Allometric exponent

K, logistic growth curve constant K, logistic growth curve constant Volume, allometric exponents Liver Kidney Bone... 

The value of 0.98 for the allometric exponent is so close to unity as to make the volume of distribution directly proportional to body weight, i.e. weight normalized volume is an invariant parameter (see Table 9.1). The mean value for the volume of distribution in the eight species is 0.82 0.21 L kg ... 

Vermeire et al. (1999) have noted that scaling on the basis of surface area or caloric demand can be considered more appropriate compared to extrapolation based on body weight however, they also noted that experimental work did not answer the question regarding which of these two methods is the most correct. Based on theoretical grounds, and supported by their own analyses, Vermeire et al. (1999) concluded that scaling on the basis of caloric demand to adjust oral NOAELs for metabolic size can be considered more appropriate compared with extrapolation based on body weight. It was also noted that an allometric exponent of 0.67, i.e., the body surface area approach, seems to better describe intraspecies relations. 

ThuS/ if the allometric exponent is less than unity/ as observed for many measures of physiologic function/ the function per unit of body weight decreases as body weight increases. 

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. 

If the allometric exponent were 0.7/ which is more typical of renal excretion and hepatic metabolism (Table 30.1)/ then increasing the body weight from 1 to 100 would result in an increase in the property from 1 to 25 and a value of the property per unit body weight only one-fourth as large. 

In this equation, Y is the parameter of interest, the coefficient a is the value of the parameter at one unit of body weight, W is body weight, and b is the allometric exponent. For convenience, this equation is linearized to... 

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