Abstract : Functional Arterial Spin Labeling (fASL) MRI can provide a quantitative measurement of cerebral blood flow. A joint detection-estimation (JDE) framework has been considered to extract task-related perfusion and hemodynamic responses not restricted to canonical response function shapes. In this work, we provide a variational expectation-maximization (VEM) algorithm for hemodynamic and perfusion responses estimation. This approach provides a lower computational load compared to previous attempts, and facilitates the incorporation of prior knowledge and constraints in the estimation. Validation on simulated and real data sets has been performed.