Reconstructing the volumetric geometry of the cerebral cortex based on magnetic resonance imaging

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1. Purpose of the article The purpose of this article is to review existing approaches to modeling brain tissue using MRI data and to identify the key criteria for evaluating the reliability of these models. Special attention is paid to international collaborations, their standards, algorithms, and impact on the reproducibility of neuroimaging research. 2. Introduction Understanding the structure of the human brain is key to deciphering the physical basis of cognitive functions, mental disorders, and individual differences. Reconstructing an accurate volumetric geometry of the cortex and white matter tracts is not only a technical challenge but also a foundation for a new neuroscience-quantitative, reproducible, and scalable. Modern methods make it possible to reconstruct the three-dimensional morphology and topology of gray and white matter with high resolution based on MRI data, which is fundamentally important for clinical diagnostics, neuroscience, and cognitive research. To ensure the accuracy and reproducibility of studies, international consortia and national initiatives have been established, which define the standards for processing and analyzing neuroimaging data. © 2026 I. V. Brak, K. G. Leladze, S. M. Islamova, A. A. Kuzminykh, G. A. Kiselev This work is licensed under a Creative Commons “Attribution-NonCommercial 4.0 International” license. 3. International collaborations in neuroimaging In recent years, an increasing number of international organizations and consortia have emerged, focusing on brain research based on morphometric data. Some of the most notable include: o One of the most notable is the ENIGMA Consortium, a collaborative network of researchers that brings together data from 70 scientific institutions around the world. ENIGMA conducts large-scale meta-analyses of neuroimaging and genetic data from over 12,826 participants (and approximately 25,000 participants when including data from the CHARGE consortium for replication). The main areas of the consortium’s work are psychiatric disorders, brain genetics, and neurodevelopment. ENIGMA develops and applies standardized (harmonized) protocols for analyzing MRI data, which allows for consistent measurements and meta-analyses of brain structures in multicenter studies [1]. o The Human Connectome Project (HCP) is an NIH Neuroscience Blueprint-funded interdisciplinary initiative aimed at systematically mapping the macroscopic contours of the human brain and their relationship to behavior in a large population of healthy adults. The project uses multimodal MRI data, including structural MRI, resting-state functional MRI (rfMRI), task-based functional MRI (tfMRI), and diffusion MRI (dMRI). The project develops and optimizes modern algorithms and data processing pipelines for accurate reconstruction of cortical geometry (with a resolution of 0.7 mm isotropically) and white matter tractography [2]. o The Brainnetome Project is a Chinese initiative launched in 2010 by the Ministry of Science and Technology of China. The project aims to create a new functional-anatomical atlas of the brain (brainnetome atlas) based on multimodal MRI data (including structural, diffusion, and functional MRI) and the analysis of structural and functional connectivity patterns. The project develops a highly accurate parcellation of cortical and subcortical regions, taking into account their connections [3, 4]. o CHIMGEN (China Imaging Genetics Project)-a Chinese project that employs structural and functional neuroimaging, genetic analysis, and psychometric testing to build brain models that account for both genetic and environmental factors [5]. o SRPBS (Strategic Research Program for Brain Sciences) is a Japanese national research program that has created one of the largest multicenter databases of multidisciplinary neuroimaging (primarily resting-state fMRI). The program has supported the development of standardized data collection protocols across multiple scanners, as well as methods for harmonizing data between centers to identify biomarkers for mental disorders o COCORO (Cognitive Genetics Collaborative Research Organization)-a Japanese multicenter project focusing on cognitive disorders and the reconstruction of cortical morphology in patients with psychoses, schizophrenia, and bipolar disorder [6], and bipolar disorder [7]. These projects not only define standards for data acquisition and processing but also provide accessible databases, analysis tools, and software environments (e.g., FreeSurfer [8], FSL, BrainSuite), enabling researchers worldwide to reproduce reconstructions and conduct comparative studies. However, despite these achievements, a critical evaluation of the employed methodologies remains essential-from voxel- and surface-based morphometry to more complex probabilistic models based on machine learning and deep learning. Even minor artifacts or preprocessing biases can affect the topology of the reconstructed model, and the use of AI may amplify systematic errors. Therefore, the accuracy of structural reconstruction becomes a critical factor in establishing trust in the conclusions of neuroimaging analysis. 4. Computational framework for cortical reconstruction The technical framework for reconstructing and analyzing the volumetric geometry of the cerebral cortex involves a sophisticated computational pipeline. This study utilizes high-precision software environments that integrate statistical computing with differential geometry. The primary tools are detailed below: o Computational Anatomy Toolbox (CAT12): As an advanced extension of the SPM12 (Statistical Parametric Mapping) package within the MATLAB environment, CAT12 provides a streamlined pipeline for both Voxel-Based Morphometry (VBM) and Surface-Based Morphometry (SBM). It employs an Adaptive Maximum A Posterior (AMAP) segmentation approach and a Partial Volume Estimation (PVE) model to account for mixed tissue types. For surface reconstruction, CAT12 utilizes a projection-based thickness (PBT) method, which allows for accurate cortical thickness estimation even in regions with high curvature without the need for manual edits. o FreeSurfer Suite (v7.4/8.0): An essential tool for creating topologically correct 3D meshes of the brain. The