Simultaneously Quantifying K 1 , k 2 , and Blood Volume in Myocardial Imaging with Overlapping Volumes of Interest: Practical Identifiability

Objective 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,K1andk2, respectively, and the blood-volume fraction, V. Theoretically, these parameters can be determined from time-activity curves (TACs) of the blood pool and the myocardium from injection and uptake of a perfusion tracer, if the matrix describing the relationship between the true TACs and the observed TACs is known. Herein, we numerically confirm these theoretical predictions and study the impact of experimental noise and matrix element uncertainty on these three parameters. Approach Using a one-compartment model, we simulated TACs for different values ofK1,k2, andV. A mixing matrix involving recovery coefficients and spillover fractions was used to describe the transformation of the true concentration to the observed concentrations. Kinetic model fitting was employed to measure the three physical parameters, and we measured the bias of these fit results with respect to the true simulated values. We investigated a range of mixing matrices, rates of uptake and washout, and blood volume fractions. Main results We confirmed the theoretical prediction thatK1,k2, andVcan be simultaneously measured accurately if and only if all elements of the mixing matrix are known. There was an approximately linear effect of uncertainty in the measurement of the three physical parameters to the noise level on the TACs. Consistent with previous results, greater mixing via the mixing matrix or the blood-volume fraction resulted in greater uncertainty. Significance This work shows we can accurately measure the physical parameters likeK1while also quantifying the uncertainty in their measurement due to noise on the TACs and mixing-matrix uncertainty.