The application of allometric scaling principles to predict pharmacokinetic parameters across species.

Expert Opin. Drug Metab. Toxicol. Downloaded from informahealthcare.com by University of Connecticut on 10/10/14 For personal use only.

Review

1.

Introduction

2.

Basic principles of interspecies allometric scaling

3.

Allometric scaling of CL

4.

Allometric scaling of VD

5.

Allometric scaling of elimination half-life

6.

Factors (or pitfalls) that might affect the prediction of PK parameters

7.

Application in veterinary medicine

8.

Expert opinion

The application of allometric scaling principles to predict pharmacokinetic parameters across species Qingbiao Huang & Jim E Riviere† Institute of Computational Comparative Medicine, Kansas State University, Manhattan, KS, USA

Introduction: Interspecies allometric scaling provides a simple and fast option to interpolate or extrapolate drug dose or pharmacokinetic parameters to a species of interest. Over the years, new scaling methods have been developed in order to improve the performance of these predictions. It is critical to choose appropriate allometric scaling approach(es) to analyze the available pharmacokinetic data. Areas covered: This review provides updated information on the latest allometric scaling methods developed for the most frequently interpolated or extrapolated pharmacokinetic parameters. The different degrees of success and advantages/disadvantages of different methods are compared and contrasted. The pitfalls that affect the accuracy of prediction and the solutions to avoid the risk of prediction errors are discussed. The application of allometric scaling in veterinary medicine is presented. Expert opinion: Although interspecies allometric scaling needs further refinements and has limitations, it is still a potential tool and rational option for the estimate of pharmacokinetic parameters in species for which there are no data available or to better interpret preclinical efficacy and safety trials. Allometric scaling can offer insight into possible mechanisms of species-dependent drug disposition. Keywords: allometric scaling, clearance, comparative pharmacology, elimination half-life, interspecies pharmacokinetics, veterinary medicine, volume of distribution Expert Opin. Drug Metab. Toxicol. (2014) 10(9):1241-1253

1.

Introduction

Allometry, an engineering term derived from the Greek alloios (meaning different), is the study of size and its consequences. It was first coined by Huxley and Tessier in 1936 [1] and applies to properties whose proportions change as a function of size, as opposed to isometry whose relationship to size remains constant. During drug discovery and development, allometric scaling has been shown to be a practical approach to predict the pharmacokinetic (PK) profile of drugs in a species of interest, particularly in the absence of either species-specific PK data or prior drug experience in that species [2]. Sarrus and Rameaux initially developed their theory of ‘surface law’ for energy metabolism rates of mammals [3]. In 1938, Benedict plotted total heat production versus average body weight and demonstrated that basal metabolic rate (BMR) could be amenable to allometric scaling and did not scale linearly with body mass [4]. The metabolic rate for mammals was fitted by the allometric equation Pmet = 70M0.75 as described by Kleiber [5]. It is now well documented that many physiological processes (such as heart rate, blood circulation time, respiratory rate, glomerular filtration rate [GFR], heat production, energy metabolism rate) and 10.1517/17425255.2014.934671 © 2014 Informa UK, Ltd. ISSN 1742-5255, e-ISSN 1744-7607 All rights reserved: reproduction in whole or in part not permitted

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Q. Huang & J. E. Riviere

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Interspecies allometric scaling has been widely used in the prediction of pharmacokinetic parameters of a species of interest. Body weight, rather than body surface area, is commonly chosen for allometric scaling. Many pitfalls may affect the performance of prediction and those factors should be careful considered when selecting the allometric scaling method. Clearance (CL) is the primary parameter for which most allometric analyses have been conducted. Volume of distribution (VD) is usually amenable to allometric scaling when protein binding of drug is low. Elimination half-life is a hybrid pharmacokinetic parameter of CL and VD and the relationship between half-life and body weight often results in poor correlation. Allometric scaling is less risky when used in veterinary medicine when species smaller and larger are used for predicting pharmacokinetics on an unknown species.

This box summarizes key points contained in the article.

organ sizes (such as heart weight, lung weight, kidney weight, surface area) exhibit an allometric relationship with the body size or body mass of various species. The assumption for using interspecies allometric scaling is that there are anatomical, physiological and biochemical similarities among animals and simple mathematical models can be utilized to describe these relationships [6]. Besides physiological parameters, PK parameters of interest can also be scaled across species using this approach. PK focuses on the processes of absorption, distribution, metabolism and elimination (ADME) of drugs and chemicals in the body. Many important PK parameters, including clearance (CL), volume of distribution (VD) and elimination half-life (t1/2), have been intensively studied and regularly predicted from animals to animals and from animals to humans. It is not surprising that interspecies PK scaling can also be described by allometric equations because most PK parameters are dependent on physiological functions that are in turn determined by BMR. Historically, body surface area was used as a criterion for the direct extrapolation of drug dosage from animals to humans in cancer chemotherapy. The US FDA recommends the exponent 0.67 for body surface area to scale doses across species [7]. The quantitative comparison of toxicity data acquired during clinical studies of 18 anticancer agents with those obtained in mice, rats, dogs and rhesus monkeys uncovered close interspecies correlations when doses were related to body surface, much closer than when doses were related to body weight [8]. This finding has subsequently guided numerous trials of anticancer and other agents. However, body surface area is not directly measured but rather is estimated with allometric equations. For a given species, there may be several equations (DuBois, Haycock, Gehan and George and 1242

