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Data-driven techniques for translational neuroscience and personalized neuro-health

Vishal Subedi, Shashipraba N. K. Rajakaruna, Pratyusha Sarkar, Subhankar Chattoraj, Anjali Khasa, Siddhartha Nandy, Hamza Farooq, Animikh Biswas, Sanjay Chaudhuri, Asim K. Dey, Karuna Joshi, Christophe Lenglet, Ansu Chatterjee

arXiv:2608.13749v1q-bio.NCcs.AIcs.LGstat.APstat.ML

TL;DR

Early diagnosis of neurodegenerative disease remains difficult when individualized brain changes may be subtle and clinically important. This review synthesizes complementary statistical, geometric, topological, artificial-intelligence, and mechanistic modeling approaches, finding a shared translational goal of personalized neuro-health models.

  • Problem

    Early diagnosis of Alzheimer’s and Parkinson’s disease remains difficult despite the need for earlier, more sensitive, and individually meaningful quantitative methods.

    Source: §1 · p. 2

  • Method

    The review synthesizes four complementary methodological pillars spanning statistical inference, geometric and topological representation, artificial intelligence, and mechanistic dynamical modeling.

    Source: §1 · p. 3

  • Results

    Across the four pillars, the approaches converge on personalized neuro-health as a shared translational goal rather than competing methodological alternatives.

    Source: §1 · p. 3

  • Takeaways & Limitations

    The synthesis supports combining methodologically diverse tools to develop personalized, mechanistically grounded, and clinically actionable models of individual brain health.

    Source: §1 · p. 3

    Neuroimaging AI remains limited by small samples, high-dimensional features, substantial estimate uncertainty, and documented data leakage.

    Source: §4.6 · p. 25

Abstract

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Neurodegenexrative diseases such as Alzheimer's disease and Parkinson's disease are diagnosed most reliably only after substantial, often irreversible, neuronal loss has already occurred, creating an urgent need for quantitative tools that can detect subtle, early, and individual-specific brain changes from neuroimaging data. This review surveys a broad and rapidly evolving toolkit of data-driven techniques for translational neuroscience and personalized neuro-health, organized around four complementary methodological pillars. Throughout, we emphasize how these methodologically diverse approaches converge on a common translational goal: personalized, mechanistically grounded, and clinically actionable models of individual brain health, and we close by discussing the principal open statistical, computational, and clinical challenges that remain.

1 INTRODUCTION

Neurodegenerative diseases are difficult to diagnose early, motivating quantitative neuroimaging methods that seek sensitive, individualized, mechanistic, and dynamic markers of brain health. The review organizes these methods into four complementary pillars spanning neuroimaging statistics, network and topology, artificial intelligence, and dynamical-system modeling.

Section 2: fMRI analysis and dimension reduction

  • Section 2 covers fMRI analysis from voxel-wise regression and Bayesian models through empirical-likelihood inference and covariate-assisted dimension reduction for personalized brain-function models.CAP and BCAP link low-dimensional functional-connectivity representations to individual covariates such as age and sex.Source: §1 · p. 2

Section 3: Network science, geometry, and topology

  • Section 3 surveys Ricci curvature, persistent homology, and knowledge graphs for characterizing network robustness, multiscale brain organization, disease classification, and interoperable multi-site data exchange.Applications include healthy aging, neurodevelopmental and neurological conditions, tumor morphology, and Alzheimer’s disease classification.Source: §1 · pp. 2–3

Section 4: Artificial intelligence

  • Section 4 reviews deep learning, generative AI, and longitudinal image-change detection for diagnosing, staging, and modeling Alzheimer’s and Parkinson’s disease progression and treatment response.The surveyed generative methods include GANs, variational autoencoders, and denoising diffusion models for synthetic neuroimage generation, augmentation, and interpretable progression modeling.Source: §1 · p. 3

Section 5: Dynamical systems and mechanistic models

  • Section 5 presents biophysical, neural-mass, whole-brain, and disease-progression models learned from noisy neuroimaging data, culminating in personalized generative digital brain twins.Digital twins integrate covariate-informed modeling, mechanistic dynamics, and AI-based estimation into a translational framework.Source: §1 · p. 3

