Simultaneously quantifyingK1,k2, and blood volume in myocardial imaging with overlapping volumes of interest: structural identifiability.

Dynamic imaging in emission computed tomography allows the determination of physiological parameters that have important clinical implications. In myocardial imaging, three parameters of interest are the uptake and washout rates, K1 and k2, respectively, and the blood-volume fraction, V. These parameters can be determined from time-activity curves (TACs) of the blood (i.e., the input function) and the myocardium. However, the volumes of interest for the dynamic images may show overlap of these regions; this overlap can be expressed as a mixing matrix. Herein, we address the requirements for mathematical uniqueness of the solutions. The relationship of the TACs of the myocardium and blood pool with model parameters is evaluated under the structural identifiability criterion, which requires equal observed TACs to have a one-to-one mapping with the model parameters. This leads to constraints on the model parameters. Those constraints lead to system invariants, specifying the relationship between the true solution of the equations and other candidate solutions consistent with the observations for the TACs. Structural identifiability is achieved for K1, k2, and V if all parameters of the mixing matrix are known. These results provide a complete structural identifiability analysis for a one-tissue compartment model with mixing matrix that accounts for partial-volume effects and spill-in/out of VOI. Prior results showed a more relaxed condition when k2 was assumed to be zero.