Environmental Geochemistry and Health, 1992, t4(3), pages 71-80

Scaling toxicity data across species Willard R. Chappell Department of Physics and Center for Environmental Sciences, Universityof Colorado at Denver, PO Box 173364, Denver, CO 80217-3364, USA

Abstract The response of various species to doses of chemicals can often give the impression that some (such as cattle in the case of molybdenum) are much more susceptible than others to these chemicals. These impressions usually rely on an underlying assumption that equivalent doses are based on mg of the chemical per kg body weight of the animal. That is, that doses scale as the first power of body weight. This assumption is more often wrong than right. When viewed in a more general way, where the scaling is proportional to a power of the body weight and the exponent determined empirically, it is often found that equivalent doses scale with an exponent in the range of 0.6 to 0.8. As a result, larger animals are indeed more susceptible to toxicity on a mg kg- body weight basis, but this is not because of unique differences in the species, but only because of different body sizes. This method of scaling is called allometry or allometric scaling. An early version of this approach was based on body surface area where the exponent is 2/3. More recently, pharmacokinetics has revealed that the reason for the different response of larger animals is related to the slower metabolic and clearance rates for larger animals which give rise to larger biological half-lives for chemicals in the body and to higher tissue concentrations per given dose.

Introduction

Many scientists working in the area of environmental geochemistry and health are familiar with dae apparently higher sensitivity of cattle and sheep to molybdenum toxicity than laboratory animals. That is, when expressed on a mg of molybdenum intake per kilogram of body weight, the subchronic lethal dose of molybdenum (in a soluble species such as sodium m o l y b d a t e ) is approximately 7 mg kg -I day-1 for a cow compared to 125 mg kg-1 day-1 for a rat (Chappell, 1985). The phenomenon of apparently greater sensitivity in some species compared to others is not confined to molybdenum. Barium chloride presents a similar picture. The acute lethal dose for barium chloride in a rat is 44 mg kg -1 (Venugopal and Luckey, 1978) and in a human is 8 mg kg -t (Soltman, 1957). This type of behaviour tends to lead to attempts to define the 'ideal' or ~ animal model for a particular chemical in order to understand how this chemical will affect humans. Great effort has been spent on trying to ascertain exactly which physiological differences (or similarities) are responsible for the different (or similar) responses of different species to the same chemical. The search for the 'ideal' animal model has been unsuccessful. There is, however, hope for an improved understanding of the applicability of laboratory animal data to humans. This hope arises from research which indicates that what were thought to be differences, are, if viewed in the right way, actually similarities. In most cases the most important difference between species such as rats, humans and cattle, is the most obvious one, namely their size.

Haldane (1928) noted that "the most obvious differences between different animals are differences in size, but for some reason zoologists have paid singularly little attention to them." When comparisons are made between species of different sizes for a variety of different physiological parameters, a wide variation across body size is seen. For example, the heartbeat rate of a mouse (of approximately 0.02 kg body weight) is about 600 beats per minute compared to 80 per minute for a human (70 kg). This appears to be a major physiological difference and, indeed, it is. It would appear to be impossible to predict the heartbeat rate of a human from that of a mouse. What about the other species? If, however, representative heartbeat rates for mice, rats, rabbits, monkeys and dogs are plotted on log-log coordinates, a straight line can be fitted to the data (Mordenti and Chappell, 1989), and when extrapolated to a mass of 70 kg gives a predicted value of 83 heartbeats per minute for a 70 kg human. The equation resulting from linear regression analysis of this heartbeat rate data is: Heartbeat rate = 240M -~

(1)

where M is the mass in kg. This, then, is an equation linking a physiological parameter to body size. Such expressions have been given the name 'atlometric equations'. Allometry is the study of size and its consequences. Numerous relationships between various physiological parameters (e.g. organ weights, metabolic rates and respiratory functions) have been empirically developed (Peters, 1983). This approach is also referred to as interspecies scaling. Several review papers of the application of the allometric method to the interspecies scaling of

72

Scaling toxicity data across species

toxicological and pharmacological data have recently appeared. Among these are Davidson et al. (1986), Mordenti and Chappell (1989), Boxenbaurn and D'Souza (1990) and Chappell and Mordenti (1991). The apparent reason for the existence of the aliometric relationships is the need to satisfy certain underlying scientific principles such as energy conservation, water balance and the laws of mechanics (Gould, 1966). Thus, for many physiological parameters, while there are differences among species of different sizes, these differences often follow a pattern which enables the prediction of the outcome for humans based on size. The challenge is to find the appropriate functional dependence on size. In the previous consideration of the molybdenum data, expressed in mg Mo kg q body weight day-I, there was an implicit assumption that the equivalent toxic dose was proportional to the body mass. This dependence has the same general form as Equation (1), namely: Y = aMb

(2)

