Inverse scattering transform - Revision history

84.114.217.193: correction

2014-11-18T09:23:11Z

correction

← Older revision		Revision as of 11:23, 18 November 2014
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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.

	~~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]]~~.

	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:~~

	~~: <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)]]~~

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2013-07-26T23:08:47Z

Adding 0 arxiv eprint(s), 1 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

← Older revision		Revision as of 01:08, 27 July 2013
Line 1:		Line 1:
	~~The writer is known as Irwin~~. ~~Puerto Rico is exactly where he's been~~ [~~http:~~//~~citymama~~.~~com~~.ua/~~profile_info~~.~~php?ID~~=~~38588 at home std test~~] [~~http:~~//~~www~~.~~animecontent~~.~~com~~/~~blog~~/~~348813 at home std testing~~] ~~std testing residing for years and he will never move. For many years he's been over~~ the ~~counter std test operating as~~ a ~~receptionist~~. ~~It's~~ not a ~~common factor but what she likes doing~~ is [~~http~~://~~www~~.~~herpes~~-~~coldsores~~.~~com~~/~~celebrities-with-herpes.html base jumping]~~ and ~~now she is trying to make cash with it.~~<br><br>~~My web site;~~ [~~http:~~//~~gcjcteam.org~~/~~index~~.~~php?mid~~=~~etc_video&document_srl~~=~~655020&sort_index~~=~~regdate&order_type~~=~~desc~~ http://~~gcjcteam~~.~~org~~/~~index~~.~~php?mid=etc_video&document_srl=655020&sort_index=regdate&order_type=desc~~]		{{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=1–7 \|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]].

			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:

			: <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)]]

58.185.41.82 at 03:13, 31 July 2012

2012-07-31T03:13:00Z

New page

The writer is known as Irwin. Puerto Rico is exactly where he's been [http://citymama.com.ua/profile_info.php?ID=38588 at home std test] [http://www.animecontent.com/blog/348813 at home std testing] std testing residing for years and he will never move. For many years he's been over the counter std test operating as a receptionist. It's not a common factor but what she likes doing is [http://www.herpes-coldsores.com/celebrities-with-herpes.html base jumping] and now she is trying to make cash with it.<br><br>My web site; [http://gcjcteam.org/index.php?mid=etc_video&document_srl=655020&sort_index=regdate&order_type=desc http://gcjcteam.org/index.php?mid=etc_video&document_srl=655020&sort_index=regdate&order_type=desc]