Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)5291410.22363/2658-4670-2026-34-3-298-315ROHGCAComputer ScienceИнформатика и вычислительная техникаResearch ArticleReconstructing the volumetric geometry of the cerebral cortex based on magnetic resonance imagingВосстановление объёмной геометрии коры головного мозга по результатам магнитно резонансной томографииhttps://orcid.org/0000-0002-5146-009624461311200AAM-4659-2021BrakIvan V.БракИ. В.

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

i.v.brak@gmail.comLeladzeKonstantin G.ЛеладзеК. Г.Student of Department of Mathematical Modeling and Artificial Intelligence of RUDN University1142230347@pfur.ruhttps://orcid.org/0009-0007-6953-5731IslamovaSaniya M.ИсламоваС. М.

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

1132249576@rudn.ruhttps://orcid.org/0009-0008-0642-0328KuzminykhAlexey A.КузьминыхА. А.

Student, Novosibirsk State University

a.kuzminykh@g.nsu.ruhttps://orcid.org/0000-0001-9231-866257195683637Y-6971-2018KiselevGleb A.КиселёвГ. А.

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

kiselev@isa.ruRUDN UniversityРоссийский университет дружбы народовPrivolzhsky Research Medical UniversityПриволжский исследовательский медицинский университетNovosibirsk State UniversityНовосибирский государственный университет15102026343VOL 34, NO3 (2026)ТОМ 34, №3 (2026)29831519102026Copyright ©; 2026, Brak I.V., Leladze K.G., Islamova S.M., Kuzminykh A.A., Kiselev G.A.Copyright ©; 2026, Брак И.В., Леладзе К.Г., Исламова С.М., Кузьминых А.А., Киселёв Г.А.2026Brak I.V., Leladze K.G., Islamova S.M., Kuzminykh A.A., Kiselev G.A.Брак И.В., Леладзе К.Г., Исламова С.М., Кузьминых А.А., Киселёв Г.А.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/52914

This review article focuses on the analysis of approaches for reconstructing the volumetric geometry of the cerebral cortex and white matter tracts based on magnetic resonance imaging (MRI) data. Particular attention is given to voxel-based morphometry (VBM) and surface-based morphometry (SBM)-two key methodologies for the quantitative analysis of brain structure. The algorithmic principles of each method are considered, along with their advantages, limitations, and metric characteristics, including cortical thickness, surface area, and gyrification index. A separate focus is placed on comparing the sensitivity and accuracy of VBM and SBM in identifying morphological changes related to cognitive and neuropsychiatric traits. Additionally, the article discusses the promising tensor-based surface morphometry (TBSM), which is based on differential geometry methods and provides high spatial resolution without topological distortion. This work emphasizes the importance of accurate and reproducible structural brain reconstruction in the context of biomedical technology and neuroscience development.

Настоящая обзорная статья посвящена анализу подходов к восстановлению объёмной геометрии коры головного мозга и проводящих путей на основе данных магнитно-резонансной томографии. Основное внимание уделено воксельно-ориентированной (VBM) и поверхностно-ориентированной (SBM) морфометрии - двум ключевым направлениям в количественном анализе структуры мозга. Рассматриваются алгоритмические принципы каждого подхода, их достоинства, ограничения, а также метрические характеристики, включая толщину коры, площадь поверхности и индекс гирификации. Отдельный акцент сделан на сравнении чувствительности и точности VBM и SBM в выявлении морфологических изменений, связанных с когнитивными и нейропсихическими особенностями. Также рассматривается перспективный тензорно-ориентированный подход (TBSM), опирающийся на методы дифференциальной геометрии и обеспечивающий высокую разрешающую способность без искажения топологии. Работа подчёркивает значимость точной и воспроизводимой структурной реконструкции мозга в контексте развития биомедицинских технологий и нейронауки.

