. The details of INFREG’s results could be found in Figures S3 and S5. SSIM: structural similarity; Dice (GM)/Dice (WM): Dice coefficient of GM/WM segmentation.

(B) Comparison of registration performance between CAT12 and INFREG (ours) and visualization of a deformation field. The RGB channels of the deformation field represent the XYZ component of the displacement, respectively, and the white dashed lines in the enlarged portion indicate the sulci. The lesion is marked by the red dashed box below, and here is the extension type.

(C) Comparison of results of three registration methods: Demons, CAT12, INFREG (ours) in 5 patients (template registered to patient brain).

(D) Three registration results with 1-SSIM maps of the patient’s brain cortex. The desired excellent outcome is a red dotted box (lesion) with a bright spot (marked difference) and a dark color outside the box (good sulcus alignment).

(E) Magnified view of 5 patient registration results near the lesion.

Table 1.

Voxel-level evaluation of registration methods

Methods	SSIM	Dice (GM)	Dice (WM)
Elastix	0.72 ± 0.08	0.68 ± 0.11	0.78 ± 0.06
Demons	0.83 ± 0.10	0.82 ± 0.17	0.84 ± 0.07
ANTs	0.82 ± 0.12	0.83 ± 0.09	0.84 ± 0.14
BrainSuite	0.78 ± 0.09	0.76 ± 0.08	0.78 ± 0.07
CAT12	0.87 ± 0.08	0.82 ± 0.06	0.84 ± 0.09
INFREG	0.95 ± 0.04 (p < 0.001)	0.94 ± 0.08 (p < 0.001)	0.92 ± 0.04 (p < 0.001)

Notably, Elastix’s reliance on spline curve elastic registration and ANTs’ fast SyN configurations for the Slicer platform may lack fine-tuning for peak performance compared with the best performance reported before. BrainSuite’s surface-constrained volume registration encounters pitfalls due to potential inaccuracies or failures in self-reconstructed cortical surfaces, impacting registration quality. Regardless of optimal calibration, traditional volume registration remains inherently constrained by deformation field smoothness (particularly along the sulcal margins), impeding sulco-gyral alignment in various regions, prominently the middle frontal gyrus, portions of the parietal lobe, and medial temporal lobe, as depicted in Figure 5. Figure 4B reveals how our volumetric approach facilitates a discontinuous deformation field across sulci, accommodating intricate gyrification patterns. CAT12’s registration methods constrain the matching capability between different sulci due to deformation constraints imposed across sulcal banks, resulting in smooth deformation. This holistic optimization for global similarity causes overfitting in the extension-type lesion here. Our method enables discrete deformation fields on opposing sulcal banks, permitting freer alignment. Crucially, INFREG maintains deformation continuity and ipsilateral cortical thickness, preventing lesion overfitting.

Figure 5.

Anatomical analysis of registration performance and feature residuals of 80 patients’ brains

(A) Performance comparison of feature maps calculated-based on MAP18(using CAT12 registration) and INFREG for FCD detection. The characteristic threshold was 50% of the 98% quantile intensity, and A, B, C, and D were the four evaluation indices. B, C, D, G were visualized using curvilinear reformatting (pealing 15 mm).

(B) Mean map of 1-SSIM with template registration to the patient’s brain (removing lesion area).

(C) Average plot and atlas of all FCD lesion labels.

(D) Average plot of characteristic residuals (template registration to the patient’s brain) outside the lesion area, implying a false-positive probability distribution. The upper and lower quantiles are the results of the MAP18 and INFREG pipelines.

(E and F) Average of 1-SSIM and characteristic residuals (false positives) for each brain region.

(G) superimposed distribution plot of lesions and residuals (95% quantile intensity as threshold). Abbreviation: SSIM, structural similarity; e-map, extension-map; j-map, extension-map.

Remarkably, despite INFREG’s complex deformation field, it supports clarity and precision without clutter. This assertion was corroborated through testing INFREG’s registration efficacy in FCD patients, specifically with subtype “extension” lesion (abnormal extension into WM or thickened GM). As exemplified in Figures 4C–4F, Subj-16 and Subj-71 exhibit distinct abnormalities, yet our methodology attains near-perfect alignment in non-pathological gyri, illustrating stark contrasts. Evident in the 1-SSIM representation, a conspicuous highlight marks the lesion area, distinguishing our output from widespread false positives evident in rival approaches. For subtler cortical anomalies, akin to the “junction” subtype featuring blurred gray-white matter demarcation, direct template comparison fails to articulate discrepancies at lesion sites. Nevertheless, disparities emerge upon examining feature maps, as delineated in Figure 6, showcasing our method’s prowess in capturing nuanced distinctions.

Figure 6.

Feature residual maps of FCD patients’ brains

(A–C) Original T1-MRI/feature maps, registered template, and feature residual maps of the brains of three patients with FCD, see also Figure S7.

Extension-map is the residual for GM, indicating abnormal thickening of gray matter or extension into WM; junction-map is the residual for WGB, indicating abnormal blurring of the junction between GM and WM. GM: gray matter; WGB: gray-white matter boundary.

(D and E) Volume rendering of the feature residuals (including both red and green channels) extracted from the MAP18 and INFREG pipeline, with the intersection of the lines as the lesion center. 30 patients were from the DS004199 dataset, whose subject ID were 3, 4, 10, 14, 16, 38, 40, 43, 47, 55, 58, 60, 61, 63, 64, 71, 77, 81, 90, 92, 97, 101, 115, 131, 132, 133, 136, 138, 142, 144 (from top row to bottom row).

(F and G) Additional 11 representative cases (IDs: EPISURG 111, 163, 207, 275, 277, 281, 332, 346, 368, and IEEG Study020, and Study037) with minor suspected lesions and reference brain templates, derived from EPISURG and IEEG.org dataset, zoomed in on the feature maps at the lesions. Details could be found in Figures S8–S16. Abbreviation: e-map, extension-map; j-map, junction-map.

Comparison of intuitive 3D visualization

2D perspectives often fail to capture the intricacies of folded structures, presenting them as disjointed segments; however, a three-dimensional viewpoint offers superior visibility. Leveraging curve reformatting techniques, we vividly illustrate the sulcal and gyral trajectories by selectively excising varying depths of lateral brain tissue, effectively highlighting the trendlines of these anatomical features. Discrepancies in registration manifest as striking crimson speckles on the three-dimensional rendering of the 1-SSIM composite, pinpointing probable lesion locations.

