Regulatory Toxicology and Pharmacology 68 (2014) 468–474
Contents lists available at ScienceDirect
Regulatory Toxicology and Pharmacology journal homepage: www.elsevier.com/locate/yrtph
Vertical allometry: Fact or fiction? q Iftekhar Mahmood ⇑, Harold Boxenbaum Office of Blood Review & Research (OBRR), Center for Biologic Evaluation and Research, Food & Drug Administration, 1401 Rockville Pike, Rockville, MD, USA
a r t i c l e
i n f o
Article history: Received 12 December 2013 Available online 15 February 2014 Keywords: Vertical allometry Allometric scaling Clearance Volume of distribution
a b s t r a c t In pharmacokinetics, vertical allometry is referred to the clearance of a drug when the predicted human clearance is substantially higher than the observed human clearance. Vertical allometry was initially reported for diazepam based on a 33-fold higher human predicted clearance than the observed human clearance. In recent years, it has been found that many other drugs besides diazepam, can be classified as drugs which exhibit vertical allometry. Over the years, many questions regarding vertical allometry have been raised. For example, (1) How to define and identify the vertical allometry? (2) How much difference should be between predicted and observed human clearance values before a drug could be declared ‘a drug which follows vertical allometry’? (3) If somehow one can identify vertical allometry from animal data, how this information can be used for reasonably accurate prediction of clearance in humans? This report attempts to answer the aforementioned questions. The concept of vertical allometry at this time remains complex and obscure but with more extensive works one can have better understanding of ‘vertical allometry’. Published by Elsevier Inc.
1. Introduction To develop a new therapeutic compound for human use, relevant pharmacological, pharmacokinetics, and toxicological studies are initially conducted in small laboratory animals such as mice, rats, rabbits, dogs, or monkeys. These initial studies are helpful in screening the potential therapeutic compounds in the process of drug development. Pharmacokinetic interspecies scaling is frequently used to predict pharmacokinetic parameters from animals to humans during drug development and is becoming a useful tool especially for the selection of the first time dose in humans. Interspecies allometric scaling is based on the assumption that there are anatomical, physiological, and biochemical similarities among animals, which can be described by mathematical models (Boxenbaum, 1984). Similarities in structure and form in animals have been studied and reported for at least three hundred years. The simple hypothesis of scaling was that all physiological parameters were proportional to body size or body mass (Boxenbaum, 1984).
q The views expressed in this article are those of the authors and do not reflect the official policy of the FDA. No official support or endorsement by the FDA is intended or should be inferred. ⇑ Corresponding author. E-mail address: [email protected] (I. Mahmood). Deceased.
http://dx.doi.org/10.1016/j.yrtph.2014.02.005 0273-2300/Published by Elsevier Inc.
Clearance (CL) is the most important pharmacokinetic parameter. The knowledge of clearance for a drug is very important during drug discovery or screening process because clearance can be used to select first-in-human dose from animals (Boxenbaum, 1984). The inverse of the clearance indicates the total exposure (area under the curve (AUC) of a drug (AUC = Dose/CL). Those drugs which are eliminated quickly may have a low absolute bioavailability and shorter duration in the systemic circulation resulting in a short duration or lack of efficacy. Due to this importance of clearance, over the years enormous attention has been given to predict clearance from animals to humans. When anthropoid primate brain mass was allometrically plotted against body mass, it was noted that human brain mass was almost 3.4 times greater than the allometrically predicted human brain mass (predicted = 0.45 kg, observed = 1.53 kg) (Boxenbaum and Dilea, 1995). The larger human brain than other species may be due to special capability of adaptation and Calder (1984) called this special adaptation process ‘vertical allometry’. In pharmacokinetics, vertical allometry is referred to the clearance of a drug when the predicted human clearance is substantially higher than the observed human clearance. Vertical allometry was initially noted for human clearance of diazepam (Boxenbaum and Dilea, 1995). The predicted clearance of diazepam in humans (860 mL/min) is 33-fold higher than the observed clearance (26 mL/min) (Klotz et al., 1976). In recent years, it has been found that many other drugs besides diazepam, can be
I. Mahmood, H. Boxenbaum / Regulatory Toxicology and Pharmacology 68 (2014) 468–474
