Fitting 4-compartment kinetics with a 3-compartment model

FDG kinetics in the brain are most commonly described with a 3-compartment model, although in the heart a double barrier exists between the vascular and intracellular spaces, implying a 4-compartment model with an additional interstitial compartment. The authors have studied the effect of fitting 4-compartment kinetics with the 3-compartment model, to discover the relations between the two model rate constants (k's). Computer simulation was used in our study. For each set of 4-compartment k's they simulated a noise-free composite tissue response curve for the 4-compartment kinetics; they fit the 3-compartment model to this curve to get estimates of the 3-compartment k's and examined their values relative to those of the 4-compartment model. The authors also investigated two approximation methods for getting the relations. In the first method, they equated coefficients of four Laplace-transform terms of the two models' differential equations. In the second method equated one more term, giving the nonlinear system to which they applied Newton's method to calculate 3-compartment k's. The results show that each 3-compartment fit to simulated 4-compartment data had high correlation (R>0.995), and the estimated 3-compartment k for FDG extraction from plasma represents the plasma extraction k in the 4-compartment model, while all other relationsmore » between 3- and 4-compartment k's are more complex. In most cases the approximation methods gave similar results. The authors conclude that with 4-compartment kinetic data it is difficult to reject the 3-compartment model, so when using this model, results should be interpreted with knowledge of the underlying physiology.« less