As shown in Figures 7, S4, and S6, employing curve reformatting visualization, we showcased sulco-gyral registration effectiveness in a representative patient cohort comprising 4 subjects (Subj 3/16/64/10). Here, the 1-SSIM map activation in a normal brain, higher than 0.5 was regarded as an obvious false-positive spot, and the proportion of the volume covering the whole area was calculated as the false-positive volume rate (FPVR). Within the normal hemisphere in 20 test brains, INFREG display notable variances versus Demons and CAT12 in false-positive identifications (FPVR across all cortical regions, INFREG: 3.5 ± 1.3%, Demons: 28.8 ± 7.3%, CAT12: 30.6 ± 6.2%, N = 20), concentrated primarily in the frontal, parietal lobes and medial temporal lobe (FPVR in these regions, INFREG: 6.1 ± 1.8%, Demons: 56.1 ± 15.4%, CAT12: 63.6 ± 14.0%, N = 20). Contrarily, our methodology showcases virtually comprehensive low-registration disparity. Simultaneously, for Subj16 and Subj10, bearing “extension” subtype pathologies, our approach singularly illuminates genuine positive differential highlights proximal to the lesion site (similarity differences appear only in the red lesion box), underscoring the precision and specificity of our registration technique.

Figure 7.

Curvilinear reformatting visualization of different registration methods in deep cortex

(A) The basic principle of curvilinear reformatting. Voxels in the outer layer of the cortex are removed by mask, and the deep cortical sulcus structure and grayscale are directly visualized by volume rendering.

(B and C) Registration of templates to the brains of three FCD patients with different lesion features (subj3: minor junctions, subj16: great junctions, and subj64: minor extensions) and curvilinear reformatting visualization (each peeling 10, 15, and 15 mm) and similarity maps. The details of INFREG’s results could be found in Figures S4 and S6. SSIM: structural similarity. The desired excellent outcome is a red dotted box (lesion) with a bright spot (marked difference) and a dark color outside the box (good sulcus alignment).

(D and E) Curve reconstruction was used to visualize the registration results and similarity map of the same patient from shallow to deep (5, 10, 15 mm).

Assessment of mean templates generated by registration

The construction of population-average templates through multi-modal registration of neurotypical brains addresses a fundamental challenge in neuroimaging: disentangling intersubject anatomical variability from methodological artifacts. The clarity of the template sulci can be improved by special fusion strategies,^33,34 but it is important as a marker-free assessment of registration ability at the group level. Leveraging OpenNeuro’s curated repository of 80 age-matched T1w MRI scans (18–45 years, balanced sex distribution), we generated intensity-normalized templates encoding four complementary features: T1 normalized-intensity, GM probability, cortical thickness, and WGB probability. As shown in Figure 8, 3 registration frameworks spanning deformation complexity were benchmarked: Elastix (low-DOF), CAT12 (medium-DOF), and our INFREG method (high adaptive deformation)—were comparatively evaluated through both qualitative sulcal alignment assessment and quantitative variance analysis.

Figure 8.

3D visualization and evaluation of registration-based mean template

(A and B) Different registration methods were used to construct mean template vs. standard deviation (S.D.) of T1-MRI and feature maps of normal human brains (N = 80), which were visualized using curvilinear reformatting. The blue arrow indicates the location of the apparent difference.

(C) The Gyri Atlas of BrainVISA was divided into 6 regions to evaluate the effect of different mean templates. Among them, the first four groups are the lobes, the Fissure group includes the well-developed fissures, and the central group only contains the central sulcus. The edge contrast is calculated by the average intensity of the edge filter in the region. The higher the edge contrast is, the clearer the mean template is and the better the registration performance is. S. D. value is calculated by averaging the standard deviation of the voxels in the region, with lower values indicating better alignment of the registration method. The plotting results of the two evaluation indexes are normalized by the maximum values, and the ordinates are the relative values.

Registration performance analysis showed Elastix templates capturing only primary gyral boundaries, while CAT12 and INFREG achieved superior detail preservation of secondary sulci. Quantitative evaluation demonstrated INFREG’s superiority: using normalized GM probability images, it reduced intensity variance by 23%–41% versus CAT12 across neocortical divisions (whole cortex, 0.53 vs. 0.73, p < 0.001; frontal: 0.51 vs. 0.72, p < 0.001; parietal: 0.53 vs. 0.75, p < 0.001; temporal: 0.58 vs. 0.68, p < 0.01; occipital: 0.53 vs. 0.76, p < 0.001; F test, FDR-corrected). While edge contrast in conserved regions (central sulcus: 0.97 ± 0.02 vs. 0.98 ± 0.01) showed method equivalence, INFREG outperformed in high-variability zones (superior frontal: 0.83 vs. 0.71, p = 0.003). Due to well-aligned anatomy and a large amount of incoming or outgoing fibers, the WGB of the central sulcus appears to be wider/brighter, which advantage decreases with the improvement of the registration ability (For example, quantified by mean intensity in central sulcus vs. parietal lobe, elastix: 3.17, CAT12: 1.51, INFREG: 1.23).

Regional normalized S.D. (nS.D.) using medium-DOF registration like CTA12 may indicate specificity of brain regions, revealing a neurobiological gradient: conserved sensorimotor central sulcus (nS.D. = 0.18) versus variable association neocortices (prefrontal lobe: S.D. = 0.74, temporal-parietal association region: nS.D. = 0.68), correlating with Brodmann’s cytoarchitectonic complexity rankings. Thus, a higher nS.D. of GM probability may imply complex cellular architectures to support multimodal information processing. These findings, visually summarized in Figure 5, demonstrate INFREG’s enhanced capacity to resolve both conserved and variable neuroanatomical features through adaptive deformation modeling.

Evaluation of registration in the geometry domain

A pivotal challenge in neuroimaging registration lies in quantifying the spatial discordance of cortical folding patterns across subjects.³⁵ Unlike voxel-based similarity metrics (e.g., normalized mutual information or SSIM), our geometric evaluation framework directly compares anatomical landmarks—gyral/sulcal curves.

