Patlak plot

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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 problems involving irreversible uptake, such as in the case of deoxyglucose. It is used for the evaluation of nuclear medicine imaging data after the injection of a radioactive or radioopaque tracer.

The analysis is feasible if the behavior of the tracer can be approximated by two compartments, a "central" compartment that is in rapid equilibrium with blood plasma, and a "peripheral" 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:

$R(t) = K \int c(t)dt + V_0 c(t)$

where $t$ is time, $R (t)$ is the amount of tracer in region of interest, $c (t)$ is the concentration of tracer in plasma or blood, $K$ is the clearance determining the rate of entry into the peripheral 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 $c (t)$ , one obtains:

${R(t) \over c(t)} = K {\int c(t)dt \over c(t)} + V_0$

The unknown constants $K$ and $V 0$ can be obtained by linear regression from a graph of ${R(t) \over c(t)}$ against ${\int c(t)dt \over c(t)}$ .

[edit] See also

[edit] References

C. S. Patlak, R. G. Blasberg, J. D. Fenstermacher (March 1983). "Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data". Journal of Cerebral Blood Flow and Metabolism 3 (1): 1–7.
C. S. Patlak, R. G. Blasberg (1985). "Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. Generalizations". Journal of Cerebral Blood Flow and Metabolism 5 (4): 584–590.