Boyd formulas) available to predict body surface area. Most importantly, it has recently been argued that there is no advantage in using body surface area over a simple mathematical function of body weight [9,10]. The link between body surface area and metabolic rate is the evolutionary adaptation of animals to their sizes. Compared to body weight, body surface area is an indirect and imperfect correlation of metabolic rate. Allometry is commonly used for determining the firsttime-in-human (FTIH) dose for Phase I human clinical drug trials [11]. In clinical medicine, it is feasible to use adult data to predict drug PK parameters in children, which can significantly decrease the occurrences of toxicity and mortality for new drugs used early in children. Allometry has a definite role in zoo animal and wildlife medicine. Currently, there are fewer than 15 therapeutic compounds approved in the USA for zoo and wildlife species and limited research has been done to provide PK data for nondomestic species. A similar scenario exists for treating minor animal species. Veterinarians are frequently faced with the need to estimate PK parameters in larger species because data for large cats, camels and elephants are particularly scarce. Interspecies allometric scaling provides a powerful tool in this scenario to extrapolate the use of approved agents to non-approved species [12]. Finally, allometric scaling of PK parameters across preclinical laboratory animal species is also used for interpreting safety and efficacy data across animal models. In this work, we review the principle of interspecies allometric scaling and its application in veterinary medicine. The latest updates for allometric scaling methods for the estimates of PK parameters: CL, VD and (t1/2) are discussed in detail. The advantages and limitations of the application of allometric scaling to predict PK parameters are also included.

Basic principles of interspecies allometric scaling

2.

Allometric scaling equation As mentioned above, the similarities among animals can be generalized and expressed mathematically by the allometric relationship. It is based on the power-law function, which can be represented as follows: (1) 2.1

Y = a ×W b

where Y is the parameter of interest, W represents the average body weight of a species, and a and b are the allometric coefficient and exponent of the equation, respectively. In order to illustrate the relationship between parameter (Y) and body weight (W), Equation 1 (simple allometry) turns into a linear function after logarithmic transformation so that estimates of a and b can be computed by linear regression. The logarithmic transformation of Equation 1 is written as follows:

Expert Opin. Drug Metab. Toxicol. (2014) 10(9)

Application of allometric scaling principles to predict PK parameters across species

12 Y = 0.5 × Wb

Parameter of interest (Y)


10

b = 0.75 b = 1.25 b = 1.00

8

6

4

2

0 0

2

4

6 8 Body weight (W)

10

12

Figure 1. The allometric scaling exponent b (i.e., the slope) describes how the parameter of interest (Y) scales over different values of body weight (W) and defines the type of scaling relationship. This plot uses allometric scaling equation Y = 0.5 Wb as an example. When the exponent is 1, Y increases in direct proportion to body weight and this is an isometric relationship; when the exponent is 1.25, Y increases out of proportion with body weight and this is a positive allometry; when the exponent is 0.75, Y increases slower than body weight and this is a negative allometry.

(2)

log Y = loga + b logW

where b is the slope and log a is the y-intercept. The value b of the equation defines the type of scaling relationship between Y and W, which can be illustrated by Figure 1. The exponent b simply provides a means of mathematically describing the rate of change between W and a given Y. Y increases proportionally with W (isometry) when b is equal to 1; Y increases faster than W (positive allometry) when b is larger than 1; Y increases slower than W (negative allometry) when b is smaller than 1. The exponents of allometric scaling are not constant and have no inherent physiological meaning [2]. When PK parameters or doses in clinical medicine are expressed per kilogram of body weight, it is implicitly assumed that b equals 1 and an isometric relationship holds. This assumption is frequently overlooked. Two practical considerations when performing allometric scaling 2.2.1 Risks of mathematical error 2.2

It is an assumption behind the log-log transformation that a constant coefficient of variation about the value of the parameter of interest associated with body weight holds true (i.e., the variability of the parameter is identical across species). If this assumption is not valid, the use of allometry is not appropriate. In practice, the logarithmic transformation of the data will stabilize variance as well as visually minimize the deviations from the regression line. A high correlation coefficient

value (r) does not guarantee that all the data points will be close to the regression line and cannot be used independently as an indicator of accuracy [13]. The extrapolation of this regression line to obtain a predicted value of PK parameter in an individual species may have great uncertainty associated with it. In addition, regression analysis does not treat the weight of each animal species comparably. However, direct fitting of the power function with incorporation of a statistical weighting strategy has not been shown to improve the prediction performance. The exponent b for a given drug is not universal and will depend on the particular mix of species used in the allometric scaling. This limitation is often not appreciated. Selection of species Ideally, the selected species should have similar physiology (e.g., mammals, birds, etc.), be closely related and differ only in size. Numerous (three or more) species are used across a wide range of body weight (0.1 -- 5000 kg), with at least three orders of magnitude recommended [14] in order to obtain a better linear relationship on a log-log scale. A change in the slope of the line can occur by altering the weight range of the animal species. However, it is hard to predict a priori which species should be best included for the prediction. In addition, the majority of large animals (cattle, horse and elephant) are herbivores, whereas the smaller animals are either omnivores (mouse, rat and monkey) or carnivores (dog and cat). Differences in diet can influence drug metabolism and renal elimination [15]. 2.2.2


