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.

翻译：功能磁共振成像（fMRI）通过随脑区及个体变化的血流动力学响应间接测量神经元活动。忽略这种血流动力学变异性会导致下游连接性估计产生偏差。此外，血流动力学参数本身可作为重要的影像学生物标志物。因此，从静息态fMRI（rsfMRI）中估计空间变化的血流动力学是一个重要但具有挑战性的盲反演问题，因为潜在的神经活动与血流动力学耦合均未知。本研究提出了一种从rsfMRI推断皮层表面血流动力学耦合的方法。该方法通过对潜在神经信号进行边缘化处理，并基于所得边缘似然进行推断，避免了神经活动与血流动力学联合恢复的高度不稳定性。为实现可扩展的高分辨率估计，我们采用深度神经网络结合条件归一化流来精确逼近这一难处理的边缘似然，同时通过在皮层表面定义的、允许稀疏表示的先验来增强空间一致性。血流动力学估计的不确定性通过双重自助法进行量化。所提方法在合成数据与真实fMRI数据集上进行了广泛验证，结果表明其在血流动力学估计及下游连接性分析方面较现有方法有明显改进。