classified as drugs which exhibit vertical allometry. The predicted clearances of drugs like valproic acid (Loscher, 1978), tamsulosin (Hoogdalem et al., 1997), susalimod (Pahlman et al., 1998), GV 150526 (Ivarone et al., 1999), and UCN-01 (Fuse et al., 2005) are 29, 16, 11, 54, and 3200 times higher than the observed human clearances, respectively. The role and importance of vertical allometry in allometric scaling is not known but it certainly complicates the prediction of human drug clearance. 2. Objectives Vertical allometry has been observed with only a handful of drugs and the reason(s) for the occurrence of vertical allometry are not known. The major problems in allometric scaling associated with vertical allometry are: To define and identify vertical allometry in the absence of human data. The magnitude of difference between predicted and observed human clearance values before a drug could be declared ‘a drug which follows vertical allometry’. If somehow one can identify vertical allometry from animal clearance values then how this information can be used for reasonably accurate prediction of clearance in humans? This report attempts to answer the aforementioned questions. In this report, we also assess the impact on the volume of distribution of drugs which are known to follow vertical allometry based on the prediction of human drug clearance. 3. Definition of vertical allometry Generally, the clearance (after human data are available) of a drug is used to describe if the drug follows vertical allometry. There is no clear definition of vertical allometry and at this time it is not possible to identify a priori (before the availability of human data) which drug will follow vertical allometry? A drug is considered to follow vertical allometry when its predicted clearance is several times (no clear understanding of how many times, may be P5 times or 10 times) higher than the observed human clearance. In this report, we will consider a drug following vertical allometry if the predicted clearance is P5-fold higher than the observed clearance (Tang and Mayersohn, 2006a,b). We will acknowledge that this cut off point is arbitrary. 4. Methods From the literature, ten drugs were selected for this study. These drugs were diazepam (Klotz et al., 1976), valproic acid (Loscher, 1978), tamsulosin (Hoogdalem et al., 1997), GV 150526 (Ivarone et al., 1999), and UCN-01 (Fuse et al., 2005), susalimod (Pahlman et al., 1998), warfarin (Nagashima and Levy, 1969; Sakai et al., 1983; Thjjssen et al., 1983), antipyrine (Bachmann, 1989; Balani et al., 2002), compounds #36 and #108 (Jones et al., 2011; Ring et al., 2011). All drugs were given to animals and humans by intravenous route.
469
4.1.1. Simple allometry In this approach, clearances of different species were plotted against body weights on a log–log scale (Eq. (1))
log Y ¼ log a þ b log W
ð1Þ
where ‘a’ is the intercept, ‘b’ is the slope of the line, and ‘W’ is the body weight. 4.1.2. Rule of exponents The rule of exponents includes simple allometry (Section 4.1.1) and two correction factors in terms of maximum life span potential (MLP) or brain weight (Mahmood and Balian, 1996). Based on the exponents of the simple allometry, Mahmood and Balian (1996) proposed the following conditions under which only one of the three methods can be used for the prediction of human drug clearance. The proposed methods (as outlined below) help in improving the prediction of human drug clearance as compared to a single simple allometric approach. 1. Simple allometry will predict human drug clearance more accurately than CL MLP or CL brain weight if the exponent of the simple allometry is within 0.55–0.70. 2. CL MLP will predict human drug clearance more accurately compared to simple allometry or CL brain weight if the exponent of the simple allometry lies between 0.71 and 0.99. 3. CL brain weight will predict human drug clearance more accurately compared to simple allometry or CL MLP when the exponent of the simple allometry is P1.0. 4. If the exponents of allometry are 1.3 then the predicted clearance, despite the application of brain weight as a correction factor, will be over-predicted and in some instances may be of practical significance. Susalimod is excreted by biliary excretion and for this kind of drugs a physiological correction factor has been suggested (Mahmood, 2005a,b). Therefore, for the prediction of susalimod clearance, this correction factor was applied with the ROE (exponent of the simple allometry was 0.749). 4.1.3. Product of maximum life-span potential (MLP) and clearance In this approach, the observed clearance values of at least three animal species are multiplied by their respective maximum life-span potential and are plotted as a function of body weight (Eq. (1)). From the allometric equation, human clearance x MLP value is estimated and then divided by the MLP in humans (8.18 105 h) to predict human drug clearance. b
CL ¼
a ðhuman body weightÞ 5
8:18 10
ð2Þ
where, ‘a’ is the coefficient and ‘b’ is the exponent obtained from the plot of body weight and product of MLP and clearance. In Eq. (2), the human MLP value (8.18 105) has been given in hours but one can use any unit of time (e.g. years, months, days) provided the unit of time for clearance is consistent across the species for a given drug.
