We present a computational method for real-time, patient-specific simulation of 2D ultrasound (US) images. The method uses a large number of tracked ultrasound images to learn a function that maps position and orientation of the transducer to ultrasound images. This is a first step towards realistic patient-specific simulations that will enable improved training and retrospective examination of complex cases. Our models can simulate a 2D image in under 4ms (well within real-time constraints), and produce simulated images that preserve the content (anatomical structures and artefacts) of real ultrasound images.