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Leveraging Persistent Homology for Differential Diagnosis of Mild Cognitive Impairment

Ninad Aithal, Debanjali Bhattacharya, Neelam Sinha, Thomas Gregor Issac

TL;DR

This work targets differential diagnosis of mild cognitive impairment and its subtypes by leveraging persistent homology on resting-state fMRI time series. It introduces a pipeline that converts ROI-wise fMRI signals into 3D point clouds via sliding window embedding, computes persistence diagrams for Betti descriptors $H_0$, $H_1$, and $H_2$ through Vietoris–Rips filtration, and uses Wasserstein distances to quantify both inter-subject and inter-ROI topological differences. A two-branch CNN integrates flattened 1D features from Wasserstein matrices and 2D CNN features from distance maps to classify HC vs MCI and EMCI vs LMCI, achieving up to $95\%$ accuracy on the ADNI dataset and $85\%$ on the in-house TLSA dataset for HC vs MCI, with notable performance on MCI subtypes ($76.5\%$, $91.1\%$, and $80\%$). The analysis highlights $H_0$ as the most informative topological descriptor, reveals ROI-level DMN signatures associated with progression, and demonstrates superior performance relative to state-of-the-art fMRI-based approaches, suggesting persistent homology as a promising biomarker framework for dementia staging and differential diagnosis.

Abstract

Mild cognitive impairment (MCI) is characterized by subtle changes in cognitive functions, often associated with disruptions in brain connectivity. The present study introduces a novel fine-grained analysis to examine topological alterations in neurodegeneration pertaining to six different brain networks of MCI subjects (Early/Late MCI). To achieve this, fMRI time series from two distinct populations are investigated: (i) the publicly accessible ADNI dataset and (ii) our in-house dataset. The study utilizes sliding window embedding to convert each fMRI time series into a sequence of 3-dimensional vectors, facilitating the assessment of changes in regional brain topology. Distinct persistence diagrams are computed for Betti descriptors of dimension-0, 1, and 2. Wasserstein distance metric is used to quantify differences in topological characteristics. We have examined both (i) ROI-specific inter-subject interactions and (ii) subject-specific inter-ROI interactions. Further, a new deep learning model is proposed for classification, achieving a maximum classification accuracy of 95% for the ADNI dataset and 85% for the in-house dataset. This methodology is further adapted for the differential diagnosis of MCI sub-types, resulting in a peak accuracy of 76.5%, 91.1% and 80% in classifying HC Vs. EMCI, HC Vs. LMCI and EMCI Vs. LMCI, respectively. We showed that the proposed approach surpasses current state-of-the-art techniques designed for classifying MCI and its sub-types using fMRI.

Leveraging Persistent Homology for Differential Diagnosis of Mild Cognitive Impairment

TL;DR

This work targets differential diagnosis of mild cognitive impairment and its subtypes by leveraging persistent homology on resting-state fMRI time series. It introduces a pipeline that converts ROI-wise fMRI signals into 3D point clouds via sliding window embedding, computes persistence diagrams for Betti descriptors , , and through Vietoris–Rips filtration, and uses Wasserstein distances to quantify both inter-subject and inter-ROI topological differences. A two-branch CNN integrates flattened 1D features from Wasserstein matrices and 2D CNN features from distance maps to classify HC vs MCI and EMCI vs LMCI, achieving up to accuracy on the ADNI dataset and on the in-house TLSA dataset for HC vs MCI, with notable performance on MCI subtypes (, , and ). The analysis highlights as the most informative topological descriptor, reveals ROI-level DMN signatures associated with progression, and demonstrates superior performance relative to state-of-the-art fMRI-based approaches, suggesting persistent homology as a promising biomarker framework for dementia staging and differential diagnosis.

Abstract

Mild cognitive impairment (MCI) is characterized by subtle changes in cognitive functions, often associated with disruptions in brain connectivity. The present study introduces a novel fine-grained analysis to examine topological alterations in neurodegeneration pertaining to six different brain networks of MCI subjects (Early/Late MCI). To achieve this, fMRI time series from two distinct populations are investigated: (i) the publicly accessible ADNI dataset and (ii) our in-house dataset. The study utilizes sliding window embedding to convert each fMRI time series into a sequence of 3-dimensional vectors, facilitating the assessment of changes in regional brain topology. Distinct persistence diagrams are computed for Betti descriptors of dimension-0, 1, and 2. Wasserstein distance metric is used to quantify differences in topological characteristics. We have examined both (i) ROI-specific inter-subject interactions and (ii) subject-specific inter-ROI interactions. Further, a new deep learning model is proposed for classification, achieving a maximum classification accuracy of 95% for the ADNI dataset and 85% for the in-house dataset. This methodology is further adapted for the differential diagnosis of MCI sub-types, resulting in a peak accuracy of 76.5%, 91.1% and 80% in classifying HC Vs. EMCI, HC Vs. LMCI and EMCI Vs. LMCI, respectively. We showed that the proposed approach surpasses current state-of-the-art techniques designed for classifying MCI and its sub-types using fMRI.
Paper Structure (11 sections, 6 equations, 6 figures, 3 tables)

This paper contains 11 sections, 6 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Dataset description
  3. Proposed Methodology
  4. Extraction of time series
  5. Point cloud construction from time series
  6. Persistent homology
  7. ROI-Specific Inter-Subject Interactions
  8. Subject-Specific Inter-ROI Interactions
  9. Classification
  10. Results and Discussion
  11. Acknowledgement

Figures (6)

  • Figure 1: Block schematic of the proposed methodology
  • Figure 2: Illustrating the Wasserstein distance as derived from the persistence diagram of fMRI time series for homology dimension-0, showing interactions among ROIs within the DMN for one representative subject. The 34 ROIs within the DMN exhibit a consistent spatial arrangement, wherein nearby brain regions are grouped together. The arrangement of these 34 ROIs remains consistent across all subjects. A low value of Wasserstein distance suggests synchronized neural activity and coordination between brain regions, while a high value of distance indicates distinct activity patterns and potential functional independence.
  • Figure 3: The proposed deep learning architecture
  • Figure 4: ROI-specific Wasserstein distance (dim-0) across all subjects of HC (n=50) and MCI (n=50) from each considered brain network- showing the visible difference in pattern of Wasserstein distance between HC and MCI subjects. These ROIs are (A) Post cingulate 108 (DMN), (B) inf cerebellum 121 (CB), (C) IPL 96 (FP), (D) Occipital1 106 (OP), (E) Post cingulate 80 (CO) and (F) Pre-SMA 41 (SM).
  • Figure 5: Visualization of P-plot at 99% C.I for Default mode network for EMCI (top row) and LMCI bottom row. The column 1, 2 and 3 show the P-plot for homology dimension 0, 1 and 2, respectively. Column 4, 5, and 6 highlight the ROI-pair that showed significant differences $(p<0.01)$ in topology across all subjects of between (i) HC and EMCI, (ii) HC and LMCI. The visualization clearly depicts significant ROIs which are seen to be more concentrated in fewer brain regions as homology dimension increases in case of LMCI as compared to EMCI.
  • ...and 1 more figures