Abstract
Prediction of human volume of distribution at steady state (Vss) before first administration of a new drug candidate to humans has become an important part of the drug development process. This study examines the assumptions behind interspecies scaling techniques used to predict human Vss from preclinical data, namely the equivalency of Vss,u and/or fut across species. In addition, several interspecies scaling techniques are evaluated side by side using a set of 67 reference compounds where observed Vss from rats, dogs, monkeys, and humans were compiled from the literature and where plasma protein binding was determined across species using an ultracentrifugation technique. Species similarity in Vss,u or fut does not appear to be the norm among rats, dogs, monkeys, or humans. Despite this, interspecies scaling from rats, dogs, and monkeys is useful and can provide reasonably accurate predictions of human Vss, although some interspecies scaling approaches were better than others. For example, the performance of the common Vss,u or fut equivalency approaches using average Vss,u or fut across three preclinical species was superior to allometric scaling techniques. In addition, considering data from several preclinical species, using the equivalency approach, was superior to scaling from any single species. Although the mechanistic tissue composition equations available in the Simcyp population-based pharmacokinetic simulator did not necessarily provide the most accurate predictions, and the equations used likely need refinement, they still provide the best opportunity for a mechanistic understanding and prediction of human Vss.
Introduction
Prediction of human pharmacokinetics has become an important part of the drug development process, to aid in estimating the potential therapeutic dose and safety margins before the first dose to humans. The volume of distribution at steady state (Vss) is typically one of the key parameters predicted and, along with clearance, governs the effective half-life and dosing interval of the prospective drug.
A number of approaches to predicting Vss have been proposed recently or have become widely used (Sui et al., 2008). Some of the most commonly used approaches attempt to predict human Vss from animal data through interspecies scaling techniques such as allometry. Allometry is the extrapolation of pharmacokinetic parameters to one species by fitting a power function to the relationship between the pharmacokinetic parameter from other species and a measure of the size of the species, such as body weight (Boxenbaum, 1982). The main assumption in this approach is that the factors or mechanisms governing the pharmacokinetics of a drug scale proportionally to body size. For example, since the volumes organisms occupy correlate with their body weights, it is logical to conclude that the Vss of a drug given to these organisms will also correlate with their body weights, if the volume of each organism is the major determinant of Vss. However, it is understood that Vss is an apparent term that often bears little resemblance to the actual volume of an organism. The observed Vss for drugs has ranged from ∼3 liters (plasma volume) to as high as >7000 liters in adult humans (Obach et al., 2008), whereas human body volume is ∼70 liters. Therefore, body volume is not the only factor governing drug distribution.
Another factor governing drug distribution is protein binding. Per the free drug hypothesis, it is thought that only unbound drug is able to equilibrate between blood and tissues, and for noneliminating tissues, relative total drug concentrations observed in blood versus tissues (CT/Cb) are determined, in part, by relative binding to blood and tissue components (fub/fut). This realization led to various forms of a popular physiological definition of volume of distribution based on relative protein binding (Oie and Tozer, 1979). Because plasma protein binding and tissue binding are biochemical processes that bear little relation to body weight, for allometric scaling of Vss to be valid, one must make the assumption that fub/fut will be similar across species. The same assumption of similarity across species must be made for other nonscalable processes that influence drug distribution, such as permeability, active transport, pH-dependent partitioning, and enterohepatic recycling (Roberts et al., 2002; Gong et al., 2007; Grover and Benet, 2009). It is well known that plasma protein binding can vary between species. However, limited studies have indicated that tissue binding (as measured in vitro) could be similar across species (Fitchl and Schulmann, 1986). This led to the notion that scaling unbound volume of distribution at steady state (Vss,u) or calculated fraction unbound in tissues (fut) might be more accurate or scientifically justifiable as ways to scale distribution across species, as long as the assumptions of species similarity in other processes are acceptable. However, the equivalency of Vss,u or fut across species has not been systematically evaluated for a wide range of reference drugs, an aim of the present study.