pipeline involves intensity normalization, skull stripping, and the generation of the white matter (inner) and pial (outer) surfaces. FreeSurfer’s unique strength lies in its spherical registration system, which aligns cortical folding patterns to a standardized atlas (fsaverage), enabling high-resolution group-level vertex-wise analysis. o Standardized Neuroanatomical Templates: Spatial normalization and anatomical localization are anchored to the MNI152 (Montreal Neurological Institute) template. For surface-based analysis, the Desikan-Killiany (DK) and Destrieux atlases are utilized to automatically parcellate the cortex into functionally and anatomically distinct regions of interest (ROIs). o Additional Processing Libraries: The integration of FSL (FMRIB Software Library) for brain extraction (BET) and ANTs (Advanced Normalization Tools) for non-linear registration ensures robust preprocessing and minimizes spatial distortion across diverse MRI datasets. o TRACULA (TRActs Constrained by UnderLying Anatomy): Integrated within the FreeSurfer environment, this tool is utilized for the automated reconstruction of major white matter pathways using a global probabilistic tractography approach, which accounts for anatomical priors to improve the reliability of connectivity models. 5. Morphometric analysis of the human brain Brain morphometry refers to a set of quantitative methods aimed at measuring the geometric characteristics of brain structures based on neuroimaging, most commonly magnetic resonance imaging (MRI). Unlike visual assessment, the morphometric approach enables numerical evaluation of volume [9-12], Thickness [9-13], surface area [10-12, 14, 15], and curvature [10-13] of various brain regions, as well as their spatial arrangement (topography) [11, 14, 16, 17] and symmetry [11, 14, 15, 18]. These metrics [19] become particularly important for identifying both individual and group-level differences-within the normative range and in neurodegenerative and neuropsychiatric conditions, such as Alzheimer’s disease [20], depressive [2] and schizotypal disorders. One of the key objectives of morphometry is the construction of anatomically accurate, reproducible, and comparable brain models suitable for both fundamental research and clinical diagnostics. Differences in the morphology of the cortex, subcortical structures, and white matter tracts can reflect a wide spectrum of cognitive, behavioral, and pathological characteristics. For example, the works by Sao et al. [21] and Fischl et al. [13] clearly demonstrate how variations in cortical thickness- both global and local patterns-can predict cognitive status and disease; and study [22] shows that the trajectory of cortical thickness changes correlates with cognitive abilities (memory, attention, executive functions). In [23], it is shown that reductions in gray matter volume in the caudate nucleus and prefrontal cortex in children and adolescents negatively affect executive functioning and cognitive control, which complicates academic performance. Beyond its diagnostic utility, morphometry plays an important role in understanding the principles of brain organization. When combined with behavioral, genetic, and psychometric data, it enables the identification of links between brain anatomy and function, between biology and psyche. This is especially relevant in the era of big data, where current scientific organizations and consortia are working to identify reproducible patterns of brain organization across thousands and tens of thousands of subjects, developing new-including stochastic-methods for their detection [24-27]. Moreover, morphometric techniques form the foundation of modern approaches to building digital twins of the brain - high-precision models that are becoming increasingly relevant with the integration of artificial intelligence technologies into medicine. The reliability of such models depends on the accuracy of morphometric analysis, the quality of input data, and the correctness of the algorithms used. Therefore, the development and evaluation of morphometric methods is a critical task not only for neuroscience but also for the entire biomedical technology industry [28, 29]. This article reviews the principal approaches to cortical brain morphometry: voxel-based and surface-based, as well as the data quality criteria and processing pipelines that determine the reliability of cortical reconstruction results. 6. MRI-based morphometric approaches to brain reconstruction The standard approaches in morphometric analysis are voxel-based and surface-based morphometry. Both allow for the assessment of structural brain changes. Voxel-based morphometry analyzes tissue volume at the voxel level, while surface-based morphometry focuses on cortical surface characteristics such as thickness and curvature. Both methods operate within a single spatial scale and do not detect patterns emerging at different levels of organization, which limits their analytical power [21]. 1. Voxel-based morphometry Voxel-Based Morphometry (VBM) is a technique for quantitatively assessing anatomical differences in the brain by analyzing brain tissue structure directly in the volume of three-dimensional MRI data at the voxel level. The general VBM processing pipeline includes the following steps: 1. The VBM workflow begins with spatial normalization, in which individual MRI scans are transformed into a standard anatomical space [14]. This is achieved using non-linear registration algorithms based on image intensities and anatomical templates, allowing for the alignment of corresponding brain regions across individuals. 2. At the next stage, tissue segmentation is performed, dividing brain tissue into major classes: gray matter, white matter, and cerebrospinal fluid. This step employs classification algorithms, most commonly based on statistical modeling of voxel intensity values and their spatial characteristics. 3. The segmented images then undergo spatial smoothing, which increases the sensitivity of statistical analysis by reducing inter-subject variability in the localization of specific structures. 4. In the final step, statistical analysis is carried out to compare the volumes or densities of gray matter at the voxel level either between subject groups or in relation to a continuous variable. The output is a statistical map highlighting brain regions with significant structural differences. Thus, the VBM pipeline enables automated and objective comparison of anatomical features directly from 3D MRI data, bypassing the surface reconstruction stage that is characteristic of surface-based morphometry. 