Allometry

Allometry is an empirical approach to predicting pharmacokinetic parameters across species. It has developed from a much wider discipline that correlates shape to a power-function of some measure of size or mass. For example, Kleibers law states that the basal metabolic rate across animal species scales to the power 0.75 to body weight.  

Allometry is a widely used technique in drug development. Numerous physical and physiological parameters, and certain pharmacokinetic parameters (F) have been found to be related to body weight according to eqn (13.7) and (13.8). 

A number of adjustments have been proposed for allometric relationships when the slopes are extreme. When slopes of flow dependent allometric relationships exceed 0.7 (between 0.7 and 1.0) a further correction is often applied. The correction, suggested by Mahmood, uses the maximum lifespan potential (MLP) and has the mathematical form described by eqn (13.9) and (13.10). 

Where BRW = animal species brain weight, and BW = animal body weight in kg. 

The overall effect of MLP correction serves to reduce the slope of the allometric relationship by 0.3, as the MLP correction has a greater effect on the higher body weight species. Why and when the application of this correction is scientifically valid is not clear, and can best be viewed as an empirical adjustment. 

One of the most frequently used methods for predicting human pharmacokinetics from animal data is allometry. This technique was initially used to explain the relationship between body size and organ weights in animals [62-67]. The approach is based on finding a correlation between a physiological and the pharmacokinetic parameter of interest. Generally the relationship takes the form of  

The allometric coefficient and exponent are determined empirically, and are not thought to have any physiological correlate. 

The drawback of this approach is that it is essentially empirical, and does not allow for differences in metabolic clearance between the species, i.e., it assumes that clearance is proportional to blood flow. This works well for compounds that are highly extracted in the liver, and/or where passive renal clearance is the major pathway [5, 68]. An approach for compounds that are actively secreted into the urine has also been proposed [69], although the precise values of some of the physiological scaling factors have been questioned [70]. 

Unfortunately, when clearance is largely metabolic and low, allometry can significantly over-predict the human value [71]. Recent investigations have attempted to address this by combining allometric approaches with in vitro metabolism data [5], 

A recent debate on allometric scaling has suggested that a great deal of further work is necessary before allometry can be used with confidence in a prospective 

Interpretation is always required. In some simple systems, concepts of similitude place design on a sound theoretical basis. But in more complex situations, rigorous similitude may not be attainable. In these cases, it is often possible to model parts of a complex system and use model-dependent information in a design process that incorporates sound theoretical principles but often contains judgment and experience as well. The approach is illustrated by a discussion of the extrapolation of data from one biological system to another. 

This chapter contains a brief discussion of allometry, physiological pharmacokinetics, and the use of in vitro systems to predict drug metabolism in experimental animals and human study participants. 

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 

Note that a is not dimensionless its value depends on the units in which P and BW are measured, while the exponent, m, is independent of the system of units. 

Note further that if m = 1, then P is proportional to BW. If m 1,P increases less rapidly than does BW. If m 1, P increases more rapidly than does BW. Adolph listed empirical coefficients and exponents for several physiological parameters and some of these are summarized in Table 30.1. 

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Chave J, Andalo C, Brown S, Cairns M, Chambers J, Eamus D et al. Tree allometry and improved estimation of carbon stocks and balance in tropical forests. Oecologia, 2005.145 pp. 87-89. 

Boxenbaum, H., Interspedes scaling, allometry, physiological time, and the ground plan of pharmacokinetics,... 

Wajima and coauthors offer an alternative approach to utilize animal VD data to predict human VD [13]. Several compound descriptors that included both chemical structural elements as well as animal VDSS values were subject to multiple linear regression and partial least squares statistical analyses, with human VDSS as the independent parameter to be predicted using a dataset of 64 drugs. Methods derived in this manner were compared to simple allometry for overall accuracy. Their analyses yielded the following regressions ... 

Allometry Determinants of VD (e.g., tissue and blood volumes binding capacity) scale with body weight across species VDSS in two or more animal species [2-5]... 

Much of the inter-species variation in pharmacokinetic properties can be explained as a consequence of body size (allometry). Consequently it is possible to scale pharmacokinetic parameters to the organism s individual anatomy, biochemistry and/or physiology in such a manner that differences between species are nuUified. Several excellent reviews on allometric scaling are available in the literature [2-7]. Allometric relationships can be described by an equation of the general form ... 

