Allometric equation

A hallmark of PB-PK models is the ability to scale up animal-based models to humans, thus allowing tissue drug concentrations to be predicted in the absence of data that are difficult or impossible to collect. Initial efforts to apply interspecies extrapolations to anticancer drugs have been greatly extended to chemical risk assessment based on PB-PK models [14]. Empirical allometric equations based on animal body weight have been the mainstay to scale organ weights and... 

Table 2. Allometric equations used in this chapter.

Adolph (1949, as cited in Davidson et al. 1986, Voisin et al. 1990, ECETOC 2003) compiled a list of 34 morphological, physiological, and biochemical parameters, which correlated with interspecies body weight in accordance with the following general allometric equation ... 

Today, well over 100 biological parameters of mammals are known to be linearly related to body weight and highly predictable on an mterspecies basis (Davidson et al. 1986, Voisin et al. 1990, Calabrese et al. 1992). The allometric equation has traditionally been used for extrapolation of experimental data concerning physiological and biochemical functions from one mammalian species to another. In addition, the allometric equation has also been used extensively as the basis for extrapolation, or scaling, of e.g., a NOAEL derived for a chemical from studies in experimental animals to an equivalent human NOAEL, i.e., a correction for differences in body size between humans and experimental animals. 

When correction for differences in body size is based on body weight, the exponent n in the allometric equation is 1 and the human dose Xhuman (expressed in mg) can be calculated as follows ... 

The allometric equation relating the body surface area (BSA) to the body weight (W) is as follows ... 

Species-Specific Allometric Equations for Eeed Consumption... 

General Allometric Equations for Feed and Drinking-Water Consumption... 

Figure 2.5. Linear transform of simple allometric equation.

In a study investigating the allometric relationships of pharmacokinetic parameters for five therapeutic proteins, the allometric equations for clearance and volumes of distribution, however, were found to be different for each protein [102]. This variability was attributed to possible species specificity and immune-mediated clearance mechanisms. Species specificity refers to the inherent differences in structure and activity across species. Minute differences in the amino acid sequence may render an agent inactive when administered to foreign species, and may even generate an immunogenic response. Immunogenicity has been clearly demonstrated in a study with the tumor necrosis factor receptor-immunoglobulin fusion protein lenercept. This all-human sequence protein elicits an immune response in laboratory animals which ultimately results in the rapid clearance of the protein [103]. 

Thus, to a first approximation, questions about the origins and mechanisms of endothermy can be reduced to questions about the underlying determinants of a in the allometric equation given above. 

In summary, the total quantity of mitochondrial membrane surface area and the per unit area flux of protons through futile cycle channels are higher in mammals than in reptiles of similar body size. These differences in the quantitative and qualitative properties of mitochondria seem capable of accounting for much of the difference in mass-specific metabolic rate between mammals and reptiles that is, they may provide a mechanistic account for the observed four- to fivefold difference in the a term in the allometric equation, M = aW0 75. 

Body size (weight) Excretion (or respiration) rate (T) can be related to body weight (W) according to the allometric equation ... 

Adolph (1) observed that many physiological processes and organ sizes show a relatively simple power-law relationship with body weight when these are compared among mammals. The allometric equation proposed by Adolph is... 

Method II If the exponent lies between 0.7 and 1.0, the allometric equation for predicting clearance is normalized according to the maximum life span potential for each animal species, as initially proposed by Boxenbaum (7). 

As discussed in Chapter 30 and elsewhere (13), interspecies scaling is based upon allometry (an empirical approach) or physiology. Protein pharmacokinetic parameters such as volume of distribution (Pd), elimination half-life (b/2)/ and elimination clearance (CL) have been scaled across species using the standard allometric equation (14) ... 

In Table 32.6 the predicted parameter estimates derived from the allometric equations in Table 32.5 are compared with the corresponding parameter estimates reported in humans. The observed values of Pi for the macromolecules listed fall within the expected range of observed results. However the observed clearances of Factor IX (FIX) and interleukin-12 (IL-12) were not predicted from allometry. Factors such as species specificity in the endothelial binding of FIX (22) or saturation of clearance mechanisms may account for the inability to predict these parameters in humans. 

TABLE 32.5 Allometric Equations for Representative Macro mo le cule s... 

Allometric equations determined from pharmacokinetic parameter estimates reported in published literature. 

TABLE 32.8 Comparison between the Predicted EGF PK Parameters from the Allometric Equations and Estimated PK Parameters Determined in Cancer Patients... 

Determined from the allometric equations in Table 7, Duconge J et al. Biopharm Drug Dispos 2004 25 177-86. 

The bispyridinium oxime HI-6, which is a powerful reactivator of imaged organophosphate-inhibited acetylcholinesterase, is eliminated by renal excretion. The allometric equations expressing the relationship between pharmacokinetic parameters describing the elimination of HI-6 and body weight of various mammalian species (mouse, rat, rabbit, Rhesus monkey, Beagle dog, sheep and man) are ... 

When developing a new therapeutic compound, relevant toxicokinetic studies are performed in different species such as mice, rabbits, dogs, and monkeys. The results of such studies lead to interspecies scaling in PK parameters based on the assumption that there are physiological and biochemical analogies between mammals, which can be expressed mathematically by allometric equations (58). The allometric approach is based on the power function, where the PK parameters Y are plotted against the body weight W of the different species ... 

Besides animal studies, in vitro studies give information about the doses and concentrations that show antitumor activity and concentration-response relationships can be established. Knowing the therapeutic range of concentration from the concentration-response relationship, and being able to predict the behavior of the drug in humans from the allometric equations, an optimal design may be implemented for the FTIH study. 

Food intake was based upon an allometric equation using the average body weight in kg (U.S. EPA 1986) F = 0.056 x bw06611. 

Allometric scaling is commonly used to account for variations in biologic systems. If X is the variable of interest, the allometric equation assumes that this variable scales with a power of the mass M ... 

Many physiological processes and organ sizes scale across species according to the well-known power-law relationship or allometric equation [66] ... 

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