2. Surface-based morphometry Surface-Based Morphometry (SBM) is an MRI analysis approach focused on the geometry and metrics of the cortical surface. There are several key variations and techniques implementing SBM, differing in analytical goals, types of metrics, and underlying algorithms [30]. SBM is frequently employed for morphometric reconstruction. For instance, study [14] describes the use of this approach for automated segmentation of the cerebral cortex based on structural magnetic resonance imaging data. The input consists of high-quality T1-weighted brain MRI scans, which are first subjected to artifact correction, intensity normalization, skull stripping, and generation of a three-dimensional model of the gray-white matter boundary. In SBM, cortical surface reconstruction is performed such that each MRI volume is represented as an inflated (“unfolded”) surface of the brain, allowing access to structures typically hidden within sulci and gyri. A critical requirement for the input images is high spatial resolution (approximately 1 mm voxel size), minimal motion artifacts, and clear contrast between gray and white matter. Cortical surfaces are matched to one another via mapping to a spherical template [31], followed by automatic registration based on curvature and the geometry of sulcal and gyral patterns [32]. The outputs of the SBM approach are anatomically accurate maps delineating cortical regions of interest, each corresponding to specific gyri or sulci. In [14], 34 such regions were automatically labeled in each hemisphere. These maps exhibit high precision and reproducibility: the average spatial discrepancy between automated and manual labeling does not exceed one millimeter, and the intraclass correlation coefficient (ICC) is approximately 0.835, indicating strong agreement and validity of the developed method. These results highlight the effectiveness of SBM in both research and clinical contexts that require precise and reproducible anatomical localization on the cortical surface. Like VBM, SBM is highly dependent on the quality of the input data. Study [10] explores surface- based morphometry in depth, with an emphasis on cortical surface reconstruction and cortical thickness estimation. A central focus is the correction of topological defects that arise during cortical surface reconstruction from MRI data. As in [14], the input consists of T1-weighted brain MR images, which must meet high spatial resolution requirements and demonstrate stable intensity characteristics. However, the method is also capable of adapting to intensity variations caused by histological differences and scanner artifacts. A notable innovation described in the study is the approach to correcting surface topology. Rather than attempting to construct a surface with an assumed correct topology from the outset, the authors begin with a surface that may contain defects and iteratively transform it into a spherical shape. This process enables identification of regions with topological errors, which are then locally corrected. This technique significantly improves the geometric accuracy of the reconstructed model and reduces manual labor, thereby enhancing the automation of the surface reconstruction process and making it suitable for large-scale clinical and research studies [33]. The output of this method is an accurate model of the cortical surfaces, including both the inner (gray-white matter boundary) and outer (pial) surfaces. A key outcome is the high accuracy of cortical thickness measurements-reaching a resolution of less than a quarter millimeter-confirmed by multiple validation studies, including comparison with histological data. This enables the detection of morphometric changes associated with various pathological conditions, age-related differences, or neuropsychological traits with exceptionally high sensitivity and reproducibility. SBM Results Enable, in Particular, the following: § Analyzing language lateralization and cortical asymmetry by calculating cortical thickness and other morphometric parameters in regions associated with language function. The resulting data are used to assess structural asymmetry of the brain, enabling precise identification of interhemispheric differences in cortical thickness in language-related areas [18]. § Studying the relationship between cortical folding and the location of cytoarchitectonic fields (Brodmann areas). The authors of [16] use SBM to construct spatial models of cortical surfaces onto which boundaries of cytoarchitectonic fields, derived from postmortem histological studies, are projected. A key finding of the study is that the cortical surface-its folds and gyri-can serve as reliable predictors of the location of different cytoarchitectonic fields. Thus, a general workflow (processing pipeline) of SBM can be outlined as follows: 3. The input data consist of T1-weighted magnetic resonance images (MRI) of the human brain. During preprocessing, correction of artifacts and distortions is performed, along with intensity inhomogeneity normalization and removal of non-relevant structures such as the skull and meninges, in order to isolate the gray and white matter regions [10, 14]. Figure 1. The process of transforming brain geometry into a spherical representation using the inflation procedure (source: compiled by the authors). 4. At the next stage, segmentation and reconstruction of the inner cortical surface are carried out-this surface represents the gray-white matter boundary. It is reconstructed first, as it is the most clearly distinguishable structure in MRI due to the high contrast between gray and white matter and the absence of topological ambiguities that are characteristic of the outer (pial) surface. The reconstruction process employs a method of adaptive surface deformation, in which the surface is gradually fitted to the local intensities of gray and white matter [17]. This method involves modifying the geometry by optimizing the following functionals: 1. An energy functional is employed to minimize metric distortions (distance-based metric). Specifically, the mean squared error functional Jd is used: 1 V 1 t 0 2 Jd = V ∑ ∑ 2 (din - din) , i=1 n∈N(i) in in where V - amount of vertices, dt - distance between vertices at time t, d0 - initial distance between vertices, and N (i) - neighborhood of vertex i. 2. The area-oriented energy functional Ja is used to minimize surface area distortions during surface unfolding: 1 T 1 t t 0 2 T 2 Ja = ∑ P(Ai ) (Ai - Ai ) , i=1 where T is the number of triangles in the surface mesh, At is the area of triangle i at time t, i A0 is the initial (reference) area of triangle i, and P(At At < 0) is a penalty function i i ) = ( i that activates when the triangle area becomes negative, which indicates the presence of surface folding. 