4.1. Prediction of human clearance The human clearance was predicted by simple allometry (Mahmood and Balian, 1996), the rule of exponents (Mahmood and Balian, 1996), fu corrected intercept method (FCIM) (Tang and Mayersohn, 2006a,b), and unbound clearance using the rule of exponents where necessary.
4.1.4. Product of brain weight and clearance In this approach, the clearances of at least three animal species are multiplied by the brain weight of the species and the product is plotted as a function of body weight on a log–log scale (Eq. (1)). From the allometric equation, human clearance brain weight value is estimated and then divided by the human brain weight
470
I. Mahmood, H. Boxenbaum / Regulatory Toxicology and Pharmacology 68 (2014) 468–474
(1.53 kg) to predict human drug clearance. In Eq. (3), both the brain weight and body weight are in kilograms.
CL ¼
a ðhuman body weightÞ 1:53
b
ð3Þ
where, ‘a’ is the coefficient and ‘b’ is the exponent obtained from the plot of body weight and product of brain weight and clearance. 4.1.5. fu corrected intercept method (FCIM) Tang and Mayersohn (2005) suggested ‘fu Corrected Intercept Method’ (FCIM) for the prediction of human drug clearance. Using 61 drugs, the authors derived a universal equation to predict human clearance for a wide variety of drugs
Predicted human drug CL ¼ 33:35 ða=Rf u Þ
0:77
ð4Þ
where; ‘a’ is intercept obtained from the log–log plot of CL vs body weight using at least three animal species, and; Rfu = ratio of unbound fraction in plasma between rats and humans (rat/human) The constant of Eq. (4) is 33.35 and the exponent is 0.77. 4.1.6. Correction for protein binding Unbound clearances (CLu) of drugs were calculated according to the following equation
CLu ¼ Clearance=fraction unbound in plasma protein
ð5Þ
The unbound clearances of different species were plotted on a log–log scale against body weight (Eq. (1)). The predicted clearance was then multiplied by the fraction unbound in humans to get total clearance in humans. Where necessary, the rule of exponents was used to predict human unbound clearance. 4.1.8. Prediction of human volume of distribution Total and unbound human volumes of distribution were predicted by simple allometry as described in Eqs. (1) and (5) (replacing clearance by volume of distribution). 5. Results 5.1. Clearance In Table 1, the names of drugs which are considered to follow vertical allometry, their routes of elimination, calculated partition coefficients (C logP), and the ratio of unbound fraction in plasma between rats and humans (Rfu) are described. In Table 2, protein binding of drugs in different species is shown. The exponents of allometry and predicted and observed clearances of 8 drugs by
different methods are shown in Table 3. In Table 4, fold-error in the prediction of clearances of 8 drugs by different methods is summarized. The exponents of allometry and predicted and observed volume of distribution along with fold-error are shown in Table 5. For antipyrine and warfarin, different combination of species was used and the predicted and observed clearance values for these two drugs are shown in Tables 6 and 7, respectively. The exponents of simple allometry (Table 3) ranged from 0.594 to 1.470. This range of allometric exponents has also been observed with drugs which are not considered vertical allometry. Therefore, the exponents of simple allometry are no guide to identify vertical allometry. The application of simple allometry produced a substantial prediction error for all 8 drugs (Table 3). As compared to simple allometry, the ROE, where needed, helped in improving the prediction of clearances of the studied drugs, but the error in the predicted clearances was still several fold higher than the observed clearances (Tables 3 and 4). On the other hand, using the approach of Clu fu and the ROE (where needed), the total clearance was predicted fairly well (Tables 3 and 4). The FCIM approach predicted the human clearances of 7 out of 8 drugs with far more accuracy than the SA and ROE. However, FCIM appears to be as good as the method of Clu fu and the ROE (Tables 3 and 4). Drugs such as diazepam, valproic acid, tamsulosin, GV150526, and UCN-01 are currently considered to follow vertical allometry and are extensively metabolized and are extensively protein bound. Susalimod, a drug which is excreted in the bile, can also be considered a drug that exhibits vertical allometry since its predicted clearance by SA is 67 mL/min (11-fold prediction error) and observed clearance is 6 mL/min. The predicted clearance of susalimod using physiological correction factor with ROE and FCIM was 11 and 60 mL/min, respectively. Although FCIM predicted the clearance of susalimod slightly better than the SA it was far less accurate than the physiological correction factor with the ROE. The predicted clearance of UCN-01 was highly erratic and the fold error was >50 by FCIM and ROE combined with unbound clearance. The fold-error in the predicted clearance of CPD #36 was 29.3 by simple allometry but the prediction error was reduced to 6.7 after using ROE combined with unbound clearance. The exponent of allometry for CPD #36 was 1.470 and Mahmood and Balian (1996) have mentioned that if the exponents of allometry for clearance are >1.3 then one should expect a high predicted clearance even after the application of the ROE and this was true for CPD #36. FCIM under-predicted the clearance of CPD #36 but the predicted clearance was the most accurate than all other methods. For CPD #108, the predicted clearance by FCIM and ROE combined with unbound clearance provided fairly accurate prediction of clearance.
