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The first pharmacokinetic model described in the scientific literature [2] was in fact a PBPK model. It led, however, to computations intractable at that time. The focus shifted then to simpler models, [3] for which analytical solutions could be obtained (such solutions were sums of exponential terms, which led to further simplifications.)
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Allometric scaling is any change that deviates from isometry. A classic example discussed by Galileo in his Dialogues Concerning Two New Sciences is the skeleton of mammals. The skeletal structure becomes much stronger and more robust relative to the size of the body as the body size increases. [ 13 ]
Allometric engineering is the process of experimentally shifting the scaling relationships, for body size or shape, in a population of organisms. More specifically, the process of experimentally breaking the tight covariance evident among component traits of a complex phenotype by altering the variance of one trait relative to another.
The simplest PK compartmental model is the one-compartmental PK model. This models an organism as one homogenous compartment. This monocompartmental model presupposes that blood plasma concentrations of the drug are the only information needed to determine the drug's concentration in other fluids and tissues. For example, the concentration in ...
Central to PK/PD models is the concentration-effect or exposure-response relationship. [4] A variety of PK/PD modeling approaches exist to describe exposure-response relationships . PK/PD relationships can be described by simple equations such as linear model, Emax model or sigmoid Emax model . [ 5 ]
Because the proportionality constants β and the scaling exponents α are often denoted using Greek letters, it is desirable to use β as the proportionality coefficient versus α, since α could be misread as the symbol for "proportional". A well-known allometric equation relates metabolic rate to body mass: Y = βM 3/4.
In synoptic scale we can expect horizontal velocities about U = 10 1 m.s −1 and vertical about W = 10 −2 m.s −1. Horizontal scale is L = 10 6 m and vertical scale is H = 10 4 m. Typical time scale is T = L/U = 10 5 s. Pressure differences in troposphere are ΔP = 10 4 Pa and density of air ρ = 10 0 kg⋅m −3. Other physical properties ...