Allometric plot

Fig. 4 Allometric plots of the pharmacokinetic parameters clearance, volume of the central compartment ( /c), volume of distribution at steady state Vss), and elimination half-life of rPSGL-lg. Each data point within the plot represents an averaged value ofthe pharmacokinetic parameter with increasing weight from mouse, rat, monkey (3.74 kg), monkey (6.3 kg), and pig, respectively. The solid line is the best fit with a power function to relate pharmacokinetic parameters to body weight (from [54]).

Figure 4 shows the allometric plots of pharmacokinetic parameters for the recombinant, soluble, and chimeric form of P-selectin glycoprotein ligand-1 (rPSGL-Ig), an antagonist to P-selectin for the treatment of P-selectin-mediated diseases like thrombosis, reperfusion injury, and deep vein thrombosis. Human rPSGL-Ig pharmacokinetic parameters could accurately be predicted on the basis of data from mouse, rat, monkey, and pig using allometric power functions [54]. 

Figure 2.4(C). Allometric scaling of flight metabolism in Euglossine bees (Euglossa, Exaerete, Eulaema, Eufriesea) plotted on the same log-log scale as the maximum flight muscle hexokinase H K max activity. Each point corresponds to the average value of a single species. Open circles represents V02 data measured in nine species by Casey et al. (1985). Filled circles represents hexokinase maximal activity measured in 28 species by Darveau, Suarez, and Hochachka (unpublished data). Note that no difference in slopes between the two data sets could be detected. (Unpublished data are courtesy of R.K. Suarez and C.A. Darveau.)...

These concepts are illustrated in Figure 30.1/ which shows a plot of an illustrative physiologic property versus body weight/ both in arbitrary dimensionless termS/ on a log-log plot. Equation 30.1 is linearized in this foriU/ with a slope equal to the allometric exponent/ a. If the property were proportional to body weight/ as is often the case for the distribution volume of a drug/ increasing the body weight from 1 to 100 would result in a concomitant increase in the property. 

While the interspecies variability in metabolism precludes the possibility of a simple allometric relationship for the plasma kinetics of ARA-C, the non-metabolic clearance by the kidney does exhibit a power-law relationship with body weight. Figure 30.7 shows the kidney clearance of ARA-C and its deami-nated product ARA-U on a log-log plot as a function of body weight for mice, monkeys, dogs, and humans. The slope is 0.80, which is essentially the same as the value of 0.77 for inulin (1). 

Fig. 3.4 Double logarithmic plots showing the allometric relationship between (a) half-life and (b) body (systemic) clearance of HI-6 and body weight of seven animal species. (Reproduced with permission from Baggot (1994).)...

Using limited data, allometric scaling may be useful in drug discovery. We assume that, for the formula Y = aWb, the value of the power function (or slope of the line from a log vs. log plot) is drug independent, unlike the intercept o , which is drug dependent. By doing this, we can use data from a single species (rat) to successfully predict the pharmacokinetics of compound X in humans... 

Figure 8.3 Allometric relationship between body surface area and species body weight on a log vs. log plot...

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 ... 

Mordenti et al. (1991) compared the pharmacokinetics of relaxin, a protein proposed for use in pregnant women at or near term to increase cervical ripening, across species using allometric scaling. Figure 5.1 plots the systemic clearance for mouse, rat, rabbit, rhesus monkey, and humans. Taking the natural log of both sides of Eq. (5.1) leads to... 

Figure 5.2 Prospective allometric scaling of relaxin clearance using only animal data. Data presented by Mordenti et al. (1991). Top plot is Ln-Ln scale. Bottom plot is linear scale. Solid line is 95% prediction interval. Prediction intervals are symmetric in the Ln-domain but become asymmetric when exponentiated back to the original domain. Arrow indicates where an adult human female (62.4 kg) falls on the line.

Representative line plots for the power model and after Ln-Ln transformation are shown in Fig. 7.3. Power models are often used because of the allometric relationship between many physiological parameters and body weight. Adolph (1949) proposed that anatomic and physiologic variables were related to body weight by power functions. For example, brain weight is related to total body weight by the model... 

A plot of data from appropriate animal species as shown above can provide estimates of the allometric parameters, allowing prediction of the pharmacokinetic parameters in other species including humans. This approach has been applied successfully for both chemical entities " and biologicals. - - ... 

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