Tissue flow vector field is generated by solving the inverse problem of a voxelized transport equation using multi-delay ASL data and an optimization method. The accuracy of the flow estimation is validated on a vasculature model. For calculating flow vector field in vivo, time resolved 3D (4D) tracer concentration data is acquired using a multi-delay pseudo continuous ASL sequence. The background suppression pulse is interleaved into labeling pulse to generate short post label delay. The output flow magnitude map shows a more anterior-poster-uniform CBF than the traditional Kety’s method.