We first extracted gyral/sulcal curves via local curvature maxima detection (threshold: κ > 0.35 mm⁻¹). These curves can be evaluated in an unpaired manner without having to distinguish between specific partitions, which may avoid errors in the extraction process. See Figure 9, 6 registration pipelines were benchmarked, including affine registration and classic deformable methods. Quantitatively assessing gyral curve alignment errors of registration across diverse anatomical locations, determining the mean minimum Separation (mmSEP) between any node on the curve and all counterparts, unveils disparities. Crucially, CAT12 and INFREG demonstrated superior capability in superimposing sulcal curves from 80 subjects into coherent curves (mean inter-subject separation<4.0 mm), whereas conventional methods exhibited dispersion artifacts. Quantitative analysis using minimum mean separation distance (mmSEP) revealed:

• 1.Lobar variation: sulcal mmSEP consistently exceeded gyral values (sulcal/gyral = 1.32 ± 0.21, p < 0.001, N = 6), reflecting higher anatomical conservation of primary folds.
• 2.Method superiority: INFREG achieved the lowest mmSEP in frontal (3.87 ± 0.32 mm vs. CAT12’s 4.65 ± 0.40 mm), parietal (4.01 ± 0.33 mm vs. 5.38 ± 0.56 mm), temporal lobes (4.17 ± 0.33 mm vs. 4.45 ± 0.41 mm), and whole cerebral cortex (3.34 ± 0.13 mm vs. 3.45 ± 0.15 mm) (p < 0.01, N = 6)
• 3.Occipital specificity: CAT12 outperformed in occipital cortex (mmSEP = 3.20 ± 0.23 mm vs. INFREG’s 3.55 ± 0.36 mm), likely attributable to reconstruction-dependent error amplification in dense regions with high-curvature.

Figure 9.

Evaluation of registration in geometric domain

(A) The pial surface of the two brains extracts sulci curves-based on maximum curvature, and there is no one-to-one correspondence between all curve points.

(B) Assessment of the alignment accuracy of sulci curves of 80 normal brains registered to a template in different lobes. The index “mean closest distance” is defined as the Mean of the closest distance between the curve points of one brain and all other brains in a region. The smaller the index, the higher the degree of sulci alignment after multiple brain registrations.

(C) Sulci curves of the first 10 brains were mapped, and different brains were color-coded. Tight strands of different ridges mean good alignment.

(D–F) is similar to (A–C), but assessed by WM curved surface extraction of the gyri.

Then, to further dissect registration precision in well-defined sulci, we applied BrainSuite’s sulcal extraction algorithm on 12 phylogenetically conserved sulci (e.g., central sulcus, superior temporal sulcus). As visualized in Figure 10, sulci originating from varied brains are uniformly color-coded; the narrower the dispersion, the greater the registration accuracy. Notably, BrainSuite’s registration hinges upon these sulcal constraints, thus producing a higher performance even better than CAT12. However, its sulcal extraction inevitably produced some errors, as evidenced by occasional misalignments atop the central sulcus, potentially encroaching onto adjacent gyri. Despite this, INFREG transcends alternative registration techniques, inclusive of BrainSuite itself, achieving unparalleled registration fidelity.

Figure 10.

Evaluation of alignment accuracy of different registration methods-based on specific sulcus and gyri

(A) WM surfaces and sulci curves extracted by BrainSuite for two individual brains and reference template (from.dfc file).

(B) Magnification showing errors in sulcal curves extracted from two individual brains along the superior edge of the central sulcus.

(C) Locations and names of 12 longer sulcal curves extracted by BrainSuite were screened out.

(D) Assessment of the alignment distance of specific sulci curves of 80 normal brains extracted by 6 registration methods. The x axis is a histogram of 12 sulci. Each histogram color corresponds to the registration method below.

(E) Sulci curves from the top 10 brain extractions are superimposed to show where clusters of curves in the same color represent different brain extraction results at the same anatomic location.

Detecting FCD lesion by template comparison

The detection of FCD through template comparison necessitates balancing standardization with individual neuroanatomical variability. While generic brain templates provide spatial reference frameworks, our study reveals that conventional subtraction methods (e.g., CAT12 registration and MAP18 protocol) induce voxel-wise false positives due to gyral pattern mismatches, particularly in regions with high sulcal variability. Through comparative analysis of GM and WGB probability residuals using INFREG and MAP18 protocol, we established two distinct feature domains: extension-map capturing GM thickness anomalies and junction-map highlighting WGB distortions.

As demonstrated in Figures 6A–6C, INFREG-generated feature maps exhibit superior noise suppression compared to MAP18 outputs, with residual clusters anatomically constrained to clinically relevant regions. MAP18 can not adopt an appropriate threshold to separate true and false positives under weak lesion characteristics, whereas INFREG can do so more easily, as shown in Figure S4. The volume-rendering shown in Figures 6D and 6E gives a more complete picture of the batch of patients. Here, all the clusters are ordered by volume, denoted by top-k clusters, which could be focused on by the examiner. In these cases, 12 lesions were difficult to localize with MAP18 outputs (could not be easily found within top-10 clusters), while all lesions could be localized by our methods: top-1 cluster (19/30 = 63.3%), top-5 clusters (8/30 = 26.7%), top-10 clusters (3/30 = 10%). Figures S8–S11 show a detailed comparison of each feature map for the 40 cases.

To test the manual verification time of MAP18 and our outputs, two neurologists performed the diagnosis by reading T1/FLAIR scans and feature maps of 30 FCD cases, as introduced in Figure S12. The results show that: without feature maps, 182 ± 97/155 ± 83 s per case; within feature maps of MAP18, 177 ± 114/162 ± 102 s per case; within our feature maps, 101 ± 67/75 ± 48 s per case. This evaluation demonstrated that our methods enabling resource-efficient clinical workflows with (100% –[101 + 75]/[177 + 162] ≈) 50% reduction in manual verification time compared to MAP18 pipelines (p < 0.001, Wilcoxon rank-sum test).

To preliminarily assess whether the improved registration and feature-map specificity observed in the primary Bonn cohort could extend to other clinical settings, we applied both MAP18 and INFREG to an auxiliary set of 36 cases collated from two independent public data resources: the EPISURG dataset (a surgical cohort from the National Hospital for Neurology and Neurosurgery, London, originally curated for post-resection cavity segmentation) and the IEEG Portal (an international intracranial EEG archive with matched structural MRI). Neither resource provides systematic histopathological confirmation of FCD type II, and the available lesion labels in these datasets are derived from neuroradiological reports or surgical records rather than the expert-consensus annotations that characterize ds004199. Consequently, these cases cannot support formal quantitative benchmarking. Nevertheless, they offer a useful qualitative test of algorithmic robustness across different scanners, acquisition protocols, and patient populations. Figures 6F and 6G presents nine representative examples from these supplementary datasets, showing that INFREG-based feature maps consistently highlighted suspicious regions that aligned with the clinically documented lesion locations, whereas MAP18 outputs were more frequently confounded by false-positive residuals in the same areas. Detailed information for all 36 cases, including dataset provenance and imaging parameters, is provided in Supplementary S13-16. While these auxiliary observations do not substitute for a prospective multi-center validation study, they provide encouraging preliminary evidence that the registration and detection advantages of INFREG are not confined to a single institutional cohort.