brain morphometrySBMVBMcortical thicknessMRIanatomical reconstructionneuroimaging reproducibilityморфометрия мозгаSBMVBMтолщина корыМРТанатомическая реконструкциявоспроизводимость нейровизуализацииThis research was supported by the strategic project “Innovative Technologies in Strengthening the Mental Health of Children and Adults,” “Priority-2030” program of the Privolzhsky Research Medical University.S. Hellard et al., “The ENIGMA Consortium: large-scale collaborative analyses of neuroimaging and genetic data,” Brain Imaging and Behavior, vol. 8, pp. 153-182, 2014.D. C. Van Essen, S. M. Smith, D. M. Barch, T. E. J. Behrens, E. Yacoub, and K. Ugurbil, “The WU-Minn Human Connectome Project: An overview,” NeuroImage, vol. 80, pp. 62-79, 2013. DOI: 10.1016/j.neuroimage.2013.05.041T. Jiang, “Brainnetome: A new -ome to understand the brain and its disorders,” NeuroImage, vol. 80, pp. 263-272, 2013. DOI: 10.1016/j.neuroimage.2013.04.002A. Johnson, T. Pollard, L. Shen, et al., “MIMIC-III, a freely accessible critical care database,” Scientific Data, vol. 3, p. 160 035, 2016. DOI: 10.1038/sdata.2016.35Q. Xu, L. Guo, J. Cheng, et al., “CHIMGEN: a Chinese imaging genetics cohort to enhance cross-ethnic and cross-geographic brain research,” Molecular Psychiatry, vol. 25, no. 3, pp. 517-529, 2020. DOI: 10.1038/s41380-019-0627-6N. Madeira, J. Duarte, R. Martins, G. Costa, A. Macedo, and M. Castelo-Branco, “Morphometry and gyrification in bipolar disorder and schizophrenia: A comparative MRI study,” NeuroImage: Clinical, p. 102 220, Jan. 2020. DOI: 10.1016/j.nicl.2020.102220D. Koshiyama, K. Miura, K. Nemoto, et al., “Neuroimaging studies within Cognitive Genetics Collaborative Research Organization aiming to replicate and extend works of ENIGMA,” Human Brain Mapping, vol. 43, no. 1, pp. 182-193, 2022. DOI: 10.1002/hbm.25040C. Gaser, R. Dahnke, P. M. Thompson, F. Kurth, E. Luders, and the Alzheimer’s Disease Neuroimaging Initiative, “CAT: a computational anatomy toolbox for the analysis of structural MRI data,” GigaScience, vol. 13, giae049, Aug. 2024. DOI: 10.1093/gigascience/giae049 eprint: https ://academic.oup.com/gigascience/article-pdf/doi/10.1093/gigascience/giae049/60707960/giae049.pdf.N. Upadhyay, A. Munivenkatappa, B. I. Devi, D. K. Subbakrishna, and J. Rajeswaran, “Analysis of various automated structural computing methods in patient with early traumatic brain injury,” The Open Access Journal of Science and Technology, vol. 2, 2014. DOI: 10.11131/2014/101069B. Fischl, “FreeSurfer,” NeuroImage, vol. 62, no. 2, pp. 774-781, 2012. DOI: 10.1016/j.neuroimage. 2012.01.021Y. Wang, L. Hao, Y. Zhang, C. Zuo, and D. Wang, “Entorhinal cortex volume, thickness, surface area and curvature trajectories over the adult lifespan,” Psychiatry Research: Neuroimaging, vol. 292, pp. 47-53, 2019. DOI: 10.1016/j.pscychresns.2019.09.002N. Makris, J. Kaiser, C. Haselgrove, et al., “Human cerebral cortex: A system for the integration of volume- and surface-based representations,” NeuroImage, vol. 33, no. 1, pp. 139-153, 2006. DOI: 10.1016/j.neuroimage.2006.04.220B. Fischl and A. M. Dale, “Measuring the thickness of the human cerebral cortex from magnetic resonance images,” Proceedings of the National Academy of Sciences, vol. 97, no. 20, pp. 11 050- 11 055, 2000. DOI: 10.1073/pnas.200033797R. S. Desikan, F. Ségonne, B. Fischl, et al., “An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest,” NeuroImage, vol. 31, no. 3, pp. 968-980, 2006. DOI: 10.1016/j.neuroimage.2006.01.021B. Fischl, C. Destrieux, E. Halgren, et al., “Automatically parcellating the human cerebral cortex,” Cerebral Cortex, vol. 14, no. 1, pp. 11-22, 2004. DOI: 10.1093/cercor/bhg087B. Fischl, N. Rajendran, E. Busa, et al., “Cortical folding patterns and predicting cytoarchitecture,” Cerebral Cortex, vol. 18, no. 8, pp. 1973-1980, 2008. DOI: 10.1093/cercor/bhm225B. Fischl, M. I. Sereno, and