(where M is the body mass), except that the exponent b is equal to one. The study of allometry has basically involved the application of Equation (2) to various physiological parameters to determine the constants a and b for those parameters. This determination is normally accomplished by linear regression analysis on the logs of the variables M and Y. Thus, allometry is primarily an empirical science. Of course, if b is different for every physiological parameter, relatively little has been gained. Fortunately nature is not that quixotic and there are patterns to the value for the allometric exponent b. Volumes (such as blood volume, tidal volume and lung capacity) tend to scale with values for b between 0.8 and 1. Volume rotes (such as energy metabolism, minute volume, cardiac output and clearance) tend to scale with values for b between 0.6 and 0.8. Times (such as heartbeat time, breath time and biological half-lives of chemicals) tend to scale with values for b between 0.2 and 0.4 (Chappell and Mordenti, 1991). The values for the constant a are relatively unimportant because ratios can be used to eliminate the need for a. Methods Four principal methods for interspecies scaling have been used: surface area, allometric, allometric pharmacokinetics and physiologically based pharamacokinetics. Only the first three of these techniques will be discussed here. The reader interested in p h y s i o l o g i c a l l y based pharmacokinetics is refered to a recent publication by the National Academy of Sciences (1987).

Body surface area scaling Surface area scaling is based on the assumption that certain physiological parameters are proportional to body surface area giving rise to an equation of the form: Y = aM 2/3 (3) The origin for surface area scaling is a paper published in 1838 by two French scientists, Sarrus and Rameaux, in which they argued that energy metabolism in homeotherms

is proportional to body surface area, which in turn is proportional to the two-thirds power of body mass. Their reasoning was that heat loss from the body is proportional to the body surface area and necessarily equal to energy production in the body. They also reasoned that since energy production by the body is proportional to oxygen consumption, that oxygen consumption would also be proportional to body surface area. They went on to propose the exponents for scaling respiration rate, pulse rate and pulse volume. For example, assuming that heart volume or stroke volume is proportional to body mass and blood current intensity (stroke volume times heart rate frequenc50 is proportional to the oxygen consumption (which is proportional to body surface area), they found that heartbeat frequency is proportional to the negative 1/3 power of the body mass. Note that while this differs somewhat from the al!ometric result in Equation (1), it is not a large difference, and over small ranges of body size gives approxima~ly the same result as the exponent --0.25. In using this method it is useful to have values for the surface areas of different species and different body weights within each species, Quiring (1941) and Meeh (1879) discuss the difficulties and uncertainties inherent in these measurements. Meeh proposed the formula: S = KM 2rJ

(4)

where S is the body surface area in square centimeters (cm2) and M is the body mass in grams (g). The constant K was allowed to vary from one species to another. Meeh found that for human adults K = 12.3 and for infants K = 11.9. Quiring (1944) and Spector (1956) reported values for K for several species. Typically these values ranged from 9 to 12. Calder proposed that good approximations to surface area would result by simply using K = 10 for all species. Chappell (1985) proposed the equation: S = 1.85(M/70) 2/3 m 2

(5)

where M is the body mass in kilograms (kg). The surface area method for scaling toxicity data assumes that equivalent toxicological doses in different species are proportional to the body surface area of the animals. Typically the dose is expressed in terms of mg m-2 or mg day-1 m -2 depending on whether the dose is acute or chronic. Thus, if a safe and effective dose of a drug for a 10-kg child (with a surface area of 0.51 m 2 from Equation (5)) is X mg day-~, the surface area equivalent dose for a 70 kg human (with a surface area Of 1.85 m 2) is not 7X mg day-1, but rather (1.85/051)X mg day-I or 3.6X mg day-t.

Allometric scaling Allometry did not develop to any extent until the invention of linear regression analysis. As pointed out by Huxley (1932), the fundamental equation of allometric scaling is the power equation given in Equation (2). tf the physiological parameter of interest is energy metabolism, as was the case for the first application of linear regression analysis (Brody and Proctor, 1932; Kleiber, I932), then the data input are results of measurements on energy metabolism of various species (the variable Y) and the body

W, R. Chappell masses of the species (M). Obviously, the linear regression analysis is performed on the logrithms of Y and M. For the application to scaling of toxicological data, the dependent variable Y is the appropriate toxicological measure such as LDs0 (dose lethal to 50% of the population), LDlo (dose lethal to 10% of the population), MTD (maximum tolerated dose), LOAEL (least observed adverse effect level) or NOAEL (no observed adverse effect level). The application of the allometric scaling model involves determining one or more of these dose levels for several species of as widely varying size as possible (to allow for interpolation or extrapolation over as wide a range as required). The empirical data are then used to obtain the allometric coefficients and exponents in Equation (2). The equivalent dose for humans is then obtained by using human values for body mass, M, in the allometric equation.