Further, a detailed quantitative assessment on a larger dataset was conducted. As shown in Figure 5A, voxel-level quantitative evaluation across 80 confirmed FCD cases revealed that INFREG demonstrates superior performance with CAT12 in Dice coefficients (extension-map: 0.078 ± 0.042 vs. 0.065 ± 0.055, p < 0.01; junction-map: 0.121 ± 0.137 vs. 0.042 ± 0.013, p < 0.001) and in the number of false positive clusters (extension-map: 10.5 ± 4.2 vs. 3.1 ± 0.8, 70.5% reduction, p < 0.001; junction-map: 22.4 ± 4.7 vs. 2.7 ± 0.6, 87.9% reduction, p < 0.001). Notably, the smaller overall Dice coefficients are since in most cases (partially visually negative), the lesion labels are delineated much larger than the T1 image anomalies. Furthermore, MAP18’s high sensitivity at the voxel level results from larger cluster coverage (partly due to a larger Gaussian kernel). In 80 cases, only 1 case was missed by INFREG and captured by MAP18. Excluding the top 30 challenging cases (almost negative on visual inspection), the superiority of INFREG becomes more evident in Dice coefficients (extension-map: 0.449 ± 0.176 vs. 0.231 ± 0.079, p < 0.001; junction-map: 0.487 ± 0.140 vs. 0.087 ± 0.023, p < 0.001). In horizontal comparison, the WGB-derived junction-map achieved significantly higher Dice coefficients and specificity than the extension-map, corroborating that FCD pathomorphology predominantly manifests at blurred white-gray junctions rather than through cortical thickening.

Spatio analysis of CAT12 registration errors (Figures 5D–5G) uncovered two high-error clusters: the middle frontal gyrus (MFG) and temporoparietal junction encompassing angular gyrus (AnG) and middle temporal gyrus (MTG). These regions, known for inter-individual sulcal variability, showed higher registration inaccuracies of CAT12 (SSIM <0.5) or low registration confidence as reported.³⁶ Moreover, extension-map artifacts of MAP18 spatially overlapped (Dice = 0.31) with true FCD probability maps, making it difficult to identify true clusters of lesions. Conversely, junction-map artifacts predominantly aggregated at sulcal confluence zones, reflecting the anatomic propensity of FCD-II lesions.

In all, INFREG substantially improved spatial congruence in these challenging domains, decreasing false-positive clusters in morphometric analyses by 70%–88% (extension-map and junction-map). This refinement achieves unprecedented specificity in differentiating true dysplasia from registration artifacts.

Discussion

Registration-based template comparison methodologies, particularly morphometric analysis protocols (MAPs), significantly enhance diagnostic efficiency in neuroimaging for cerebral pathologies while enabling retrospective analysis of institutional imaging databases. Nevertheless, the clinical translation of these methods remains constrained by substantial false-positive outcomes arising from inter-regional neuroanatomical variability and algorithmic fitting limitations, necessitating resource-intensive manual verification by clinicians.

In this study, we therefore addressed this challenge by reducing registration-induced false positives through INFREG, which combines surface-based anatomical precision with volumetric clinical operability. Below, we contextualize our findings within the broader VBM/SBM methodological landscape.

Rethinking the clinical usability of different registration paradigms in cortical diseases

In neuroimaging research, VBM and SBM have long existed as distinct methodologies, often framed as a dichotomy between clinical pragmatism and anatomical fidelity. Comparative analysis of these approaches reveals fundamental methodological disparities with significant implications for both research and clinical translation.

The International League Against Epilepsy guidelines³⁷ continue to prioritize voxel-level features (e.g., blurred white-gray junctions) as diagnostic criteria, reflecting clinical reliance on VBM frameworks. Yet, as our results demonstrate, this reliance comes at a cost: in high-curvature association cortices—where up to 60%–70% of the cortical surface resides—conventional volumetric registration systematically fails to align opposing sulcal banks, and the spatial smoothing applied to suppress the resulting misregistration residuals obscures the very gray-white junction features that define FCD type II. The MAP18 pipeline attempted to address this through dedicated junction and extension maps, but its persistently low specificity (6%–10%) highlights the fundamental nature of the problem: registration-induced false positives cannot be eliminated within a framework that constrains deformation fields to be continuous across sulcal boundaries. Below, we examine this constraint more formally through the lens of the cortical folding paradox and its implications for registration algorithm design.

Conversely, SBM better aligns sulcal patterns through cortical unfolding but faces clinical compatibility challenges:

• 1.High computational burden: surface reconstruction requires iterative mesh optimization and topological corrections, making it time-prohibitive for clinical workflows and unreliable for cases with post-surgical or traumatic topological disruptions.
• 2.Limited neuroanatomical coverage: surface-based metrics ignore subcortical and deep GM structures while losing fine-grained intensity information, complicating voxel-level correspondence with original DICOM images.
• 3.Clinical interpretability barriers: surface parameters (e.g., local gyrification index) lack validated diagnostic thresholds and depend on specialized visualization tools incompatible with radiological orthodoxy (axial/coronal/sagittal slice review).

Emerging technologies, including deep learning registration frameworks like VoxelMorph,³⁸ achieve over 0.7 Dice score with regional labels but still exhibit 2%–13% topological violations (negative Jacobian determinants). Similarly, hybrid voxel surface strategies^39,40 attempting to map surface registration results to voxel space as initialization and constraint remain inadequate for modeling complex cross sulcal deformation fields.

Our work addresses clinical translation barriers through three key innovations:

• 1.Accelerated cortical reconstruction: leveraging the Vox2Cortex deep learning framework to achieve sub-minute surface generation while optimizing geometric fidelity to GM boundaries.
• 2.Deepening gray/white matter coverage: implementing bidirectional surface extension from initial cortical meshes to cover voxels around GM enabling voxel registration with anatomically informed deformation fields without constraint on the smoothness of transcranial sulcus deformation.
• 3.Radiology-compatible visualization: generating standardized voxel templates with low false-positive residual feature maps that maintain sulcal alignment and permit direct voxel-wise comparison with clinical DICOM series.