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Table 1. Summary of advantages and disadvantages of various allometric scaling approaches used for the prediction of CL. Scaling methods Simple allometry


Product of CL and MLP or brain weight Rule of exponents

Correction for protein binding Incorporation of in vitro data (hepatocytes, microsomes and rCYP) to in vivo CL

Monkey liver blood flow Incorporation with physicochemical properties of a drug Dedrick plot

Advantages

Disadvantages

Quite common, found in lots of literatures Simple and fast Worked for most VD interpolation or extrapolation Improve the predictive power for drugs which are extensively hepatic metabolized and renally eliminated Improve the prediction greatly

Account for vertical allometry Improve the prediction accuracy of drugs with high extraction rate Apply to drugs that are primarily metabolized by liver

Good prediction for drugs biliary excreted Consider the CL related to the properties of a drug (in silico) Use to scale concentration--time profile by using physiological time.

Least successful for drugs that are biliary excreted, extensively hepatic metabolized and renally eliminated with significant reabsorption More prediction errors in large animals A mathematical adjustment, no physiological significance The predictive accuracy depending on the species used Not applicable for drugs that are renally excreted Require fu values that are available for each species included in the scaling In vitro CL of hepatic models for several species required to be measured (timeconsuming and labor-consuming) Cannot be applied for drugs primarily excreted by kidneys or eliminated both by hepatic and renal routes Only used for human CL prediction Computation-intensive Only used in adjustment of species difference in concentration--time profile

CL: Clearance; MLP: Maximum life-span potential; rCYP: Recombinant enzymes; VD: Volume of distribution.

When there is a limited number of species associated with the regression analysis, each data point has a great impact on the prediction of PK parameters, especially for animals whose body weight is closer to a potentially deviant observation. When a midpoint species (e.g., dog in veterinary medicine) is the source of the error, the change is primarily in the intercept rather the slope; consequently, the resulting magnitude of prediction error is comparable throughout the range of body weight examined. Rats had no significance in predicting human PK parameters as long as the body weight of the rat is not the smallest in the species chosen to determine the allometric relationship [16]. When one examines a number of allometric studies, it is striking how important species selection and balance is to an analysis. An ‘outlier’ study close in body weight to the species being predicted can have a large adverse impact on predictability.

3.

Allometric scaling of CL

In drug discovery and clinical application, the knowledge of CL for a drug is very important. In PK, CL refers to the removal of drug from a fixed volume of blood, plasma or serum per unit time. It is the best estimate of the efficiency of drug elimination from the body. If the drug has high CL, it will be eliminated quickly from the system circulation and has less accumulation in the body. With the increasing 1244

amount of literature available, many new allometric scaling approaches have been reported and tested. These approaches will be discussed. The advantages and shortcomings of each method have been summarized in Table 1. Developed methods for CL estimation There are many allometric equations developed for interspecies scaling of CL. 3.1

Simple allometry Simple allometry (CL = aWb) is widely used for the initial step to access the correlation between PK parameters and body weight for drugs renally excreted and biologics (protein, peptide and oligonucleotide) [17]. Compared to traditional drugs (small-molecule drugs), the therapeutic proteins (macro-molecule drugs, molecular weight cutoff of 1000 Da) are mainly eliminated by proteolysis, which is not speciesspecific. However, simple allometric scaling was least successful for drugs metabolized by liver with low extraction rate (Figure 2A). 3.1.1

Product of CL and maximum life-span potential, brain weight, GFR, bile flow or UDP-glucuronyltransferase

3.1.2

Compared to animals, humans have enhanced longevity and brain weight (BrW), which reflects a major evolutionary



A. 10000

Observed CL (mL/min)

Enprofylline

100

RO25-6833 Cefpiramide

10

Tamsulosin Reboxetine Diazepam

Valproate GV150526A

Susalimod Warfarin

1 1

100

10

1000

10000

Predicted CL (mL/min)

B. 100 Amiodarone

Vinblastine

10 Observed VSS (L/Kg)


1000

Mifepristone

1

Gabapentia

0.1

0.01 0.01

0.1

1 Predicted VSS (L/Kg)

10

100

Figure 2. Observed human CL (A) and Vss (B) as a function of observed values. The dataset for CL included 100 drugs listed in Ref. [43] and the dataset for Vss included 67 drugs listed in Ref. [49]. The solid circles represent hepatic elimination, the open circles represent renal elimination and the straight circles represent mixed eliminations. Solid and dashed lines represent unity and threefold error, respectively. The names of the drugs, which were significant beyond threefold error, were labeled. CL: Clearance; Vss: Volume of distribution at steady state.