Table 1 Names of drugs which are considered to follow vertical allometry, their partition coefficients (C logP), and routes of elimination. Drugs
Species
Routes of elimination
C logP
Rfu
Acid/base
Diazepam Tamsulosin Valproic acid GV150526A UCN-01 CPD #36** CPD#108** Warfarin Susalimod Antipyrine
Rat, dog, rabbit, GP* Rat, rabbit, dog Mouse, rat, dog Rat, dog, monkey Mouse, rat, dog Rat, dog, monkey Mouse, rat, dog Rat, dog, monkey Mouse, rat, dog, monkey Mouse, rat, rabbit, dog, monkey
Metabolism Metabolism Metabolism Metabolism Metabolism Unknown Unknown Metabolism Biliary Metabolized
3.16 2.17 2.98 5.17 1.04a 1.48 3.91 2.89 3.54 0.20
4.3 17.6 7.04 13.5 87.5 1.81 1.56 15.1 1.74 NA
Base Base Acid Acid Base Base Acid Acid Acid Neutral
Rfu, Ratio of unbound fraction in plasma between rats and humans (rat/human). C logP values taken from Tang and Mayersohn (2006a,b). GP, Guinea pig, NA, Antipyrine does not bind to plasma protein. ** Taken from PhRMA initiative (Ring et al., 2011 and Jones et al., 2011). a This is a log P value (n-octanol/phosphate buffered saline (PBS)). *
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I. Mahmood, H. Boxenbaum / Regulatory Toxicology and Pharmacology 68 (2014) 468–474 Table 2 Protein binding of 8 drugs in different species. Drugs
% Unbound
Diazepam Tamsulosin Valproic acid GV150526A UCN-01 Susalimod CPD #36 CPD#108
Man
Mouse
Rat
Dog
Monkey
Rabbit
3.2 1.1 5.2 0.002 5-fold). In short, the above examples indicate that the choice and number of species in allometric scaling may lead to vertical allometry. Furthermore, there is no known method or rule which can help in the selection of combination of species which in turn can help in avoiding the occurrence of vertical allometry. 6.2. Does vertical allometry exist only with high protein bound and extensively metabolized drugs? From Table 1, it can be seen that at least 7 out of 10 (route of elimination not available for 2 drugs) drugs which are considered to follow vertical allometry are extensively metabolized (susalimod is biliary excreted). In Table 2, the protein binding data indicate that all 8 drugs in humans are extensively protein bound. However, the notion that for a drug to exhibit vertical allometry, the drug must be extensively protein bound and extensively metabolized in humans may not be true. For example, antipyrine is metabolized but does not bind to plasma protein. Susalimod is biliary excreted but extensively protein bound in humans but exhibit vertical allometry. Warfarin is highly protein bound in humans and is extensively metabolized but may not be a drug which follows vertical allometry. The accuracy of the measurement of protein binding when a drug is extensively bound (P99%) should also be considered. The methods of measurement of protein binding and the concentrations of a drug at which protein binding is measured can also have impact on the interpretation of the data. 6.3. Identifying the vertical allometry 6.3.1. C logP and Rfu In real life, it will not be known if a drug will follow vertical allometry unless human data are available. At this time there is no established method available that can identify vertical allometry a priori. Tang and Mayersohn (2006a,b) have proposed that if a drug has a partition coefficient (C logP) greater than 2 and ratio of unbound protein (Rfu) between rat and human is P5 then a drug should be considered to follow vertical allometry. There are however, several caveats in the proposal of Tang and Mayersohn. The Rfu and C logP of susalimod is 1.74 and 3.54, respectively (Table 1). Although Rfu of susalimod is
Contents lists available at ScienceDirect
Regulatory Toxicology and Pharmacology journal homepage: www.elsevier.com/locate/yrtph
Vertical allometry: Fact or fiction? q Iftekhar Mahmood ⇑, Harold Boxenbaum Office of Blood Review & Research (OBRR), Center for Biologic Evaluation and Research, Food & Drug Administration, 1401 Rockville Pike, Rockville, MD, USA
a r t i c l e
i n f o
Article history: Received 12 December 2013 Available online 15 February 2014 Keywords: Vertical allometry Allometric scaling Clearance Volume of distribution