A. M. Dale, “Cortical surface-based analysis II: Inflation, flattening, and a surface-based coordinate system,” NeuroImage, vol. 9, no. 2, pp. 195-207, 1999. DOI: 10.1006/nimg.1998.0396D. N. Greve, L. Van der Haegen, Q. Cai, et al., “A surface-based analysis of language lateralization and cortical asymmetry,” Journal of Cognitive Neuroscience, vol. 25, no. 9, pp. 1477-1492, 2013. DOI: 10.1162/jocn_a_00400A. Klein, S. S. Ghosh, F. S. Bao, et al., “Mindboggling morphometry of human brains,” PLOS Computational Biology, vol. 13, no. 2, pp. 1-40, Feb. 2017. DOI: 10.1371/journal.pcbi.1005350Y. He, Y. Huang, Z. Guo, H. Zhu, D. Zhang, C. Xue, X. Hu, C. Xiao, and X. Chai, “MRI-Negative Temporal Lobe Epilepsy: A Study of Brain Structure in Adults Using Surface-Based Morphological Features,” Journal of Integrative Neuroscience, vol. 23, no. 11, p. 206, 2024. DOI: 10.31083/j.jin2311206T. Cao, J. C. Pang, A. Segal, Y. C. Chen, K. M. Aquino, M. Breakspear, and A. Fornito, “Mode-based morphometry: A multiscale approach to mapping human neuroanatomy,” bioRxiv, 2023. DOI: 10.1101/2023.02.26.529328P. Shaw, D. Greenstein, J. Lerch, et al., “Intellectual ability and cortical development in children and adolescents,” Nature, vol. 440, pp. 676-679, 2006. DOI: 10.1038/nature04513A. C. Jagger-Rickels, M. Y. Kibby, and J. M. Constance, “Global gray matter morphometry differences between children with reading disability, ADHD, and comorbid reading disability/ADHD,” Brain Lang., vol. 185, pp. 54-66, 2018. DOI: 10.1016/j.bandl.2018.08.004A. Daoudi and S. Mahmoudi, “Enhancing brain segmentation in MRI through integration of hidden Markov random field model and whale optimization algorithm,” Computers, vol. 13, no. 5, p. 124, 2024. DOI: 10.3390/computers13050124P. Kurella, “Convolutional neural networks grid search optimizer based brain tumor detection,” International Transactions on Electrical Engineering and Computer Science, 2023. DOI: 10.62760/iteecs.2.4.2023.68R. S. Cruz, L. Lebrat, P. Bourgeat, V. Doré, J. Dowling, J. Fripp, C. Fookes, and O. Salvado, “Going Deeper With Brain Morphometry Using Neural Networks,” pp. 711-715, 2021. DOI: 10.1109/ISBI48211.2021.9434039B. Mosch, V. Hagena, S. Herpertz, and M. Diers, “Brain morphometric changes in fibromyalgia and the impact of psychometric and clinical factors: a volumetric and diffusion-tensor imaging study,” Arthritis Research and Therapy, vol. 25, 2023. DOI: 10.1186/s13075-023-03064-0B. Marteau, S. Vashista, M. Chen, et al., “Brain Digital Twin Combining Artificial Intelligence and Extended Reality,” pp. 1-8, Dec. 2024. DOI: 10.1109/ICIR64558.2024.10976965Y. Xiong, B. Liu, D. Wang, T. Zhang, W. Wu, T. Liu, P. Li, G. Shi, and Y. Fan, “Digital Twin Brain: Bridging Biological and Artificial Intelligence via Brain Science,” arXiv preprint arXiv:2308.01941, 2023.R. Riccelli, N. Toschi, S. Nigro, A. Terracciano, and L. Passamonti, “Surface-based morphometry reveals the neuroanatomical basis of the five-factor model of personality,” Social cognitive and affective neuroscience, vol. 12, Jan. 2017. DOI: 10.1093/scan/nsw175S. Fujita, A. Hagiwara, M. Hori, et al., “Three-dimensional High-resolution Simultaneous Quantitative Mapping of the Whole Brain with 3D-QALAS: An Accuracy and Repeatability Study.,” Magnetic Resonance Imaging, vol. 63, Aug. 2019. DOI: 10.1016/j.mri.2019.08.031K. Li, Y. Peng, S. Li, L. Zeng, R. Cao, B. Yu, Y. Zhang, Z. Zhong, and H. Lin, “Correlation between cerebral cortex changes and cognitive dysfunction in patients with obstructive sleep apnea hypopnea syndrome,” Neural Regeneration Research, vol. 18, no. 11, pp. 2469-2474, 2023. DOI: 10.4103/1673-5374.369493R. A. Yotter, R. Dahnke, P. M. Thompson, and C. Gaser, “Topological correction of brain surface meshes using spherical harmonics,” Human Brain Mapping, vol. 32, no. 7, pp. 1109-1124, Jul. 2011, Research