1. Patients with late-onset depression and mild cognitive impairment exhibit specific structural alterations in brain regions.

2. The neural network and reverse correlation-based approach effectively identifies subtle intergroup differences.

3. Temporal lobe structural alterations may reflect an early stage in the transition from late-onset depression to cognitive impairment.

With an ageing population, the healthcare burden related to late-life conditions continues to rise. Late-life depression (LLD), defined as depression occurring in adults aged 60 and above, is one of the most common mental disorders among older adults. The risk of depression increases with age in this group. LLD is a known risk factor for Alzheimer’s disease and vascular dementia [1], and when coexisting with mild cognitive impairment (MCI), it significantly predicts dementia [2, 3, 4]. LLD can be divided into early-onset depression, which recurs or persists into old age, and late-onset depression (LOD), characterised by a first depressive episode occurring at 60 or older. early-onset depression may be associated with genetic predisposition, a family history of mental illness, and stress-related factors [5, 6]. Our recent study identified distinct differences between early-onset depression and LOD in dynamic network modularity and rich-club node distribution, assessed via resting-state functional magnetic resonance imaging [7]. These differences correlated with cognitive function in only one subtype, suggesting distinct mechanisms of cognitive impairment in early-onset depression and LOD. Given that LOD poses a higher risk for cognitive decline than early-onset depression, this study focused on analysing the structural correlates of cognitive impairment specifically in LOD.

Graph theory enables the quantitative analysis of brain network topology. The key metrics in this respect include: global efficiency; nodal strength; clustering coefficient; shortest path length; and local efficiency. These metrics capture how efficiently information is integrated both globally and locally, and relate closely to cognitive abilities and clinical symptoms. Rich-club properties and modularity further describe the brain’s balance between integration and segregation.

Our previous work demonstrated synergistic effects of LLD and MCI on brain ageing. Structural covariance networks revealed that grey matter alterations in LLD-MCI resemble those observed in Alzheimer’s disease [8]. Memory impairment in LLD correlates with white matter rich-club reorganisation, where the connectivity strength of rich-club and local networks, shortest path length, global efficiency, and local efficiency, is associated with cognitive function [9], indicating both grey and white matter involvement in LLD-related cognitive decline. Although functional magnetic resonance imaging (fMRI) studyin LLD-MCI have reported similar network alterations, no cognitive correlations were identified [10]. Our recent dynamic network analysis showed that modularity correlates with memory in early-onset depression but not in LOD, with similar patterns observed in rich-club analysis (see Research Foundation). This suggests distinct structural substrates for cognitive impairment in early-onset depression versus LOD. However, the specific brain regions driving changes in rich-club organization and modularity remain unidentified. Pinpointing the key nodes influencing rich-club organization is crucial for understanding the neuropathology of LLD and for developing targeted neuromodulation therapies, such as Transcranial Magnetic Stimulation/transcranial Direct Current Stimulation.

Advances in methodology have broadened the applications of machine learning [11]. Clinically, machine learning supports diagnosis, prognosis prediction, and the assessment of treatment response [12, 13, 14]. It also enables the quantification of disease-induced neural damage [15]. Our preliminary studies applied machine learning to evaluate brain ageing, confirming synergistic LLD-MCI effects on cognitive decline [8]. Although MRI-derived network properties partially reflect cognitive function in LLD [9], conventional comparisons fail to pinpoint the structural signatures of impairment. In this study, we employed neural networks to investigate the structural and functional features of cognitive impairment in LOD.

Owing to the strong interpretability of back propagation neural networks, a classification model can be established. However, unlike regression models, the presence of hidden layers in back propagation networks makes it challenging to interpret connection weights and classifier thresholds in real-world terms. Nevertheless, their excellent generalisation performance makes back propagation networks a powerful tool for gaining deeper insights into underlying principles of complex systems. To explore their potential as feature-extraction tools in brain networks, we applied the reverse correlation method, using classification results to infer internal representations. Reverse correlation is a data-driven technique for visualising mental representations. In this approach, participants are shown a series of stimuli created by adding random noise patterns to a base image, typically a face with a neutral expression. These variations were generated by superimposing random noise patterns onto the base image [16].

