BPnd (Ichise MRTM0 Ref): Ichise Multi-linear Reference Tissue Model

The MRTM₀ reference model approach of Ichise et al. [18] is based on the Logan plot and applies for receptor studies. The assumption is, that there is a reference TAC C'(t) from a region without receptors (k₃=0 in the 2-Tissue compartment model), and a TAC C(t) from a receptor-rich region (k₃>0). If the Logan plot is applied for both TACs, then the input curve can be eliminated and the following multi-linear expression can be derived.

V and V' are the total distribution volumes of C(t) and C'(t), k'₂ is the clearance rate constant from the reference region to plasma, and b is the intercept term, which becomes constant for T > t* (equilibration time).

The multi-linear relationship above can be solved using multi-linear regression, yielding three regression coefficients. From the first coefficient the binding potential can be calculated by

assuming that the non-displaceable distribution volumes in the tissue and reference regions are identical.

For radioligands with 1-tissue kinetics such as ¹¹C DASB the multi-linear equation is correct from T = 0, i.e., t* = 0, and b is equal to (-1/k₂ ), where k₂ is the clearance rate constant from the tissue to plasma. Furthermore, R₁ = K₁/K'₁, the relative radioligand delivery, can be calculated from the ratio of the second and third regression coefficients.