Despite the empirical nature of interspecies scaling, and the required assumptions, it has been a valuable tool for predicting human Vss, and there are many success stories. Ward and Smith (2004) evaluated the ability to predict human Vss from several common preclinical species used during drug development in the pharmaceutical industry and suggested that scaling from monkey data was the most accurate approach. Unfortunately, their analysis of 103 compounds did not consider potential species differences in plasma protein binding. Other studies have examined single- or multiple-species scaling based on the assumption of Vss,u or fut equivalency across species using proprietary compounds, with limited species, or only having oral half-life data available in humans for comparison (Obach et al., 1997; McGinnity et al., 2007; Hosea et al., 2009). In such studies, scaling Vss from rats or dogs is proposed to be more accurate (Hosea et al., 2009; Sui et al., 2010), depending on the study. These conflicting reports about the best scaling methods or species to use require some reconciliation. In addition, the aforementioned interspecies scaling methods for predicting Vss have not been evaluated side by side using a sizable dataset of diverse reference compounds that also considers plasma protein binding. The present work aims to do so. Finally, interspecies scaling methods were compared with the mechanistic tissue partition methods for prediction of human Vss proposed by Poulin and Theil (2002) and Rodgers and Rowland (2007).
Materials and Methods
Materials.
All compounds were obtained from commercial sources as appropriate. Sprague-Dawley rat, beagle dog, cynomolgus monkey, and human plasma (pooled) were purchased from Bioreclamation, Inc. (Hicksville, NY).
Source of In Vivo Data.
Published literature was searched for reported values for volume of distribution at steady state (Vss) in rats, dogs, monkeys, and humans. Sources include reviews and original articles. If Vss was reported in liters, it was converted to l/kg using the mean body weight of the animals as reported in the source. In some cases in which Vss was not specifically reported, it was estimated by noncompartmental analysis of a digitally extracted version of the plasma concentration time plot provided in the source. The final dataset contains 67 drug-like molecules of diverse structures and chemical properties. The dataset included 16 acidic, 8 neutral, 31 basic, and 12 zwitterionic compounds. The molecular weight in this dataset ranged from 144 to 811 Da. Polar surface area ranged from 6 to 321 Å. Calculated solubility at pH 7.4 ranged from 6 ′ 10−6 to >1000 mg/ml. Calculated log P (clogP) ranged from −1.1 to 7.8. Calculated log D (clogD) at pH 7.4 ranged from −5.1 to 6.2. The compounds represented a number of therapeutic classes, including but not limited to, antibiotic, anti-inflammatory, anticancer, antiarrhythmic, antidepressant, sedative, anticoagulant, antihypertension, antiviral, anticonvulsant, antipsychotic, and anesthetic drugs.
Determination of Fraction Unbound in Plasma (fup).
Fractions unbound in plasma (fup) were determined in triplicate using an ultracentrifugation technique. Blank plasma was spiked with compound to achieve a final concentration of 5 μM, and was centrifuged at 600,000g for 5 h at 37°C. Halfway through the spin, at 2.5 h, the topmost (lipid) layer was removed by aspiration. After the complete 5-h spin, aliquots of the middle (water) layer were transferred into an equal volume of blank plasma and extracted with 5 volumes of acetonitrile containing internal standard. Aliquots of the original spiked plasma were mixed with an equal volume of blank plasma and 2 volumes of plasma ultrafiltrate and extracted with 10 volumes of acetonitrile. Extracts were centrifuged to precipitate proteins and analyzed by the liquid chromatography-tandem mass spectrometry method described below. Observed fraction unbound was calculated from the ratio of concentration observed in the water layer following centrifugation relative to total concentration in original spiked plasma.
Sample Analysis.
Sample extracts from in vitro experiments were analyzed by multiple reaction monitoring on a liquid chromatography-tandem mass spectrometry system consisting of dual Shimadzu LC-10AD high-performance liquid chromatography pumps and a DGU-14A degasser (Shimadzu, Columbia, MD), a CTCPAL autoinjector (LEAP Technologies, Carrboro, NC), and an API3000 or API4000 LC-MS/MS system, equipped with an electrospray ion source and operated by the Analyst software package (Applied Biosystems, Foster City, CA). Chromatography was conducted on a Sprite Armor C18 (20′ 2.1 mm, 10 μm) analytical column (Analytical Sales and Products, Pompton Plains, NJ) with a 0.5 μm guard filter, using the following mobile-phase gradient program: mobile phase A (MPA), H20 with 0.1% formic acid; mobile phase B (MPB), acetonitrile with 0.1% formic acid; 0 min = 98% MPA, 2% MPB; 0.3 min = 98% MPA, 2% MPB; 0.7 min = 5% MPA, 95% MPB; 1.3 min = 5% MPA, 95% MPB; 1.4 min = 98% MPA, 2% MPB; 1.7 min = end of run; there were approximately 2 min between sample injections. For the first 0.5 min of each sample run, the LC eluent was diverted from the ion source to waste. Each compound was detected in either positive or negative ion mode after tuning the MS electronics to the mass transition with the largest intensity.
