### MLAIR (Multiple Linear Analysis for Irreversible Radiotracers)

The MLAIR method has been developed by Kim et al. [1] for tracers undergoing irreversible trapping. It is an elternative to the Patlak plot analysis which is dependent on the specification of an equilibration time t* which may vary among tissues, and may suffer from bias when applied to noisy data. It has applied for the analysis of FDG, which can be modeled as a 2-tissue compartment model with k_{4}=0, and 11C-labeled MeNTI [1].

Operational Model Curve

The authors develop two approaches, both of which are included in the **Irreversible Ki (MLAIR)** model. The 2-tissue compartment model structure with k_{4}=0 is assumed. A blood volume fraction v_{B} is taken into account, but applied to the metabolite-corrected input curve C_{p}(t) rather than the whole-blood activity.

The operational equation of method **MLAIR1** for the the measured tissue TAC C_{T}(t) is given by

The linear coefficients are related to the model parameters as follows, allowing to calculate the influx K_{i} from P_{3} and P_{4}.

In order to avoid the P_{4}/P_{3} division of MLAIR1 which might intorduce artefacts for noisy data, a second second multilinear operational equation MLAIR2 was developed which estimates K_{i} as a direct regression parameter. **MLAIR2 **has the following operational equation for the integrated tissue activity curve:

Parameter Fitting

As soon as the **Irreversible Ki (MLAIR)** model is selected it fits the MLAIR1 and MLAIR2 model curves to the data using singular value decomposition and shows the regression coefficients. The parameter of interest is K_{i} which is calculated with both methods: **Ki(MLAIR1)** and **Ki(MLAIR2).**

The curve area initially shows the tissue TAC together with the **MLAIR1 **fit, whereas the MLAIR2-related curves are hidden because the have a completely different dynamic range. However, they can easily be shown by enabling the respective check boxes in the curve control area, as illustrated above.

Reference:

1. Kim SJ, Lee JS, Kim YK, Frost J, Wand G, McCaul ME, Lee DS: Multiple linear analysis methods for the quantification of irreversibly binding radiotracers. J Cereb Blood Flow Metab 2008, 28(12):1965-1977. DOI