Allometric pharmacokinetics With the advent of modern analytical techniques, it was found that while the equivalent doses (for the same response) among different animals varied greatly (expressed as mg kg-1), there was often considerable agreement for the total or unbound plasma concentration of the chemical. That is, it was found that the same plasma concentration often elicited the same physiological response. Pharmacokinetics (or toxicokinetics) is the study of the absorption, distribution, metabolism and excretion of a chemical in the animal and gives a way to determine the plasma concentration as a function of dose. Total or unbound plasma concentration is found to be related to basic pharmacokinetic parameters such as clearance, distribution volume and biological half-life. These parameters, in turn, are often found to obey allometric relationships of the form given in Equation (2). If the plasma concentration can be expressed in terms of parameters which obey allometric relationships, then an allometric relationship can be found for the plasma concentration and an expression derived for equivalent doses as a function of body mass. For example, if linear pharmacokinetics apply, for chronic dosing the average plasma concentration is given by: Cav = FD/CL = FD/kV = FDTI/2/(0.69)V

(6)

where F is the fraction absorbed, D is the dose in mass per unit time (e.g. mg day-t), CL is the clearance in units of volume per time (e.g. L day-l), k is the rate constant for first order loss of the chemical from the blood, V is the volume of distribution and T1/2 is the biological half-life (Wagner et al., 1965). Thus, given that the concentration of the chemical is the correct measure of its effectiveness and that it can be expressed in terms of measurable parameters that obey allometric relationships, the approach is to measure these parameters in a variety of species of different body sizes. Then the allometric expressions for these parameters (such as clearance) can be empirically derived, by linear regression analysis. The scaling of these parameters to humans is accomplished by simply substituting the appropriate human value for the body mass (M) into the allometric equations.

73

Table 1 Energy metabolism in dogs. a Weight (kg) 31.2 24.0 19.8 18.2 9.6 6.5 3.2

Metabolic rate (kcal kg -1)

Metabolic rate (kcal m-2)

36.7 40.9 45.6 45.9 65.2 66.1 88.1

1,040 1,110 1,210 1,000 1,180 1,150 1,210

a Adapted from Schmidt-Nielsen (1970)

Table 2 Energy metabolism in various species, a Species

Weight (kg)

Horse Man Dog Hen

441 64 15 2

Metabolism (kcal m-2) 948 1,040 1,040 1,010

a Adapted from Kleiber (1947)

For chemicals that involve hepatic clearance, both brain weight and body weight may have to be used to obtain the correct scaling (Boxenbaum and D'Souza, 1990). In these cases the physiological parameters of interest are power functions of both brain weight and body weight.

Physiologically-based pharmacokinetics (PB-PK) While this approach is outside the scope of this paper, a brief description of the method is appropriate in order to distinguish the PB-PK method from the three methods that are being discussed. The p h y s i o l 0 g i c a l l y - b a s e d , pharmacokinetic approach is based on the construction of differential equations which are mass-balance models in which it is generally assumed that organs and tissues with similar behavior can be lumped together into compartments interconnected by the fluid motion between and through the compartments. Each compartment can be considered to have a vascular section, an interstitial space and a cellular space (NAS, 1987). The equations are solved using appropriate algorithms with various constants being determined from the literature or fit to animal models. When the species-specific parameters in the model are replaced by human values, a prediction for humans is obtained. No further discussion of this approach will be given. Readers interested in this method are referred to the literature (e.g. NAS, 1987).

74

Scaling toxicity data across species Results and Discussion

Surface area Most of the early experimental work on the surface area method was inspired by the work by Sarrus and Rameaux (1838) on energy metabolism. Because of the need to develop suitable calorimetric methods, this proposal was not tested until 1883 when Rubner measured the energy metabolism rate in dogs. Rubner's results, shown in Table 1, illustrate two important phenomena. One is that the metabolic rate per kilogram body weight increases with decreasing size (this ever-increasing demand for nourishment places minimum size for mammals at the size of a shrew). The other is that when the metabolic rate is divided by surface area, it is nearly a constant. These two phenomena are two sides of the same coin since surface area is approximately proportional to M 2/3. In fact, Rubner proposed that the energy produced by homeotherms is 1,000 cal m-2 day-1. Voit (1901) performed the same measurements on animals from four different species. His data, shown in Table 2, illustrate that the phenomena described above hold over a range of body mass of two orders of magnitude. Perhaps the earliest record of body surface area being used to calculate drug dosage was the work by Hufeland in 1830. He is quoted by Butler and Richie (1960) as having proposed that "on the basis of clinical experience a scale of doses of drugs according to size, expressed as a percentage of adult dose being closely proportional to body surface area". The clinical experience often encountered when body weight was used to scale dosage was that a 70 kg adult, given a dose 14 times that which was sate and effective for a 5 kg child, had a toxic response. Conversely, a child given 1/14 the dose safe and effective for a 70 kg adult often had an inadequate pharmacologic response. The use of body surface area would predict a dose ratio of 6 rather than 14. The dose scaling proposed by Hufeland (Butler and Richie, 1960) was very close to what would result from the application of Equation (3). The surface area approach has had an irregular pattern of use over time. It would appear to gain acceptance only to fall into disuse for a time before eventually being rediscovered. Moore in 1909 and Dreyer and Walker in 1914 recommended its use. Crawford et at. (1950) described an extensive programme being carried out at Massachusetts General Hospital to test the surface area dosage method. One study described by C r a w f o r d involved approximately 60 patients who were divided into four groups (infants, young children, older children and adults) based on surface area. These patients were all receiving, as part of their t r e a t m e n t , either s u l p h a d i a z i n e or acetylsaticylic acid at regular intervals around the clock. They found a linear relationship between blood concentrations and dosage based on body surface area. In the case of sulphadiazine, a dose level of 4.25 g m-2 day-~ resulted in a blood level of this drug of 10 mg 100 mL-1. Thus, if a blood level of 10 mg 100 mL-1 were required in a 10 kg child, the appropriate dose would be (4.25 g m-2 day-l) x (0.5 m 2) = 2.13 g day-1. For a 70 kg adult to have the same blood level of the drug, the dose would need