3. The total energy functional combines both the metric distortion and surface area preservation terms: J = d ⋅ Jd + a ⋅ Ja, where d and a are weights that determine the contribution of each component. 5. Next, topological correction of the surface is performed, which constitutes a critical step in the SBM processing pipeline. The initially reconstructed surface may contain topological defects, such as “bridges” between gyri or holes within sulcal surfaces. A specialized approach is applied in which the surface is mapped onto a spherical model [17], enabling straightforward detection and localization of such topological errors. The mapping can be performed either by inflating the cortical surface until it approximates a sphere, or conversely, by deflating the spherical model until it conforms to the pial surface [34, 35]. The identified defects are then corrected using local algorithms that take into account the intensity profile of the original MRI image, allowing for the restoration of correct surface topology without the loss of meaningful cortical regions [36]. Figure 2. Example of SBM application in the analysis of individual variability in cortical structures in patients with major depressive disorder: lateral and medial views (a); axial and coronal views (b) (source: compiled by the authors). 6. Once a topologically correct inner surface of the brain has been obtained, the outer (pial) surface - representing the external boundary of the gray matter-is reconstructed. This is achieved by progressively deforming the inner surface outward until it reaches the interface between gray matter and cerebrospinal fluid, again using the adaptive algorithms described above, which account for both signal intensity variations and cortical folding curvature. As a result of this stage, two mutually aligned surfaces (the gray-white matter boundary and the pial surface) are formed, enabling precise computation of cortical thickness at any point on the cortical surface [15, 16]. 7. The final stage of the SBM pipeline is the morphometric analysis. The reconstructed surfaces are registered and mapped into a standard anatomical space, allowing for statistical comparisons across different subjects and groups. At this stage, the following parameters are computed using numerical methods [13]: § Cortical thickness is defined as the shortest distance between the white matter surface and the pial surface. For each point p on the cortical surface, its local thickness is calculated as T(p) = dist(S, Spial). § Cortical volume is computed as the surface integral of cortical thickness over the pial surface: V = ∫ T(p) dS. § Surface area is calculated as the surface integral over the pial surface: A = ∫ dS. The accuracy of this method reaches a level of less than a quarter of a millimeter, ensuring high reproducibility and sensitivity to changes that may reflect age-related, pathological, or neuropsychological characteristics of the cerebral cortex. Below are the main parameters and metrics analyzed using SBM: § Cortical thickness-the most commonly used SBM parameter, calculated as the distance between the gray-white and gray-CSF boundaries of the cortex [37]. It is used, for example, to study age- related changes, neurodegenerative diseases (including Alzheimer’s disease), and neuroplasticity. § Surface area-reflects both the developmental and individual characteristics of the brain structure. Figure 3. Example of SBM application for analyzing individual variability in subcortical structures of the cerebral hemispheres in patients with major depressive disorder (source: compiled by the authors). § Gyrification index [6]-quantifies the degree of cortical folding and is calculated as the ratio of the total pial (folded) surface area to the area of its convex hull: GI = A [38]. This index is Aconv particularly relevant in studies of brain development and psychiatric disorders [39]. § Curvature-describes the shape of the cortex, including convexity and concavity. In [13], curvature is derived directly from the second derivative of the surface, which can be obtained using numerical methods [40]. Several variants of SBM can be distinguished, differing in the operations performed during morphometric analysis: § Classical approach [10]. Utilizes segmentation of T1-weighted images to build individual surface models; suitable for evaluating cortical thickness, surface area, and curvature. § Statistical SBM with nonparametric testing [41]. Employs analysis of displacement vector fields along with permutation testing to assess the significance of observed changes. § Multimodal SBM [39]. Integrates data from functional MRI, diffusion MRI, or metabolic imaging to enable a more comprehensive understanding of structure-function relationships. § Morphometry of subcortical surfaces [42]. Applied to structures such as the hippocampus and amygdala, using 3D surface modeling and mesh node correspondence. 