Overview

  • The review frames personalized neuro-health as a shared goal in which statistical inference, geometric and topological representations, artificial intelligence, and mechanistic modeling provide complementary capabilities.This reflects a shift from localized, stationary effects toward individualized accounts of how brain organization and function evolve and are altered by disease.Source: §1 · pp. 2–3

2 FMRI DATA ANALYSIS AND DIMENSION REDUCTION TECHNIQUES

This section reviews fMRI’s high-dimensional BOLD data structure and the progression from voxel-wise linear modeling to Bayesian, empirical-likelihood, and covariate-assisted dimension-reduction methods. These approaches aim to model spatial dependence, improve robustness, and identify individualized connectivity patterns linked to demographic traits.

2 FMRI DATA ANALYSIS AND DIMENSION REDUCTION TECHNIQUES

  • fMRI provides high-dimensional, hemodynamically mediated BOLD measurements across voxels and time, often accompanied by task and subject characteristics.Illustrative scans use a (64, 64, 33) voxel grid, typical of fMRI studies.Source: §2 · pp. 3–4

2.1 fMRI regression and SPM-based techniques and extensions

  • Classical fMRI analysis fits mass-univariate linear models at each voxel to produce whole-brain statistical parametric maps, but inference depends on assumptions and multiple-comparison correction.Voxel responses are modeled with task-related covariates, and temporally dependent noise may be represented with autoregressive processes.Source: §2 · pp. 4–5, §2.1 · pp. 5–6

2.2 Bayesian Inference for fMRI

  • Bayesian fMRI models couple neighboring voxels and can incorporate spatiotemporal, multilevel, and variable-selection structure, while sparse spatial priors can regularize activation and reduce dimension.Whole-brain posterior inference is generally analytically intractable at scale, motivating MCMC and variational Bayes methods.Source: §2.2 · p. 6

2.3 An illustrative example of empirical likelihood inference in fMRI data

  • Empirical-likelihood inference constructs the null distribution from background voxels, then applies Benjamini-Hochberg adjustment to generate FDR-controlled voxel-wise activation maps.In the illustrative scan, EL produced a more robust alternative to parametric frameworks with strong data and model assumptions [245].Source: §2.3 · pp. 7–8, Figure 1 · p. 8

2.4 Covariate assisted principal regression for brain functional connectivity

  • CAP and BCAP reduce fMRI connectivity dimension while explicitly linking latent covariance directions to subject-level covariates such as age and sex.BCAP jointly extracts a d-dimensional subspace with d ≪ p, separating covariate-driven directions from residual variation through an SPD-aware formulation [358, 250].Source: §2.4 · pp. 8–9

2.4.1 An illustrative example

  • Across 16 subjects, SSGP showed no significant demographic association, whereas GICA and SCFP identified sex-related connectivity differences further modulated by age.The three parcellations were SSGP, GICA, and SCFP; their differing results demonstrate that dimension-reduction choices affect downstream insights.Source: §2.4.1 · p. 10, Figure 2 · p. 10

3 APPROACHES USING GRAPHS, NETWORKS, TOPOLOGY, GEOMETRY · 3.1 Network curvature in structural and functional brain connectomics

Network curvature extends conventional graph analysis by modeling the intrinsic geometry of brain networks, revealing robustness, fragility, functional alterations, aging-related reorganization, and multiscale community structure. Across structural and functional connectomics, these geometric methods support clinically relevant biomarkers and a unifying framework for brain organization.

3.1 Network curvature in structural and functional brain connectomics

  • Ricci curvature quantifies local geometric organization by transporting probability mass between neighboring regions, complementing graph metrics with measures of network robustness and fragility (34).It addresses the limited insight conventional degree, clustering, path-length, modularity, and centrality measures provide into intrinsic geometry, information flow, and resilience.Source: §3.1 · pp. 10–11

3.1.1 Architectural robustness of structural brain networks

  • Curvature-based structural connectomics identifies robust and fragile regions while detecting age-related, ASD-related, treatment-associated, and MS-related alterations beyond conventional graph analyses (104; 300; 105).Positive curvature represents robust organization, whereas negative curvature indicates structural vulnerability; local and global metrics differentiated cognitively impaired from non-impaired patients and correlated with cognitive decline.Source: §3.1.1 · p. 11

