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Learned Hemodynamic Coupling Inference in Resting-State Functional MRI

William Consagra, Eardi Lila

TL;DR

This paper addresses the problem of spatially varying hemodynamic coupling in resting-state fMRI by marginalizing over the unknown neural signals and learning a per-vertex marginal likelihood $p(y|\tilde{\theta})$ using a conditional neural spline normalizing flow. A Gaussian-process prior on the transformed HRF field $\tilde{\theta}$ and a sparse cortical discretization enable scalable MAP estimation, while a double-bootstrap procedure provides calibrated uncertainty intervals. Simulator calibration via spectral moment matching ensures physiologically plausible data generation, and a suite of experiments on synthetic and HCP data demonstrates improved hemodynamic reconstruction and downstream connectivity analyses compared with state-of-the-art alternatives. The approach offers a practical path to deconvolve rsfMRI signals with subject- and region-specific dynamics, potentially yielding biomarkers and more accurate brain connectivity maps, underlining its significance for neuroscience and neuroimaging analytics.

Abstract

Functional magnetic resonance imaging (fMRI) provides an indirect measurement of neuronal activity via hemodynamic responses that vary across brain regions and individuals. Ignoring this hemodynamic variability can bias downstream connectivity estimates. Furthermore, the hemodynamic parameters themselves may serve as important imaging biomarkers. Estimating spatially varying hemodynamics from resting-state fMRI (rsfMRI) is therefore an important but challenging blind inverse problem, since both the latent neural activity and the hemodynamic coupling are unknown. In this work, we propose a methodology for inferring hemodynamic coupling on the cortical surface from rsfMRI. Our approach avoids the highly unstable joint recovery of neural activity and hemodynamics by marginalizing out the latent neural signal and basing inference on the resulting marginal likelihood. To enable scalable, high-resolution estimation, we employ a deep neural network combined with conditional normalizing flows to accurately approximate this intractable marginal likelihood, while enforcing spatial coherence through priors defined on the cortical surface that admit sparse representations. Uncertainty in the hemodynamic estimates is quantified via a double-bootstrap procedure. The proposed approach is extensively validated using synthetic data and real fMRI datasets, demonstrating clear improvements over current methods for hemodynamic estimation and downstream connectivity analysis.

Learned Hemodynamic Coupling Inference in Resting-State Functional MRI

TL;DR

This paper addresses the problem of spatially varying hemodynamic coupling in resting-state fMRI by marginalizing over the unknown neural signals and learning a per-vertex marginal likelihood using a conditional neural spline normalizing flow. A Gaussian-process prior on the transformed HRF field and a sparse cortical discretization enable scalable MAP estimation, while a double-bootstrap procedure provides calibrated uncertainty intervals. Simulator calibration via spectral moment matching ensures physiologically plausible data generation, and a suite of experiments on synthetic and HCP data demonstrates improved hemodynamic reconstruction and downstream connectivity analyses compared with state-of-the-art alternatives. The approach offers a practical path to deconvolve rsfMRI signals with subject- and region-specific dynamics, potentially yielding biomarkers and more accurate brain connectivity maps, underlining its significance for neuroscience and neuroimaging analytics.

Abstract

Functional magnetic resonance imaging (fMRI) provides an indirect measurement of neuronal activity via hemodynamic responses that vary across brain regions and individuals. Ignoring this hemodynamic variability can bias downstream connectivity estimates. Furthermore, the hemodynamic parameters themselves may serve as important imaging biomarkers. Estimating spatially varying hemodynamics from resting-state fMRI (rsfMRI) is therefore an important but challenging blind inverse problem, since both the latent neural activity and the hemodynamic coupling are unknown. In this work, we propose a methodology for inferring hemodynamic coupling on the cortical surface from rsfMRI. Our approach avoids the highly unstable joint recovery of neural activity and hemodynamics by marginalizing out the latent neural signal and basing inference on the resulting marginal likelihood. To enable scalable, high-resolution estimation, we employ a deep neural network combined with conditional normalizing flows to accurately approximate this intractable marginal likelihood, while enforcing spatial coherence through priors defined on the cortical surface that admit sparse representations. Uncertainty in the hemodynamic estimates is quantified via a double-bootstrap procedure. The proposed approach is extensively validated using synthetic data and real fMRI datasets, demonstrating clear improvements over current methods for hemodynamic estimation and downstream connectivity analysis.
Paper Structure (34 sections, 31 equations, 5 figures, 1 table)

This paper contains 34 sections, 31 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Work
  4. Our Contribution
  5. Models and Background
  6. Modeling Neural Population Dynamics
  7. Modeling the Hemodynamic Response
  8. Statistical Model for Observed Data
  9. Methodology
  10. Learned Marginal Likelihood
  11. Prior Distribution
  12. Point Estimation
  13. Hyperparameter Selection
  14. Calibration of Smoothness Prior
  15. Calibration of Simulator
  16. ...and 19 more sections

Figures (5)

  • Figure 1: Simulation from the data generative model. (Left) Neural activity sampled from \ref{['eqn:signal_generative_model']}. (Middle) Hemodynamic response obtained by convolving the neural activity with the HRF \ref{['eqn:double_gamma_hrf']} under forward model \ref{['eqn:LTI_HR_model']}. (Right) Simulated BOLD measurements generated according to \ref{['eqn:bold_forward_model']} ($t_r=0.72\,\mathrm{s}$).
  • Figure 2: Hemodynamic response kernel for several $\theta$ for model \ref{['eqn:double_gamma_hrf']} (left panel) and \ref{['eqn:canonical_gamma_basis']} (right panel).
  • Figure 3: (Left) Estimates of the $\theta$-field for the one-parameter hemodynamic coupling model \ref{['eqn:double_gamma_hrf']} on the HCP test-retest data for three randomly selected subjects. Inter-subject variability is noticeably larger than within-subject between-scan variability. (Right) Length of the $95\%$ pointwise intervals calculated from the procedure in Section \ref{['ssec:uq']} on the Scan 1 data.
  • Figure 4: A) Time-to-peak (in seconds) of mean hemodynamic field, B) pointwise standard deviation of the hemodynamic field $\tilde{\theta}(x)$, C) and the first $5$ eigenfunctions $\tilde{\varphi}_k$, describing the main modes of inter-subject variability, estimated from $100$ unrelated HCP-YA subjects under the one-parameter model \ref{['eqn:double_gamma_hrf']}.
  • Figure 5: (Left) $-\log_{10}$-transformed p-values for testing GC from each mesh vertex to average signal in Left Ventral Area 6. (Right) Regions in the Glasser atlas with at least 50% of vertices exhibiting significant GC to Left Ventral Area 6, for the three considered signal representations.