Patlak plot
Encyclopedia
A Patlak plot is a graphical
analysis technique based on the compartment
model that uses linear regression
to identify and analyze pharmacokinetics
problems involving irreversible uptake, such as in the case of deoxyglucose. It is used for the evaluation of nuclear medicine
imaging
data after the injection of a radioactive or radioopaque tracer
.
The analysis is feasible if the behavior of the tracer can be approximated by two compartments, a "central" compartment that is in rapid equilibrium with blood plasma
, and a "peripheral" compartment where tracer enters without ever leaving during the time of the measurements. The amount of tracer in the region of interest
is accumulating according to the equation:
where
is time, 
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 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 
.
Graph of a function
In mathematics, the graph of a function f is the collection of all ordered pairs . In particular, if x is a real number, graph means the graphical representation of this collection, in the form of a curve on a Cartesian plane, together with Cartesian axes, etc. Graphing on a Cartesian plane is...
analysis technique based on the compartment
Compartment (pharmacokinetics)
In pharmacokinetics, a compartment is a defined volume of body fluids. It is distinguished from anatomic compartments, which are bounded by fasciae...
model that uses linear regression
Linear regression
In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...
to identify and analyze pharmacokinetics
Pharmacokinetics
Pharmacokinetics, sometimes abbreviated as PK, is a branch of pharmacology dedicated to the determination of the fate of substances administered externally to a living organism...
problems involving irreversible uptake, such as in the case of deoxyglucose. It is used for the evaluation of nuclear medicine
Nuclear medicine
In nuclear medicine procedures, elemental radionuclides are combined with other elements to form chemical compounds, or else combined with existing pharmaceutical compounds, to form radiopharmaceuticals. These radiopharmaceuticals, once administered to the patient, can localize to specific organs...
imaging
Medical imaging
Medical imaging is the technique and process used to create images of the human body for clinical purposes or medical science...
data after the injection of a radioactive or radioopaque tracer
Tracer
Tracer may refer to:* Histochemical tracer, a substance used for tracing purposes in histochemistry, the study of the composition of cells and tissues...
.
The analysis is feasible if the behavior of the tracer can be approximated by two compartments, a "central" compartment that is in rapid equilibrium with blood plasma
Blood plasma
Blood plasma is the straw-colored liquid component of blood in which the blood cells in whole blood are normally suspended. It makes up about 55% of the total blood volume. It is the intravascular fluid part of extracellular fluid...
, and a "peripheral" compartment where tracer enters without ever leaving during the time of the measurements. The amount of tracer in the region of interest
Region of interest
A Region of Interest, often abbreviated ROI, is a selected subset of samples within a dataset identified for a particular purpose.For example:* on a waveform , a time or frequency interval...
is accumulating according to the equation:
where
is time, is the amount of tracer in region of interest, is the concentration of tracer in plasma or blood, is the clearanceClearance (medicine)
In medicine, the clearance is a measurement of the renal excretion ability. Although clearance may also involve other organs than the kidney, it is almost synonymous with renal clearance or renal plasma clearance. Each substance has a specific clearance that depends on its filtration characteristics...
determining the rate of entry into the peripheral compartment, and
is the distribution volume of the tracer in the central compartment. The first termTerm (mathematics)
A term is a mathematical expression which may form a separable part of an equation, a series, or another expression.-Definition:In elementary mathematics, a term is either a single number or variable, or the product of several numbers or variables separated from another term by a + or - sign in an...
of the right-hand side represents tracer in the peripheral compartment, and the second term tracer in the central compartment.
By dividing
Division (mathematics)
right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...
both sides by
, one obtains:The unknown constants
and can be obtained by linear regressionLinear regression
In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...
from a graph
Graph of a function
In mathematics, the graph of a function f is the collection of all ordered pairs . In particular, if x is a real number, graph means the graphical representation of this collection, in the form of a curve on a Cartesian plane, together with Cartesian axes, etc. Graphing on a Cartesian plane is...
of
against .See also
- Logan plot
- Positron Emission TomographyPositron emission tomographyPositron emission tomography is nuclear medicine imaging technique that produces a three-dimensional image or picture of functional processes in the body. The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide , which is introduced into the body on a...
- Multi-compartment modelMulti-compartment modelA 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. Each compartment is assumed to be a homogenous entity within which the entities being modelled are equivalent...
- Binding potentialBinding potentialIn pharmacokinetics and receptor-ligand kinetics the binding potential is a combined measure of the density of "available" neuroreceptors and the affinity of a drug to that neuroreceptor.- Description :Consider a ligand receptor binding system...
- DeconvolutionDeconvolutionIn mathematics, deconvolution is an algorithm-based process used to reverse the effects of convolution on recorded data. The concept of deconvolution is widely used in the techniques of signal processing and image processing...
- Albert GjeddeAlbert GjeddeAlbert Gjedde is a Danish neuroscientist. He is Professor of Neurobiology and Pharmacology at the Faculty of Health Sciences and Head of Department of Neuroscience and Pharmacology at the University of Copenhagen...
External links
- PMOD, Patlak Plot, PMOD Kinetic Modeling Tool (PKIN).
- Gjedde-Patlak plot, Turku PET Centre.