to be 8 g day-t (using a surface area of 1.85 m2). A linear relationship of the same kind was found for acetylsalicylic acid. Crawford et al. (1950) also found that accepted dosages (e.g. the average analgesic dose for morphine at that time) of several commonly used drugs (e.g. morphine mad thyroid) were consistent with body surface area scaling. They also noted that this was the case with an extensive list of therapeutic agents (they did not, however, publish the list) over a wide range of body weights and stated that no exceptions had been found to that time, Talbot et al. (1953), Snively (1957), Baker el at. (1957) and Talbot and Richie (1959) also reported the use of surface area to determine the dosages of therapeutic fluids, blood and electrolytes. These investigators all reported that body surface area was preferable to body weight for dosage scaling. An interesting consequence of using body weight scaling was reported by West and Pierce (t962): These investigators had wished to study the effect of lysergic acid diethylamide (LSD) on an elephant. They chose the dose which produced a rage response in a cat (which they hoped to duplicate in the elephant) and multiplied that dose (0.1 nag LSD kg-1 body weight) by the weight of the elephant (2,970 kg) to arrive at a dose of 297 mg LSD which they administered to the elephant. The elephant immediately went into convulsions and died within 2 hours. Harwood (1963) pointed out that the outcome might have been different if body surface area scaling had been used. In spite of the considerable empirical data supporting the surface area technique, there was considerable dissent. Forbes (1959) and Oliver et al. (1958) both criticized the use of this method. The most important studies regarding surface area scaling were those involving chemotherapeutic agents. Because these drugs are often effective only at levels near or above toxic doses, it is crucial that the dosage calculation be as accurate as possible. Moreover, more and better information exists about the toxicity of these drugs to humans than for most chemicals because of the high doses and the controlled conditions under which they are administered. Pinkel (1958) reviewed the literature to determine 'generally accepted' levels for therapeutic doses in animals and humans. Pinkel found that when these doses were expressed in terms of mg m-2 body surface area day-l, that there was remarkable similarity among and within species. The differences were generally less than 20%. The only exception was for 6-mercaptopurine where the same dose per body weight per day (3 nag kg-1 day-l) was used for humans over weights ranging from 8 to 70 kg. This practice lead to an adult dose in mg m-2 day-1 that was 70% higher than for a child in the same units. Pinkel suggested that this difference might explain why adults generally developed earlier and more severe toxic responses to this drug than children. The classic study regarding chemotherapeutic agents was published by Freireich et al. (1966). They reviewed published and unpublished data on the toxicity of various anticancer drugs to humans and animals. They chose to compare the Maximum Tolerated Dose (MTD) for humans

W. R. Chappell Table 3 Comparison of predicted and actual lethal

doses of molybdenum for various species (from Chappell, 1985).

Species

Weight (kg)

Surface area (m 2)

Rat Guinea Pig Rabbit Man Cow

0.1 0.3 2 70 500

0.023 0.05 0.17 1.85 7

Lethal dose Predicted Actual (mg kg-1 day-1) 90 45 14 7.6

125 70 50--60 ? 4-10

75

The extent and quality of the data on anfitumor agents is generally far better than for other chemicals, particularly the trace elements. There are, however, some data on trace elements with which to test the surface area scaling hypothesis. The two chemicals, molybdenum and barium, mentioned at the beginning of this paper are examples. Table 3 contains data on the lethal doses of molybdenum. The third column in Table 3 illustrates the results of using the surface area method to predict the lethai dose for four other species from the lethal dose for rats. The fourth column in Table 3 contains the actual lethal close for comparison. The calculation for humans simply involves the following: [(125 mg kg -1 day-1) x (0.1 kg)/(0.023 m2)] x [(1.85 m2)/(70 kg)] = 14 mg kg -1 day-l.

Table 4 Comparison of lethal dosesa of barium chloride for various speciesb (from Chappell, 1985).

Species Rat Rabbit Cat Dog Guinea Pig Man c

Lethal dose mg kg-1 44 38 33 10 36 8

mg m-2 190 450 390 200 300 300

a LDI00.

b Adapted from Venugopal and Luckey (1978). c Sollman (1957).

with either the LDlo (dose to kill 10%) or MTD for animals (the LD10 being appropriate for small animals and the MTD for large animals). It was necessary to use a normalisation procedure to take into account different dosage schedules. They found that with this normalisation the data strongly supported the use of surface area scaling as opposed to body weight scaling of dosages. This study was so convincing that body surface area is still the most widely used method for calculating dosages for chemotherapeutic agents in humans.