3.1.2 Applications to functional brain networks

  • Functional curvature measures reveal ASD-related, region-specific connectivity abnormalities in default-mode, somatomotor, and ventral-attention networks that overlap cognitive impairments and effective non-invasive stimulation targets (99).Forman-Ricci and Ollivier-Ricci curvature capture complementary, non-interchangeable geometric properties and detect higher-order alterations missed by conventional edge-weight analyses.Source: §3.1.2 · pp. 11–12

3.1.3 Characterizing Healthy Aging and Community Detection

  • Age-related Ollivier-Ricci and Forman-Ricci changes concentrate in movement, somatosensory, and affective regions, with curvature values correlating directly with behavioral measures (348).These findings support curvature descriptors as sensitive markers of functional reorganization across healthy aging and pathological states.Source: §3.1.3 · p. 12
  • Ricci-flow community detection accuracy and robustness depend strongly on network topology, establishing a geometric framework for multiscale organization alongside modularity maximization and Bayesian stochastic block models (SBM) (44).Evaluations across large-scale fMRI datasets used curvature flow (152, 240) to study the evolution and overarching structure of brain networks.Source: §3.1.3 · p. 12

3.1.4 Theoretical Extensions

  • A geometric phase-transition framework extends curvature analysis across brain networks, biomedical knowledge graphs, and disease comorbidity networks, suggesting a unifying language across biological scales (2).Related evaluations find Gromov-hyperbolic, Ollivier-Ricci, Forman-Ricci, and curvature-flow methods complementary across biological, biomedical, and brain networks (4).Source: §3.1.4 · p. 12, §3.1.3 · p. 12

3.1.5 Implementation and Computational Accessibility

  • Open-source Python workflows support scalable graph-theoretical and topological analyses of resting-state fMRI, brain-atlas visualization, and future incorporation of discrete Ricci curvature (60, 61).These frameworks improve computational accessibility by providing practical construction, analysis, and visualization pipelines, although they primarily target graph theory and topological data analysis.Source: §3.1.5 · p. 13

3.2 Topological data analysis (TDA) and related developments in neuroscience

TDA provides multiscale representations of neural structure, activity, and connectivity by tracking persistent topological features across filtrations. In neuroimaging and brain networks, these representations support morphology analysis, prediction, segmentation, comparison, clustering, and population-level inference.

3.2.1 Preliminaries on TDA

  • Persistent homology converts data into filtered simplicial or cubical complexes and quantifies multiscale holes using Betti numbers and persistence diagrams.Vietoris–Rips filtrations capture point-cloud relationships, while cubical filtrations support regular-grid images through intensity thresholds.Source: §3.2.1 · pp. 13–14

3.2.2 TDA for neuroimage data

  • In structural and functional neuroimaging, topology-aware summaries address intensity limitations while enabling tumor-shape inference, unsupervised segmentation, disease-related analysis, and dynamic brain-state characterization.SECT improved survival prediction over conventional geometric descriptors, while fMRI Mapper representations linked activation-trajectory topology to task performance.Source: §3.2.2 · pp. 14–16

3.2.3 TDA for brain networks

  • Brain-network filtrations provide threshold-robust multiscale topology for alignment, group testing, clinical clustering, and population inference.TDA revealed fewer connected components and denser correlations in maltreated children’s networks, while expected persistent barcodes showed significant male–female resting-state network differences.Source: §3.2.3 · pp. 16–17

3.3 Knowledge Graph representations for Clinical Interoperability

Knowledge graphs and Semantic Web technologies provide machine-interpretable, queryable representations for interoperable clinical data, policies, and biomedical evidence. In translational neuroscience, hypergraphs extend these representations to capture multimodal, higher-order relationships relevant to neurodegenerative disease.