3. Comparison of VBM and SBM The review article [43] discusses the limitations of Voxel-Based Morphometry (VBM) in detecting distributed brain changes due to its univariate analysis framework. The authors propose the use of multivariate models, such as deformation-based morphometry, to better understand inter-regional dependencies within the brain. The article also outlines the core characteristics of VBM, emphasizing its nature as a univariate approach that applies statistical parametric mapping to spatially normalized brain images. VBM is designed to detect region-specific structural differences in gray matter after spatial normalization, segmentation, and smoothing. Importantly, the authors note that VBM is not intended for analyzing dependencies between different brain regions. Rather, it identifies local differences in gray matter that are independent of changes in other areas. They also stress that VBM does not replace shape analysis or provide detailed volumetric evaluation of well-defined anatomical structures. In conclusion, the effectiveness of VBM in neuroanatomical research is acknowledged, but the authors argue that analyzing complex spatial interactions requires multivariate approaches. Surface-Based Morphometry (SBM), on the other hand, offers several substantial advantages over VBM, especially in the context of cortical analysis [37, 43-45]: § SBM accounts for the natural geometry and topology of the cortex, enabling more precise and biologically meaningful measurements of thickness, surface area, and curvature. In contrast, VBM operates in a volumetric space without respecting the specific characteristics of sulci and gyri, which reduces sensitivity to subtle local changes in cortical structure. § SBM provides significantly better spatial registration of anatomical structures across subjects. This is achieved by projecting cortical surfaces onto a spherical model and precisely aligning folds and gyri, thereby minimizing inter-individual variability in cortical folding patterns. VBM, by contrast, relies on less sensitive normalization methods that are not well-suited for fine-scale cortical geometry, often resulting in suboptimal alignment between subjects. § SBM exhibits higher sensitivity to small-scale changes in cortical thickness associated with both normal and pathological states. Since SBM enables direct measurement of cortical thickness as the distance between the pial surface and the gray-white boundary, it achieves submillimeter accuracy that VBM cannot provide. Thus, VBM does not utilize information about the specific shape of brain structures-only about their density and volume. It may be susceptible to errors from inaccurate normalization or segmentation and relies on mass univariate testing that ignores inter-regional dependencies [46-48]. In contrast, SBM, due to its superior handling of cortical topology and geometry, more precise spatial registration, and greater sensitivity to subtle morphometric changes, is considered the preferred method for detailed analysis of cortical anatomy and is widely used in tools such as FreeSurfer [10]. Additionally, in a study on traumatic brain injury, SBM demonstrated greater sensitivity than VBM in detecting structural changes associated with neuropsychological test performance. This suggests that SBM may be a more accurate approach for correlating brain anatomy with cognitive functions [9]. 4. Accuracy of VBM and SBM approaches Accuracy is a quantitative measure of how well a given approach can detect true morphometric differences between groups or conditions (e.g., patients vs. healthy controls). Several key metrics influence and define accuracy: § Sensitivity - probability of a type I error (false positive) § Specificity - probability of a type II error (false negative) § Reproducibility - stability of results across repeated scans § Spatial accuracy - how precisely the method localizes the effect The authors of study [9] claim that SBM has greater sensitivity to cortical changes. In a study involving patients with traumatic brain injury, only SBM was able to detect significant correlations between cortical thickness and cognitive test performance, while VBM did not. This indicates a higher sensitivity of SBM in cortical structure analysis. Furthermore, study [43] demonstrated that the accuracy of VBM is highly dependent on the quality of spatial normalization and smoothing [49]. Errors at these stages can blur local changes and reduce spatial precision, which limits the reliability of VBM-based findings. Lastly, the review study [39] shows that SBM is more accurate in measuring cortical thickness and gyrification, whereas VBM may be more effective for assessing subcortical and global volumetric changes. The authors conclude that the best practice is to use both methods in combination for a comprehensive assessment. A comparison table summarizing the analytic properties of the reviewed morphometric methods is presented below. Comparative analysis of Voxel-Based Morphometry (VBM) and Surface-Based Morphometry (SBM) Table 1 Characteristic Voxel-Based Morphometry (VBM) Surface-Based Morphometry (SBM) Analysis space Volume (3D voxels) Surface (vertices, polygons) Measured parameters Density, gray matter volume Thickness, area, curvature, gyrification Accuracy Lower for cortical analysis, sensitive to registration Application Assessment of overall volumetric changes Higher, especially for submillimeter cortical thickness Detailed cortical analysis and folding patterns Software tools SPM, FSL, CAT12 (VBM module) FreeSurfer, CAT12 (SBM module), BrainVISA Robustness to distortions Lower due to nonlinear normalization Higher, performed on native cortical geometry Computational load Relatively Lower Higher; requires intensive surface reconstruction Anatomical accuracy Limited (surface features not accounted for) High (direct vertex-wise analysis) Sensitivity Lower after Gaussian smoothing Higher, uses surface-constrained smoothing Best use case Global atrophy, subcortical structures Subtle cortical changes, neurodevelopment 7. Quality check and reliability of structural reconstruction To ensure the accuracy and reproducibility of volumetric and surface-based models, a rigorous multi- stage Quality Check (QC) protocol is essential. Structural reconstruction is highly sensitive to image artifacts, and even minor preprocessing biases can lead to significant errors in cortical thickness or volume estimation. The QC framework implemented in modern morphometric studies consists of the following key components: 0. Raw data screening and artifact detection The initial stage involves a systematic evaluation of T1-weighted MRI scans before any automated processing. This includes: § Motion Artifacts: Identifying “ringing” or “ghosting” effects caused by subject movement, which can blur the gray-white matter boundary. § Signal-to-Noise Ratio (SNR): Calculating the SNR and Contrast-to-Noise Ratio (CNR) to ensure sufficient image clarity for tissue segmentation. § Field Inhomogeneity: Correcting for B1 magnetic field non-uniformity (bias field), which can cause intensity variations across the brain. 