Geometric Brain Signatures for Diagnosing Rare Hereditary Ataxias and Predicting Function

BackgroundHereditary cerebellar ataxias (HCAs) are rare neurodegenerative disorders characterised by progressive motor impairment and overlapping clinical phenotypes. Although genetic testing provides etiological diagnosis, diagnostic delays frequently arise before targeted testing, owing to non-specific presentation and limited clinician familiarity. Imaging-derived biomarkers that capture phenotypic expression and network-level consequences of disease could support earlier recognition of hereditary ataxia, guide appropriate genetic testing, and provide sensitive measures of disease evolution. Building on evidence that cortical geometry shapes functional organisation, we hypothesised that geometric signatures derived from structural magnetic resonance imaging (sMRI) could discriminate HCA subtypes and yield progression-sensitive biomarkers, while enabling scalable prediction of function. MethodsWe decomposed sMRI and task-evoked functional MRI data from three independent cohorts using cortical geometric eigenmodes, intrinsic spatial patterns defined by cortical surface geometry, to obtain structural and functional geometric signatures. Structural signatures were used to train neural networks for disease classification and to derive biomarkers sensitive to annual progression. We further modelled structure-to-function mappings to predict functional geometric signatures from sMRI and evaluated their diagnostic and longitudinal utility. FindingsOur framework achieved high diagnostic performance, distinguishing healthy controls from Friedreich ataxia (FRDA) with a maximum AUC of 0.93 and separating FRDA from spinocerebellar ataxia type 1 (SCA1) and SCA3, with AUCs up to 0.81, showing cross-cohort generalisability. Structure-to-function-signature prediction achieved coefficient of determination up to 0.62 and correlation reaching 0.86 across health and disease, while predicted functional signatures improved classification beyond structural signatures alone and enabled partial reconstruction of individual task-activation map. Geometric brain signatures showed greater progression sensitivity than conventional volumetric MRI measures. InterpretationThis geometry-driven framework offers novel, objective, multiscale biomarkers for diagnostic-decision-support and monitoring HCAs and provides proof-of-concept for the feasibility of predicting fMRI-equivalent biomarkers in disease from routine sMRI, which is far more practical in movement-disorder populations. FundingFriedreich Ataxia Research Alliance USA. Research in ContextO_ST_ABSEvidence before this studyC_ST_ABSWe searched PubMed, Scopus, IEEE Xplore, and Google Scholar, for peer-reviewed studies published up to 2025 using combinations of terms related to hereditary cerebellar ataxia (HCAs), Friedreich ataxia (FRDA), spinocerebellar ataxia (SCA), diagnosis, progression, MRI biomarkers, structural MRI (sMRI), functional MRI (fMRI), machine learning (ML), deep learning (DL), task activation maps, prediction, and geometric eigenmodes. We found that while sMRI studies in HCAs consistently showed patterns of cerebellar, brainstem, and supratentorial atrophy, highlighting their potential diagnostic value as non-invasive biomarkers, existing studies on imaging-based diagnostic tools for HCAs typically used small sample size, single-site data and focused on narrow classification tasks rather than generalisable frameworks for differential diagnosis. Clinically meaningful objective biomarkers sensitive to disease progression are also limited, with most outcome measures relying on subjective clinical rating scales or conventional MRI metrics with restricted sensitivity and reproducibility. In addition, fMRI reveals important network-level abnormalities in disease, however, motion artefacts, task-performance difficulties and long acquisition times limit its applicability in movement-disorder populations. Recent work in healthy populations showed that structural data could predict task-fMRI activation using DL, yet disease-specific and clinically deployable investigations remain unexplored. In parallel, advances in brain geometric eigenmode research underscore that cortical geometry provides a principled structural basis that shapes multi-scale functional organisation. However, no study has investigated cortical geometric signatures as tools to address three major challenges in hereditary ataxia research and clinical care: diagnostic delay, lack of progression-sensitive objective biomarkers, and practical limitations of functional imaging acquisition. Added value of this studyUsing a combined geometric and ML framework, we showed that cortical geometric signatures captured multiscale brain organisation that constitute novel, generalisable biomarkers for differential diagnosis across HCA subtypes. Our models reliably distinguished healthy controls from individuals with FRDA, demonstrated consistent performance across independent cohorts, and further separated FRDA from multiple SCA subtypes. Importantly, we provided proof-of-concept for structure-to-function prediction and showed that fMRI-equivalent functional signatures could be inferred from sMRI in both health and disease, enabling reliable approximation of individual task-activation maps without requiring fMRI acquisition. Incorporating these predicted functional signatures improved diagnostic accuracy beyond structural measures alone. Both structural and predicted functional biomarkers demonstrated greater sensitivity to annual disease progression than conventional volumetric metrics, with comparable performance to clinical scales. Implications of all the available evidenceCortical geometric signatures pave the way for a clinically deployable neuroimaging diagnostic decision-support tool that could guide clinicians toward targeted genetic testing and potentially reduce diagnostic delay in HCAs. These biomarkers provide objective, rater-independent measures of disease evolution that are more scalable and reproducible than clinical ratings alone, and more sensitive than conventional imaging measures, with important implications for improving clinical trial design and monitoring therapeutic efficacy. The ability to infer functional signatures from sMRI allows clinicians to probe aspects of functional organisation and network disruption using routine sMRI, which is substantially more practical in movement-disorder populations, thereby introducing a novel fMRI-equivalent biomarker that may further improve diagnosis and progression monitoring.