SIME

The SIME works on the assumption that the parent AIF is common to all of the TACs and can be expressed using a mathematical function. In its original implementation, Feng et al. used an input function model [13] which is a sum of a gamma variate function and two exponentials. This function has six parameters and can be written as Eq. 1.

The six parameters of the AIF function are estimated together with the kinetic parameters by fitting the TACs for multiple brain regions simultaneously. Therefore, when a two-tissue compartment (2-TC) model with four rate constants (K₁–k₄) is used to model m number of regions of interest (ROIs), 4m+6 parameters are included in the optimisation. The cost function can be written as follows:

where E¯i(t _j) is the estimated model output, M_i(t _j) is the measured PET activity concentration at the jth time frame of the ith region. Symbol m represents the number of TACs to be fitted, n represents the number of time frames for each TAC and w_i,j are the weights applied to the model and were set to 1 in our implementation to apply uniform weighting. In order to account for the measured activity in a PET scan, E¯i(t _j) is computed by averaging E_i over the length of the scanning interval:

where tj−=tj−Δtj/2, tj+=tj+Δtj/2 and Δt_j is length of frame j. C_WB represents the whole blood TAC, C_P is the parent AIF, h is the impulse response of the 2-TC model and V_b is the cerebral blood volume. As the original SIME does not include any prior measurement of C_WB, C_P was used to replace it in Eq. 4.