Patlak Plot
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Patlak Plot
A Patlak plot (sometimes called Gjedde–Patlak plot, Patlak–Rutland plot, or Patlak analysis) 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. 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. The amount of tracer in the region of interest is accumulating according to the equation: : R(t) = K \int_0^t C_p(\ ...
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Journal Of Cerebral Blood Flow And Metabolism
The ''Journal of Cerebral Blood Flow & Metabolism'' is a monthly peer-reviewed medical journal the official journal of the International Society for Cerebral Blood Flow & Metabolism and publishes Peer review, peer-reviewed research and review papers. covering research on experimental, theoretical, and clinical aspects of brain circulation, metabolism and imaging. The editor-in-chief is Jun Chen (University of Pittsburgh). According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 6.200. References External links * International Society for Cerebral Blood Flow & Metabolism
Neuroscience journals Publications established in 1981 Nature Research academic journals English-language journals Monthly journals Delayed open access journals Academic journals associated with learned and professional societies {{neuroscience-journal-stub ...
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Clearance (medicine)
In pharmacology, clearance is a pharmacokinetic measurement of the volume of plasma from which a substance is completely removed per unit time. Usually, clearance is measured in L/h or mL/min. The quantity reflects the rate of drug elimination divided by plasma concentration. Excretion, on the other hand, is a measurement of the amount of a substance removed from the body per unit time (e.g., mg/min, μg/min, etc.). While clearance and excretion of a substance are related, they are not the same thing. The concept of clearance was described by Thomas Addis, a graduate of the University of Edinburgh Medical School. Substances in the body can be cleared by various organs, including the kidneys, liver, lungs, etc. Thus, total body clearance is equal to the sum clearance of the substance by each organ (e.g., renal clearance + hepatic clearance + lung clearance = total body clearance). For many drugs, however, clearance is solely a function of renal excretion. In these cases, clearance is ...
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Systems Theory
Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structure, function and role, and expressed through its relations with other systems. A system is "more than the sum of its parts" by expressing synergy or emergent behavior. Changing one component of a system may affect other components or the whole system. It may be possible to predict these changes in patterns of behavior. For systems that learn and adapt, the growth and the degree of adaptation depend upon how well the system is engaged with its environment and other contexts influencing its organization. Some systems support other systems, maintaining the other system to prevent failure. The goals of systems theory are to model a system's dynamics, constraints, conditions, and relations; and to elucidate principles (such as purpose, measure ...
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Mathematical Modeling
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statistical m ...
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Turku PET Centre
Turku ( ; ; sv, Åbo, ) is a city and former capital on the southwest coast of Finland at the mouth of the Aura River, in the region of Finland Proper (''Varsinais-Suomi'') and the former Turku and Pori Province (''Turun ja Porin lääni''; 1634–1997). The region was originally called Suomi (Finland), which later became the name for the whole country. As of 31 March 2021, the population of Turku was 194,244 making it the sixth largest city in Finland after Helsinki, Espoo, Tampere, Vantaa and Oulu. There were 281,108 inhabitants living in the Turku Central Locality, ranking it as the third largest urban area in Finland after the Capital Region area and Tampere Central Locality. The city is officially bilingual as percent of its population identify Swedish as a mother-tongue. It is unknown when Turku gained city rights. The Pope Gregory IX first mentioned the town ''Aboa'' in his ''Bulla'' in 1229 and the year is now used as the foundation year of Turku. Turku is the olde ...
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Albert Gjedde
Albert Gjedde: is a Danish-Canadian neuroscientist. He is Professor of Neurobiology and Pharmacology at the Faculty of Health Sciences and Center of Neuroscience at the University of Copenhagen. He is currently also Adjunct Professor of Neurology and Neurosurgery in the Department of Neurology, Montreal Neurological Institute, McGill University, Montreal, Quebec, Canada, Adjunct Professor of Radiology and Radiological Science in the Division of Nuclear Medicine, Department of Radiology and Radiological Science, Johns Hopkins University, Baltimore, Maryland, US, Adjunct Professor of Translational Neuropsychiatry Research, University of Southern Denmark, Odense, Denmark, and adjunct professor of psychiatry at Tabriz University of Medical Sciences, Tabriz, East Azerbadjan, Iran. Born in the Copenhagen suburb of Gentofte in 1946, Albert Gjedde spent time as an undergraduate student in Berkeley, California, United States (1964–65, 1968), Stellenbosch, Cape Province, South Africa (196 ...
