BPnd (Ichise MRTM2 Ref): Ichise MRTM with fixed k2'

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BPnd (Ichise MRTM2 Ref): Ichise MRTM with fixed k2'

Starting from the operational equation of the blood-based Logan plot, Ichise et al. derived three multi-linear reference tissue model variants MRTM0, MRTM and MRTM2 [1]. They all assume an initial equilibration time t* from which on the derived multi-linear relation holds. However, if kinetics in the target tissue can be described by a 1-tissue compartment model (an assumption required for the SRTM), all data can be used for the fitting (t*=0). Otherwise an adequate t* value has to be determined.

Assuming the presence of receptor-devoid reference region TAC CT'(t), the target tissue TAC CT(t) is plotted as a function of the transformed tissue TACs as illustrated below. For the calculation of BPND it is assumed that the non-displaceable distribution volumes in the tissue and reference regions are identical.


When applied to noisy data such as single-pixel TACs in parametric mapping, the MRTM method still suffers from a high variability. Assuming a known value of the reference tissue clearance rate k2' the MRTM operational equation can be reformulated as the MRTM2 operational equation:

Equation MRTM2

with only two regression coefficients VT/(VT'b) and 1/b for T > t*. The multi-linear relationship above can be fitted using multi-linear regression, yielding three regression coefficients. The binding potential is then calculated from the ratio of the two regression coefficients as

Equation MRTM BP

For receptor ligands with 1-tissue kinetics such as [11C]DASB the multi-linear equation is correct from t*=0, and the clearance rate constant from the tissue to plasma k2 is equal to the negative value of the second regression coefficient, -(1/b). Furthermore, R1 = K1/K'1, the relative radioligand delivery, equals the first regression coefficient divided by k2'.

For pixelwise applications the same two-step approach applied in the SRTM2 model is applied:

1.Calculate in the model preprocessing step the clearance rate k2' of the reference TAC by the MRTM method with VOI data which has a limited level of noise.

2.Fix  k2': Use the estimated k2' value for the pixelwise MRTM calculations, reducing the number of fitted parameters from 3 to 2.

Alternatively, k2' can be determined for externally (for instance in PKIN), manually entered and fixed.

Acquisition and Data Requirements

Image Data

A dynamic data set acquired long enough that the equilibrium relation is approximately fulfilled.

Target tissue

Optional: TAC from a receptor-rich region (such as basal ganglia for D2 receptors). For visualization of model fitting and optionally for fitting k2' and t*

Reference tissue

Mandatory: TAC from a receptor-devoid region (such as cerebellum or frontal cortex for D2 receptors).

Note: specification of an appropriate reference TAC is crucial for the result!


Optional: VOI definition excluding the reference tissue which can be used for getting an estimate of k2'.

Model Preprocessing

PXMOD MRTM2 Model Pre-Processing


The least squares estimation should be restricted to a range after an equilibration time. t* marks the beginning of the range used in the multi-linear regression analysis. It can be fitted based on the Max. Err. criterion if a Target tissue is specified.

Max. Err.

The maximal relative error allowed if t* is fitted.

R1 Cutoff

Alternative method for masking based on the R1 estimate.

k2' for mapping

k2 of the reference tissue. It can be specified in four different ways, as explained in section Specification of k2'.

Percent masked pixels

Exclude the specified percentage of pixels based on histogram analysis of integrated signal energy. Not applied in the presence of a defined mask.

The result of a model fit during Model Preprocessing is shown in the Model Results panel for inspection. The initial points which are not taken into account (before the t* time) are indicated in grey. If no Target tissue is specified, the panel remains empty.

PXMOD MRTM2 Model Pre-Processing Result

Model Configuration

PXMOD MRTM2 Model Parameters


Binding potential BPnd = k3/k4 .


R1 = K1/K1' relative ligand delivery (for 1-tissue kinetics). The calculated image often looks similar to a perfusion image and can sometimes used for matching purposes. It is recommended to restrict the range of fitted values.


Clearance rate in the pixel (for 1-tissue kinetics).


1.Ichise M, Liow JS, Lu JQ, Takano A, Model K, Toyama H, Suhara T, Suzuki K, Innis RB, Carson RE: Linearized reference tissue parametric imaging methods: application to [11C]DASB positron emission tomography studies of the serotonin transporter in human brain. J Cereb Blood Flow Metab 2003, 23(9):1096-1112. DOI