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. 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：功能磁共振成像通过血流动力学响应间接测量神经元活动，该响应在不同脑区和个体间存在差异。忽略这种血流动力学变异性会降低下游连接性估计的准确性。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，从静息态功能磁共振成像数据中估计空间异质性的血流动力学是一个重要但具有挑战性的盲反问题，因为潜在的神经活动与血流动力学耦合关系均未知。本研究提出了一种从静息态功能磁共振数据推断大脑皮层表面血流动力学耦合的方法。该方法通过边缘化潜在神经信号，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先验（允许稀疏表示）来增强空间一致性。所提方法在合成数据与真实功能磁共振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提升。