Prediction of Vss from Preclinical Species.
Several methods were compared for their ability to predict human Vss from that in rats, dogs, and monkeys.
Allometric Scaling of Vss.
For each drug, Vss in preclinical species was plotted in log-log scale versus body weight. The allometric power function was fit to the data (eq. 1). where Vss is in liters, W is body weight in kilograms, and a and b are the allometric coefficient and exponent, respectively. The Vss in humans was extrapolated using the fitted function for each drug. Body weights for rats, dogs, monkeys, and humans were set to 0.25, 10, 5, and 70 kg, respectively.
Allometric Scaling of Vss,u.
Allometric scaling of Vss,u uses the same principle as allometric scaling of Vss, only substituting Vss with Vss,u, where Vss,u = Vss/fup.
Vss,u Equivalency Approach.
This approach assumes Vss,u in humans will be the same as Vss,u in animals. The Vss,u equivalency approach was conducted for each individual species (i.e., single-species scaling) and used the mean Vss,u across all three species (i.e., multispecies scaling).
fut Equivalency Approach.
This approach assumes fut in humans will be the same as fut in animals. Two common approaches to calculating fut were considered, eqs. 2 and 3 (collectively termed the “Oie-Tozer-style equations” here for simplicity). Both use observed Vss and fup and some physiological data to calculate apparent fut. where Vp is the total volume of plasma in the animal and Vt is the rest of the animal volume (which can be considered as essentially 1 − Vp, assuming 1 kg of body weight equals 1 liter of volume); or where, Ve is the extracellular fluid volume, Vr is the remaining fluid volume, and Re/i is the ratio of protein binding in extracellular fluid to that in plasma. Re/i is assumed to be 1.4 and the same across species. Physiological volumes used in the calculations are shown in Table 1 (Obach et al., 1997). The fut equivalency approach was conducted for eqs. 2 and 3 using each individual species (i.e., single-species scaling) and using the mean fut across species (i.e., multispecies scaling). Negative values for fut or fut values of >1 were not excluded from subsequent calculations.
Simcyp.
For comparison, Vss was also calculated according to the tissue composition equations proposed by Poulin and Theil (2002) and corrected by Berezhkovskiy (2004) (or “method 1”) and Rodgers and Rowland (2007) (or “method 2”), as programmed in Simcyp version 8.0 (Simcyp Ltd., Sheffield, UK). Please refer to these publications for a detailed description of their approaches. In brief, both methods 1 and 2 calculate total partitioning of a drug into a particular tissue as the sum of partitioning into individual tissue components, such as neutral lipids, phospholipids, or tissue water. Partitioning of a drug into these components is assumed to be driven by a drug's lipophilicity. Both methods use the octanol/water partition coefficient (Po:w) as a surrogate for partitioning into neutral lipids, except in adipose tissue, which uses the vegetable oil/water partition coefficient (Pvo:w). Because phospholipids are composed of both hydrophilic and lipophilic properties, partitioning into all phospholipids is described as a combination of partitioning into water (70%) and neutral lipids (30%), assuming the same hydrophilic/lipophilic balance as commercial lecithin. A drug's binding to specific macromolecular proteins common to the plasma and interstitial tissue space (such as albumin) is also considered, as estimated from plasma protein binding experiments. Method 2 also considers the ionization state of the drug (drug pKa versus tissue pH), and interactions between acidic phospholipids and drugs with at least one basic pKa of >7.0 are estimated from blood-to-plasma concentration ratio data. Considering all these factors, differences in distribution from one tissue type to the next will depend on the abundance of these components in each tissue. Steady-state tissue-to-blood concentration ratio, Kp (Pt-b in some related citations), is calculated as a function of total partitioning and binding in a tissue versus the total partitioning and binding in blood. Vss is then calculated by incorporating the Kp values determined for each tissue into an Oie-Tozer-style equation. Physicochemical properties used for these methods were calculated using ACD Labs Chemistry version 12 (Advanced Chemistry Development, Inc., Toronto, Canada) and are shown in Table 2.
Prediction accuracy was measured by calculating the fold error as predicted human Vss/observed human Vss. The various methods for predicting Vss were compared by tallying the number of compounds falling within 1.5-, 2-, and 3-fold prediction error.
Results
Plasma Protein Binding and Calculation of Vss,u and fut.
