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A Patlak plot (sometimes called Gjedde–Patlak plot, Patlak–Rutland plot, or Patlak analysis) is a
graphical Graphics () are visual images or designs on some surface, such as a wall, canvas, screen, paper, or stone, to inform, illustrate, or entertain. In contemporary usage, it includes a pictorial representation of the data, as in design and manufactu ...
analysis technique based on the compartment model that uses
linear regression In statistics, linear regression is a statistical model, model that estimates the relationship between a Scalar (mathematics), scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A mode ...
to identify and analyze
pharmacokinetics Pharmacokinetics (from Ancient Greek ''pharmakon'' "drug" and ''kinetikos'' "moving, putting in motion"; see chemical kinetics), sometimes abbreviated as PK, is a branch of pharmacology dedicated to describing how the body affects a specific su ...
of tracers involving irreversible uptake, such as in the case of deoxyglucose. It is used for the evaluation of
nuclear medicine Nuclear medicine (nuclear radiology, nucleology), is a medical specialty involving the application of radioactivity, radioactive substances in the diagnosis and treatment of disease. Nuclear imaging is, in a sense, ''radiology done inside out'', ...
imaging Imaging is the representation or reproduction of an object's form; especially a visual representation (i.e., the formation of an image). Imaging technology is the application of materials and methods to create, preserve, or duplicate images. ...
data after the injection of a
radioopaque Radiodensity (or radiopacity) is opacity to the radio wave and X-ray portion of the electromagnetic spectrum: that is, the relative inability of those kinds of electromagnetic radiation to pass through a particular material. Radiolucency or hypod ...
or
radioactive tracer A radioactive tracer, radiotracer, or radioactive label is a synthetic derivative of a natural compound in which one or more atoms have been replaced by a radionuclide (a radioactive atom). By virtue of its radioactive decay, it can be used to ...
. 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. The amount of tracer in the
region of interest A region of interest (often abbreviated ROI) is a sample within a data set identified for a particular purpose. The concept of a ROI is commonly used in many application areas. Existing as a vicinity, or within one. For example, in medical imagin ...
is accumulating according to the equation: : R(t) = K \int_0^t C_p(\tau) \, d\tau + V_0 C_p(t) where t represents time after tracer injection, R(t) is the amount of tracer in
region of interest A region of interest (often abbreviated ROI) is a sample within a data set identified for a particular purpose. The concept of a ROI is commonly used in many application areas. Existing as a vicinity, or within one. For example, in medical imagin ...
, C_p(t) is the concentration of tracer in plasma or blood, K is the clearance determining the rate of entry into the peripheral (irreversible) compartment, and V_0 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 C_p(t), one obtains: : = K + V_0 The unknown constants K and V_0 can be obtained by
linear regression In statistics, linear regression is a statistical model, model that estimates the relationship between a Scalar (mathematics), scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A mode ...
from a
graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discret ...
of against \int_0^t C_p(\tau) \, d\tau / C_p(t).


See also

* Logan plot *
Positron emission tomography Positron emission tomography (PET) is a functional imaging technique that uses radioactive substances known as radiotracers to visualize and measure changes in metabolic processes, and in other physiological activities including blood flow, r ...
*
Multi-compartment model A multi-compartment model is a type of mathematical model used for describing the way materials or energies are transmitted among the ''compartments'' of a system. Sometimes, the physical system that we try to model in equations is too complex, so ...
*
Binding potential In pharmacokinetics and receptor-ligand kinetics the binding potential (BP) is a combined measure of the density of "available" neuroreceptors and the Affinity (pharmacology), affinity of a drug to that neuroreceptor. Description Consider a ligan ...
*
Deconvolution In mathematics, deconvolution is the inverse of convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deconvolution ...
* Albert Gjedde


References


Further literature

* {{Cite Q , Q48779416


External links

* PMOD
Patlak Plot
PMOD Kinetic Modeling Tool (PKIN). *

', Turku PET Centre. Mathematical modeling Systems theory Plots (graphics) Pharmacokinetics