1. Automated quality indices (QA metrics) Modern tools like CAT12 provide objective numerical indices to evaluate reconstruction quality: § Weighted Average Image Quality Rating (IQR): A composite score based on noise, resolution, and inhomogeneity. Reconstructions with an IQR below “Satisfactory” (typically < 70%) are excluded from the analysis. § Euler Number: In surface-based morphometry, the Euler number is used as a quantitative measure of topological complexity. A lower Euler number indicates more topological defects (holes or bridges) in the reconstructed cortical mesh. 2. Visual inspection and boundary verification Despite automated metrics, visual inspection remains the “gold standard”. This process involves: § Segmentation Accuracy: Verifying that the automated tool correctly distinguished between gray matter, white matter, and cerebrospinal fluid (CSF). § Pial and White Matter Surface Alignment: Ensuring that the reconstructed surfaces accurately follow the anatomical boundaries of the cortex. Particular attention is paid to the temporal lobes and areas near the dural sinuses, where segmentation errors are most frequent. 3. Topological correction and statistical robustness To maintain the integrity of the 3D model, any detected topological defects must be repaired. Spherical inflation and deflation techniques are used to ensure the mesh is a manifold. Finally, the reliability of the measurements is assessed using the Intraclass Correlation Coefficient (ICC), ensuring that the morphometric markers are stable across repeated scans or different processing sessions. By implementing this comprehensive QC protocol, researchers can minimize the risk of “false positive” structural changes and ensure that the reconstructed geometry reflects true biological variation rather than technical noise. 8. Multiscale approach The study by [21] introduces a method implementing tensor-based surface morphometry (TBSM), a modern approach for analyzing structural changes in the cerebral cortex. TBSM is based on concepts from differential geometry and tensor calculus, allowing for direct examination of geometric changes in the cortical surface while avoiding distortions inherent in traditional methods that require surface flattening. The TBSM processing pipeline begins with automatic segmentation of cortical surfaces from T1- weighted MRI scans, which are pre-classified into gray matter, white matter, and cerebrospinal fluid. These surfaces are then modeled as continuous triangular meshes, followed by a mathematical description of surface deformation over time. A key innovation is the use of tensor geometry, which enables the computation of local changes in surface area, cortical thickness, and curvature. A core advantage of TBSM is its ability to measure local changes in morphometric parameters directly on cortical surfaces with high sensitivity. The approach also incorporates diffusion-based smoothing on cortical surfaces, which improves the signal-to-noise ratio and enhances the accuracy of statistical inference. As a result, TBSM enables precise localization of areas with significant cortical thickness increases or decreases, as well as changes in curvature and surface area-particularly relevant for studies of brain development and neurodegenerative diseases. Tensor-based surface morphometry (TBSM) differs from traditional surface-based morphometry (SBM) in both its mathematical framework and data analysis methods. While SBM uses classical geometry to reconstruct the cortical surface and evaluate parameters such as thickness, area, and curvature, TBSM relies on more advanced differential and tensor geometry. This allows deformations to be described using tensors, providing greater precision in investigating both local and global changes in brain shape. Moreover, TBSM avoids distortions typical of traditional methods: in SBM, complex cortical structures are often projected onto simplified forms (e.g., a sphere), which can distort geometric properties [50]. In contrast, TBSM analyzes data directly on the original cortical surface, without simplification, reducing error and enabling more accurate registration. An additional advantage of TBSM is its heightened sensitivity to subtle morphometric changes. Thanks to diffusion-based smoothing adapted to curved surfaces, this method allows for more precise localization and quantitative assessment of even small changes in cortical shape and thickness- capabilities that are unattainable with standard smoothing in SBM. Finally, the tensor-based framework of TBSM enables the integration of multiple morphometric characteristics-cortical thickness, curvature, surface area, and volume-into a single analytical model. In traditional SBM, these parameters are typically analyzed separately, which limits the comprehensiveness of the analysis. Thus, TBSM represents a more advanced analytical method, providing more precise and reliable characterization of structural changes in the cerebral cortex by employing a tensor-based approach and preserving the natural geometry of cortical surfaces. 9. Results The comparative analysis presented in this review demonstrates that Surface-Based Morphometry (SBM) consistently outperforms Voxel-Based Morphometry (VBM) in the context of cortical structure analysis. SBM achieves submillimeter accuracy in cortical thickness estimation (less than 0.25 mm), whereas VBM is limited by its dependence on spatial normalization and Gaussian smoothing, which reduce spatial precision. As summarized in Table 1, SBM provides higher sensitivity, better anatomical accuracy, and more robust handling of cortical topology compared to VBM. Furthermore, the emerging Tensor-Based Surface Morphometry (TBSM) approach addresses key limitations of classical SBM by avoiding geometric distortions introduced during spherical projection. TBSM enables the integration of multiple morphometric parameters - cortical thickness, curvature, surface area, and volume - into a unified analytical framework, offering enhanced sensitivity to subtle morphometric changes. The analysis of international collaborations (ENIGMA, HCP, Brainnetome, CHIMGEN, SRPBS, COCORO) reveals that standardized data acquisition protocols and harmonized processing pipelines are essential for ensuring the reproducibility of morphometric findings across multicenter studies. The Quality Check framework, encompassing raw data screening, automated quality indices, visual inspection, and topological correction, provides a necessary methodological foundation for reliable structural reconstruction. 