a b s t r a c t In pharmacokinetics, vertical allometry is referred to the clearance of a drug when the predicted human clearance is substantially higher than the observed human clearance. Vertical allometry was initially reported for diazepam based on a 33-fold higher human predicted clearance than the observed human clearance. In recent years, it has been found that many other drugs besides diazepam, can be classified as drugs which exhibit vertical allometry. Over the years, many questions regarding vertical allometry have been raised. For example, (1) How to define and identify the vertical allometry? (2) How much difference should be between predicted and observed human clearance values before a drug could be declared ‘a drug which follows vertical allometry’? (3) If somehow one can identify vertical allometry from animal data, how this information can be used for reasonably accurate prediction of clearance in humans? This report attempts to answer the aforementioned questions. The concept of vertical allometry at this time remains complex and obscure but with more extensive works one can have better understanding of ‘vertical allometry’. Published by Elsevier Inc.
1. Introduction To develop a new therapeutic compound for human use, relevant pharmacological, pharmacokinetics, and toxicological studies are initially conducted in small laboratory animals such as mice, rats, rabbits, dogs, or monkeys. These initial studies are helpful in screening the potential therapeutic compounds in the process of drug development. Pharmacokinetic interspecies scaling is frequently used to predict pharmacokinetic parameters from animals to humans during drug development and is becoming a useful tool especially for the selection of the first time dose in humans. Interspecies allometric scaling is based on the assumption that there are anatomical, physiological, and biochemical similarities among animals, which can be described by mathematical models (Boxenbaum, 1984). Similarities in structure and form in animals have been studied and reported for at least three hundred years. The simple hypothesis of scaling was that all physiological parameters were proportional to body size or body mass (Boxenbaum, 1984).
q The views expressed in this article are those of the authors and do not reflect the official policy of the FDA. No official support or endorsement by the FDA is intended or should be inferred. ⇑ Corresponding author. E-mail address: [email protected] (I. Mahmood). Deceased.
http://dx.doi.org/10.1016/j.yrtph.2014.02.005 0273-2300/Published by Elsevier Inc.
Clearance (CL) is the most important pharmacokinetic parameter. The knowledge of clearance for a drug is very important during drug discovery or screening process because clearance can be used to select first-in-human dose from animals (Boxenbaum, 1984). The inverse of the clearance indicates the total exposure (area under the curve (AUC) of a drug (AUC = Dose/CL). Those drugs which are eliminated quickly may have a low absolute bioavailability and shorter duration in the systemic circulation resulting in a short duration or lack of efficacy. Due to this importance of clearance, over the years enormous attention has been given to predict clearance from animals to humans. When anthropoid primate brain mass was allometrically plotted against body mass, it was noted that human brain mass was almost 3.4 times greater than the allometrically predicted human brain mass (predicted = 0.45 kg, observed = 1.53 kg) (Boxenbaum and Dilea, 1995). The larger human brain than other species may be due to special capability of adaptation and Calder (1984) called this special adaptation process ‘vertical allometry’. In pharmacokinetics, vertical allometry is referred to the clearance of a drug when the predicted human clearance is substantially higher than the observed human clearance. Vertical allometry was initially noted for human clearance of diazepam (Boxenbaum and Dilea, 1995). The predicted clearance of diazepam in humans (860 mL/min) is 33-fold higher than the observed clearance (26 mL/min) (Klotz et al., 1976). In recent years, it has been found that many other drugs besides diazepam, can be
I. Mahmood, H. Boxenbaum / Regulatory Toxicology and Pharmacology 68 (2014) 468–474
classified as drugs which exhibit vertical allometry. The predicted clearances of drugs like valproic acid (Loscher, 1978), tamsulosin (Hoogdalem et al., 1997), susalimod (Pahlman et al., 1998), GV 150526 (Ivarone et al., 1999), and UCN-01 (Fuse et al., 2005) are 29, 16, 11, 54, and 3200 times higher than the observed human clearances, respectively. The role and importance of vertical allometry in allometric scaling is not known but it certainly complicates the prediction of human drug clearance. 