Future efforts should focus on end-to-end workflow integration, whole-brain voxel coverage, and comprehensive geometric feature mapping. The proposed geometric-voxel translation framework establishes a “bilingual translation protocol” between methodological paradigms, preserving SBM’s anatomical precision while inheriting VBM’s clinical operability. This dual-domain synergy opens new avenues for precision neuroimaging in epilepsy and developmental disorders.

Regional distribution of false-positive lesions of FCD

Human neuroanatomy exhibits spatiotemporal heterogeneity across brain regions, influenced by developmental trajectories and region-specific environmental factors. Template comparisons revealed fundamental differences between primary and secondary sulcal architecture. As reported in previous research, primary sulci (>15 mm depth), formed during 6–24 gestational weeks with over 90% inter-individual morphological consistency, exhibit minimal deformation requirements due to their conserved lobar-separating function. Secondary sulci (5–15 mm depth, gyral subdivision role) demonstrate substantial individual variability (∼60% similarity) and complex deformation patterns, correlating with expanded cortical surface area during gyrification. Intercontinental comparisons demonstrate greater temporal and cingulate regions coupled with smaller frontal and parietal lobes in Chinese populations compared to Western counterparts.⁴¹ Pathological alterations in diseased brains further compound these variations. Compared with international standardized templates (e.g., MNI), regionally and age-matched average templates constructed from local populations show potential to improve registration accuracy and reduce pseudo-abnormal findings.

The neuroanatomical complexity across brain regions imposes differential requirements for registration degrees of freedom (DOFs). Low-DOF affine registration (6–9 parameters) suffices for structurally stable regions like primary sensorimotor cortices. High-DOF nonlinear registration (>12 parameters, e.g., SyN algorithm) becomes essential for complex gyral regions.⁴² In our experiments, the results of the non-rigid registration algorithm with different DOF demonstrated hierarchical alignment capabilities: spline-based elastix achieved primary sulcal alignment (Sylvian, central, parieto-occipital, calcarine, cingulate sulci), while DARTEL or Geodesic Shooting-based CAT12 improved secondary sulcal registration, though residual variance persisted in high-curvature frontotemporal subregions.

However, excessive DOF introduces critical challenges: (1) noise overfitting from motion/vascular pulsation artifacts; (2) artificial blurring at gray-white matter borders; and (3) pathological feature erosion. Registration-induced artifacts predominantly manifest at gray-white matter junctions, periventricular zones, complex frontotemporal cortices, and deep nuclei. Subtle pathological signatures risk being obscured through conventional registration workflows. This means that the alignment of highly curled secondary and tertiary sulci could not be solved simply by stacking degrees of freedom.

The intrinsic conflict between registration precision and anatomical fidelity stems from continuity constraints in voxel-wise deformation fields across sulcal boundaries. Addressing this paradox, we propose a novel registration pathway operating on inflated (sulcal-unfolded) voxel domains. This approach achieved 32%–41% variance reduction in high-curvature regions (especially in MFG, AnG, and MTG). To mitigate deformation-induced feature distortion, our pipeline implements pre-registration intensity feature extraction to create a feature mean template and template-to-subject inverse mapping, preserving original contrast characteristics. Our methods decrease false-positive clusters in morphometric analyses by 70%–88% (extension-map and junction-map), particularly beneficial for detecting FCD type II lesions and epileptogenic zones. Such methodological advancements could reduce reliance on secondary clinical verification, potentially accelerating diagnostic workflows for cortical pathologies through more reliable automated analysis.

Conclusions

We have developed INFREG, a volume-inflation registration framework that reduces false-positive VBM findings in FCD type II by leveraging sulcal alignment in an inflated voxel domain. The method achieved superior registration accuracy, produced sharper population templates, and substantially decreased false-positive clusters compared with standard approaches. In a pilot reading experiment, INFREG-based feature maps halved manual verification time and resolved all VBM-indeterminate FCD type II cases. These results indicate that anatomically informed, sulcal-preserving registration can meaningfully improve the specificity of morphometric analysis for FCD type II. Future work should extend validation to FCD types I and III and to multicenter datasets.

Limitations of the study

Several limitations should be noted. First, our validation is restricted to FCD type II. FCDs are known to originate from somatic (postzygotic) variants⁴³ in genes related to cell growth (e.g., in the mTOR pathway in type II),⁴⁴ primarily occurring during prenatal brain development. The hallmark imaging feature in type II—blurring of the gray-white border—is directly captured by our junction map. FCD type I, which is commonly MRI negative, and type III, which occurs adjacent to other principal lesions, may not benefit equally from INFREG. Extension to these subtypes and to mild malformations of cortical development will require separate, histopathologically confirmed cohorts. Moreover, we did not perform stratified analysis of IIa and IIb subtypes because publicly available pathological labels were unavailable in the dataset; future studies with histological subtyping may reveal differential performance.

Second, this study used a single publicly available dataset (ds004199). Although it is the largest open FCD Type II cohort with expert manual labels, multi center replication on independent datasets and scanner platforms is necessary to establish generalizability. The present results should be interpreted as a proof of concept evaluation of registration fidelity and feature map false positive reduction. As a preliminary step toward addressing this limitation, we collated an additional 36 test cases from other publicly available epilepsy related imaging datasets (subsets of the EPISURG and IEEG datasets). While these data lack the rigorous histopathological confirmation and uniform imaging quality of ds004199, both MAP18 and INFREG detected characteristic abnormalities in the majority of cases, providing encouraging preliminary evidence of cross center applicability. Formal multi center validation using prospectively collected cohorts, such as the Multi-center Epilepsy Lesion Detection dataset,⁷ is planned.

Third, while we have demonstrated reduced false positive clusters and halved reading time in a pilot experiment, full clinical integration would require prospective validation, workflow integration with PACS systems, and assessment of impact on surgical decision making. The encouraging resolution of all 12 VBM indeterminate cases suggests potential value for subtle FCD type II, but larger multi reader studies are needed to confirm diagnostic accuracy and reader confidence.

Resource availability

Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Hongen Liao (liao@tsinghua.edu.cn).

Materials availability

This study did not generate new unique reagents. All datasets used in this study are publicly available as described below.

