Conventional quantitative MRI estimates parameters by fitting a known analytical signal model to pixels of images with different contrasts. By combining image reconstruction and the signal model into one non-linear inverse problem, model-based reconstruction methods can estimate the parameters directly from k-space. Avoiding the acquisition and reconstruction of intermediate images they require much less data. Furthermore, they can be directly combined with parallel imaging and compressed sensing, but still rely on analytical models and carefully designed MRI sequences.
Here, we generalize this framework to work with arbitrary sequences using a Runge-Kutta based simulation of spin dynamics.