Rat, dog, monkey, and human plasma protein binding were determined for 60 of the 67 reference compounds using an ultracentrifugation technique. For the remaining seven compounds, plasma protein binding values across species were obtained from the literature, where an ultracentrifugation technique was also used (except for lamifiban). The values for free fraction are summarized in Table 2. Free fraction ranged from <1% free in some species (diclofenac, fluvastatin, gemfibrozil, indomethacin, ketoprofen, naproxen, troglitazone, warfarin, felodipine, telmisartan, and verlukast) to essentially 100% free across species (lamivudine, venlafaxine, nicotine, gabapentin, and lamifiban). Among the compounds tested, 20 compounds (∼30%) showed extensive species differences in plasma protein binding, with a greater than 3-fold ratio between the species with the highest and lowest free fractions. Compounds with the largest such difference (>5-fold) were cefazolin, cefoperazone, fluvastatin, furosemide, ketoprofen, valproic acid, warfarin, felodipine, nifedipine, cefpiramide, telmisartan, topotecan, and verlukast. Other compounds (70% of the total) showed more moderate or minimal species differences in plasma protein binding (≤3-fold ratio).
Plasma protein binding and reported Vss values for rat, dog, monkey, and human were used to calculate Vss,u or fut for those species. Vss,u and fut (calculated by eq. 2 or 3) are summarized in Table 3. Calculated Vss,u ranged from 0.16 l/kg (gabapentin in dogs) to 2400 l/kg (felodipine in rats). Among the compounds investigated, 26 compounds (∼39%) showed moderate or minimal species differences (≤3-fold ratio between the species with the highest and lowest Vss,u). Calculation of fut by eq. 2 occasionally resulted in fut values of >1.0, the theoretical maximum. Values for fut, as calculated by eq. 2, ranged from 0.0004 (felodipine in rats) to 8.7 (gabapentin in dogs) and were essentially inversely proportional to values for Vss,u. Considering fut as calculated by eq. 2, 27 compounds (∼40%) showed moderate or minimal species differences (≤3-fold ratio between the species with the highest and lowest fut). These compounds were essentially the same as those showing moderate or minimal species differences in Vss,u. Calculation of fut by eq. 3 also occasionally resulted in fut values of >1.0, as well as negative values for fut. Positive values for fut, as calculated by eq. 3, ranged from 0.0002 (felodipine in rats) to 13 (lamifiban in monkeys). Considering fut as calculated by eq. 3, 16 compounds (∼24%) showed moderate or minimal species differences in fut. The compounds that showed moderate or minimal species differences in Vss,u and fut (regardless of calculation method) include troglitazone, antipyrine, caffeine, flunisolide, zidovudine, cyclophosphamide, lamivudine, midazolam, bupivacaine, citalopram, hydrodolasetron, propranolol, verapamil, irinotecan, and doxorubicin. Most of these (except for midazolam, bupivacaine, and irinotecan) also showed moderate or minimal species differences in plasma protein binding (≤3-fold ratio).
Species Differences in Vss versus Species Differences in Vss,u.
The impact of protein binding on the species difference in rat, dog, monkey, and human Vss was evaluated. Species differences in Vss were compared with species differences in Vss,u. The majority of compounds showed little change in extent of species difference with Vss,u compared with Vss, particularly when species difference in plasma protein binding was minimal or moderate. For example, considering propranolol, the ratio between the species with the highest and lowest Vss was 2.4-fold, whereas the ratio between the species with the highest and lowest Vss,u was 2.3-fold (Fig. 1, A and B). Likewise, for lorazepam, the ratio between the species with the highest and lowest Vss was 7-fold, whereas the ratio between the species with the highest and lowest Vss,u was 8.6-fold. Occasionally, minimal changes in extent of species difference also occurred when species differences in plasma protein binding were large. In these cases, there was often a change in the rank order of species, in order of increasing values for Vss or Vss,u. For example, considering imatinib, the ratio between the species with the highest and lowest Vss was 2.9-fold, whereas the ratio between the species with the highest and lowest Vss,u was 3.2-fold, essentially unchanged. However, the rank order of species, in order of increasing Vss, was rat<human<monkey<dog, whereas the rank order of species, in order of increasing Vss,u, was human<dog<rat<monkey.
However, several compounds did show meaningfully reduced species difference with Vss,u compared with Vss. For example, considering midazolam, the ratio between the species with the highest and lowest Vss was 2.6-fold, whereas the ratio between the species with the highest and lowest Vss,u was 1.2-fold (Fig. 1, C and D). Other compounds showing a similar reduction in species difference included tiludronate (15–5-fold), valproic acid (4.4–2-fold), mifepristone (22–7.2-fold), nifedipine (9.2–5-fold), and quinidine (11–4.8-fold).