3.3 Knowledge Graph representations for Clinical Interoperability

  • Semantic Web technologies, including RDF (246) and OWL (9), annotate data with machine-understandable metadata and support sound reasoning over shared data and usage policies.OWL profiles such as OWL QL and OWL RL provide different reasoning-complexity guarantees for databases and rule-based systems.Source: §3.3 · p. 18

3.3.1 Knowledge Graphs in Translational Neuroscience

  • Biomedical knowledge graphs unify entities across molecular, anatomical, clinical, and disease scales, enabling evidence integration, drug-response prioritization, and disease-centric precision-medicine modeling (66, 65, 159, 63).In neurodegenerative and psychiatric disorders, relational paths support patient stratification, mechanistic hypothesis generation, and biomarker discovery while improving interpretability for clinical and regulatory acceptance (67, 350).Source: §3.3.1 · p. 18

3.3.2 Hypergraph-Structured Representations for Neuroimaging Cohorts

  • Hypergraphs address the loss of biologically meaningful joint interactions caused by reducing higher-order neurobiological relationships to pairwise edges (20, 26, 359).Hypergraph learning and HGNN convolution propagate information across higher-order relations and fuse modalities, supporting Alzheimer’s diagnosis from incomplete multimodal data in ADNI cohorts (359, 106, 214, 172).Source: §3.3.1 · pp. 18–19, §3.3.2 · p. 19

4 ARTIFICIAL INTELLIGENCE TECHNIQUES FOR NEUROSCIENCE STUDIES · 4.1 AI for neuroimage modeling · 4.2 Deep Learning for Diagnosis and Progression Modeling of Neurodegenerative Disease

AI is central to neuroimage analysis for individualized neurodegenerative-disease detection, diagnosis, progression modeling, synthesis, and personalized brain-health applications. Deep learning learns features from multimodal data, while the literature increasingly emphasizes longitudinal modeling and concerns about reproducibility and generalization.

4.1 AI for neuroimage modeling

  • AI is increasingly important because structural imaging and clinical assessment often detect Alzheimer’s and Parkinson’s disease only after substantial neuronal loss (197, 363).The section frames early, individualized detection as the central motivation for neuroimage modeling.Source: §4.1 · pp. 20–21
  • Deep learning directly learns hierarchical features from high-dimensional imaging, speech, gait, and other multimodal clinical data without hand-engineered extraction, while generative AI supports synthesis, augmentation, and disease modeling.The review focuses on applied diagnosis and progression modeling, foundation models, generative AI, digital brain twins, and cross-cutting limitations.Source: §4.1 · p. 21

4.2 Deep Learning for Diagnosis and Progression Modeling of Neurodegenerative Disease

  • Volumetric CNNs remain the workhorse for AD/PD diagnosis, including 3-D MRI classification (91), multi-stage AD detection (168), transfer learning for PD (191), early diagnosis (7), and progression forecasting (229).Systematic and narrative reviews synthesize this large CNN literature (130, 319, 306).Source: §4.2 · p. 21
  • Reported accuracies are often high but typically come from comparatively small, single-site cohorts, raising reproducibility and generalization concerns.These limitations recur across the survey literature reviewing CNN-based neurodegenerative-disease studies.Source: §4.2 · p. 21
  • Recurrent and hybrid models address temporal and multimodal progression, with clinical, genetic, and imaging fusion tending to outperform single-modality, single-architecture models (17, 223, 201, 295, 19).CNN–LSTM systems improve AD detection (366), jointly model MRI and PET signatures (297), and support simultaneous AD/PD detection (291); NeuroNet combines 3-D CNN, LSTM, attention, and Bayesian optimization (141).Source: §4.2 · p. 21
  • Longitudinal change detection extends classical registration, change-vector, dictionary-learning, and clustering methods through autoencoders, Siamese networks, metric learning, consistency-regularized pooling, Neural ODEs, and temporally aware diffusion models (95, 205, 192, 244, 199, 212).These approaches learn unsupervised change, continuous severity trajectories, direct scan comparisons, and explicit spatio-temporal progression from serial imaging.Source: §4.2 · p. 21
  • Deep learning also connects macroscopic progression analysis with pathology through large-scale histological tau-protein mapping (322).General-purpose multimodal large language models have additionally been evaluated for identifying radiologic progression from serial brain MRI (188).Source: §4.2 · pp. 21–22

4.3 Foundation Models and Generative AI for Neuroimaging

Foundation models are emerging as adaptable neuroimaging backbones through large-scale self-supervised pretraining, while generative AI supports synthetic data generation, augmentation, progression modeling, and multimodal clinical applications.