It can be seen that the predicted values agree well with the actual values. Of course, no case of a lethal dose to humans has been reported. Thus, while a cow is indeed more sensitive than a rat on a mg kg -1 basis, that is not the case on a mg m-2 basis. Table 4 contains data on the lethal dose for barium chloride in six species. A comparison is made between the lethal dose on a body weight (mg kg -1) basis and on a surface area (rag m-2) basis. It can be seen that the body weight-based dose decreases with body weight (similar to the energy metabolism as seen in Tables 1 and 2). But, the surface area-based dose is relatively constant among species. Table 5 gives some data for thresholds for subchronic toxicity of molybdenum and compares the LOAEL (least observed adverse effect level) on the basis of body weight and body surface area. With the exception of the pig, the surface area approach gives remarkably good agreement when the rat is used to predict the LOAELs for the other species. It should be noted that developing values for LOAELs always involves a certain amount of interpretation of the literature.

Allometric method The term 'allometry' in connection with scaling was introduced by Huxley and Tessier in 1936. It means 'of a different measure.' But allometry itself existed before that time. Galileo may have been the first allometrist when he noted in his Dialogue of the Second Day (1638) that the diameters of the supporting limbs of animals and the trunks

Table 5 Comparison of predicted and actual thresholds for subchronic zoxicity of molybdenum (from ChappeU,

1985).

Species

Weight (kg)

Rat Guinea Pig Rabbit Pig Man Cow

0.1 0,3 2 60 70 500

Surface area (m 2) 0.023 0.05 , 0.17 1.7 1.85 6.9

LOAEL Predicted (mg kg-1) 1.5 0.7 0.2 0.2 0.1

Actual (rag kg-1)

(rag m-2)

1-2 1-10 1-10 2 0.14--0.2 0.07-4

4-9 6--60 11-120 71 5-8 5-290

76

Scaling toxicity data across species

of trees must become proportionately larger as their mass increases in order to support their weight (in fact, the square of the diameters must increase as the weight to the first power). Thus, the mass of the supporting limbs increases at a rate faster than that of the total body mass - thus 'of a different measure.' The first major contributions made by this approach involved energy metabolism of homeotherms, the same phenomenon considered by Sarrus and Rameaux (1839). In 1932, two nearly simultaneous publications appeared, one by Kleiber and the other by Brody and Proctor. Kleiber (1932) applied linear regression analysis to the log-transformed data set and obtained a value of 0.75 for the exponent. Brody and Proctor (1932) applied the same method to a somewhat different data set and obtained a value of 0.734. These calculations used data from species ranging in weight from a 10 g mouse to a 16 ton elephant. Other investigators applied the same technique to numerous physiological parameters. In particular, Adolph (1949) reported on the atlometric exponents for a variety of parameters with exponents ranging from 0.08 (for renal corpuscle diameter) to 1.31 for myoglobin weight. Since that time, many investigators have published results of aUometric investigations (Gunther and Guerra, 1957; Calder, 1981; Peters, 1983). In general, the reported exponents have tended to cluster about three values: 1.0 (for various volumes such as tidal volume, blood volume, and lung capacity); 0.75 (for energy metabolism rate, minute volume, blood flow, cardiac output, clearance and oxygen uptake); and -0.25 (pulse rates, breath rates, and inverse lifetimes). Whenever two different parameters scale with approximately the same exponential value, the ratio of the two parameters is nearly a constant across species (i.e. an interspecies invariant). For example, the ratio of breath time to heartbeat time is essentially independent of mass and equal to 4 heartbeats per breath for all mammals. Furthermore, in many mammalian species the number of heartbeats per maximum life span is nearly a constant equal to 900 million (and, because of what was just said, the number of breaths per lifetime is 225 million). That is, even though small mammals live a much shorter time than large animals, they have, in a lifetime performed approximately the same total number of physiological functions. Thus, in terms of their internal clocks, most mammals live the same period of time. Humans are somewhat different, living approximately three times longer in number of heartbeats (i.e. a total of about 3000 million heartbeats per lifetime). This is considered to be a reflection of neoteny (Gould, 1979; Yates and Kugler, 1986; Boxenbaum and D'Souza, 1990), which is the phenomenon of prolonged early development, This approach of finding physiological invariants or constants, is one of the methods that have been exploited in the theoretical analysis of allometric relationships. It is based on an engineering method of analysis called ~ analysis' which is frequently used in scaling up from bench scale models to pilot scale and commercial scale. The idea being that there are underlying design similarities that must be retained in order to have the larger models perform the same functions as the smaller models.

