[Paper Review] Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence

Bastian Rieck, Tristan S. Yates+5 more|arXiv (Cornell University)|Jun 14, 2020

Topological and Geometric Data AnalysisComputer Science68 references35 citations

TL;DR

The paper introduces a non-parametric, coordinate-free topological framework that encodes time-varying fMRI data as cubical persistence diagrams and uses them for clustering and brain-state trajectory analysis to reveal age-related differences.

ABSTRACT

Functional magnetic resonance imaging (fMRI) is a crucial technology for gaining insights into cognitive processes in humans. Data amassed from fMRI measurements result in volumetric data sets that vary over time. However, analysing such data presents a challenge due to the large degree of noise and person-to-person variation in how information is represented in the brain. To address this challenge, we present a novel topological approach that encodes each time point in an fMRI data set as a persistence diagram of topological features, i.e. high-dimensional voids present in the data. This representation naturally does not rely on voxel-by-voxel correspondence and is robust to noise. We show that these time-varying persistence diagrams can be clustered to find meaningful groupings between participants, and that they are also useful in studying within-subject brain state trajectories of subjects performing a particular task. Here, we apply both clustering and trajectory analysis techniques to a group of participants watching the movie 'Partly Cloudy'. We observe significant differences in both brain state trajectories and overall topological activity between adults and children watching the same movie.

Motivation & Objective

• Motivate robust, noise-tolerant representations of time-varying fMRI data that do not rely on voxel-by-voxel correspondence.
• Introduce cubical persistence as a topological descriptor for fMRI volumes across time.
• Demonstrate that time-varying topological features can be clustered to reveal group differences and to study within-subject brain state trajectories.
• Show that topological features can improve age prediction and illuminate developmental differences in brain processing.

Proposed method

• Convert each fMRI volume into a cubical complex where voxels are vertices and six-neighbour adjacencies define edges.
• Assign a time-step specific filtration value to each cubical element by taking the maximum voxel activation within the element.
• Compute time-slice persistent homology to obtain time-varying persistence diagrams per participant.
• Vectorize and summarize persistence diagrams with statistics such as the infinity norm ||D||∞ and the p-norm ||D||p (p=1) for static analyses.
• Transform persistence diagrams into persistence images to enable dynamic trajectory analysis and machine learning methods.
• Use clustering, age-prediction regression, and brain-state trajectory visualization (PHATE) to analyze age-related differences.

Experimental results

Research questions

• RQ1 Can time-varying fMRI data be robustly represented without voxel-wise correspondences using cubical persistence?
• RQ2 Do time-varying topological features reveal age-related differences in brain activity during naturalistic movie watching?
• RQ3 Are topological representations more informative for age prediction than baseline voxel/functional-connectivity approaches?
• RQ4 What do cohort brain state trajectories tell us about development of cognitive processing?
• RQ5 How does variability in topological features relate to event boundaries in naturalistic stimuli?

Key findings

• Time-varying persistence diagrams derived from cubical complexes capture meaningful, noise-robust topological information from fMRI data.
• Topological features separate adults from children in embeddings, more clearly than baseline correlation-based representations.
• Summary statistics of persistence diagrams (notably ||D||∞) improve age-prediction performance compared to baselines.
• Cohort brain-state trajectories show distinct, age-related trajectory shapes and higher entropy in older participants for cognitively demanding processing.
• Event-processing variability analysis reveals stronger cross-cohort differences in occipital-temporal masks around event boundaries.
• Persistence images enable dynamic trajectory analyses and reveal developmental differences in brain-state evolution.