Foundation Models

  • Foundation models pretrained on broad neuroimaging and neurophysiological corpora enable fine-tuning or zero-shot inference across downstream tasks.Examples span fMRI, EEG, and intracranial recordings, including BrainLM, Brain-JEPA, SwiFT, LaBraM, NeuroLM, BrainBERT, and EEGPT (242, 93, 193, 179, 178, 331, 332).Source: §4.3 · p. 22

Generative AI

  • GANs, VAEs, and diffusion models generate synthetic neuroimages, augment datasets, address imbalance and rare subtypes, and model Alzheimer’s and Parkinson’s disease progression (335, 14, 73, 155, 349, 29, 251).Applications include synthetic AD MRI, amyloid-related progression dynamics, brain-age prediction, improved downstream prediction, and anomaly detection (272, 31, 37, 166, 164, 27).Source: §4.3 · p. 22
  • Generative models are extending beyond diagnosis to functional brain regeneration, adaptive cognitive recovery, privacy-preserving federated EEG classification, and disease-literacy or communication systems (190, 310, 36).These applications broaden generative AI toward clinical simulation, multi-institutional learning, and patient-facing communication.Source: §4.3 · p. 22
  • Connectome- and multimodality-aware diffusion models address multimodal fusion, including high-resolution structural MRI generation and clinical-aware missing-modality imputation (262, 72, 367, 361).ConnectomeDiffuser, BrainNetDiff, and adaptive clinical-aware latent diffusion extend generation toward multimodal neuroimaging problems.Source: §4.3 · p. 22

4.4 AI, Digital Twins, and Digital Clones of the Brain

AI-driven brain digital twins are personalized generative models calibrated to individual imaging data to simulate, predict, and potentially steer brain function. Their clinical promise is substantial, but sparse-data personalization, surrogate validation, and unresolved regulatory requirements remain major barriers.

Digital twins

  • Brain digital twins use subject-specific structural and functional imaging to build individualized whole-brain models for diagnosis, prognosis, treatment planning, and clinical inference across ageing and disease, including Alzheimer’s and Parkinson’s disease (333, 279, 365).The Virtual Brain provides earlier infrastructure for connectome-constrained whole-brain simulation (279).Source: §4.4 · pp. 22–23

AI methods

  • AI supports digital-twin construction through segmentation, registration, parcellation, transferable foundation-model representations, and generative models for individualized data synthesis, calibration, validation, and computationally efficient simulation surrogates.These methods address limited subject-specific data and may enable virtual-cohort studies or near-real-time clinical use.Source: §4.4 · p. 23

Clinical application

  • A personalized digital-twin-brain framework identified state-specific neurostimulation targets for abnormal brain dynamics in tinnitus, linking individualized computational modeling to a candidate therapeutic intervention (355).Source: §4.4 · p. 23

Limitations

  • Major barriers include identifiability and overfitting from sparse individual imaging, validation of deep-learning surrogates against mechanistic models, and unresolved clinical and regulatory validation for treatment decisions.Digital twins are therefore both clinically compelling and methodologically demanding.Source: §4.4 · p. 23

4.5 Change detection in medical images

Medical-image change detection automates comparison across successive scans to identify clinically meaningful differences, but must distinguish pathology from artifacts and physiological deformation. Methods have progressed from registration and subtraction to deep, temporal, and continuous-time models that track and predict disease evolution.