Stahl (1963) wrote extensively on this concept. Heusner (1982) has argued that the analysis of energy metabolism by Brody and Proctor (1932) and Kleiber (1932) was incorrectly performed because the parameter a in the allometric equation, Y = aM b, should have been allowed to vary from one species to another. He used an analysis of covariance model which lead to an equation of the form: "," = a M ~

(8)

where the constant a varies with species. In essence, he argued against interspecies scaling. Feldman and McMahon (t983), however, pointed out that there was a monotonic increase in Huesner's coefficient a as a function of mass. Using the same data set as Huesner and a re-parameterisation of the model used by Huesner, they showed that the mass coefficient a varied as the 0.08 power of mass. Thus Huesner's model was equivalent to that obtained by Brody and Proctor (1932). Hayssen and Lacey (1985) have reviewed the work of several investigators on the allometric equation for energy (basal) metabolism rates. They noted that many of these studies shared a weakness in the use of multiple data points for the same species. Hayssen and Lacey argued that this practice confounded the trends and violated the assumption of statistical independence of the samples. Hayssen and Lacey's own data set led to an exponent of 0.7 rather than 0.75. But they also noted significant deviation from this value by many species. With the exception of Heusner (1982), there is general support for the concept of aUometric relationships across species. There is, however, disagreement regarding the values of the exponents and coefficients. When possible, the selection of the values of a and b to be used in Equation (2) should be approached empirically. That is to says appropriate measurements made on several species over as wide a range of body weights as is feasible, and then the values of interest regressed against body weights to obtain an empirically-derived equation yielding the predicted human values. The application of allometric methods to scaling toxicity data involves choosing the appropriate dependent variable y in the allometric equation, y = a M ~ . This dependent variable might be the LDl0 (the dose required to kill 10% of the animals), the MTD (maximum tolerated dose) or the LOAEL (lowest observed adverse effect levei). The most extensive study involving the application of allometric methods to toxicity data was reported by Krasovskii (1976). He described an extensive programme carried out at the Sysin Institute in Moscow. Unfortunately, none of the allometric equations obtained or other data have been published even though Krasovskii claimed to have studied more than 100 substances. He reports to have found that, on average, the allometxic equation and the body surface area method gave approximately the same result implying an allometric exponent close to 0.7. Fie reported that the use of regression analysis was valid for 80--85% of the substances and that the predicted values differed from actual values by less than a factor of 3 or 4. Book (1952) applied the allometric method to the scaling of nitrogen dioxide toxicity data. He used data for

W. R. Chappell Table 6 Allometric exponents for fourteen drugs used in Freireich et at. (1966) study (from Mordenti, 1986). Agent

Exponent

Significance level

Actinomycin D BCNU Busulfan Cyclophosphamide 5-fluorouracil 5-FUdR Mechlorethamine Melphalan 6--mercaptopurine Methotrexate IVfitomycin C Nitromin L-phenylalanine Thio-TEPA

0.776 0.784 0.727 0.765 0.841 0.782 0.815 0.721 0.868 0.704 0.707 0.663 0.604 0.621

0.011 0.005 0.053 0.117 0.015 0.001 0.054 0.004 0.034 0.145 0.0005 0.007 0.0005 0.001

the concentrations and times of exposure to kill 50% of the exposed populations for five species (mouse, rat, guinea pig, rabbit and dog). He found that the lethal dose (LDs0) in units of mL rain -1 satisfied an allometric equation with an exponent of 0.84. In view of the fact that Krasovskii's data (1976) are unavailable, the most convincing publication to date of the relevance of the allometric method to scaling toxicity data is that by Mordenti (1986). Mordenti used the extensive data set analysed by Freireich et al. (1966) in their classic paper on the use of body surface area scaling. Of the eighteen drugs analysed by Freireich et al., there was sufficient data on fourteen of them (Table 6) to perform regression analysis. Statistically significant results were obtained for ten of these chemicals. In this case the dependent variable y in the allometric equation was either the MTD or the LDI0 dose in mg. The values for the exponent in the allometric equation varied between 0.6 and 0.87. While the body surface area result (0.67) falls within that range, the data do not support that choice over others, such as 0.75. But these results clearly show that body surface area was a far better choice (at least for these chemicals) than body weight, which was the argument made by Freireich et al. (1966). Recently, Travis and White (1988) repeated the analysis described above and obtained similar results to those of Mordenti (1986). While Mordenti proposes an empirical approach without supporting any particular value for the allometric exponent, Travis and White argue that these results support the choice of 0.75 in toxicity scaling. Chappell (1989), on the other hand, contends that Travis and White are overstating the accuracy of the data by using two significant figures and suggests the use of 0.7 in the absence of empirical data. Unfortunately, the data for chemicals other than c h e m o t h e r a p y agents are very sparse, generally inconsistent and non-uniform in terms of molecular form,

77

route of delivery and end point observed. However, the data for barium chloride in Table 4 do allow the opportunity to test the allometric method on at least this inorganic chemical. When reasonable assumptions are made concerning animal weight (to convert from mg kg-1 to rag), and a linear regression of the logs of the toxic dose and mass is performed, the result is an allometric equation with an exponent of 0.7. Thus, in a gross sense, the reason that larger animals have toxic doses in mg kg-t that are less than those of smaller animals is that the allomeuic equations for dose (in rag) as a function of mass (in kg) frequently have exponents less than one. Consequently, when the dose is divided by mass to give mg kg -t units, the allometric equation for this redefined dose frequently has a negative exponent.