In addition, several compounds showed meaningfully increased species difference with Vss,u compared with Vss. For example, considering felodipine, the ratio between the species with the highest and lowest Vss was 5.5-fold, whereas the ratio between the species with the highest and lowest Vss,u was 23-fold (Fig. 1, E and F). Other compounds showing a similar increase in species difference included cefoperazone (3–6.1-fold), gemfibrozil (9.8–17-fold), warfarin (2.5–5.2-fold), chlorpromazine (3.6–15-fold), cefpiramide (4.5–12-fold), temisartan (3.4–12-fold), and verlukast (7.4–14-fold).
Prediction of Human Vss by Allometric Scaling.
Human Vss was predicted by allometric scaling of Vss or Vss,u from three preclinical species (rat, dog, and monkey) versus body weight. The results of allometric scaling are shown in Table 4 and Fig. 2. In addition, the prediction accuracy was assessed by determining the percentage of compounds falling into 1.5-, 2-, and 3-fold prediction error (Table 5), where fold error is defined as predicted Vss/observed Vss. With allometric scaling of Vss, 30, 60, and 73% of all compounds fell within 1.5-, 2-, and 3-fold error, respectively. With allometric scaling of Vss,u, 28, 55, and 75% of all compounds fell within 1.5-, 2-, and 3-fold error, respectively. Incorporating plasma protein binding information did not seem to improve the overall chance of prediction success using allometric scaling. The allometric exponents b ranged from 0.21 to 1.4 and from 0.26 to 1.5 for scaling of Vss and Vss,u, respectively. With allometric scaling of both Vss and Vss,u, there was a clear relationship between the fold error in prediction and the value of the best fit for the allometric exponent b from the three preclinical species (Fig. 2, C and D). Exponents of <1 tended to result in an underprediction of human Vss, whereas exponents of >1 tended to result in an overprediction of human Vss.
Prediction of Human Vss by Interspecies Scaling of Vss,u or fut.
Human Vss was predicted using the Vss,u equivalency approach, assuming human Vss,u will be equivalent to the Vss,u from each individual preclinical species (i.e., single-species scaling from rats, dogs, or monkeys) or equivalent to the average Vss,u across the three preclinical species (multispecies scaling). The results of interspecies scaling of Vss,u are shown in Table 6 and Fig. 3. In addition, the prediction accuracy was assessed by determining the percentage of compounds falling within 1.5-, 2-, and 3-fold prediction error (Table 5). Considering all compounds, no single species appeared to predict human Vss better than any other. Using the Vss,u equivalency approach, 36 to 37%, 54 to 64%, and 79 to 81% of all compounds fell within 1.5-, 2-, and 3-fold error, respectively, depending on the species. Using the average Vss,u across three preclinical species showed some improvement compared with single-species scaling, with 40, 72, and 87% of all compounds falling within 1.5-, 2-, and 3-fold error, respectively.
Human Vss was also predicted using the fut equivalency approach, assuming human fut will be equivalent to the fut from each individual preclinical species (i.e., single-species scaling from rats, dogs, or monkeys) or equivalent to the average fut across the three preclinical species (multispecies scaling). The results of interspecies scaling of fut are shown in Table 5 and Figs. 4 and 5. In addition, the prediction accuracy was assessed by determining the percentage of compounds falling into 1.5-, 2-, and 3-fold prediction error (Table 6). The fut was calculated using either eq. 2 or 3. Considering all compounds, no single species appeared to predict human Vss better than any other. Using the fut equivalency approach, where fut is calculated by eq. 2, 39 to 43%, 54 to 66%, and 81 to 84% of all compounds fell within 1.5-, 2-, and 3-fold error, respectively, depending on the species. Using the average fut (eq. 2) across three preclinical species showed some improvement compared with single-species scaling, with 55, 75, and 90% of all compounds falling within 1.5-, 2-, and 3-fold error, respectively. Substantially similar results were observed when fut was calculated using eq. 3 (Tables 5 and 6; Fig. 5). Using the average fut (eq. 3) across three preclinical species also showed some improvement compared with single-species scaling, with 58, 78, and 90% of all compounds falling within 1.5-, 2-, and 3-fold error, respectively. Finally, interspecies scaling using the average Vss,u or fut (regardless of calculation method) seemed to provide a better chance of falling within 1.5-, 2-, or 3-fold error compared with allometric scaling versus body weight when predicting human Vss.
Predicting Human Vss Using Mechanistic Tissue Composition Equations in Simcyp.