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Deconvolution
In mathematics, deconvolution is the operation inverse to 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 method with a certain degree of accuracy. Due to the measurement error of the recorded signal or image, it can be demonstrated that the worse the SNR, the worse the reversing of a filter will be; hence, inverting a filter is not always a good solution as the error amplifies. Deconvolution offers a solution to this problem. The foundations for deconvolution and time-series analysis were largely laid by Norbert Wiener of the Massachusetts Institute of Technology in his book ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'' (1949). The book was based on work Wiener had done during World War II but that had been classified at the time. Some of the early attempts to apply these theories were in the fields of ...
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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 of a drug to that neuroreceptor. Description Consider a ligand receptor binding system. Ligand with a concentration ''L'' associates with a receptor of concentration or availability ''R'' to form a ligand-receptor complex with concentration ''RL''. The binding potential is then the ratio ligand-receptor complex to free ligand at equilibrium and in the limit of L tending to 0, and is given symbol BP: BP=\frac\bigg, _ This quantity, originally defined by Mintun, describes the capacity of a receptor to bind ligand. It is a limit (L << Ki) of the general receptor association equation: RL=\frac and is thus also equivalent to: BP=\frac These equations apply equally when measuring the total receptor density or the residual receptor density available after binding to second ligand - availability.
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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 it is much easier to discretize the problem and reduce the number of parameters. Each compartment is assumed to be a homogeneous entity within which the entities being modeled are equivalent. A multi-compartment model is classified as a lumped parameters model. Similar to more general mathematical models, multi-compartment models can treat variables as continuous, such as a differential equation, or as discrete, such as a Markov chain. Depending on the system being modeled, they can be treated as stochastic or deterministic. Multi-compartment models are used in many fields including pharmacokinetics, epidemiology, biomedicine, systems theory, complexity theory, engineering, physics, information science and social science. The circuits sys ...
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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 Metabolism, metabolic processes, and in other physiological activities including blood flow, regional chemical composition, and absorption. Different tracers are used for various imaging purposes, depending on the target process within the body. For example, 18F-FDG, -FDG is commonly used to detect cancer, Sodium fluoride#Medical imaging, NaF is widely used for detecting bone formation, and Isotopes of oxygen#Oxygen-15, oxygen-15 is sometimes used to measure blood flow. PET is a common medical imaging, imaging technique, a Scintigraphy#Process, medical scintillography technique used in nuclear medicine. A radiopharmaceutical, radiopharmaceutical — a radioisotope attached to a drug — is injected into the body as a radioactive tracer, tracer. When the radiopharmaceutical undergoes beta plus decay, a positron is ...
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Logan Plot
A Logan plot (or Logan graphical analysis) is a graphical analysis technique based on the compartment model that uses linear regression to analyze pharmacokinetics of tracers involving reversible uptake. It is mainly used for the evaluation of nuclear medicine imaging data after the injection of a labeled ligand that binds reversibly to specific receptor or enzyme. In conventional compartmental analysis, an iterative method is used to fit the individual model parameters in the solution of a compartmental model of specific configuration to the measurements with a measured plasma time-activity curve that serves as an forcing (input) function, and the binding of the tracer can then be described. Graphical analysis is a simplified method that transforms the model equations into a linear equation evaluated at multiple time points and provides fewer parameters (i.e., slope and intercept). Although the slope and the intercept can be interpreted in terms of a combination of model parameters ...
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Division (mathematics)
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication. At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another. This number of times need not be an integer. For example, if 20 apples are divided evenly between 4 people, everyone receives 5 apples (see picture). The division with remainder or Euclidean division of two natural numbers provides an integer ''quotient'', which is the number of times the second number is completely contained in the first number, and a ''remainder'', which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of the second number can be allocated. For example, if 21 apples are divided between 4 people, everyone receives ...
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