In this study, the neural network model served as the “participant” classifying healthy human brain networks that had been perturbed by the addition of random noise. By integrating these noise patterns, we extracted brain network features associated with cognitive impairment.

Given that interregional brain connectivity underpins higher-order neural functions, this study leveraged the predictive power of neural networks to identify dysregulated connectivity in LOD-related cognitive impairment. Using reverse correlation, we extracted discriminative features from the model to uncover structural network signatures of LOD pathology.

This cross-sectional study was conducted at the Brain Hospital affiliated with Guangzhou Medical University, China. This study was approved by the ethics committee of the Guangdong Provincial People’s Hospital and written informed consent was obtained from each participant. The inclusion criteria for patients with LOD were as follows: (1) age $\ge$60 years; (2) diagnosis of major depressive disorder according to the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5); (3) confirmation of major depressive disorder by psychiatrists at the Brain Hospital affiliated with Guangzhou Medical University; (4) the ability to complete neuropsychological assessments; (5) first depressive episode occurring at or after the age of 60. The exclusion criteria included: (1) the inability to complete neuropsychological testing; (2) a history of severe psychiatric disorders (e.g., bipolar disorder and schizophrenia) excluding depression; (3) a family history of severe psychiatric disorders (e.g., bipolar disorder and schizophrenia) excluding depression; (4) primary neurological disorders (e.g., stroke and brain tumours); (5) medical conditions potentially affecting mood (e.g., hypothyroidism, syphilis, and anaemia); (6) contraindications for MRI (e.g., non-cooperation or intracorporeal metallic implants); (7) Hamilton rating scale for depression (HAMD) $>$7; (8) Clinical Dementia Rating (CDR) score $>$0.5; (9) Hachinski Ischaemic Scale score $>$4.

Patients with LOD were further stratified into the following groupings:

MCI group: diagnosed using Petersen’s 1999 criteria [17]: (1) self- or informant-reported memory complaints; (2) objective cognitive impairment $\ge$1.5 standard deviation units below age- and education-matched norms; (3) CDR = 0.5 and Global Deterioration Scale stages 2 and 3; (4) preserved activities of daily living; and (5) absence of dementia.

Cognitively normal group (NON-MCI): patients with LOD not meeting the MCI criteria.

Healthy controls (HCs) met the following criteria: (1) age $>$60 years with no history of depression; (2) exclusion criteria similar to the LOD group; and (3) CDR $\le$0.5 (to exclude dementia-depression comorbidity).

The final study cohort was comprised of the following participants: (1) 42 patients with LOD and 90 HCs from prior studies who met all criteria; (2) one patient with LOD who was excluded owing to incomplete diffusion tensor imaging (DTI) scanning.

All participants underwent clinical assessments, neuropsychological testing, and neuroimaging within 1 week of enrolment.

This study established a standard brain network matrix for healthy ageing using DTI structural images from 90 HCs. By integrating randomised matrices with the difference network between LOD and HC groups and combining them with the standard matrix, we generated random networks constrained within known LOD connectivity parameters. By employing feature comparison with established LOD networks and neural network filtering, we identified LOD-characterised random networks. An aggregation of these matrices revealed distinct network features for LOD-MCI and LOD-NON-MCI. The core innovation of the present study lies in applying reverse correlation to identify those network features that determine training efficiency in well-trained neural networks. This study proposed the application of the reverse correlation method as a tool for interpreting machine learning and identifying potential discrepancy trends in preliminary experiments with limited sample sizes. We aimed to detect divergence trends in sample collection at an early stage in the research, analyse experimental samples based on research objectives, and promptly adjust relevant conditions for sample collection.