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advantage. In these situations, the prediction of CL can be improved by incorporating the maximum life-span potential (MLP) or BrW of a species (CL MLP = a Wb or CL BrW = a Wb) when better scaling cannot be obtained on a log-log scale by using simple allometry, as reported by Mahmood and Balian [18]. In the study of the prediction of cefazolin CL (observed value = 61 ml/min) in humans, predicted CL was 141 ml/min (mean absolute error [MAE] = 131%) by simple allometry versus 50.55 ml/min (MAE = 17.1%) by allometry with MLP as a correction factor [18]. Other correction factors are also reported in the literature, including GFR for renally excreted drugs (CL/GFR = a wb) [2] and bile flow rate and microsomal uridine diplosphate glucuronyltransferase (UDPGT) activity for biliary excreted drugs (CL BileFlow = a Wb and CL UDPGT = a Wb) [2,19,20]. Although the normalization of CL by these correction factors is merely a convenient mathematical manipulation that may not have any physiological relevance, they no doubt improve the predictive performance of scaling, compared to simple allometry. However, they do suggest that another biological phenomenon not directly related to BMR is important in drug disposition, requiring these adjustments.

Rule of exponents The random use of different correction factors has been argued to be of no practical value and it is important to identify the proper situations for which each method should be adopted. Mahmood and Balian investigated 40 drugs and found that the exponent of simple allometry ranged from 0.35 to 1.39 [21]. Based on these exponents, it was found that there are conditions under which only one of the three methods can be used for a reasonably accurate prediction of CL, which is termed the ‘rule of exponents’ (ROE). In this approach, no correction factor is necessary and the CL is best predicted by simple allometry when the value of allometric exponent b is between 0.55 and 0.71; MLP should be incorporated into the scaling equation when b is between 0.71 and 1.00; BrW should be incorporated into the scaling method when b is larger than 1.00. The CL is likely to be underestimated when the exponent rises above 1.30. Conversely, the CL is likely to be overestimated when the exponent falls below 0.55 [22]. Mahmood compared the ROE method with other reported scaling methods for 50 drugs and found that the ROE obtained lower MAE (25%) than simple allometry (106%), CL MLP (40%) and CL BrW (49%), respectively [23]. It can be seen that the random application of either method produced larger errors than the ROE. The prediction error generated by the ROE method was far less than one or two species methods using fixed coefficients and exponents [24]. One disadvantage of the ROE is that the correction factors depend on the species included in the analysis, which can interfere with the accuracy of the prediction. It must be acknowledged that the 0.55, 0.71 and 1.00 are arbitrary cutoffs. 3.1.3

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Monkey liver blood flow approach Comprehensive analyses of the role of correction factors in the allometric prediction of CL from rat, dog and monkey to human were conducted by investigating 103 compounds [25,26]. Simple allometry and allometry including various correction factors (MLP, BrW and GFR) were chosen and compared. Scaling was performed universally across all compounds and on subsets segregated by allometric exponent, CL, physicochemical properties and so on. About 776 allometric combinations with 27,913 outcomes were generated. A predicted-to-observed CL ratio of 0.5- to 2-fold was preselected as the criterion for predictive success. The results showed the success rate of allometric scaling ranged from 18 to 53%. None of the correction factors resulted in substantially improved predictivity. None of the methods attempted in this study, which used smaller species to extrapolate to the larger human, achieved a success rate greater than that observed by simple estimating human CL based on monkey hepatic extraction. The monkey liver blood flow (MLBF) approach appeared to be the best method for the prediction of human CL in this study. However, Mahmood reevaluated this study and found this conclusion inaccurate because an arbitrarily acceptance criteria of 100% error between the predicted and observed CL was applied [27]. After data reevaluation, the prediction of human CL was improved by the use of the correction factors. As expected, the MLBF approach was least successful for renally excreted drugs [26] because the disposition had nothing to do with liver blood flow. One must acknowledge that if data exist in primates closely related to humans, this result is not surprising and data from the appropriate animal should be used. The same logic would apply to estimating PK in carnivores, ruminants or unique non-terrestrial mammals (e.g., aquatic, aerial). However, the ‘primate equivalent’ species for other animals have not been clearly defined. 3.1.4