10. Discussion The findings of this review highlight several important considerations for the field of brain morphometry. While VBM remains a computationally efficient tool suitable for rapid assessment of global volumetric changes and subcortical structures, its univariate nature and sensitivity to registration errors limit its applicability for fine-grained cortical analysis. In contrast, SBM, by respecting the natural geometry and topology of the cortex, provides more biologically meaningful measurements. A key observation is that no single morphometric approach is universally optimal. As demonstrated by the reviewed studies, VBM may be more effective for assessing subcortical and global volumetric changes, while SBM excels in detecting subtle cortical thickness variations associated with neurodegenerative and neuropsychiatric conditions. The best practice, as suggested by the literature, is to employ both methods in combination for a comprehensive assessment. The TBSM approach represents a significant methodological advancement. By operating directly on the original cortical surface without simplification to spherical models, it reduces geometric distortion and enables more precise registration. However, TBSM is still an emerging technique, and further validation across diverse datasets and clinical populations is needed to establish its reliability for routine use. The importance of rigorous quality control cannot be overstated. Even minor preprocessing biases or image artifacts can propagate through the reconstruction pipeline and lead to erroneous morphometric conclusions. The multi-stage QC protocol described in this review - from raw data screening to topological correction - should be considered a mandatory component of any morphometric study. 11. Conclusion and future work The main approaches to reconstructing the volumetric geometry of the cerebral cortex based on magnetic resonance imaging have been reviewed, focusing on the comparative analysis of voxel- based morphometry (VBM) and surface-based morphometry (SBM). It has been shown that while VBM remains a computationally efficient tool for rapid assessment of global volumetric changes, it is inherently limited by its univariate nature and dependence on spatial normalization, which often leads to the underestimation of subtle morphological differences. In contrast, SBM provides more accurate and anatomically meaningful results by considering the natural topology and geometry of cortical structures. By directly measuring parameters such as cortical thickness, surface area, and gyrification index, SBM achieves submillimeter precision and increased sensitivity to neurodegenerative and neuropsychiatric changes. Furthermore, the emerging tensor-based surface morphometry (TBSM) approach offers significant prospects for mitigating geometric distortions inherent in traditional methods, allowing for the integration of various morphometric metrics into a unified, multiscale analytical process where cortical deformations are treated as interconnected biological events. The current review highlights that the transition from traditional voxel-based analysis to surface- oriented and multiscale frameworks is a necessary step for high-precision neuroimaging. However, the field is rapidly moving beyond pure structural metrics toward integrated platforms that combine automated reconstruction with clinical intervention planning. Our future research will be centered around the development and implementation of the NextBrain ecosystem, which aims to bridge the gap between theoretical morphometry and practical neurosurgery. In the upcoming stages of this research, we plan to conduct a comprehensive analysis of automated methods for reconstructing brain white matter tracts, including TRACULA, AFQ, and TractSeg. Particular attention will be given to probabilistic tractography constrained by anatomical priors, enabling the simultaneous reconstruction of the cortical mantle and the underlying white matter connectivity to provide a complete structural connectome. To ensure the reliability of these complex models, the study will address critical preprocessing steps for diffusion-weighted imaging (DWI), such as motion artifact correction, eddy current compensation, and both affine and non-linear transformations. These technical refinements will allow for the formulation of standardized quality criteria for input data, which is essential for the clinical translation of morphometric markers. A pivotal direction in the NextBrain project is the development of specialized algorithms for anatomical tumor parcellation and mapping. By utilizing the geometric constraints of the reconstructed cortex, we plan to implement automated segmentation of oncological lesions and analyze their spatial relationship with functionally active cortical zones. This level of detail is crucial for personalized medicine, where the anatomical labeling of a tumor is directly linked to its impact on the surrounding neural architecture. Furthermore, the volumetric models generated via the NextBrain atlas will serve as the technical foundation for stereotactic and functional neurosurgery. By providing high-resolution 3D reconstructions of the pial surface and subcortical structures, the system will enable more accurate trajectory calculation and minimize the risk of damaging eloquent brain areas during invasive procedures. The experimental part of our future work will involve the reconstruction of structural models across multiple international datasets, followed by automatic validation and comparative analysis of white matter tracts. This rigorous validation process will help identify the most accurate and reproducible solutions suitable for real-time fusion with intraoperative data, creating a dynamic navigation environment for neurosurgeons. In conclusion, the advancement of tools like NextBrain signifies a fundamental shift toward personalized neuroanatomy. In this emerging paradigm, 3D reconstruction is not merely a research metric but a vital component of clinical decision-making and surgical precision. By integrating multiscale morphometry with tractography and oncological mapping, we move closer to a comprehensive digital model of the human brain that can directly inform and improve patient outcomes in complex neurological conditions.