2. Objectives Vertical allometry has been observed with only a handful of drugs and the reason(s) for the occurrence of vertical allometry are not known. The major problems in allometric scaling associated with vertical allometry are: To define and identify vertical allometry in the absence of human data. The magnitude of difference between predicted and observed human clearance values before a drug could be declared ‘a drug which follows vertical allometry’. If somehow one can identify vertical allometry from animal clearance values then how this information can be used for reasonably accurate prediction of clearance in humans? This report attempts to answer the aforementioned questions. In this report, we also assess the impact on the volume of distribution of drugs which are known to follow vertical allometry based on the prediction of human drug clearance. 3. Definition of vertical allometry Generally, the clearance (after human data are available) of a drug is used to describe if the drug follows vertical allometry. There is no clear definition of vertical allometry and at this time it is not possible to identify a priori (before the availability of human data) which drug will follow vertical allometry? A drug is considered to follow vertical allometry when its predicted clearance is several times (no clear understanding of how many times, may be P5 times or 10 times) higher than the observed human clearance. In this report, we will consider a drug following vertical allometry if the predicted clearance is P5-fold higher than the observed clearance (Tang and Mayersohn, 2006a,b). We will acknowledge that this cut off point is arbitrary. 4. Methods From the literature, ten drugs were selected for this study. These drugs were diazepam (Klotz et al., 1976), valproic acid (Loscher, 1978), tamsulosin (Hoogdalem et al., 1997), GV 150526 (Ivarone et al., 1999), and UCN-01 (Fuse et al., 2005), susalimod (Pahlman et al., 1998), warfarin (Nagashima and Levy, 1969; Sakai et al., 1983; Thjjssen et al., 1983), antipyrine (Bachmann, 1989; Balani et al., 2002), compounds #36 and #108 (Jones et al., 2011; Ring et al., 2011). All drugs were given to animals and humans by intravenous route.
469
4.1.1. Simple allometry In this approach, clearances of different species were plotted against body weights on a log–log scale (Eq. (1))
log Y ¼ log a þ b log W
ð1Þ
where ‘a’ is the intercept, ‘b’ is the slope of the line, and ‘W’ is the body weight. 4.1.2. Rule of exponents The rule of exponents includes simple allometry (Section 4.1.1) and two correction factors in terms of maximum life span potential (MLP) or brain weight (Mahmood and Balian, 1996). Based on the exponents of the simple allometry, Mahmood and Balian (1996) proposed the following conditions under which only one of the three methods can be used for the prediction of human drug clearance. The proposed methods (as outlined below) help in improving the prediction of human drug clearance as compared to a single simple allometric approach. 1. Simple allometry will predict human drug clearance more accurately than CL MLP or CL brain weight if the exponent of the simple allometry is within 0.55–0.70. 2. CL MLP will predict human drug clearance more accurately compared to simple allometry or CL brain weight if the exponent of the simple allometry lies between 0.71 and 0.99. 3. CL brain weight will predict human drug clearance more accurately compared to simple allometry or CL MLP when the exponent of the simple allometry is P1.0. 4. If the exponents of allometry are 1.3 then the predicted clearance, despite the application of brain weight as a correction factor, will be over-predicted and in some instances may be of practical significance. Susalimod is excreted by biliary excretion and for this kind of drugs a physiological correction factor has been suggested (Mahmood, 2005a,b). Therefore, for the prediction of susalimod clearance, this correction factor was applied with the ROE (exponent of the simple allometry was 0.749). 4.1.3. Product of maximum life-span potential (MLP) and clearance In this approach, the observed clearance values of at least three animal species are multiplied by their respective maximum life-span potential and are plotted as a function of body weight (Eq. (1)). From the allometric equation, human clearance x MLP value is estimated and then divided by the MLP in humans (8.18 105 h) to predict human drug clearance. b
CL ¼
a ðhuman body weightÞ 5
8:18 10
ð2Þ
where, ‘a’ is the coefficient and ‘b’ is the exponent obtained from the plot of body weight and product of MLP and clearance. In Eq. (2), the human MLP value (8.18 105) has been given in hours but one can use any unit of time (e.g. years, months, days) provided the unit of time for clearance is consistent across the species for a given drug.