Incorporation with physicochemical properties of a drug

3.1.5

Wajima et al. developed an innovative ‘molecule-centric’ method by using descriptors of drugs mechanistically related to CL to extrapolate CL [28]. The underlying basis of this approach is that the CL of a drug is partly determined by its own physicochemical properties. The descriptors include molecular weight, partition coefficient (cLogP) and number of hydrogen-bound acceptors for every drug. Using various types of regression, including multiple linear regression analysis, partial least square analysis or artificial neural networks, regression equations were derived to predict CL in humans. Correction for protein binding Protein binding prevents drug diffusion across membranes barriers and restricts drug distribution to the sites of action and excretion. Protein binding of a drug varies considerably among animal species and is unrelated to size; thus, the CL 3.1.6




of drug that exhibits high protein binding may not be amenable to straightforward scaling. It is conceivable to predict unbound drug CL across species. Theoretically, unbound CL should be predicted with more accuracy than the total CL, but in practice this may not be the case. Systematic comparative studies to evaluate the predictive performance with or without taking protein binding into consideration across laboratories indicated that the unbound CL could be predicted with slightly better accuracy than or almost similar as the total CL [29-32]. Moreover, the correction for binding may simply add more variability to the unbound drug CL for that species. Incorporation of in vitro data to in vivo CL The linkage of in vitro data to in vivo CL has been proposed and provides a more rational (mechanistic) approach. The intrinsic CL is measured using in vitro models, including microsomes, recombinant enzymes and hepatocytes. For extensively metabolized compounds, adjusting the in vivo CL in the different species for the relative rates of metabolism in vitro dramatically improved the prediction of human CL compared to the approach in which CL is directly extrapolated using body weight [33,34]. This method accounts for interspecies difference in hepatic metabolism. However, the MAE values for in vitro and MLP approaches were similar (43 and 46%, respectively) but better than simple allometry and BrW methods, after the reevaluation by Mahmood [35]. There is a clear disadvantage in that in vitro CL must be measured from several species, which is labor-intensive and time-consuming. Moreover, absence of Phase II metabolism on liver microsomes could result in enzyme inhibition due to the accumulation of the oxidative metabolites in some in vitro models. 3.1.7

Dedrick plot The Dedrick plot is a species invariant time method to estimate CL by accounting for species differences in physiological time by transforming the time axis of the concentration-time profile from Newtonian chronological time to a unit of physiological ‘species-invariant time’ [36]. The correction of physiological time makes the concentration-time profiles from different species superimposed in a homogeneous and species-independent drug disposition profile [29,37,38]. 3.1.8

Vertical allometry Vertical allometry was first coined by Calder, who found that the human brain is much larger than other species related to their body weights [39]. In PK, it refers to the CL of a drug when the predicted human CL is substantially (arbitrarily ‡ 5-fold) higher than the observed human CL [40]. Diazepam was the first drug reported as exhibiting vertical allometry. The predicted CL of diazepam in humans (860 ml/min) by simple allometry scaling is 33-fold higher than the observed CL (26 ml/min) [11]. Besides diazepam, there are many drugs exhibiting vertical allometry, including warfarin, valproic acid, tamsulosin, susalimod and 7-hydroxystaurosporine. Those drugs have predicted CLs (obtained by simple 3.2

allometry) that are at least fivefold greater than their observed CLs in humans. There are still many questions that remain unanswered and complicate the prediction of CL in humans compared to smaller mammals for drugs exhibiting vertical allometry. Currently, no established approaches are available to identify vertical allometry a priori and most of studies were retrospective allometric analyses. Tang and Mayersohn demonstrated the ‘fu-corrected intercept method’ (FCIM) as an alternative two-species scaling approach that uses the allometric exponent of CL and the ratio of fu between rats and humans. The equation to predict human CL for drugs is shown as Equation 3: (3)

CLhuman

⎛ a ⎞ = 33.35 × ⎜ ⎝ Rfu ⎟⎠

0.77

Where a is the intercept obtained from the log-log plot of CL versus body weight using at least three animal species and Rfu is the ratio of unbound fraction in plasma between rats and humans. The constant and the exponent of the equation are 33.35 and 0.77, respectively [41,42]. They also found that drugs in the study with the ratio of unbound fraction in plasma between rats and humans (Rfu) > 5 and cLogP > 2 followed vertical allometry [43]. FCIM predicted the CL of those drugs known to demonstrate vertical allometry with a fair degree of accuracy. This approach, however, failed to predict the CL of biliary or renally excreted drugs. For biologics, including therapeutic proteins, blood products and mAbs, FCIM does not predict well due to the need for protein binding data. Mahmood suggested the use of unbound + ROE approach to obtain a prediction accuracy of CL, similar to FCIM, worked well for the prediction of biliary and renally excreted drugs [44]. FCIM is a simplified version in that protein binding data are required in rats and humans only, whereas Mahmood’s method requires protein binding data for all the species used in the allometric scaling. 4.