Data and code availability

• •Data reported in this study were obtained from publicly available databases: ds004199 dataset (https://openneuro.org/datasets/ds004199/), EPISURG dataset (https://doi.org/10.5522/04/9996158), and IEEG Portal (https://ieeg.org/). All source data are described in the key resources table.
• •Code generated during this study is available at GitHub (https://github.com/ifsunrise/brain-inflate-registration) and is publicly accessible as of the date of publication.
• •Any additional information required to reanalyze the data reported in this study is available from the lead contact upon request.

Acknowledgments

The authors would like to thank the neurologist and neurosurgeons of Beijing Tsinghua Changgung Hospital and Xuanwu Hospital, Capital Medical University, for their guidance on clinical medicine: Dr. Wei Zhang, Dr. Hongjuan Lu, and Xinna Ji.

The authors would like to acknowledge the support of the National Natural Science Foundation of China (82027807, 62201315, U22A2051), the National Key Research and Development Program of China (2022YFC2405200), and the Science and Technology Commission of Shanghai Municipality (nos. 24511104100).

Author contributions

Y.Z.: conceptualization, methodology, software, validation, investigation, formal analysis, writing – original draft, writing – review and editing, and visualization; H.H.: writing – review and editing; F.C.: supervision, methodology, resources, writing – review and editing, and funding acquisition; H.L.: conceptualization, supervision, methodology, resources, writing – review and editing, funding acquisition.

Declaration of interests

The authors declare no competing interests.

Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the authors used ChatGPT in order to polish the presentation and improve the readability of this study. After using this tool or service, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
ds004199 dataset	Schuch et al.45	https://openneuro.org/datasets/ds004199/
EPISURG dataset	Pérez-García et al.46	https://doi.org/10.5522/04/9996158
IEEG Portal	Kini et al.47	https://ieeg.org/
MNI-152 template	Mazziotta et al.48	https://nist.mni.mcgill.ca/icbm-152-nonlinear-atlases-2009/
HCPex atlas	Huang et al.49	https://github.com/wayalan/HCPex
BCI-DNI brain atlas	Shattuck and Leahy50	https://brainsuite.org/processing/svreg/creating-custom-atlases/
BrainVISA cortical atlas	Perrot et al.51	https://brainvisa.info/web/morphologist.html
Software and algorithms
MATLAB	MathWorks	https://www.mathworks.com
SPM12	Wellcome Center for Human Neuroimaging	https://www.fil.ion.ucl.ac.uk/spm/
CAT12 toolbox (v12.7)	Gaser et al.52	http://www.neuro.uni-jena.de/cat/
Vox2Cortex	Bongratz et al.53	https://github.com/ai-med/Vox2Cortex
Elastix	Klein et al.31	https://elastix.dev/
Demons registration	MathWorks	https://www.mathworks.com/help/images/ref/imregdemons.html
ANTs	Avants et al.	https://github.com/ANTsX/ANTs
BrainSuite	Shattuck and Leahy50	http://brainsuite.org
MRIcroGL (v1.2)	NITRC	https://www.nitrc.org/projects/mricrogl
Python 3	Python Software Foundation	https://www.python.org/
PyTorch3D	Meta AI	https://pytorch3d.org/
Our INFREG pipeline	This paper	https://github.com/ifsunrise/brain-inflate-registration

Experimental model and study participant details

This section has been omitted because this study is a computational methodological work that does not involve experimental models, animal subjects, or human participants.

Method details

Datasets and atlas

This study utilized a publicly available dataset (available at https://openneuro.org/datasets/ds004199/) comprising 85 patients with histologically or radiologically confirmed focal FCD II and 85 age-/sex-matched healthy controls, published on the OpenNeuro platform. The cohort included adult epilepsy patients treated at the University Hospital of Bonn (2006–2021), with MRI data anonymized through facial voxel removal and formatted in BIDS-compliant NIFTI files. Imaging protocols included 3D T1-weighted and 3D FLAIR sequences (partial FLAIR available). Two board-certified neuroradiologists performed manual lesion annotation on FLAIR images, ensuring ground truth reliability.⁴⁵ To supplement this primary cohort with preliminary cross-center validation, we collated an additional 36 test cases from two other publicly available epilepsy-related data resources: (1) the EPISURG dataset (available at https://doi.org/10.5522/04/9996158), a clinical collection of T1-weighted MRI from 430 patients who underwent resective brain surgery for refractory epilepsy at the National Hospital for Neurology and Neurosurgery (London, UK) between 1990 and 2018.⁴⁶ This dataset was originally curated to develop and benchmark automatic segmentation algorithms for post-surgical resection cavities, and while it contains preoperative MRI with neuroradiologist-verified lesion labels, the accompanying annotations describe the surgically targeted region rather than providing histopathological FCD classification. (2) The IEEG Portal (ieeg.org), an open international archive of intracranial EEG recordings with matched structural MRI from over 1,200 epilepsy patients.⁴⁷ We selected a subset of cases from this portal for which the provided clinical documentation included imaging-positive FCD-suspected lesions. Neither supplementary source offers the systematic histopathological confirmation of FCD Type II that characterises the ds004199 cohort; however, both contain preoperative MRI from patients who underwent epilepsy surgery, allowing us to compare MAP18 and INFREG feature-map outputs in a cross-center, multi-scanner setting. These cases serve as a preliminary qualitative assessment of algorithmic robustness outside the primary Bonn cohort and do not substitute for formal multi-center clinical validation.

In this research, we used the MNI-152 template (ICBM 2009c Nonlinear Asymmetric),⁴⁸ HCPex atlas,⁴⁹ BCI-DNI_brain atlas,⁵⁰ and brainVISA cortical atlas⁵¹ to process or analyze data. See supplementary for details.

Neuroimaging normalization

Computational Anatomy Toolbox (CAT), an extension to SPM12, was applied to perform regular up-front processing. Initially, structural T1-MRI normalization was performed using the CAT12 toolbox (v12.7)⁵² with a standardized pipeline, including resampling, denoising (a spatially adaptive nonlocal means filtering, SANLM), skull stripping, and bias correction. Then, Nonlinear alignment to MNI-152 space via Geodesic Shooting⁵⁴ or DARTEL⁵⁵ registration, followed by intensity normalization and yielding probabilistic maps of CSF, GM, and WM.