4.5 Change detection in medical images

  • Change detection reduces manual comparison and supports disease monitoring, therapy-response assessment, recurrence surveillance, and quantitative measurement of disease evolution in clinical trials (254, 210).A central challenge is separating genuine pathology from artifacts caused by positioning, protocol variation, and physiological deformation (253).Source: §4.5 · p. 23

4.5.1 Classical techniques for image change detection

  • Classical approaches register images before subtraction, while statistical, unsupervised, and geometric methods address noise, limited training data, boundaries, and physiological deformation (326), (151), (219), (362), (233).These methods include multivariate analysis with PCA and differential geometry on tetrahedral meshes for canonical representations, tumors, and anatomical feature clustering.Source: §4.5.1 · p. 24

4.5.2 Deep learning for change detection

  • Deep-learning pipelines learn image features automatically, using dictionary-PCA fusion, siamese networks, and PaIRNet to detect changes, classify severity, order sequences, and assess disease progression (236), (205), (192).Applications include brain MRI, retinopathy, osteoarthritis, brain cancer, Alzheimer’s disease, and embryo development.Source: §4.5.2 · p. 24
  • Temporal models predict progressive changes and disease conversion from longitudinal images, including longitudinal pooling, synthetic lesion alterations with pseudo-labels, temporal similarity loss, and continuous-time ODE models (244), (318), (100), (199).These approaches address Alzheimer’s disease, alcohol use disorder, adolescent neurodevelopment, multiple sclerosis, retinal OCT, geographic atrophy, and segmentation of continuously changing states.Source: §4.5.2 · p. 24

4.6 Limitations · 4.7 Open Problems and Future Directions

Neuroimaging AI is constrained by small, heterogeneous datasets, leakage, unstable interpretability, weak cross-site generalization, computational cost, and limited biological or causal validation. Future progress depends on scalable and privacy-preserving multimodal learning, faithful and mechanistic models, rigorous validation, and clinically deployable standards.

4.6 Limitations

  • Small samples, high dimensionality, and data leakage make neuroimaging accuracy estimates uncertain and can inflate reported classification performance (325, 263, 264, 187).Reproducible brain–behavior associations require larger cohorts than typical published studies, while deep networks provide only modest gains over tuned classical models at realistic sample sizes (217, 204, 158, 294).Source: §4.6 · p. 25
  • Interpretability is unstable because Grad-CAM and SHAP can produce substantially divergent brain maps for the same trained model (296, 215, 317).This concern is amplified for large foundation models with zero-shot, emergent behaviors.Source: §4.6 · p. 25
  • Models often generalize poorly across sites and scanners, while uneven pretraining populations, substantial computational costs (35), and predictive accuracy alone limit clinical and biological validity (10, 171, 51).These limitations include robustness to diagnostic-criterion shifts and do not establish causal validity.Source: §4.6 · p. 25

4.7 Open Problems and Future Directions

  • Neuroimaging-specific scaling laws for BrainLM, Brain-JEPA, and LaBraM remain poorly characterized, including the pretraining scale needed to close deep-learning–classical-method performance gaps (45).This open problem follows from the modest gains of deep networks at realistic sample sizes.Source: §4.7 · p. 25, §4.6 · p. 25
  • Interpretability should become demonstrably faithful, with architecture-level constraints such as BrainGNN’s region-selection pooling offering one promising direction (206).The goal is to move beyond merely available post hoc explanations.Source: §4.7 · p. 25
  • Multimodal foundation models combining volumetric, connectome, and genetic or phenotypic data remain underdeveloped, while federated privacy-preserving learning could enable multi-site scaling without centralized pooling (312, 247).The cited early efforts include multimodal autoencoders and cross-modality GAN imputation.Source: §4.7 · p. 25
  • Translation requires causal and mechanistic understanding, biophysical and dynamical-systems integration, unsupervised subtyping, biologically grounded validation, and regulatory standards for deployed tools and digital twins (51, 189, 171, 12, 15, 102).These frameworks must preserve the individual-level predictive precision motivating the field (107).Source: §4.7 · p. 25

5 DYNAMICAL SYSTEMS AND MECHANISTIC MODELING OF NEUROIMAGE DATA

Dynamical-systems models characterize time-varying brain activity, connectivity, pathology, and atrophy while linking neuroimaging patterns to plausible mechanisms and causal processes. The section spans neural activity, disease progression, statistical learning, and personalized digital-brain models, alongside major identifiability, data, and validation challenges.