For comparison, human Vss was also predicted using methods 1 and 2 as available in Simcyp version 8.0 population-based pharmacokinetic simulator (Simcyp Ltd.). Physicochemical properties used for these methods were calculated using ACD Labs Chemistry version 12 and are shown in Table 2. Plasma protein binding and blood-to-plasma concentration ratio values used for these methods are also provided in Table 2. The results of the predictions of human Vss by methods 1 and 2 are shown in Table 6 and Fig. 6. In addition, the prediction accuracy was assessed by determining the percentage of compounds falling within 1.5-, 2-, and 3-fold prediction error (Table 5). Considering all compounds, method 1 resulted in 19, 40, and 67% of all compounds falling within 1.5-, 2-, and 3-fold error, respectively. Correspondingly, method 2 resulted in 15, 43, and 64% of all compounds falling within 1.5-, 2-, and 3-fold error, respectively. Some compounds showed considerable error in prediction (>4-fold error) using the tissue composition equations, particularly using method 2, including diclofenac, fluvastatin, troglitazone, mifepristone, nifedipine, indinavir, amiodarone, nicardipine, and vinblastine. Most of these compounds had a clogD at pH 7.4 of >3.5. The relationship between fold prediction error from method 1 or 2 and clogD at pH 7.4 is shown in Fig. 6, C and D. The relationship between prediction error and clogD at pH 7.4 was less pronounced with method 1. However, method 1 also tended to overpredict the Vss for several compounds with a clogP of ∼4.0 or higher (figure with clogP not shown).
Discussion
The aims of the present study were to examine the assumptions regarding equivalency of Vss,u and fut across species and to examine side by side several common approaches for predicting human Vss from preclinical data. To do this, observed rat, dog, monkey, and human Vss values were compiled from the literature, and plasma protein binding was determined across species, for a wide range of 67 reference compounds.
Despite this common assumption, Vss,u or fut equivalency does not necessarily seem to be the norm. Only 39% of the compounds tested exhibited moderate to minimal species difference in Vss,u (≤3-fold ratio between the species with the highest and lowest value). Furthermore, only 24 to 40% of the compounds exhibited moderate to minimal species difference in fut, depending on how fut is calculated, whereas 70% of the compounds showed moderate to minimal species difference in fup. This seems to indicate that species similarity in fup is more likely to be observed than species similarity in fut (as calculated by the Oie-Tozer-style equations), despite early evidence that binding to tissues (as determined in vitro) could be quite similar across species (Fitchl and Schulmann, 1986). There are several possibilities for these findings. One possibility is that some reported values for Vss may not be accurate because of limited blood sampling or insufficiencies in the analytical method used. Another possibility is that plasma (or tissue) protein binding as determined in vitro might, in some cases, not accurately reflect the in vivo situation. In cases of inaccurate determination of Vss or protein binding, apparent species differences in calculated Vss,u or fut would be an artifact of limitations in the experimental methodology, rather than true species differences in distribution.
A third possible source of discrepancy is that fut calculated by the Oie-Tozer-style equations is practically quite different than fut determined in vitro. When determined in vitro using tissue homogenates, fut represents simply the fraction of drug unbound to tissue material, including tissue solids, and soluble proteins in the intracellular and extracellular spaces. In this case, as with plasma protein binding measurements, the theoretical maximum for free fraction is 1. However, fut calculated from observed Vss and plasma protein binding is a derived term resembling an average fut across all tissue tissues and, therefore, might not represent the binding to any specific tissue. In addition, calculated fut might capture any number of other mechanisms affecting distribution that are unrelated to tissue binding. For example, several compounds exhibited calculated fut values of >1 in at least one species. Additionally, using eq. 3, negative values for fut were also observed (Table 3) for some compounds, including cefotetan, cefazolin, furosemide, naproxen, cefpiramide, gabapentin, and lamifiban. These compounds also exhibited Vss values that were among the lowest in the dataset. Waters and Lombardo (2010) also reported similar anomalies in calculated fut. Such anomalies certainly illustrate a limitation with this particular model for low Vss drugs. However, they might not only reflect a lack of binding to tissue proteins but also a lack of penetration (i.e., permeability) into tissue compartments. For drugs that do not penetrate into intracellular tissue spaces, calculated fut could be forced above 1 by the fraction of intracellular tissue volume. In the original derivation of eq. 3 (Oie and Tozer, 1979), the authors suggested that for drugs restricted to the extracellular fluid, Vr should be set to zero, making tissue binding irrelevant. However, toward the application of interspecies scaling, it might be difficult to judge whether or not a drug is restricted to the extracellular fluid based on Vss and fup alone.