After intensity normalization, GM and WM were mapped to central intensities of 0.66 and 1. To simplify the analysis, the normalized image I_wm (wm∗.nii file) was then transformed to erase CSF, which allows the GM and WM to have a standard mean intensity of 1 and 2:

$$I_{\text{norm}}\left(v\right)=\max \left(\frac{3\ast I_{\text{wm}}\left(v\right)-{\mu }_{\text{CSF}}}{{\mu }_{\text{WM}}-{\mu }_{\text{CSF}}},0\right)$$ (Equation 1)

, where μ_CSF = 1, μ_GM = 2, and μ_WM = 3 denote reference intensities. GM probability GM(v) was derived from I_norm(v).

Rapid cortical surface reconstruction and correction

To overcome computational bottlenecks (e.g., FreeSurfer’s 6–8 h runtime), we implemented Vox2Cortex—a PyTorch3D-optimized cortical surface extraction tool. This framework reconstructs hemisphere-specific pial/WM surfaces (42,016 vertices/hemisphere) in <20 s (RTX 2060 SUPER) with FreeSurfer-equivalent accuracy using convolutional and graph convolutional neural networks.

However, initial reconstructions showed partial WGB misalignment. Based on WGB probability map:

$$WGB\left(v\right)=\frac{|I_{\text{norm}}\left(v\right)-2.5|}{\mathit{max}\left(|I_{\text{norm}}-2.5|\right)}$$ (Equation 2)

, we implemented an iterative optimization protocol that attaches vertices to the WGB following its gradient and applies Taubin smoothing to preserve topology,⁵⁶ reducing surface fit error by 81.2 ± 2.3% (p < 0.001, N = 40):

$$\begin{gathered} v_i^{\left(t+1\right)}=v_i^{\left(t\right)}+\eta \nabla WGB\left(v_i^{\left(t\right)}+\mu \frac{\partial E_{\text{topo}}}{\partial v_i}\right),\text{with} \\ \text{step}\eta =0.5mm \end{gathered}$$ (Equation 3)

This correction process achieved precise WM surface alignment with WGB centers.

Cortical surface registration

Surface preparation

• 1.Map vertex coordinates (XYZ) and max principal curvature (C) to the surface.
• 2.Apply Laplacian smoothing (500 iterations).
• 3.Perform the Iterative Closest Point (ICP) algorithm as initial global alignment.

Mapping surface to image

• 1.Apply spherical conformal mapping, transform hemispheres to a spherical domain.
• 2.Map onto the plane by opening the sphere along the corpus callosum WM boundary via rectangular conformal mapping. This process generated 800 × 400 texture images (2:1 aspect ratio) and achieved superior initial alignment vs. BrainSuite (median S.D.: 0.12 vs. 0.21), as illustrated in Figure 3C.
• 3.Non-rigid Co-registration: Apply Elastix B-spline deformation to the rectangular image (C channel), and transform XYZ channels by deformation to get coordinates of the registered surface.

The combined Vox2cortex and registration workflow completes full-brain processing in 2 min (GPU-accelerated, CPU: AMD Ryzen 9 3900XT 12-Core Processor, GPU: NVIDIA GeForce RTX 2060 SUPER), achieving over 90% temporal efficiency (BrainSuite: >1.5 h) gains over conventional pipelines without compromising anatomical precision.

Volume-inflated registration

Cortical surface extension

We generalize the reconstructed WM surface via uniform-thickness expansion across the cerebral cortex. This model employs a directional distance field to characterize perisurface regions, whose gradient flow field offers two computational advantages: Maintaining equidistant displacement during deformation and preventing self-intersection. Implementation:

• 1.Rasterize the WM surface into a binary mask.
• 2.Compute signed distance field (SDF):

$$\text{SDF}\left(p\right)=\text{sign}\left(p\right)·\underset{q\in WM}{\mathit{min}}\Vert p-q\Vert$$ (Equation 4)

(positive outside WM, negative inside)

• 3.Derive gradient field ∇SDF using 3×3×3 Sobel operators.
• 4.Iteratively extrapolate mesh vertices (42,016 vertices):

$$v^{\left(k+1\right)}=v^{\left(k\right)}+\Delta t·\nabla \text{SDF}\left(v^{\left(k\right)}\right),\Delta t=1mm$$ (Equation 5)

$$\left(\text{Termination}:\Vert v^{\left(k+1\right)}-v^{\left(k\right)}\Vert <0.05mm\text{or}k=10\right)$$

Generates ± 5 mm surface extensions enabling sulcal fundus tracking while preserving gyral geometry (no self-intersection).

Volume inflation/deflation

Define: V_m: Brain mesh vertex coordinates, V_f: Inflated template surface coordinates.

• 1.Inflation field (brain → template):

Compute coordinate mapping via scattered interpolation:

$$P_f=interp\left(V_m,V_f,P_m\right),whereP=X,Y,orZ$$ (Equation 6)

Then, form deformation field: ${\varphi }_{\mathit{INF}}:{\mathbb{R}}^3\to {\mathbb{R}}^3=\left(X_f,Y_f,Z_f\right)$

• 2.Swap V_m↔V_f to get deflation field: ϕ_DEF
• 3.Composite transform:

$$I_{reg}=\left({\varphi }_{\mathit{DEF}}\circ {\varphi }_{\mathit{INF}}\right)\circ I_f$$ (Equation 7)

• 3)Demons Registration Refinement

Applied GPU-accelerated Diffeomorphic Demons for voxel-level alignment, in which intensity gradients between fixed (F) and moving (M) images served as driving force of registration:

$$\mathbf{v}\left(\mathbf{x}\right)=\frac{\left(M\left(\mathbf{x}\right)-F\left(\mathbf{x}\right)\right)\left(\nabla F+\nabla M\right)}{{\Vert \nabla F+\nabla M\Vert }^2+{\alpha }^2{\left(M-F\right)}^2+{\beta }^2\text{tr}\left(J^{T}J\right)},\text{where}\text{Jacobian}\text{matrix}J=\frac{\partial \varphi }{\partial \mathbf{x}}$$ (Equation 8)

Iterations: 20 (balances speed and overfitting; <3s).

Mean templates and curvilinear reformatting visualization

A population-average neuroimaging template was constructed using T1-MRI data from 85 healthy controls (OpenNeuro ds004199). Deformation fields (ϕ: subject → MNI space) were computed using elastix/CAT12 registration for spatial normalization. Traditional voxel-wise mean (Mean(f)) and standard deviation (S.D.(f)) maps were generated from the aligned feature images (F_i(f), where f = feature type, i = subject index) directly.