5 DYNAMICAL SYSTEMS AND MECHANISTIC MODELING OF NEUROIMAGE DATA

  • Static local analyses miss temporal evolution and causal mechanisms, whereas dynamical-systems theory models brain activity and pathology as evolving, partially stable processes (181).Neuroimaging dynamical systems are typically formulated as nonlinear, stochastic state-space models.Source: §5 · pp. 25–26
  • Whole-brain models couple region-level neural masses through structural connectomes to represent multistability, excitability, oscillations, and physiological parameters while supporting causal inference and experiment design.Examples include Hopf (Stuart–Landau) and R¨ossler models, with applications to neurodegenerative and clinical conditions (85, 281, 261, 252, 308).Source: §5 · p. 26
  • Disease-progression models operate over months to decades, capturing pathology spread along anatomical networks, while staging models infer biomarker ordering from cross-sectional data when onset times are unknown (5, 127, 182, 41, 213, 328, 274, 275, 360, 271, 111, 174, 352).AD pathology is described as a spatiotemporal process unfolding simultaneously across genetic, cellular, tissue, and organ scales (280).Source: §5 · pp. 26–27

5.1 Statistical and machine learning tools for learning dynamical systems

  • Kalman filtering and modern extensions provide recursive Bayesian latent-state inference, while dedicated frameworks and related studies learn disease-progression dynamics (185, 135, 131, 284, 169, 96, 70, 170, 249, 195, 308, 202, 252, 320).Dynamic causal modeling offers a low-dimensional, hypothesis-driven state-space approach to task-based effective connectivity (123, 120, 81, 309, 203).Source: §5 · p. 26, §5.1 · p. 27

5.2 Challenges and Open Problems

  • Key challenges include causal interpretation, sparse and irregular longitudinal data, parameter non-identifiability, multimodal integration, validation, scalability, and uncertainty in disease onset and model predictions (5, 293).Open questions include whether activity changes are compensatory or degenerative, how stimulation reduces protein burden, and why cognition can persist despite high pathology.Source: §5.2 · p. 27
  • Personalized digital brain twins aim to calibrate adaptive generative whole-brain models, including Hopf, R¨ossler, and Wilson–Cowan instantiations, to individual structural and functional imaging for inference (365, 333).Their development remains a major challenge.Source: §5.2 · p. 27

6 CONCLUDING COMMENTS

The review brings diverse statistical, geometric, topological, artificial-intelligence, and dynamical-systems methods together around personalized, mechanistically interpretable, and clinically actionable neuro-health. Translation will require advances in statistical reliability, methodological robustness, computational scalability, multimodal validation, and secure data sharing.

6 CONCLUDING COMMENTS

  • The reviewed methods converge on earlier disease detection, individually meaningful brain characterization, and mechanistically interpretable models of progression.This convergence spans classical and Bayesian regression, empirical likelihood, covariate-assisted dimension reduction, network analysis, artificial intelligence, and dynamical-systems modeling.Source: §6 · pp. 27–28
  • Personalized and dynamic modeling now extends from covariate-linked connectivity and individual biomarkers to single-subject AI prediction and subject-specific digital twins.Geometric, topological, and dynamical representations complement conventional voxel-wise and region-wise inference by exposing network fragility, multiscale organization, and mechanistic trajectories.Source: §6 · p. 28
  • Generative AI and mechanistic modeling increasingly converge through disease simulation, synthetic training data, and learned representations incorporated into dynamical-systems and digital-twin frameworks.These approaches are presented as complementary to, rather than replacements for, classical statistical inference.Source: §6 · p. 28
  • Translation remains limited by model misspecification, multiple comparisons, unreliable thresholding, identifiability, preprocessing sensitivity, uncertainty quantification, and sparse clinical sampling (98, 115, 208).Scaling Bayesian, topological, and dynamical methods to whole-brain resolution and large multi-site cohorts also remains computationally demanding.Source: §6 · p. 28
  • Personalized digital brain twins (333, 365) additionally require multimodal integration, clinical and regulatory validation, and interoperable, secure cross-institutional data sharing.The review identifies knowledge-graph and semantic-web approaches as directly relevant to these data-sharing needs.Source: §6 · p. 28
  • Cross-disciplinary collaboration is essential to convert this interconnected toolkit into reliable, interpretable, and clinically deployable tools for neurodegenerative disease management.The intended applications include early detection, monitoring, and personalized management.Source: §6 · p. 28

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