No structural network differences were observed between the LOD-MCI and LOD-NON-MCI subgroups. However, our previous brain-age prediction studies had identified significant disparities, suggesting that conventional methods fail to capture abnormalities in clinically distinct cohorts. In contrast, the reverse correlation-based neural network approach successfully detected differential inter-nodal connections. Although statistical validation is still pending, these preliminary results highlight the need for larger-scale investigations.

Matrix significance comparisons revealed the greatest structural network deviations between LOD-MCI (2645/10,000 matrices) and HC groups, and these findings are consistent with the results of prior research. The left inferior, middle, and anterior temporal pole showed the most pronounced differences, suggesting that disrupted intra-temporal white matter connectivity may serve as a potential anatomical biomarker to distinguish HC from LOD-MCI. Although studies on LLD-related cognitive impairment have implicated the cingulate cortex, hippocampus, and prefrontal cortex, these regions lack disease specificity, as they also appear in conditions such as frontotemporal dementia [18] and Lewy body dementia [19]. The encodement of memory depends on coordinated hippocampal engagement [20], frontal lobe integration of entorhinal-hippocampal inputs [21], and medial temporal-hippocampal spatial processing [22]. Given that LOD-MCI is a known risk factor for Alzheimer’s disease, and considering the limited sample size of this study, our findings suggest that structural changes within the dominant temporal lobe may reflect an early stage in the transition from LOD to Alzheimer’s disease. These preliminary results may also provide valuable clues for advancing our understanding of the pathogenesis of LOD-MCI.

The structure–function relationships of the human brain manifest as complex networks that enable efficient segregation and integration of information. Neuroimaging-derived connectivity matrices capture these architectures and can be quantified using graph theory, where nodes represent anatomical or functional regions of interest and edges denote structural or functional connections [23, 24]. Network properties have been shown to correlate with cognition and symptomatology: Li et al. [25] linked LLD white matter connectivity to processing speed, while another study reported associations between functional network metrics and depression severity [10]. Our replication of Cp/Eg differences between LLD and HC groups supports established findings. The absence of significant LOD subgroup differences may be attributable to limited statistical power, whereas machine learning with reverse correlation successfully detected subtle intergroup variations.

This study utilised multilayer neural networks combined with a reverse correlation approach, demonstrating that LOD-MCI may be linked to structural alterations in the temporal lobe, thereby providing valuable insights into its pathological mechanisms. Importantly, the proposed framework illuminates the decision-making logic of multilayer neural networks and effectively tackles the difficulty of detecting subtle inter-group differences when sample sizes are limited. Further, the reverse correlation method is not specific to neural networks and can be applied across other domains. Given the growing accessibility of high-performance and cost-efficient machine learning models, the reverse correlation technique introduced in this study presents a practical and accessible alternative for exploratory research in the field.

The data and materials used in this study are available from the corresponding author upon reasonable request.

NM designed and performed the research study. YW analyzed the data and drafted the manuscript. Both authors contributed to critical revision of the manuscript for important intellectual content. Both authors read and approved the final manuscript. Both authors have participated sufficiently in the work and agreed to be accountable for all aspects of the work.

This study was conducted in accordance with the Declaration of Helsinki and approved by the Ethics Committee of Guangdong Provincial People’s Hospital (ethics approval number: KY2023-576-03). All participants or their legal guardians provided signed informed consent.

Thanks to all the peer reviewers for their opinions and suggestions.

This research was funded by Guangzhou Science and Technology Program - Basic and Applied Basic Research Project (2023A04J0509), Guangzhou Science and Technology Program - Basic and Applied Basic Research Project (202202011280), and Heyuan Philosophy and Social Sciences Planning Project (HYSK25Z16). The funding agency had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

The authors declare no conflict of interest.

Supplementary material associated with this article can be found, in the online version, at https://doi.org/10.31083/AP44585.