P harmacokinetic allometry One of the deficiencies of the two methods just discussed is that for toxicity scaling they are 'black box' methods. While there are theoretical arguments for energy metabolism scaling, there is no theoretical underpinning for scaling toxicity data. With the advent of modern analytical equipment, it was found that while the equivalent doses (for the same response) between different animals varied greatly. There was considerable agreement between total or unbound plasma concentrations of a chemical across species when equivalent (on the basis of surface area or allometric scaling) doses were given. This was illustrated for humans in the study by Crawford et al. (1950) that was discussed earlier where similar blood concentrations of sulphadi~ine and acetylsalicylic acid were found for doses based on surface area scaling. Pharmacokinetic methods can be used to show that (for first-order kinetics) the average plasma concentration is related to the clearance and the dose. Thus, if the clearance obeys an allometric equation, so does the concentration. For chronic dosing, the average plasma concentration is equal to the f r a c t i o n (F) absorbed from the gastrointestinal tract into the systemic blood (including effects of first pass metabolism) multiplied by the dose rate (D) (e.g. mg day-1) divided by the clearance. The clearance (CI) in turn is proportional to the volume of distribution (V) (the effective volume through which the chemical is distributed in that compartment) divided by the half-life (TI/2) of the chemical in the blood. That is: Car = FD/C1 = FD/kV = 1.44 FDTi~fV

(9)

where k is the rate constant for first-order loss of the chemical from the blood and is related to Tl/2 by k = 0.69/T172 (Wagner, 1965). It is important to note that Equation (9) holds, in general, only under certain conditions: (a) the transfer from the blood is first order; (b) F, Car, C1, V and TI/2 are constants for each dose; and (c) the dynamics of input, transport and excretion are described by a system of simultaneous, linear, differentiS.l equations. From Equation (9) it can be seen that if C1 obeys an allometric equation, then so will Car. But why should C1 obey an allometric equation? The mason is that the volume of distribution (V) and the half-life obey allometric

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Scaling toxicity data across species Table 7 Pharmacokinetic equivalent dosing regimes for ceftizoxime in animals and humans (adapted from Mordenti, 1986). Parameters

Mouse

Rat

Weight (kg) Dose (mg kg-1) No. doses/24 hrs

0.023 88.1 20

0.18 37.5 15

Species Monkey

equations and it is very reasonable that they should. As mentioned earlier, the heartrate increases with decreasing size and the heartbeat time obeys an allometric equation with an exponent of 0.25. As a result of the faster heartbeats, various other physiological processes occur faster in smaller animals compared to large animals. Typically time periods involved (e.g. Ttt2) obey allometric equations with exponents between 0.2 and 0.4. Most frequently the exponent is close to 0.25. While the volume of distribution (V) is not exactly the blood volume, it clearly becomes larger with increasing size, and there is considerable evidence that distribution volumes for many compartments obey allometric equations with exponents generally in the range of 0.8 to 1.0; most frequently, the exponent is close to 1.0. As a result of the relationship between clearance, biological half-life and distribution volume, clearance also frequently obeys an allometric equation. The exponents are typically in the range 0.6-0.8 and frequently close to 0.75. Thus, the reason that smaller animals can generally tolerate larger doses (in mg kg -1 body weight) of a toxin is that they are able to clear most chemicals from their bodies much more quickly (in mL day-1 kg -t body weight) than larger animals. That is, the much longer biological half-lives of chemicals in large animals compared to small animals means that a given dose to a larger animal will lead to a higher concentrations of the chemical in the tissues than for small animals. When only single or a few doses are given, or when the doses are given infrequently, the blood concentrations become time dependent. In that case, an important parameter is the AUC (area under the curve), which is the integral over time of the tissue concentration. Under the conditions for which Equation (9) holds it is possible to show (Wagner et al., 1966) that for a single dose d: CI = Fd/AUC

(10)

If the dose is given intraveneously, F = 1. Thus, in the short-term, toxicokinetic studies can be performed on several species to obtain data for an allometric analysis of that chemical in the blood. In many cases (Mordenti and Chappell, 1989) the AUC does scale allometrically across species. Because of the relationship given by Equation (10), CI should also scale allometrically (with an exponent which is the negative of that for the AUC). Assuming that the conditions under which Equation (9) are not violated by the doses being extrapolated, the same exponent obtained from the linear regression equation for the AUC can be used to scale the toxicity data generated from subchronic and chronic studies. Thus, short-term toxicokinetic studies on several species can be used to obtain the aUometric

