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| {{Expert-subject|Science|date=November 2008}}
| | Greetings. The writer's title is Phebe and she feels comfortable when individuals use the complete title. Years ago we moved to Puerto Rico and my family enjoys it. My day occupation is a meter reader. One of over the counter std test - [http://www.Sddch.org/?document_srl=345265 linked site], issues she loves most is to do aerobics and now she is trying to earn cash with it. |
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| A '''Patlak plot''' (sometimes called '''Gjedde–Patlak plot''', '''Patlak–Rutland plot''', or '''Patlak analysis''')<ref name="Patlak1983">{{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 |date=March 1983 | doi=10.1038/jcbfm.1983.1 | pmid=6822610}}</ref><ref name="Patlak1985">{{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 |date=April 1985 | doi=10.1038/jcbfm.1985.87 | pmid=4055928}}</ref> 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]] of tracers involving irreversible uptake, such as in the case of [[deoxyglucose]].<ref>{{cite journal | author=A. Gjedde | title=High- and low-affinity transport of D-glucose from blood to brain | journal=[[Journal of Neurochemistry]] | volume=36 | issue=4 | pages=1463–1471 |date=April 1981 | doi=10.1111/j.1471-4159.1981.tb00587.x}}</ref><ref>{{cite journal | author=A. Gjedde | title=Calculation of glucose phosphorylation from brain uptake of glucose analogs in vivo: A re-examination | journal=[[Brain Research Reviews]] | volume=4 | issue=2 | pages=237–274 |date=June 1982 | doi=10.1016/0165-0173(82)90018-2}}</ref> It is used for the evaluation of [[nuclear medicine]] [[medical imaging|imaging]] data after the injection of a [[radioopaque]] or [[radioactive tracer]].
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| 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|plasma]], and a "peripheral" (or irreversible) compartment, where tracer enters without ever leaving during the time of the measurements.<ref name="Patlak1983" /><ref name="Patlak1985" /> The amount of tracer in the [[region of interest]] is accumulating according to the equation:
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| : <math>R(t) = K \int_0^t C_p(\tau) \, d\tau + V_0 C_p(t)</math>
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| where <math>t</math> represents time after tracer injection, <math>R(t)</math> is the amount of tracer in [[region of interest]], <math>C_p(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 (irreversible) 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.
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| By [[division (mathematics)|dividing]] both sides by <math>C_p(t)</math>, one obtains:
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| : <math>{R(t) \over C_p(t)} = K {\int_0^t C_p(\tau) \, d\tau \over C_p(t)} + V_0</math>
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| 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_p(t)}</math> against <math> \int_0^t C_p(\tau) \, d\tau / C_p(t)</math>.
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| == See also ==
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| * [[Logan plot]]
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| * [[Positron emission tomography]]
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| * [[Multi-compartment model]]
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| * [[Binding potential]]
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| * [[Deconvolution]]
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| * [[Albert Gjedde]]
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| == References ==
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| {{Reflist}}
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| ==External links==
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| * PMOD, [http://www.pmod.com/technologies/doc/pkin/2326.htm Patlak Plot], PMOD Kinetic Modeling Tool (PKIN).
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| * ''[http://www.turkupetcentre.net/modelling/guide/patlak_plot.html Gjedde–Patlak plot]'', [[Turku PET Centre]].
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| [[Category:Mathematical modeling]]
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| [[Category:Systems theory]]
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| [[Category:Plots (graphics)]]
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