When transporter proteins are involved in the rate-determining step of compound clearance, there is clearly the potential for species differences to exist which are not related to allometry. Given the large (and growing) number of transporter proteins... 

Adjustment for Differences in Body Size Allometry/Scaling... 

Finally, no discussion of human pharmacokinetic predictions is complete without a consideration of allometric scaling [67-69]. In general, allometry is the examination of relationships between size and function and it has been applied to the prediction of human pharmacokinetic parameters from animal pharmacokinetic parameters for decades [70]. Allometry has been shown to work reasonably well for predicting human VD from animal VD data, probably because volumes of plasma and various tissue across species are allometrically scaleable to body weight, a notion reinforced... 

Deming, W.E., 1964. Statistical adjustment of data. Dovers Publications, New York. Kermack, K.A. and Haldane, J.B.S., 1950. Organic correlation and allometry. Biometrica, 37 30. 

In dmg discovery, preliminary PK studies are usually conducted in rodents to evaluate the extent of dmg exposure in vivo. This is commonly followed by PK studies in larger animals such as dog or monkey to better characterize the PK profile of the compound and to support safety studies. Pharmacokinetic scaling (also called allometry) is a discipline that is used to predict human PK profiles using preclinical data and is widely used in predicting the dmg human half-life, dose, and extent of absorption. Accurate prediction of a human PK profile is imperative to minimize dmg failure in development due to poor PK attributes. A detailed description of methods in predicting human PK is beyond the scope of this chapter but can be found in many excellent reviews (Obach et al., 1997 Miners et al., 2004 Poggesi, 2004 Raunio et al., 2004 Thomas et al., 2006 Hurst et al., 2007). A more in-depth discussion of various PK concepts and their applications can be found in various references (Gibaldi and Perrier, 1982 Rowland and Tozer, 1995 Hurst et al., 2007). 

Allometric scaling (allometry) is the discipline that predicts human PK using pre-clinical data (Ritschel et al., 1992). This approach is based on empirical observations that various physiological parameters are functions of body size. The most widely used equation in allometry is a one-term power function ... 

Actisomide was included in a set of drugs for computational predictions of human drug clearance using different allometry methods (08MI1, 09JPS2472) and for computational predictions of volume of distribution using linear and nonlinear models (09JMC4488). 

Kedderis, G.L., and J.C. Lipscomb. 2001. Application of in vitro biotransformation data and pharmacokinetic modeling to risk assessment. Toxicol. Ind. Health 17(5-10) 315-321. Lindstedt, S.L. 1987. Allometry Body size constraints in animal design. Pp. 65-79 in Pharmacokinetics in Risk Assessment. Drinking Water and Health, Vol. 8. Washington, DC National Academy Press. 

Cl) was within 2-fold of the observed values in 70 (7/10), 67 (6/9), 63 (12/19), and 55% (10/18) of cases, respectively. The accuracy of the physiologically based model was superior to that of simple allometry, especially in under 2-year-olds. 

Vitousek, P.M., Walker, L.R., Whiteaker, L.D., Mueller-Dombois, D., and Matson, P.A. (1988) Element interactions in forest ecosystems succession, allometry and input-output budgets. Biogeochemistry 5, 7-34. 

Porter RK (2001) Allometry of mammalian cellular oxygen consumption. Cell Mol Life Sci 58 815-822... 

Because of the intense interest in allometry, we should end this discussion with a final question Is there a universal biologically important principle underlying the 0.75 power law West et al. (2000) certainly believed there was such a principle when they initiated their search for an explanation for why b = 0.75 for SMR in so many organisms and so many functions. After reviewing current information on this question, however, we suspect that they answer may be no. In fact, from our analysis the thought arises that biologists and physiologists... 

Figure 7.38. Allometry of oxygen consumption rates and potassium leakage rates for liver slices from five species of mammals that differ by four orders of magnitude in body mass. (Figure modified after Couture and Hulbert, 1995.)...

Porter, R.K., A.J. Hulbert, and M.D. Brand (1996). Allometry of mitochondrial proton leak influence of membrane surface area and fatty acid composition. Am. J. Physiol. 271 (Regulatory Integrative Comp. Physiol. 40) R1550-R1560. 

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