Patlak plot 4921531 184783057 2008-01-16T18:17:47Z Davecrosby uk 2946795 Typo correction - [[Wikipedia:Typo|You can help!]] {{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&ndash;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&ndash;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]]. {{med-stub}} {{chem-stub}} [[Category:Diagrams]]