# Calculation of Patlak plot for regional TACs with plasma input

Multiple-time graphical analysis (MTGA) for irreversible
uptake (Patlak plot) with
plasma input is used to estimate tracer net uptake (influx) rate
of the PET tracer, *K _{i}*, and possibly also
metabolic rate (

*MR*) of glucose, fatty acids, or other natural substrates.

First step in the analysis is the preprocessing of plasma input curve. The procedure is dependent on the tracer and study protocol. Generalized instructions on the preparation of input curves is given here. MTGA is considered to be robust enough not to require (usually) corrections for time delay or vascular volume fraction.

The next analysis steps (drawing ROIs, calculation of regional TACs, and calculation of Patlak plot, can all be done in Carimas or PMOD.

## Command-line software

As an alternative to Carimas, Patlak plot can also be calculated using in-house command-line tools:

### 2. Preparation of regional tissue TAC data

Save the regional TAC files in the image analysis program, in DFT format with Carimas, or in TAC format in PMOD. Calculate averages over planes and regions if needed; this can also be done inside Carimas.

In brain [^{18}F]FDOPA studies with plasma input you must first subtract the reference
tissue TAC from the other regional TACs using dftbound.

Myocardial regional data can be corrected for recovery and spillover before calculating Patlak plot.

### 3. Computing the net uptake rate (*K*_{i})

_{i}

The patlak program can then be run with (at least) the following command-line parameters:

- regional tissue TAC file
- file name of (metabolite corrected) plasma TAC
- start time for the line fit (time where linear phase starts)
- end time for the line fit (time where linear phase ends, or end time of study)
- name for result file

#### Control the linearity of plots

MTGA methods produce correct results only if the slope is calculated from the linear phase of the plot, excluding the curvature in the beginning. You should always draw the Patlak plots and control the linearity and quality of the data visually.

If only late PET scan is available, then fractional uptake rate
(*FUR*) can be calculated by assuming that the y axis intercept in the graphical analysis
goes through zero. However, if a population average of intercept is known, then it can be set in
patlak with option `-ic=0`

.

*k*_{LOSS}

_{LOSS}

If trapping of the tracer is not completely irreversible during the PET scan the Patlak plot
tends to curve downwards in the end. In that case the loss rate (*k _{b}* or

*k*) of the tracer from the irreversible compartment to blood could also be estimated, if the loss rate is much smaller than the other parameters of the model (Patlak & Blasberg, 1985), i.e.

_{LOSS}*k*. However, when any downward curvature in the Patlak plots is observed, it may be more appropriate to select another analysis method designed for reversible uptake.

_{LOSS}<< K_{i}Downward curvature in Patlak plot may also be caused by systematic errors in plasma measurements, especially in metabolite analysis.

The loss rate *k _{LOSS}* could be estimated optionally with patlak program
versions until 1.7.x, but this option was removed from version 1.8.x.

#### Calculation of metabolic rate from *K*_{i}

_{i}

Metabolic rates could be calculated “manually” from the *K _{i}*, for example, by
importing Patlak result files into Excel, where

*K*values are multiplied by plasma concentration of the native substrate (for example glucose) and divided by lumped constant (

_{i}*LC*), and divided by tissue density (g/mL), if results are required per mass of tissue.

#### Computing *K*_{i} and metabolic rate at the same time

_{i}

Specify the plasma concentration of native substrate, the lumped constant, and the tissue density
on the patlak command-line using options `-Ca`

,
`-LC`

, and `-density`

.
Patlak program then writes both *K _{i}* and

*MR*values in the result file.

## Units

The units of *K _{i}* are

*(mL plasma)*(mL tissue)*.

^{-1}*min^{-1}*LC* is unitless. The units of plasma glucose concentration are (usually) *mM*,
which is equal to *mmol/L* and *µmol/mL*.
Therefore, initially, the units of metabolic rate of glucose (glucose consumption) is
*(µmol glucose)*(mL tissue) ^{-1}*min^{-1}*.
If these results are divided by tissue density,

*(g tissue)*(mL tissue)*, and multiplied by 100, the unit is converted to

^{-1}*(µmol glucose)*(100 g tissue)*, which is the most common unit for tissue glucose consumption in literature.

^{-1}*min^{-1}## Sun/Solaris Patlak program

## Steps of Patlak plot calculation using the old SUN/Solaris tool:

### Preparation of regional tissue TAC data

Convert the regional TACs in DFT format (*.dft) older *.roi.kbq format using dft2nci.

### Computing the uptake rate

The Patlak program can be found in the menu of SUN/Solaris workstations:

The same program can be used to convert the results directly to glucose consumption, if
plasma glucose concentration was measured and lumped constant (*LC*) is known.
This program has also an option for computing myocardial glucose consumption, correcting for
recovery and spillover.

# See also:

- Patlak plot using reference region input
- Calculation of Patlak plot for images
- Correcting regional myocardial data for recovery and spillover
- Fractional Uptake Rate (
*FUR*) - Calculation of regional
*FUR* - Multilinear method to calculate
*K*using lhsolki_{i} - Estimating
*K*and_{LOSS}*K*_{i}

# References:

Logan J. Graphical analysis of PET data applied to reversible and irreversible tracers.
*Nucl Med Biol.* 2000; 27:661-670.

Patlak CS, Blasberg RG. Graphical evaluation of blood-to-brain transfer constants from
multiple-time uptake data. Generalizations. *J Cereb Blood FlowMetab* 1985; 5: 584-590.

Tags: Patlak plot, MTGA, Ki

Updated at: 2018-02-06

Written by: Vesa Oikonen