About the authors

Ivan V. Brak

RUDN University; Privolzhsky Research Medical University

Email: i.v.brak@gmail.com
ORCID iD: 0000-0002-5146-0096
Scopus Author ID: 24461311200
ResearcherId: AAM-4659-2021

Candidate of Biology Sciences, Senior Lecturer at the Department of Mathematical Modeling and Artificial Intelligence of RUDN University; Researcher of Privolzhsky Research Medical University

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation; 178T Gagarina Ave, Nizhny Novgorod, 603107, Russian Federation

Konstantin G. Leladze

RUDN University

Email: 1142230347@pfur.ru
Student of Department of Mathematical Modeling and Artificial Intelligence of RUDN University 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Saniya M. Islamova

RUDN University

Email: 1132249576@rudn.ru
ORCID iD: 0009-0007-6953-5731

Student of Department of Mathematical Modeling and Artificial Intelligence of RUDN University

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Alexey A. Kuzminykh

Novosibirsk State University

Email: a.kuzminykh@g.nsu.ru
ORCID iD: 0009-0008-0642-0328

Student, Novosibirsk State University

1 Pirogova St, Novosibirsk, 630090, Russian Federation

Gleb A. Kiselev

RUDN University

Author for correspondence.
Email: kiselev@isa.ru
ORCID iD: 0000-0001-9231-8662
Scopus Author ID: 57195683637
ResearcherId: Y-6971-2018

Candidate of Technical Sciences, Senior Lecturer at the Department of Mathematical Modeling and Artificial Intelligence of RUDN University; Researcher of Federal Research Center ``Computer Science and Control'' of the Russian Academy of Sciences

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

References

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