Kinetic modelling using basis functions derived from two-tissue compartmental models with a plasma input function: General principle and application to [18F]fluorodeoxyglucose positron emission tomography

A kinetic modelling method for the determination of influx constant, Ki is given that utilises basis functions derived from plasma input two-tissue compartmental models (BAFPIC). Two forms of the basis functions are given: BAFPICI with k4 = 0 (no product loss) and BAFPICR with k4 non-zero. Simulations were performed using literature rate constant values for [18F]fluorodeoxyglucose (FDG) in both normal and abnormal brain pathology. Both homogeneous and heterogeneous tissues were simulated and this data was also used as input for other methods commonly used to determine Ki: non-linear least squares compartmental modelling (NLLS), autoradiographic method and Patlak-Gjedde graphical analysis (PGA). The four methods were also compared for real FDG positron emission tomography (PET) data. For both k4 = 0 and k4 non-zero simulated data BAFPIC had the best bias properties of the four methods. The autoradiographic method was always the best for variability but BAFPICI had lower variability than PGA and NLLS. For non-zero k4 data, the variance of BAFPICR was inferior to PGA but still significantly superior to NLLS. Ki maps calculated from real data substantiate the simulation results, with BAFPICI having lower noise than PGA. Voxel Ki values from BAFPICI correlated well with those from PGA (r2 = 0.989). BAFPIC is easy to implement and combines low bias with good noise properties for voxel-wise determination of Ki for FDG. BAFPIC is suitable for determining Ki for other tracers well characterised by a serial two-tissue compartment model and has the advantage of also producing values for individual kinetic constants and blood volume.