To reduce noise-related bias effects arising in the MRTM_{0} method Ichise et al. [33] applied a strategy known to be effective in reducing the noise-induced bias for the models requiring blood data. To this end the equation of the MRTM_{0 } was rearranged to remove the noisy tissue radioactivity term C(t) from the independent variables. This approach resulted in a new method called MRTM with operational equation

C(t) is the TAC from a receptor-rich region (k_{3}>0), and C'(t) the TAC from a region without receptors_{ }(k**3**=0 in the 2-Tissue compartment model).

The multi-linear relationship above can be solved using multi-linear regression, yielding three regression coefficients. The binding potential can then be calculated from the first two regression coefficients g_{1} and g_{2} by

Furthermore, division of the first by the third regression coefficient yields an estimate of **k**_{2}' .

Implementation Notes

After switching to the **Ichise NonInvasive MRTM** in PKIN a suitable reference region must be selected. It allows to fit a multilinear regression within a range starting at the parameters **Start Lin**. The results are the three regression coefficients, and the derived binding potential BP.

There is also an error criterion **Max Err.** to fit **Start Lin**. For instance, if **Max Err.** is set to 10% and the fit box of **Start Lin**. is checked, the model searches the earliest sample so that the deviation between the regression and all measurements is less than 10%. Samples earlier than the **Start Lin**. time are disregarded for regression and thus painted in gray.

**Note:** The reference methods MRTM2 and SRTM2 require k'_{2 }as an input parameter. The k_{2}'_{ } resulting from the MRTM method above is a suitable estimate. Therefore, when switching in PKIN from the MRTM model to MRTM2 or SRTM2, k_{2}'_{ }is automatically copied from MRTM, as long as **Model conversion** in the **Configuration **menu is enabled. See also.

Abstract [33]

"We developed and applied two new linearized reference tissue models for parametric images of binding potential (BP) and relative delivery (R1) for [11C]DASB PET imaging of 5-HT transporters in human brain. The original multilinear reference tissue model (MRTM0) was modified (MRTM) and used to estimate a clearance rate (k'_{2}) from the cerebellum (reference). Then, the number of parameters was reduced from three (MRTM) to two (MRTM_{2}) by fixing k_{2}'_{ }. The resulting BP and R_{1} estimates were compared with the corresponding nonlinear reference tissue models, SRTM and SRTM_{2}, and one-tissue kinetic analysis (1TKA), for simulated and actual [11C]DASB data. MRTM gave k'_{2} estimates with little bias (<1%) and small variability (<6%). MRTM2 was effectively identical to SRTM2 and 1TKA, reducing BP bias markedly over MRTMO from 12-70% to 1-4% at the expense of somewhat increased variability. MRTM2 substantially reduced BP variability by a factor of 2-3 over MRTM or SRTM. MRTM_{2}, SRTM_{2} and 1TKA had R_{1} bias < 0.3% and variability at least a factor of 2 lower than MRTM or SRTM. MRTM_{2} allowed rapid generation of parametric images with the noise reductions consistent with the simulations. Rapid parametric imaging by MRTM_{2} should be a useful method for human [11C]DASB PET studies.