Lecture

Tracer kinetics: One-tissue compartment model

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Description

This lecture covers the fundamentals of tracer kinetics in biomedical imaging, focusing on the one-tissue compartment model. It explains first-order tracer kinetics, the unidirectional chemical reaction from S to T, and the measurement of tracer enrichment. The lecture also delves into the linear first-order ordinary differential equations describing the model and the Laplace transformation. Examples are provided to illustrate the concepts, including the input function, intravenous bolus infusion, and the concentration of authentic tracer in arterial blood over time.

In MOOC

Fundamentals of Biomedical Imaging: Ultrasounds, X-ray, positron emission tomography (PET) and applications

This course shows how existing physical principles transcend into bio-imaging and establish an important link into life sciences, illustrating the contributions physics can make to life sciences. Practical examples will be shown to illustrate the respective imaging modality, its use, premise and limitations, and biological safety will be touched upon. During this course, you will develop a good understanding of the mechanisms leading to tissue contrast of the bio-imaging modalities covered in this course, i

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Related concepts (28)

Chemical kinetics

Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is different from chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction.

Chemical reaction

A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur.

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Rate equation

In chemistry, the rate law or rate equation for a chemical reaction is a mathematical equation that links the rate of forward reaction with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders). For many reactions, the initial rate is given by a power law such as where [\mathrm{A}] and [\mathrm{B}] express the concentration of the species \mathrm{A} and \mathrm{B}, usually in moles per liter (molarity, M).

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