Allometric scaling of VD

Besides CL, three types of VDs are generally predicted across species: VD of the central compartment (VC),VD at steady state (Vss) and VD by area (Varea) also known as Vb. Generally, the real distribution volume of a drug can be described as the following Equation 4: (4)

VD = V p + Vt ×

fup fut

whereVp is the volume of plasma, Vt is the tissue volume and fup and fut are the fraction of unbound drug in plasma and tissues, respectively [2]. Usually a change in fut has a greater effect than fup on VD. Of the three types of VD, VC is the most important volume parameter in establishing the safety or toxicity for first-time dosing, especially in humans, and can be predicted with


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much more accuracy than Vss or Vb [45]. Predicted Vc can be obtained from the administered dose divided by the drug concentration (C0) at time zero after intravenous administration (Vc = Dose/C0) in a one-compartment model. Vss, the product of CL and mean residence time (MRT), can be predicted better when protein binding is taken into account [46]. In addition, Vss can be used practically to predict half-life when CL is known (t1/2 = 0.693 Vss/CL). In general, the exponents for all three VDs (Vc,Vss,Vb) are around 1.0 (usually between 0.8 and 1.1) by using simple allometry [47], indicating that there exists a direct isometric relationship between body weight and volume. However, it is not the case for all drugs and some exceptions such as sildenafil (exponent as high as 1.26) and diazepoxide (exponent as low as 0.58) have also been reported [2]. Unlike CL, the Vss of drugs which exhibit vertical allometry may be under- or over-predicted, but the magnitudes will be lower than CL [40].Therefore, reasonable accurate prediction of Vss could be obtained even for drugs following vertical allometry. It is well established that protein-drug binding varies considerably across species as a result of differences in the drug affinity to and number of binding sites on proteins such as albumin which have species-specific structures [48]. Because there is no allometric relationship between protein binding and body weight, it is difficult to project the VD of the drug in a certain species from other species data. Across species, when VD is not corrected for the different sizes of gastrointestinal tracts and/or other membrane-defined species, problems can occur because drugs may not be accessible for diffusion. When a drug has low binding affinity to plasma and tissue proteins, or when a drug only distributes extracellularly, the VD of the drug reflects total body water or extracellular water. In these cases, the VD in human can be predicted from data in animals (Figure 2B) because both the total body water and extracellular water decrease as animal size increases in an allometric manner [49]. However, correction for protein binding is not helpful in improving the prediction of VD [2]. Distribution volumes of unbound (Vfree) and total (Vtotal) drugs sometimes may be very different. For instance, Vfree of propranolol is similar across species although Vtotal displays significantly different values among different animals and humans [50]. In contrast, there were large differences for Vfree between species for b-lactam antibiotics [51]. Besides the simple allometric approach, several methods have been suggested for the prediction of VD. Bachmann et al. proposed that VD can be predicted directly from another appropriate single species [52]. Obach et al. predicted Vss in humans by establishing proportionality between Vss and the free fraction of drugs in plasma in dogs and humans [46]. These approaches require further investigation. 5.

Allometric scaling of elimination half-life

The prediction of half-life to the first-time dosing in animals or humans is limited. Half-life is a hybrid parameter of CL 1248

and VD and not directly related to the physiological function of the body. Conceptually, it is difficult to establish a relationship between half-life and body weight [53]. Unlike CL and VD, the correlation of half-life with body weight has often been found to be poor [2]. In order to improve the accuracy of the half-life prediction across species, several indirect approaches to calculate half-life were used. As mentioned previously, CL and VD can be predicted with reasonable accuracy according to allometric scaling. Hence, half-life of many drugs can be calculated using the equation (t1/2 = 0.693 Vss/CL) [21]. Another proposed indirect approach is to predict the stochastic PK parameter MRT and then use the equation (t1/2 = MRT/1.44) to predict half-life [2].

Factors (or pitfalls) that might affect the prediction of PK parameters

6.

Biotransformation Despite the presence of the same fundamental biochemical machinery, different species have their own unique characteristics and display different intrinsic abilities to metabolize drugs [54]. Some differences are significant. For example, dogs are deficient in acetylation and rats are highly active acetylators, whereas humans are intermediate between them. Cats are deficient in glucuronidation, whereas humans exhibit efficient glucuronidation and pigs lack sulfation. Numerous studies have shown that heterogeneity in both Phase I and Phase II drug metabolism reactions might result in tremendous differences in PK parameters across species. Allometric scaling for drugs undergoing acetylation, glucuronidation or sulfation, usually displays poor goodness of fit in an allometric analysis when those species are chosen. 6.1

Genetic polymorphism The CYP450 system is the most important group of drug metabolism enzyme that mediates the hepatic metabolism of a diverse range of compounds. There are considerable interspecies variations related to genetic differences in CYP450 isoenzymes and unidentified genetic differences in drug disposition with a species. Even a small change in the gene sequence can lead to a profound change in substrate specificity, which precludes an adequate interspecies extrapolation of PK parameters. Similar phenomena are found in other drugmetabolizing enzyme systems. In addition, species differences have emerged for drug-metabolizing enzymes that are induced and inhibited [55]. If the polymorphism affects the pharmacodynamics of the drug, the effects of the drug would be very variable although the doses could still be interpolated or extrapolated across species based on simple PK parameters. 6.2

Protein binding Protein binding restricts the glomerular filtration of the drug and cannot be interpolated or extrapolated across species. Difference in protein binding would be expected to affect 6.3



CL, VD and the fraction of a dose that interact with receptors. Protein binding would also affect bioavailability after oral administration of a drug with a high extraction ratio [54]. However, this problem can be avoided and better scaling can be obtained by considering the unbound fraction (fu) [56]. The details have been discussed in the previous sections of allometric scaling of CL and VD. Saturation If the administrated dose of drug produces concentrations that saturate an elimination mechanism, the PK profile will not correlate with the dose. Such nonlinear PK makes the allometric prediction difficult and warrants how doses of drugs actually administered should be handled in an allometric analysis. This should not be an issue for most pharmacological doses except, for example, in a species such as cats in which a normally glucuronidated drug cannot be eliminated.


