Digital Phantoms

In CMRsim, digital objects are defined as a set of particles bearing physical properties, without assuming a spatial structure on simulation time. The input format for all simuations within CMRsim are python dictionaries, where the keys denote the physical properties and the values of the dictionary are np.ndarrays that have at least 1 axis. Mandatory axis has the dimensionality of the number of all particles in the object.

Generally, the required entries in the dictionary are defined by the composed simulator (as you will see in the subsequent tutorial sections). However, there are mandatory inputs with specific shapes for differing for analytic and bloch simulations as shown below:

Input to Bloch simulation

digital_phantom = {
    "M0" : np.ndarray[dtype = np.complex64, shape = (#points, )]             # rho
    "magnetization" : np.ndarray[dtype = np.complex64, shape = (#points, )]  # (M+, M-, Mz)
    "T1" : np.ndarray[dtype = np.float32, shape = (#points, )],
    "T2" : np.ndarray[dtype = np.float32, shape = (#points, )]
    "initial_positions" : np.ndarray[dtype = np.float32, shape = (#points, 3)]
}

For analytic simulations the inputs have additional axes denoted with #repetitions and #k-space-samples. The reason for these axes to be present, lies within an efficient broad casting logic allowing an efficient evaluation of multiple simulation configurations. To learn more about that checkout the tutorial page on analytic simulations.

Input to Analytic simulation

digital_phantom = {
    "M0" : np.ndarray[dtype = np.complex64, shape = (#points, #repetitions, #k-space-samples)],
    "r_vectors": np.ndarray[dtype = np.float32, shape = (#points, #repetitions, #k-space-samples, 3(XYZ))],
    "T1" : np.ndarray[dtype = np.float32, shape = (#points, #repetitions, #k-space-samples)],
    "T2" : np.ndarray[dtype = np.float32, shape = (#points, #repetitions, #k-space-samples)]
}

Quantities, that spatially vary (e.g. coil sensitivity or velocity within a velocity field) are looked up on simulation time. Physical properties that depend on the spatial structure of the digital object need to be computed outside of the simulation call and assigned to the particles on demand.