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{{Expert-subject|Science|date=November 2008}}
 
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&ndash;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&ndash;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&ndash;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&ndash;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]].
 
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 &ndash; 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:
 
: <math>R(t) = K \int_0^t C_p(\tau) \, d\tau + V_0  C_p(t)</math>
 
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.
 
By [[division (mathematics)|dividing]] both sides by <math>C_p(t)</math>, one obtains:
 
: <math>{R(t) \over C_p(t)} = K {\int_0^t C_p(\tau) \, d\tau \over C_p(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_p(t)}</math> against <math> \int_0^t C_p(\tau) \, d\tau / C_p(t)</math>.
 
== See also ==
* [[Logan plot]]
* [[Positron emission tomography]]
* [[Multi-compartment model]]
* [[Binding potential]]
* [[Deconvolution]]
* [[Albert Gjedde]]
 
== References ==
{{Reflist}}
 
==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]].
 
[[Category:Mathematical modeling]]
[[Category:Systems theory]]
[[Category:Plots (graphics)]]

Revision as of 01:08, 27 July 2013

Template:Expert-subject

A Patlak plot (sometimes called Gjedde–Patlak plot, Patlak–Rutland plot, or Patlak analysis)[1][2] 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.[3][4] It is used for the evaluation of nuclear medicine 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 plasma, and a "peripheral" (or irreversible) compartment, where tracer enters without ever leaving during the time of the measurements.[1][2] The amount of tracer in the region of interest is accumulating according to the equation:

where represents time after tracer injection, is the amount of tracer in region of interest, is the concentration of tracer in plasma or blood, is the clearance determining the rate of entry into the peripheral (irreversible) compartment, and 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 , one obtains:

The unknown constants and can be obtained by linear regression from a graph of against .

See also

References

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    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

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    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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