# Patlak plot > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Patlak_plot > Markdown URL: https://mediated.wiki/source/Patlak_plot.md > Source: https://en.wikipedia.org/wiki/Patlak_plot > Source revision: 1313832298 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) Graphical analysis technique A **Patlak plot** (sometimes called **Gjedde–Patlak plot**, **Patlak–Rutland plot**, or **Patlak analysis**)[1][2] is a [graphical](/source/Graph_of_a_function) analysis technique based on the [compartment](/source/Compartment_(pharmacokinetics)) model that uses [linear regression](/source/Linear_regression) to identify and analyze [pharmacokinetics](/source/Pharmacokinetics) of tracers involving irreversible uptake, such as in the case of [deoxyglucose](/source/Deoxyglucose).[3][4] It is used for the evaluation of [nuclear medicine](/source/Nuclear_medicine) [imaging](/source/Medical_imaging) data after the injection of a [radioopaque](/source/Radioopaque) or [radioactive tracer](/source/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](/source/Blood_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](/source/Region_of_interest) is accumulating according to the equation: - R ( t ) = K ∫ 0 t C p ( τ ) d τ + V 0 C p ( t ) {\displaystyle R(t)=K\int _{0}^{t}C_{p}(\tau )\,d\tau +V_{0}C_{p}(t)} where t {\displaystyle t} represents time after tracer injection, R ( t ) {\displaystyle R(t)} is the amount of tracer in [region of interest](/source/Region_of_interest), C p ( t ) {\displaystyle C_{p}(t)} is the concentration of tracer in plasma or blood, K {\displaystyle K} is the [clearance](/source/Clearance_(medicine)) determining the rate of entry into the peripheral (irreversible) compartment, and V 0 {\displaystyle V_{0}} is the [distribution volume](/source/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](/source/Division_(mathematics)) both sides by C p ( t ) {\displaystyle C_{p}(t)} , one obtains: - R ( t ) C p ( t ) = K ∫ 0 t C p ( τ ) d τ C p ( t ) + V 0 {\displaystyle {R(t) \over C_{p}(t)}=K{\int _{0}^{t}C_{p}(\tau )\,d\tau \over C_{p}(t)}+V_{0}} The unknown constants K {\displaystyle K} and V 0 {\displaystyle V_{0}} can be obtained by [linear regression](/source/Linear_regression) from a [graph](/source/Graph_of_a_function) of R ( t ) C p ( t ) {\displaystyle {R(t) \over C_{p}(t)}} against ∫ 0 t C p ( τ ) d τ / C p ( t ) {\displaystyle \int _{0}^{t}C_{p}(\tau )\,d\tau /C_{p}(t)} . ## See also - [Logan plot](/source/Logan_plot) - [Positron emission tomography](/source/Positron_emission_tomography) - [Multi-compartment model](/source/Multi-compartment_model) - [Binding potential](/source/Binding_potential) - [Deconvolution](/source/Deconvolution) - [Albert Gjedde](/source/Albert_Gjedde) ## References 1. ^ [***a***](#cite_ref-Patlak1983_1-0) [***b***](#cite_ref-Patlak1983_1-1) C. S. Patlak; R. G. Blasberg; J. D. Fenstermacher (March 1983). ["Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data"](https://doi.org/10.1038%2Fjcbfm.1983.1). *[Journal of Cerebral Blood Flow and Metabolism](/source/Journal_of_Cerebral_Blood_Flow_and_Metabolism)*. **3** (1): 1–7. [doi](/source/Doi_(identifier)):[10.1038/jcbfm.1983.1](https://doi.org/10.1038%2Fjcbfm.1983.1). [PMID](/source/PMID_(identifier)) [6822610](https://pubmed.ncbi.nlm.nih.gov/6822610). 1. ^ [***a***](#cite_ref-Patlak1985_2-0) [***b***](#cite_ref-Patlak1985_2-1) C.S. Patlak; R.G. Blasberg (April 1985). ["Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. Generalizations"](https://doi.org/10.1038%2Fjcbfm.1985.87). *[Journal of Cerebral Blood Flow and Metabolism](/source/Journal_of_Cerebral_Blood_Flow_and_Metabolism)*. **5** (4): 584–590. [doi](/source/Doi_(identifier)):[10.1038/jcbfm.1985.87](https://doi.org/10.1038%2Fjcbfm.1985.87). [PMID](/source/PMID_(identifier)) [4055928](https://pubmed.ncbi.nlm.nih.gov/4055928). 1. **[^](#cite_ref-3)** A. Gjedde (April 1981). "High- and low-affinity transport of D-glucose from blood to brain". *[Journal of Neurochemistry](/source/Journal_of_Neurochemistry)*. **36** (4): 1463–1471. [doi](/source/Doi_(identifier)):[10.1111/j.1471-4159.1981.tb00587.x](https://doi.org/10.1111%2Fj.1471-4159.1981.tb00587.x). [PMID](/source/PMID_(identifier)) [7264642](https://pubmed.ncbi.nlm.nih.gov/7264642). 1. **[^](#cite_ref-4)** A. Gjedde (June 1982). "Calculation of glucose phosphorylation from brain uptake of glucose analogs in vivo: A re-examination". *[Brain Research Reviews](/source/Brain_Research_Reviews)*. **4** (2): 237–274. [doi](/source/Doi_(identifier)):[10.1016/0165-0173(82)90018-2](https://doi.org/10.1016%2F0165-0173%2882%2990018-2). [PMID](/source/PMID_(identifier)) [7104768](https://pubmed.ncbi.nlm.nih.gov/7104768). ### Further literature - [A Gjedde](/source/Albert_Gjedde) (1 March 1997). ["Dark origins of the Patlak-Gjedde-Blasberg-Fenstermacher-Rutland -Rehling Plot"](https://journals.lww.com/nuclearmedicinecomm/Citation/1997/03000/Dark_origins_of_the.14.aspx). *[Nuclear Medicine Communications](/source/Nuclear_Medicine_Communications)*. **18** (3): 274–275. [doi](/source/Doi_(identifier)):[10.1097/00006231-199703000-00014](https://doi.org/10.1097%2F00006231-199703000-00014). [ISSN](/source/ISSN_(identifier)) [0143-3636](https://search.worldcat.org/issn/0143-3636). [PMID](/source/PMID_(identifier)) [9106783](https://pubmed.ncbi.nlm.nih.gov/9106783). [Wikidata](/source/WDQ_(identifier)) [Q48779416](https://www.wikidata.org/wiki/Q48779416). ## External links - PMOD, [Patlak Plot](https://web.archive.org/web/20070311063807/http://www.pmod.com/technologies/doc/pkin/2326.htm), PMOD Kinetic Modeling Tool (PKIN). - *[Gjedde–Patlak plot](http://www.turkupetcentre.net/modelling/guide/patlak_plot.html)*, [Turku PET Centre](https://en.wikipedia.org/w/index.php?title=Turku_PET_Centre&action=edit&redlink=1). --- Adapted from the Wikipedia article [Patlak plot](https://en.wikipedia.org/wiki/Patlak_plot) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Patlak_plot?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.