4.1. Prediction of human clearance The human clearance was predicted by simple allometry (Mahmood and Balian, 1996), the rule of exponents (Mahmood and Balian, 1996), fu corrected intercept method (FCIM) (Tang and Mayersohn, 2006a,b), and unbound clearance using the rule of exponents where necessary.
4.1.4. Product of brain weight and clearance In this approach, the clearances of at least three animal species are multiplied by the brain weight of the species and the product is plotted as a function of body weight on a log–log scale (Eq. (1)). From the allometric equation, human clearance brain weight value is estimated and then divided by the human brain weight
470
I. Mahmood, H. Boxenbaum / Regulatory Toxicology and Pharmacology 68 (2014) 468–474
(1.53 kg) to predict human drug clearance. In Eq. (3), both the brain weight and body weight are in kilograms.
CL ¼
a ðhuman body weightÞ 1:53
b
ð3Þ
where, ‘a’ is the coefficient and ‘b’ is the exponent obtained from the plot of body weight and product of brain weight and clearance. 4.1.5. fu corrected intercept method (FCIM) Tang and Mayersohn (2005) suggested ‘fu Corrected Intercept Method’ (FCIM) for the prediction of human drug clearance. Using 61 drugs, the authors derived a universal equation to predict human clearance for a wide variety of drugs
Predicted human drug CL ¼ 33:35 ða=Rf u Þ
0:77
ð4Þ
where; ‘a’ is intercept obtained from the log–log plot of CL vs body weight using at least three animal species, and; Rfu = ratio of unbound fraction in plasma between rats and humans (rat/human) The constant of Eq. (4) is 33.35 and the exponent is 0.77. 4.1.6. Correction for protein binding Unbound clearances (CLu) of drugs were calculated according to the following equation
CLu ¼ Clearance=fraction unbound in plasma protein
ð5Þ
The unbound clearances of different species were plotted on a log–log scale against body weight (Eq. (1)). The predicted clearance was then multiplied by the fraction unbound in humans to get total clearance in humans. Where necessary, the rule of exponents was used to predict human unbound clearance. 4.1.8. Prediction of human volume of distribution Total and unbound human volumes of distribution were predicted by simple allometry as described in Eqs. (1) and (5) (replacing clearance by volume of distribution). 5. Results 5.1. Clearance In Table 1, the names of drugs which are considered to follow vertical allometry, their routes of elimination, calculated partition coefficients (C logP), and the ratio of unbound fraction in plasma between rats and humans (Rfu) are described. In Table 2, protein binding of drugs in different species is shown. The exponents of allometry and predicted and observed clearances of 8 drugs by
different methods are shown in Table 3. In Table 4, fold-error in the prediction of clearances of 8 drugs by different methods is summarized. The exponents of allometry and predicted and observed volume of distribution along with fold-error are shown in Table 5. For antipyrine and warfarin, different combination of species was used and the predicted and observed clearance values for these two drugs are shown in Tables 6 and 7, respectively. The exponents of simple allometry (Table 3) ranged from 0.594 to 1.470. This range of allometric exponents has also been observed with drugs which are not considered vertical allometry. Therefore, the exponents of simple allometry are no guide to identify vertical allometry. The application of simple allometry produced a substantial prediction error for all 8 drugs (Table 3). As compared to simple allometry, the ROE, where needed, helped in improving the prediction of clearances of the studied drugs, but the error in the predicted clearances was still several fold higher than the observed clearances (Tables 3 and 4). On the other hand, using the approach of Clu fu and the ROE (where needed), the total clearance was predicted fairly well (Tables 3 and 4). The FCIM approach predicted the human clearances of 7 out of 8 drugs with far more accuracy than the SA and ROE. However, FCIM appears to be as good as the method of Clu fu and the ROE (Tables 3 and 4). Drugs such as diazepam, valproic acid, tamsulosin, GV150526, and UCN-01 are currently considered to follow vertical allometry and are extensively metabolized and are extensively protein bound. Susalimod, a drug which is excreted in the bile, can also be considered a drug that exhibits vertical allometry since its predicted clearance by SA is 67 mL/min (11-fold prediction error) and observed clearance is 6 mL/min. The predicted clearance of susalimod using physiological correction factor with ROE and FCIM was 11 and 60 mL/min, respectively. Although FCIM predicted the clearance of susalimod slightly better than the SA it was far less accurate than the physiological correction factor with the ROE. The predicted clearance of UCN-01 was highly erratic and the fold error was >50 by FCIM and ROE combined with unbound clearance. The fold-error in the predicted clearance of CPD #36 was 29.3 by simple allometry but the prediction error was reduced to 6.7 after using ROE combined with unbound clearance. The exponent of allometry for CPD #36 was 1.470 and Mahmood and Balian (1996) have mentioned that if the exponents of allometry for clearance are >1.3 then one should expect a high predicted clearance even after the application of the ROE and this was true for CPD #36. FCIM under-predicted the clearance of CPD #36 but the predicted clearance was the most accurate than all other methods. For CPD #108, the predicted clearance by FCIM and ROE combined with unbound clearance provided fairly accurate prediction of clearance.