supported by NIH grants EB007813, HD050735, EB008432, EB008281. DOI: 10.1002/hbm. 21095B. Fischl, A. Liu, and A. M. Dale, “Automated manifold surgery: constructing geometrically accurate and topologically correct models of the human cerebral cortex,” IEEE Transactions on Medical Imaging, vol. 20, no. 1, pp. 70-80, Jan. 2001, Research supported by NIH: P41-RR14075, R01-NS39581, R01-RR13609. DOI: 10.1109/42.906426A. M. Dale, B. Fischl, and M. I. Sereno, “Cortical surface-based analysis. I. Segmentation and surface reconstruction,” NeuroImage, vol. 9, no. 2, pp. 179-194, Feb. 1999. DOI: 10.1006/nimg. 1998.0395O. Acosta, J. Fripp, V. Doré, et al., “Cortical surface mapping using topology correction, partial flattening and 3D shape context-based non-rigid registration for use in quantifying atrophy in Alzheimer’s disease,” Journal of Neuroscience Methods, vol. 205, no. 1, pp. 96-109, Mar. 2012. DOI: 10.1016/j.jneumeth.2011.12.011A. C. Evans, “Cortical Surface Morphometry,” pp. 157-166, 2015. DOI: 10.1016/B978-0-12-397025- 1.00210-4K. Zilles, E. Armstrong, A. Schleicher, and H. J. Kretschmann, “The human pattern of gyrification in the cerebral cortex,” Anatomy and Embryology, vol. 179, no. 2, pp. 173-179, 1988. DOI: 10.1007/BF00304699M. Goto, O. Abe, A. Hagiwara, et al., “Advantages of Using Both Voxel- and Surface-based Morphometry in Cortical Morphology Analysis: A Review of Various Applications,” Magnetic Resonance in Medical Sciences, vol. 21, no. 1, pp. 41-57, 2022. DOI: 10.2463/mrms.rev.2021-0096M. Meyer, M. Desbrun, P. Schroder, and A. H. Barr, “Discrete Differential-Geometry Operators for Triangulated 2-Manifolds,” pp. 35-57, 2003. DOI: 10.1007/978-3-662-05105-4_2D. Pantazis, R. M. Leahy, T. E. Nichols, and M. Styner, “Statistical surface-based morphometry using a nonparametric approach,” vol. 2, pp. 1283-1286, 2004. DOI: 10.1109/ISBI.2004.1398780D. P. Devanand, R. Bansal, J. Liu, et al., “MRI hippocampal and entorhinal cortex mapping in predicting conversion to Alzheimer’s disease,” NeuroImage, vol. 60, no. 3, pp. 1622-1629, 2012. DOI: 10.1016/j.neuroimage.2012.01.075J. A. K.J. Friston, “Generative and recognition models for neuroanatomy,” NeuroImage, Volume 23, Issue 1, 2004, Pages 21-24, ISSN 1053-8119, vol. 23, no. 1, pp. 21-24, 2004. DOI: 10.1016/j.neuroimage. 2004.04.021N. Voets, M. Hough, G. Douaud, P. Matthews, A. James, L. Winmill, P. J. Webster, and S. M. Smith, “Evidence for abnormalities of cortical development in adolescent-onset schizophrenia,” NeuroImage, vol. 43, pp. 665-675, 2008. DOI: 10.1016/j.neuroimage.2008.08.013K. Lai, D. Niddam, J. Fuh, W.-T. Chen, J.-C. Wu, and S.-J. Wang, “Cortical morphological changes in chronic migraine in a Taiwanese cohort: Surface- and voxel-based analyses,” Cephalalgia, vol. 40, pp. 575-585, 2020. DOI: 10.1177/0333102420920005J. Ashburner and K. J. Friston, “Voxel-Based Morphometry-The Methods,” NeuroImage, vol. 11, pp. 805-821, 2000. DOI: 10.1006/nimg.2000.0582A. Mechelli, C. Price, K. J. Friston, and J. Ashburner, “Voxel-based morphometry of the human brain: Methods and applications,” Current Medical Imaging Reviews, vol. 1, pp. 105-113, 2005. DOI: 10.2174/1573405054038726D. Callaert, A. Ribbens, F. Maes, S. Swinnen, and N. Wenderoth, “Assessing age-related gray matter decline with voxel-based morphometry depends significantly on segmentation and normalization procedures,” Frontiers in Aging Neuroscience, vol. 6, 2014. DOI: 10.3389/fnagi.2014. 00124X. Han, J. Jovicich, D. Salat, A. van der Kouwe, B. Quinn, S. Czanner, E. Busa, J. Pacheco, M. Albert, R. Killiany, et al., “Reliability of MRI-derived measurements of human cerebral cortical thickness: the effects of field strength, scanner upgrade and manufacturer,” NeuroImage, vol. 32, no. 1, pp. 180-194, Aug. 2006. DOI: 10.1016/j.neuroimage.2006.02.051M. Chung, “Tensor-Based Surface Morphometry,” 2002.