6.4

Drug induces alterations in physiology Most drugs are pharmacologically inert relative to ADME processes, although some might alter physiological profiles, if they affect renal function, hepatic blood flow and so on, in one species but not in another. This could lead to broken allometric relationships between physiology and body weight. 6.5

Interspecies differences in enterohepatic recirculation

6.6

The secreted drug may be reabsorbed into the small intestine and undergo enterohepatic recycling [57]. Compounds with molecular weights > 500, amphipathic or products of hepatic conjugation are primarily excreted in the bile. Enterohepatic recirculation occurs in a drug which is primarily cleared via bile and there are marked differences in biliary excretion and in the fraction that is reabsorbed into the systemic circulation across species. For a given drug, the nature of biliary excretion may be species-specific. For instance, rats and dogs are fast biliary excreters; humans, primates, guinea pigs and rabbits are slow biliary excreters; cats are intermediate [55]. Interspecies extrapolation for the PK parameters will not work under this situation. Drug transporter Transporter proteins are involved in the rate-determining step of hepatic uptake of some compounds [58]. The presence of significantly different drug transporters among species is not possible to account for allometry. 6.7

Renal tubular reabsorption sensitive to urine pH Species differences in urine pH will affect the CL and t1/2 of some weak acids and bases by modulating distal renal tubular reabsorption. Depending on the species and the diets included in an allometric analysis, weak organic acids with pKa values from 3 to 7 could be speculated to have a decreased half-life when urine is alkaline. The opposite would happen with weak bases. 6.8

Nanoparticles Nanoparticles interact with hundreds of proteins and biomolecules to form biocoronas in the body. The formation and stabilization of biocoronas are driven mostly by thermodynamics, and the local environment and independent of any physiological rates, including BMR, which make simple extrapolations theoretically problematic [59,60]. 6.9

Other situations Age, diseases states, environmental factors and co-medication can introduce additional variability, which affect the interspecies prediction. 6.10

7.

Application in veterinary medicine

Species differences in ADME for numerous pharmaceutical agents have been well documented for domestic species. However, there are scant ADME data available for several zoo animals and large animals such as donkeys, camels and elephants. In veterinary medicine, practitioners must often take approved agents (veterinary or human) to extrapolate safe and effective dosage regimens (first-in-animal dose selection) for species of interest for which approved drugs are simply not available. For such practical reasons, simple allometry is widely used by veterinarians. One operational difference in using allometry in veterinary medicine as compared to human medicine is that the target animal species is often of intermediate size compared to other species in the analysis, whereas humans are often the largest species, thus, resulting in more accurate interpolation rather than the extrapolation seen in humans. Our group currently uses the extensive Food Animal Residue Avoidance Databank compilation of 25,000 PK records covering about 500 drugs to access how well allometry could be used for extrapolating drug disposition for veterinary drugs across species. The data analyzed only includes mammals and excludes birds due to significant physiological differences [61,62]. Drugs with blood flow-dependent and/or flowlimited hepatic metabolism exhibit excellent linear regression using simple allometric scaling [53]. Drugs (mostly antimicrobials) that are excreted primarily by renal mechanisms scaled to allometric exponents around 0.75 [62], because overall renal function is determined by blood flow, which is dependent on cardiac output with its b» 0.75 [3]. However, allometric scaling did not perform well when drugs undergo significant tubular reabsorption. In contrast, drugs depending on hepatic metabolism for all or part of their elimination are poor candidates for allometric scaling. Although liver weight and hepatic blood flow are allometrically scalable, well-documented differences in Phase I and/or Phase II, were reported in hepatic drug metabolism across species [2,14]. As discussed earlier, other factors, such as CYP450 isoenzyme expression, hepatic extraction ratio, species--species hepatic blood flow and other species--specific


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Table 2. Summary of drugs that are likely and unlikely amenable to simple allometric scaling of their CL. Drugs that are good for simple allometric scaling


Low protein-bound Renal excretion Flow-limited hepatic metabolism Drug-targeted sites having no marked interspecies difference in expression, affinity and distribution No drug transporters involved Biologics (protein, peptide and oligonucleotide)

Drugs that are poor for simple allometric scaling Highly protein-bound Extensive metabolism or combination of hepatic metabolism and renal excretion Significant biliary excretion Extensive renal secretion with reabsorption Drug-targeted sites having significant interspecies difference in expression, affinity and distribution Significant target-binding effects Active drug transporters involved Nanoparticles (biocorona formation)