Table 1 Names of drugs which are considered to follow vertical allometry, their partition coefficients (C logP), and routes of elimination. Drugs
Species
Routes of elimination
C logP
Rfu
Acid/base
Diazepam Tamsulosin Valproic acid GV150526A UCN-01 CPD #36** CPD#108** Warfarin Susalimod Antipyrine
Rat, dog, rabbit, GP* Rat, rabbit, dog Mouse, rat, dog Rat, dog, monkey Mouse, rat, dog Rat, dog, monkey Mouse, rat, dog Rat, dog, monkey Mouse, rat, dog, monkey Mouse, rat, rabbit, dog, monkey
Metabolism Metabolism Metabolism Metabolism Metabolism Unknown Unknown Metabolism Biliary Metabolized
3.16 2.17 2.98 5.17 1.04a 1.48 3.91 2.89 3.54 0.20
4.3 17.6 7.04 13.5 87.5 1.81 1.56 15.1 1.74 NA
Base Base Acid Acid Base Base Acid Acid Acid Neutral
Rfu, Ratio of unbound fraction in plasma between rats and humans (rat/human). C logP values taken from Tang and Mayersohn (2006a,b). GP, Guinea pig, NA, Antipyrine does not bind to plasma protein. ** Taken from PhRMA initiative (Ring et al., 2011 and Jones et al., 2011). a This is a log P value (n-octanol/phosphate buffered saline (PBS)). *
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I. Mahmood, H. Boxenbaum / Regulatory Toxicology and Pharmacology 68 (2014) 468–474 Table 2 Protein binding of 8 drugs in different species. Drugs
% Unbound
Diazepam Tamsulosin Valproic acid GV150526A UCN-01 Susalimod CPD #36 CPD#108
Man
Mouse
Rat
Dog
Monkey
Rabbit
3.2 1.1 5.2 0.002 5-fold). In short, the above examples indicate that the choice and number of species in allometric scaling may lead to vertical allometry. Furthermore, there is no known method or rule which can help in the selection of combination of species which in turn can help in avoiding the occurrence of vertical allometry. 6.2. Does vertical allometry exist only with high protein bound and extensively metabolized drugs? From Table 1, it can be seen that at least 7 out of 10 (route of elimination not available for 2 drugs) drugs which are considered to follow vertical allometry are extensively metabolized (susalimod is biliary excreted). In Table 2, the protein binding data indicate that all 8 drugs in humans are extensively protein bound. However, the notion that for a drug to exhibit vertical allometry, the drug must be extensively protein bound and extensively metabolized in humans may not be true. For example, antipyrine is metabolized but does not bind to plasma protein. Susalimod is biliary excreted but extensively protein bound in humans but exhibit vertical allometry. Warfarin is highly protein bound in humans and is extensively metabolized but may not be a drug which follows vertical allometry. The accuracy of the measurement of protein binding when a drug is extensively bound (P99%) should also be considered. The methods of measurement of protein binding and the concentrations of a drug at which protein binding is measured can also have impact on the interpretation of the data. 6.3. Identifying the vertical allometry 6.3.1. C logP and Rfu In real life, it will not be known if a drug will follow vertical allometry unless human data are available. At this time there is no established method available that can identify vertical allometry a priori. Tang and Mayersohn (2006a,b) have proposed that if a drug has a partition coefficient (C logP) greater than 2 and ratio of unbound protein (Rfu) between rat and human is P5 then a drug should be considered to follow vertical allometry. There are however, several caveats in the proposal of Tang and Mayersohn. The Rfu and C logP of susalimod is 1.74 and 3.54, respectively (Table 1). Although Rfu of susalimod is
