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= Multi Compartment Model = A multi-compartment model is a type ofmathematical model used for describing the way materials or energies are transmitted among the compartments of a system. Each compartment is assumed to be a homogeneous entity within which the entities being modelled are equivalent. For instance, in a pharmacokinetic model, the compartments may represent different sections of a body within which the concentration of a drug is assumed to be uniformly equal.

Hence a multi-compartment model is alumped parameters model.

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 systems can be viewed as a multi-compartment model as well.

In systems theory, it involves the description of a network whose components are compartments that represent a population of elements that are equivalent with respect to the manner in which they process input signals to the compartment.




 * Instant homogeneous distribution of materials or energies within a "compartment."
 * The exchange rate of materials or energies among the compartments is related to the densities of these compartments.
 * Usually, it is desirable that the materials do not undergo chemical reactions while transmitting among the compartments.
 * When concentration of the cell is of interest, typically the volume is assumed to be constant over time, though this may not be totally true in reality.

Most commonly, the mathematics of multi-compartment models is simplified to provide only a single parameter—such as concentration—within a compartment.

Single-compartment modelEdit
Possibly the simplest application of multi-compartment model is in the single-cell concentration monitoring (see the figure above). If the volume of a cell is V, the mass of solute is q, the input is u(t) and the secretion of the solution is proportional to the density of it within the cell, then the concentration of the solution C within the cell over time is given by





where k is the proportionality.



















Model topologies
Generally speaking, as the number of compartments increase, it is challenging both to find the algebraic and numerical solutions of the model. However, there are special cases of models, which rarely exist in nature, when the topologies exhibit certain regularities that the solutions become easier to find. The model can be classified according to the interconnection of cells and input/output characteristics:


 * 1) Closed model: No sinks or source, lit. allkoi = 0 and ui = 0;
 * 2) Open model: There are sinks or/and sources among cells.
 * 3) Catenary model: All compartments are arranged in a chain, with each pool connecting only to its neighbors. This model has two or more cells.
 * 4) Cyclic model: It's a special case of the catenary model, with three or more cells, in which the first and last cell are connected, i.e. k1n ≠ 0 or/and kn1 ≠ 0.
 * 5) Mammillary model: Consists of a central compartment with peripheral compartments connecting to it. There are no interconnections among other compartments.
 * 6) Reducible model: It's a set of unconnected models. It bears great resemblance to the computer concept offorest as against trees.

See alsoEdit

 * Mathematical model
 * Biomedical engineering
 * Biological neuron models
 * Compartmental models in epidemiology
 * Physiologically-based pharmacokinetic modelling

ReferencesEdit

 * Godfrey, K., Compartmental Models and Their Application, Academic Press, 1983 (ISBN 0-12-286970-2).
 * Anderson, D. H., Compartmental Modeling and Tracer Kinetics, Springer-Verlag Lecture Notes in Biomathematics #50, 1983 (ISBN 0-387-12303-2).
 * Jacquez, J. A, Compartmental Analysis in Biology and Medicine, 2nd ed., The University of Michigan Press, 1985.
 * Evans, W. C., Linear Systems, Compartmental Modeling, and Estimability Issues in IAQ Studies, in Tichenor, B.,Characterizing Sources of Indoor Air Pollution and Related Sink Effects, ASTM STP 1287, pp. 239–262, 1996 (ISBN 0-8031-2030-3).

= Plasma protein binding = Plasma protein binding refers to the degree to which medications attach to proteins within the blood. A drug's efficiency may be affected by the degree to which it binds. The less bound a drug is, the more efficiently it can traverse cell membranes or diffuse. Common blood proteins that drugs bind to arehuman serum albumin, lipoprotein,glycoprotein, and α, β‚ and γ globulins.

Binding (Drug Distribution)Edit
A drug in blood exists in two forms: bound and unbound. Depending on a specific drug's affinity for plasma protein, a proportion of the drug may become bound to plasma proteins, with the remainder being unbound. If the protein binding is reversible, then a chemical equilibrium will exist between the bound and unbound states, such that:


 * Protein + drug ⇌ Protein-drug complex

Notably, it is the unbound fraction which exhibits pharmacologic effects. It is also the fraction that may be metabolized and/or excreted. For example, the "fraction bound" of the anticoagulant warfarin is 97%. This means that of the amount of warfarin in the blood, 97% is bound to plasma proteins. The remaining 3% (the fraction unbound) is the fraction that is actually active and may be excreted. Note that this does not mean that 97% of the plasma proteins are bound with drug, however.

Protein binding can influence the drug'sbiological half-life. The bound portion may act as a reservoir or depot from which the drug is slowly released as the unbound form. Since the unbound form is being metabolized and/or excreted from the body, the bound fraction will be released in order to maintain equilibrium.

Since albumin is alkalotic, acidic and neutral drugs will primarily bind to albumin. If albumin becomes saturated, then these drugs will bind to lipoprotein. Basic drugs will bind to the acidic alpha-1 acid glycoprotein. This is significant because various medical conditions may affect the levels of albumin, alpha-1 acid glycoprotein, and lipoproteins.

Plasma protein binding prediction softwareEdit

 * Quantum Plasma Protein Binding
 * S+ Plasma Protein Binding
 * Albumin binding prediction

See alsoEdit

 * Blood proteins
 * Pharmacokinetics

ReferencesEdit

 * 1) ^ https://bblearn.usask.ca/bbcswebdav/pid-1957823-dt-content-rid-9318990_2/courses/86742.201709/Toutain%20Free%20Drug%20vs%20Free%20Drug%20Fraction.pdf

External linksEdit

 * The measurement of Plasma Protein Binding The performance of plasma protein binding studies including analysis of the data.