Patlak plot
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{{Expert-portal|Science}}
A '''Patlak plot''' (sometimes called Gjedde-Patlak plot, Patlak-Rutland plot, or Patlak analysis) is a [[Graph of a function|graphical]] analysis technique based on the [[Compartment (pharmacokinetics)|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]] [[medical imaging|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:
<math>R(t) = K \int c(t)dt + V_0 c(t)</math>
where <math>t</math> is time, <math>R(t)</math> is the amount of tracer in region of interest, <math>c(t)</math> is the concentration of tracer in plasma or blood, <math>K</math> is the [[Clearance (medicine)|clearance]] determining the rate of entry into the peripheral compartment, and <math>V_0</math> is the [[distribution volume]] of the tracer in the central compartment. The first [[Term (mathematics)|term]] of the right-hand side represents tracer in the peripheral compartment, and the second term tracer in the central compartment.
By [[division (mathematics)|dividing]] both sides by <math>c(t)</math>, one obtains:
<math>{R(t) \over c(t)} = K {\int c(t)dt \over c(t)} + V_0</math>
The unknown constants <math>K</math> and <math>V_0</math> can be obtained by [[linear regression]] from a [[Graph of a function|graph]] of <math>{R(t) \over c(t)}</math> against <math> {\int c(t)dt \over c(t)}</math>.
== See also ==
* [[Logan plot]]
* [[Multi-compartment model]]
* [[Binding potential]]
== References ==
* {{Cite journal
| author = C. S. Patlak, R. G. Blasberg, J. D. Fenstermacher
| title = Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data
| journal = [[Journal of Cerebral Blood Flow and Metabolism]]
| volume = 3
| issue = 1
| pages = 1–7
| year = [[1983]]
| month = March
}}
* {{Cite journal
| author = C. S. Patlak, R. G. Blasberg
| title = Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. Generalizations
| journal = [[Journal of Cerebral Blood Flow and Metabolism]]
| volume = 5
| issue =4
| pages = 584–590
| year = [[1985]]
}}
=== External links ===
* PMOD, [http://www.pmod.com/technologies/doc/pkin/2326.htm Patlak Plot], PMOD Kinetic Modeling Tool (PKIN).
* ''[http://www.turkupetcentre.net/modelling/guide/patlak_plot.html Gjedde-Patlak plot]'', [[Turku PET Centre]].
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[[Category:Diagrams]]