As a derived term, calculated fut could also reflect active uptake or efflux, concentrative uptake due to pH gradients, and distribution to compartments that are unrelated to partitioning into tissues, such as enterohepatic recycling, or intestinal or renal secretion and reabsorption, depending on the properties of the compound of interest. Any one or combination of these mechanisms could potentially be a source for species differences in apparent Vss,u or fut. The impact of these mechanisms on the calculation of Vss,u or fut would be difficult to determine without substantially more information about each compound. Another consideration is that the physiological volumes recommended for use with eq. 3 (Obach et al., 1997) only account for total body water and do not account for the volume attributed to tissue solids, where many high Vss drugs could primarily reside, leading to inaccurate estimation of fut. Finally, Waters and Lombardo (2010) suggested that an assumed value for Re/i of 1.4 might not be appropriate for all drugs. For these reasons, although the calculation of fut is mechanistic in appearance, it is difficult to derive any mechanistic insight by simply calculating fut using Oie-Tozer-style equations. These equations should still be considered as empirical when used in the application of interspecies scaling.
Despite the observation that species similarities in Vss,u or fut (as calculated by the Oie-Tozer-style equations) are not necessarily the norm, predictions of human Vss by interspecies scaling can still be useful and reasonably accurate. All interspecies scaling methods evaluated, including allometric scaling, and Vss,u or fut equivalency, by single-species scaling or averaging across species, can result in reasonably accurate predictions. However, some methods seemed to result in a better chance of obtaining the most accurate prediction than others. In particular, the Vss,u or fut equivalency approaches (using average Vss,u or fut across three preclinical species) seemed to meaningfully outperform allometric scaling of Vss or Vss,u. Allometric scaling of Vss or Vss,u resulted in the most accurate prediction only 15% of the time, whereas the Vss,u or fut equivalency approach resulted in the most accurate prediction 67% of the time. In other cases, prediction accuracies were similar. The lesser performance of allometric scaling could be due to the extrapolation using a log-log relationship. Any species differences (or errors) in Vss estimation, particularly in animals with the lowest and highest body weights, will propagate exponentially when extrapolating human Vss using the allometric power function. There was a strong relationship between the fold error in prediction and the value of the best fit for the allometric exponent b from the three preclinical species (Fig. 2, C and D). Given the observed relationship, predictions resulting from exponents outside the range of between ∼0.8 and ∼1.2 should be considered cautiously because of the risk of exponential error propagation.
With the Vss,u or fut equivalency approaches, single-species scaling from rats, dogs, or monkeys resulted in a similar chance of prediction success as allometric scaling (Table 5), in agreement with some previous reports. However, in the present study, no single species (rats, dogs, or monkeys) seemed to perform significantly better overall than any other (Table 5). This conclusion is somewhat different than other reports that have found rats, dogs, or monkeys to be the best species for predicting human Vss, depending on the study (Ward and Smith, 2004; Hosea et al., 2009; Sui et al., 2010). Although statistical analysis may periodically suggest that one species could be better than another at predicting human Vss, depending on the dataset, there is no known physiological basis for this to be so. That single-species scaling has performed similarly to allometric scaling has led some to suggest that scaling from a single preclinical species (i.e., rat) is sufficient and that considering data from additional preclinical species (such as dog or monkey) provides little benefit (Hosea et al., 2009). Certainly, accurate predictions can be obtained from a single species, and such an approach might be useful at the early stages of drug discovery. However, further analysis shows that, when predicting human Vss, the Vss,u or fut equivalency approaches using the average Vss,u or fut across three preclinical species (i.e., multispecies scaling) provides considerable improvement in extent of prediction accuracy compared with single-species scaling (Table 5). The pharmacokinetics scientist would be best advised to use all available preclinical data (as resources allow) to arrive at predicted human pharmacokinetic parameters for purposes of estimating the potential therapeutic dose and safety margins before the first dose to humans.
For comparison, Vss was also calculated according to the tissue composition equations proposed by Poulin and Theil (2002) and Rodgers and Rowland (2007). These tissue composition equations are considered to be mechanistic alternatives to interspecies scaling and facilitate the use of physiologically based pharmacokinetic models in the absence of in vivo tissue distribution data. Prediction of Vss using the tissue composition equations did not necessarily provide a better chance of lowest error in prediction than interspecies scaling methods. Methods 1 and 2 resulted in 67 and 64% of all predictions falling within 3-fold error, respectively, versus 87 to 90% for Vss,u or fut equivalency using average Vss,u or fut across three preclinical species. Method 1 or 2 provided the most accurate prediction only 7% of the time, whereas the value was 61% for Vss,u or fut equivalency.