7.5 24.3 7

Dog

Human

12 23.6 4

70 14.3 3

exponent which is then applied to scale data from long term studies on fewer species. Assuming that equivalent doses are implied by equal concentrations, the dose level Dh in the human, which is equivalent to the dose level Da in the animal, is given by the equation (Mordenti and ChappeU, 1989): Dh = Da {(Fa/Fh)(Th/Ta)(Clh/Cla)

(11)

where Th and Ta are the dosing intervals. If the dosing is continuous, then the dosing intervals are absorbed into the dose D (so the units are, for example, mg rain-l), and if the bioavailabilities are same, then, assuming an atlometric equation for the clearance leads to the result: D h = Da(Mh/Ma)b

(12)

where b is the allometric exponent for the clearance. If the allometric exponent (b) has riot been determined empirically and it is important to obtain an estimate, then a value of b = 0.7 is a reasonable choice (Chappett, I989). Some would argue tbr 0.67, others for 0.75, and still others for 1.0. But the errors inherent in the measurements do not support two-significant figure accuracy. From Equation (12) it can be seen that the smaller b, the more conservative (i.e. smaller) the value for Dh. In general, the data tend to support values for the allometric exponent b in the range of 0.6-0.8 as opposed to 1.0. Thus, 0.7 represents a conservative choice, reasonably supported by the data and does not misrepresent the degree of accuracy of the estimate by having too many significant figures. The fact that biological half-lives for chemicals are much shorter in small animals compared to large animals has many important implications. For example, if instead of continuous dosing, doses are given in intervals that are of the order of, or larger, than the biological half-life of the chemical in some of the species being tested, then not only do the doses have to be adjusted but the dosing intervals may have to be adjusted as well. This occurs when both the area under the curve and the peak concentration are required to be equal for equivalent doses. In these cases, the smaller animals have to be dosed more frequently than larger animals in order to obtain equivalent doses as demonstrated in Table 7 for the drug ceftizomine (Mordenti, 1986). The allometric method of scaling works best for renally excreted chemicals. Boxenbaum and Fertig (1984) have shown that for chemicals that involve hepatic clearance it may be necessar~j to develop multivariate allometric equations using body weight and brain weight. If the doses being given are sufficiently high to saturate metabolic processes or in any way lead to nonlinearities, than the basic assumptions of linear

W. R. Chappetl mxicoldnetics are violated and simple allometric scaling may be expected to fail. In such cases, physiologicallybased, pharmacokinetic (PB-PK) models may be useful in interspecies scaling (NAS, 1987). Discussion and Conclusions What appears at first glance to be a species-specific reaction to a drug or toxicant, such as the apparendy much greater susceptibility of cattle and sheep to molybdenum, may, if viewed in a different light, be a reflection of interspecies similarity. There are indeed differences among species. Perhaps the most important, but often ignored, difference is that of size (Haldane, 1928). As physiological processes were adapted to different sizes, certain underlying fundamental laws, such as energy conservation and water conservation, governed the way in which organ sizes and physiological rates were scaled from one body size to the next (Gould, 1966). In particular, heartbeat rates are much faster for smaller animals than for larger ones. But these rates vary in a predictable way from one mammal to another, obeying the allometric equation with an exponent of about 0.25. This and other such allometric relationships imply that various metabolic processes, such as the elimination rates of drugs and toxicants are also generally faster in small compared to large animals. As a result biological half-lives of chemicals should tend to obey allometric equations with exponents generally in the range of 0.2-0.4 (Chappell and Mordenti, 1991). The result of this dependence of half-life on body mass is that the same dose in mg kg-I body weight given to a large animal will result in a higher tissue concentration than in a small animal. A l l o m e t r y offers a relatively simple way of understanding these patterns and an empirical approach to predicting equivalent doses in different species. While there were many attempts to develop a body surface area approach, this method is apparently limited in its success and can simply be considered a special case of atlometry (with a fixed exponent of 2/3). As noted earlier, in cases where there is insufficient data to determine empirically the allometric exponent, a choice of 0.7 for the exponent is reasonable. For situations such as wildlife toxicology, where little or no data exist, particularly for most terrestrial species, allometric scaling may be particularly helpful. It is true that there are situations where the allometric method (at this time) does not work well. In particular, when the doses are such that nonlinear processes can take place, such as s a t u r a t i o n , other m e t h o d s (e.g. physiologically-based pharmacokinetics) have more success. It is possible that the simpler allometric method might be modifiable to account for saturation and other similar nonlinear processes. That remains as a challenge to this field, References Baker, R.J., Kozoll, D.D. and Meyer, K.A. 1957. qSe use of surface area as a basis for establishing the normal blood volume. Surg. Gynecol. Obst., 104., 183-189. Book, S.A. 1982. Scaling toxicity from laboratory animals to people: an example with nitrogen dioxide. J. Toxicol. Environ. Health,

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(Manuscript Noo250: submitted June 18, 199t and accepted after revision June 23, 1992.)

Scaling toxicity data across species.

The response of various species to doses of chemicals can often give the impression that some (such as cattle in the case of molybdenum) are much more...
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