Patlak plot

 ( Mathematical Modeling ) 

A Patlak plot (sometimes called Gjedde–Patlak plot, Patlak–Rutland plot, or Patlak analysis) is a graphical analysis technique based on the compartment model that uses linear regression to identify and analyze pharmacokinetics of tracers involving irreversible uptake, such as in the case of deoxyglucose. It is used for the evaluation of nuclear medicine medical imaging data after the injection of a radioopaque or radioactive tracer.

The method is model-independent because it does not depend on any specific compartmental model configuration for the tracer, and the minimal assumption is that the behavior of the tracer can be approximated by two compartments – a "central" (or reversible) compartment that is in rapid equilibrium with blood plasma, and a "peripheral" (or irreversible) compartment, where tracer enters without ever leaving during the time of the measurements. The amount of tracer in the region of interest is accumulating according to the equation:

$R(t)\; =\; K\; \backslash int\_0^t\; C\_p(\backslash tau)\; \backslash ,\; d\backslash tau\; +\; V\_0\; C\_p(t)$

where $t$ represents time after tracer injection, $R(t)$ is the amount of tracer in region of interest, $C\_p(t)$ is the concentration of tracer in plasma or blood, $K$ is the clearance determining the rate of entry into the peripheral (irreversible) compartment, and $V\_0$ is the distribution volume of the tracer in the central compartment. The first term of the right-hand side represents tracer in the peripheral compartment, and the second term tracer in the central compartment.

By dividing both sides by $C\_p(t)$, one obtains:

$\{R(t)\; \backslash over\; C\_p(t)\}\; =\; K\; \{\backslash int\_0^t\; C\_p(\backslash tau)\; \backslash ,\; d\backslash tau\; \backslash over\; C\_p(t)\}\; +\; V\_0$

The unknown constants $K$ and $V\_0$ can be obtained by linear regression from a graph of $\{R(t)\; \backslash over\; C\_p(t)\}$ against $\backslash int\_0^t\; C\_p(\backslash tau)\; \backslash ,\; d\backslash tau\; /\; C\_p(t)$.

• Logan plot
• Positron emission tomography
• Multi-compartment model
• Binding potential
• Deconvolution
• Albert Gjedde

• PMOD, Patlak Plot, PMOD Kinetic Modeling Tool (PKIN).
• Gjedde–Patlak plot, Turku PET Centre.