CL: Clearance.

hepatic physiology and anatomy also contribute to the differences across species [63]. The application of allometric scaling to predict the CL across species always has the risk of ignoring potential differences in CL mechanism and metabolic pathway. For example, ketoprofen is a NSAID marketed as a racemic mixture, R-ketoprofen and S-ketoprofen. The (S)-enantiomer is eliminated from the plasma much faster than the (R)-enantiomer in Asian elephants after intravenous administration, which is significantly different from the horse. Moreover, most species (dog, rabbit, monkey, horse and cat) convert ketoprofen from the (R)-enantiomer to the (S)-enantiomer; however, some species (cattle and llamas) do not convert at all, and the Asian elephant is the only species that reportedly converted the (S)-enantiomer to the (R)enantiomer. Thereafter, ketoprofen appears non-appropriate for allometric scaling [64]. Such species-specific differences in drug disposition will always make allometric predictions difficult in a previous unstudied species. Allometry is often used in veterinary medicine to determine which drugs scale well across species, especially when rare exotic species are being treated. In this case, the target species is often intermediate in body weight compared to available data. When a drug scales well across a large number of species, there is more confident that unique physiological or biochemical processes are not involved in the drug’s disposition, increasing confidence in using allometric techniques. A similar logic applies to accessing PK in preclinical safety and efficacy studies in laboratory animals. In contrast, when drugs do not scale well, cautions and other techniques need to be utilized to estimate drug dosages in unknown species. 8.

Expert opinion

Allometric scaling is a prediction tool that is practically utilized for the estimation of FTIH doses in clinical trials, estimating PK parameters in veterinary medicine and for experimental purposes. This extrapolation facilitates the process of dosing transition across species and often shortens the duration of drug testing by facilitating accurate PK extrapolations. There are some advantages in predicting interspecies PK parameters 1250

by using allometric scaling: i) it is simple and easy to use; ii) data analysis is short; iii) there is 80% success rate, if incorporation of hepatocytes data is available; and iv) it provides a better degree of safety and reassurance in the initial dose chosen than other empirical approaches, especially for FTIH study. It does require plasma concentration--time data from which PK parameters can be calculated. It is important to mention that the primary use of allometry in the literature is conducted to estimate the human PK from available data in smaller laboratory rodents, dogs and primates. In most cases, humans are the largest species that makes the allometric estimate an extrapolation of available data. In analyses for veterinary end points, the estimated species is often mid-range in body weight making regression a much more conservative interpolation between existing data. There are limitations in the application of allometric scaling. Simple allometric scaling for the prediction of PK parameters can be misleading for some drugs when species difference (differences in drug transport and metabolism) are not taken into account. Drugs that are highly protein-bound, having significant biliary excretion, extensive active renal secretion, active metabolism and other transport processes or have speciesspecific binding or distribution may not be good candidates for simple allometric scaling and may require ad hoc adjustment protocols. Nanoparticles may not be predictable because of extensive protein interaction. Drugs that are likely and unlikely suitable for allometric scaling are summarized in Table 2. Although allometric scaling has been shown to be useful as a retrospective tool to examine how the PK of a drug compares across species, it may generate a wide prediction interval (low precision) for point estimate when used in a prospective manner and may decrease its power for predictions [65]. There are few papers that generate any type of confidence interval for PK parameter estimate using allometry. In most cases, only point estimates were presented with bias. Very little information is currently available for the prediction of pharmacodynamic parameters across species. Therefore, it is conceptually difficult to accept that the efficacy and potency of a drug will be predicted by PK alone based on an allometric analysis of body weight of the species.




It is well known that allometric scaling is not always successful and occasionally fails to predict PK parameters. Over the years, many new and robust approaches to substantially improve the predictive performance of allometry (especially CL) have been suggested and are covered in this review, although none of the adjustments are infallible [66,67]. Allometric scaling can be used in comparing drug disposition across species, for example, when selecting animal models for preclinical studies or comparing and interpreting toxicological end points across species. The limitations of allometric scaling would be better known if increasing amounts of cases documenting the failure of interspecies scaling were published. These ‘failures’ often suggest species-specific processes in drug bio-disposition that prevent scaling. In contrast, when a drug does demonstrate simple allometric scaling, one can assume similarity in the pharmaceutical processes that govern disposition across all species -- a finding making extrapolation to an unknown species less risky. This is particularly important in many applications in veterinary and comparative medicine. Until a new and more robust approach is proposed, Bibliography Papers of special note have been highlighted as either of interest () or of considerable interest () to readers. 1.

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Declaration of interest The authors are employees of Kansas State University. This work was supported by Kansas Bioscience Authority. They do not have any relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents, received or pending, or royalties.

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Affiliation

Qingbiao Huang & Jim E Riviere† † Author for correspondence Institute of Computational Comparative Medicine, Kansas State University, Manhattan, KS 66506, USA E-mail: [email protected]

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The allometric approach for interspecies scaling of pharmacokinetic parameters.

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