There are a number of possible reasons for the lesser performance of the tissue composition equations. First, inaccuracies in calculation or measurement of physicochemical properties could result in inaccuracies in prediction of tissue partitioning, as discussed by Rodgers and Rowland (2007). Second, partitioning into octanol (or vegetable oil) might not always adequately represent the partitioning of a drug into all classes of neutral lipids found in animal tissues (i.e., triglycerides, diglycerides, monoglycerides, cholesterol, lipid components of phospholipids, etc.). Evidence for this lies in that human Vss was substantially overpredicted for several lipophilic neutral and basic compounds, particularly using method 2 (Fig. 6, C and D). This effect was most pronounced for neutral and basic compounds when clogD at pH 7.4 was greater than ∼3.5. The theory behind these models suggests that predicted Kp, and therefore Vss, will continue to increase as log P increases. This was illustrated by a simulation conducted by Rodgers and Rowland (2007), where Vss,u increased exponentially when log P exceeded 3. However, initial validations of these methods contained relatively few drugs of high lipophilicity. In contrast, some comparisons of observed adipose Kp versus log P have indicated that Kp might not increase exponentially with log P but might plateau instead (Haddad et al., 2000). This discrepancy would lead to an overprediction of Vss for highly lipophilic compounds using the tissue composition equations, as observed with the present dataset. Given the current findings, Vss predictions for highly lipophilic compounds using method 2 should be interpreted cautiously. The Vss,u or fut equivalency approaches were likely to give a more accurate prediction for this class of compounds, possibly because partitioning into human tissues by lipophilic compounds is best represented by actual in vivo data from preclinical species. Third, not all tissue phospholipids might behave exactly as commercial lecithin (see Materials and Methods). Fourth, partitioning into water might not always accurately reflect partitioning into hydrophilic tissue components (i.e., salt-buffered intracellular and extracellular fluids, hydrophilic components of phospholipids, hydrophilic protein matrices, etc.). Fifth, the possibility of specific binding to numerous tissue macromolecules is neglected. Finally, as with calculation of fut using the Oie-Tozer-style equations, the tissue composition equations still neglect other mechanisms that can contribute to distribution such as lack of permeability, active uptake or efflux, enterohepatic recycling, or intestinal or renal secretion and reabsorption.
Although the mechanistic tissue compositions did not necessarily provide the most accurate Vss prediction, some important benefits of the approach should be acknowledged. Whereas refinement of the methods should be investigated, they currently provide the best opportunity for a mechanistic understanding of distribution, short of performing a tissue distribution study in vivo. In addition, predictions are possible using only in vitro and physicochemical property data as inputs, whereas data from preclinical species are not required, providing a valuable alternative to interspecies scaling.
In summary, the assumptions regarding equivalency of Vss,u and fut across species were examined, and several common approaches for predicting human Vss from preclinical data were evaluated. Species similarity in Vss,u or fut does not seem to be the norm among rats, dogs, monkeys, or humans. Despite this, interspecies scaling from rats, dogs, and monkeys is useful and can provide reasonably accurate predictions of human Vss, although some interspecies scaling approaches were better than others. For example, the performance of the common Vss,u or fut equivalency approaches using average Vss,u or fut across three preclinical species was substantially superior to allometric scaling techniques. In addition, considering data from several preclinical species, using the equivalency approach, provided improved prediction success compared with scaling from any single species. Although the mechanistic tissue composition equations available in the Simcyp population-based pharmacokinetic simulator did not necessarily provide the most accurate predictions, and the equations used likely need refinement, they still provide the best opportunity for a mechanistic understanding and prediction of human Vss.
Authorship Contributions
Participated in research design: Berry and Zhao.
Conducted experiments: Berry and Li.
Performed data analysis: Berry.
Wrote or contributed to the writing of the manuscript: Berry and Zhao.
Footnotes
Article, publication date, and citation information can be found at http://dmd.aspetjournals.org.
doi:10.1124/dmd.111.040766.
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ABBREVIATIONS:
- Vss
- volume of distribution at steady state
- Vss,u
- unbound volume of distribution at steady state
- fup
- fraction unbound in plasma
- fut
- fraction unbound in tissues
- MPA
- mobile phase A
- MPB
- mobile phase B
- clogP
- calculated log P
- clogD
- calculated log D.
- Received May 17, 2011.
- Accepted August 5, 2011.
- Copyright © 2011 by The American Society for Pharmacology and Experimental Therapeutics