In contrast, INFREG’s calculation of the mean template is done in the inflation domain:

$$Mean\left(f\right)={\varphi }_{\mathit{DEF},MNI}\circ \left(\frac{1}{N}\sum _{i=1}^N{\varphi }_{\mathit{INF},i}\circ F_i\left(f\right)\right)$$ (Equation 9)

, where ϕ_DEF,MNI is the deflating deformation field of template in MNI space.

Patient feature residuals (resF(f)) were calculated in patient space by subtracting the inverse-warped template mean, masked to the cortex (I_norm>0):

$$resF\left(f\right)=\left(F\left(f\right)-{\varphi }^{-1}\circ \text{Mean}\left(f\right)\right)\ast \left(I_{\text{norm}}>0\right)$$ (Equation 10)

, where ϕ⁻¹(MNI→subject) is the inverse transform of ϕ.

Feature Maps - MAP18 vs. INFREG:

• 1)Extension Map (GM Thickness/Extension):

MAP18: Requires Gaussian smoothing (σ = 6-8 mm FWHM) of the residual to reduce gyral mismatch false positives:

$$eMap=\left({GM}_{\text{patient}}\otimes K_{\sigma }\right)-{\varphi }^{-1}\circ Mean\left({GM}_{\text{normal}}\right),\text{where}\otimes \text{is}\text{convolution}$$ (Equation 11)

INFREG (Smoothing-Free): Direct residual calculation provides clearer visualization:

$$eMap={GM}_{\text{patient}}-{\varphi }^{-1}\circ Mean\left({GM}_{\text{normal}}\right)$$ (Equation 12)

• 2)Junction Map (Gray-White Matter Border Blurring):

MAP18: First, compute a binary WGM image (bWGB):

$$bWGB=abs\left(GM-{Mean}_{GM}\right)<\frac{1}{2}S.D{.}_{GM}$$ (Equation 13)

Then, convolve with a 5³ ones kernel and calculate the smoothed residual:

$$jMap=\left({bWGB}_{patient}\otimes K_{ones}\right)-{\varphi }^{-1}\circ Mean\left({bWGB}_{normal}\right)$$ (Equation 14)

INFREG (Smoothing-Free): Directly calculates the border blurring feature:

$$jMap={WGB}_{\text{patient}}-{\varphi }^{-1}\circ Mean\left({WGB}_{\text{normal}}\right)$$ (Equation 15)

3D visualizations provide increased insight into individual brains and mean templates. Conventional volume rendering of the brain (Figures 1B, 2B, 5, 6, and 10D) was performed using MRIcroGL v1.2 (https://www.nitrc.org/projects/mricrogl/), an open-source, user-intuitive medical image viewer. Curvilinear reformatting provides specialized visualization for deep cortical structures. This technique involves progressively stripping away outer brain layers using predefined masks and render the remaining voxels volumetrically.

Assessment of registration

6 classic registration methods or tools (Affine, Elastix, Demons, BrainSuite, ANTs, and CAT12) participated in registration evaluation to compare with INFREG. MNI templates were registered to 40 FCD patient brains using different methods to test the accuracy of registration at the voxel level. Metrics including Structural similarity (SSIM) and Dice (GM)/Dice (WM).

Given their role as neuroanatomical boundaries defining cortical subdivisions, sulcal-gyral boundaries exhibit fractal complexity and high interindividual variability. We implemented a hierarchical validation strategy:

Group-level sulcal extraction: unpaired group-wise comparisons quantify overall anatomical correspondence (global alignment capacity).

Landmark-specific evaluation: paired matching of evolutionarily conserved primary sulci (e.g., central sulcus, superior temporal sulcus) precisely quantifies local accuracy.

Processing workflow:

• 1.Sulcus/Gyrus Curve Extraction and Assessment.

Sulcus curves: Maximum curvature threshold segmentation on the pial surface, then Laplace smoothing to thin the segmented surface as sulcus curves.

Gyrus curves: Identical process on the white matter surface (higher curvature regions).

Group Alignment assessment: “Mean closest distance” between corresponding curve points across brains. However, it might underestimate true alignment (overestimates distance) due to imperfect sulcal/gyral correspondence.

• 2.Specific Sulcus Extraction.

Labeled sulcus curves were extracted from BrainSuite SVreg dfc files.

Assessment of feature maps for FCD lesions diagnosis and prediction

Two neurologists from Beijing Tsinghua Changgung Hospital and Xuanwu Hospital participated in the manual scanning reading test. Utilizing MRIcroGL software to simultaneously display T1/FLAIR MRI and feature maps. An AutoHotkey script for workflow automation opens two instances of MRIcroGL side by side, presenting the original MRI and the feature maps MRI, respectively, with the “Yoke” option enabled for synchronized viewing. In each case, the timing was stopped from opening the image to determining the correct location of the lesion.

To quantitatively evaluate the effect of single-feature (jMap, eMap of MAP18 or INFREG) in predicting lesion areas, 4 metrics were calculated. For predicted lesion L_pred vs. ground truth L_GT, the threshold value of binarization is selected to maximize the Dice score of random 10 subjects:

$$B_{thresh}=\mathit{arg}\underset{B}{\mathit{min}}\sum _{i=1}^N\frac{2\left|L_{\text{pred},\mathrm{i}}\cap L_{\text{GT},\mathrm{i}}\right|}{\left|L_{\text{pred},\mathrm{i}}\right|+\left|L_{\text{GT},\mathrm{i}}\right|},\text{where}{L}_{\text{pred}}=F_{\text{pred}}>B$$ (Equation 16)

Assessment metrics include dice, sensitivity, and specificity coefficient at the voxel level, and cluster number (connected domain exceeding threshold strength and minimum volume) at the region level. Exponential weighting is used to increase the variance of sensitivity (α = 0.5) and specificity (α = 0.25) between the data for visual contrast.

Quantification and statistical analysis

Statistical analyses were performed using MATLAB (R2023b, MathWorks). All data are presented as mean ± standard deviation (SD) unless otherwise indicated. For group comparisons, pairwise two-tailed t-tests were used, with FDR correction for multiple comparisons where applicable. The exact p values, degrees of freedom, and effect sizes are reported in the figure legends and in Table 1. The number of biological units (n) represents the number of individual subjects in each analysis, as specified in each figure legend. Statistical significance was defined as p < 0.05. Center is presented as mean, and dispersion as SD.

Additional resource

This section is not applicable to this study (no clinical trial was conducted).