A two-compartment model was used for 82Rb to allow for accurate estimation of myocardial extraction fraction because the latter is only partially extracted by the myocardium (16 ). The two compartments of the model are the “free rubidium space” (blood perfusing the myocardium plus interstitial space) and the “trapped rubidium space” (muscle of the myocardium). The main parameters of the model are the kinetic transport constants K1 (mL/min/g) and k2 (min-1), which denote the extraction (forward) and egress (backward) rates of transport between the metabolically trapped space (myocardium) and the freely diffusible space (blood pool), respectively. In order to estimate myocardial blood flow (MBF) from measures of K1, we used the extraction fraction (E) reported previously by Yoshida et al. (17 (link)) in open-chest dogs as:
Equation 1 was solved for MBF using the fixed point iteration approach (18 ). Since the equation is not solvable for high values of MBF, we used the following linear extrapolation for K1 > 0.92 ml/g/min:
The tissue time activity curve in each voxel, CT(t), was modeled as a combination of 3 contributions: the contribution from myocardial tissue, modeled using a two-compartment model, and contributions from left and right ventricular cavities, modeled as fractions of measured left (LV) and right (RV) ventricle functions:
where CTi (t) is the value of the polar map sector i (1 ≤ i ≤ 17) at time t, CTi is the time activity curve of sector i, Ca (t) is the measured left ventricle input function, and Cr (t) is the measured right ventricle input function, k2i, fyi, and rvi are the kinetic parameters for sector i, where K1i [mL/min/g] characterizes myocardial tissue extraction (inflow), k2i [min-1] characterizes myocardial tissue egress (outflow), fvi [dimensionless] represents the contribution to the total activity from the blood input function Ca (t), and rvi [dimensionless] represents the contribution from the activity in the right ventricle, Cr (t), which in general differs from the input function Ca (t). Both Ca (t) and Cr (t) were determined by GFADS.
The tissue time activity curve in each voxel, CT(t), was modeled as a combination of 3 contributions: the contribution from myocardial tissue, modeled using a two-compartment model, and contributions from left and right ventricular cavities, modeled as fractions of measured left (LV) and right (RV) ventricle functions:
where CTi (t) is the value of the polar map sector i (1 ≤ i ≤ 17) at time t, CTi is the time activity curve of sector i, Ca (t) is the measured left ventricle input function, and Cr (t) is the measured right ventricle input function, k2i, fyi, and rvi are the kinetic parameters for sector i, where K1i [mL/min/g] characterizes myocardial tissue extraction (inflow), k2i [min-1] characterizes myocardial tissue egress (outflow), fvi [dimensionless] represents the contribution to the total activity from the blood input function Ca (t), and rvi [dimensionless] represents the contribution from the activity in the right ventricle, Cr (t), which in general differs from the input function Ca (t). Both Ca (t) and Cr (t) were determined by GFADS.
