An Algorithm for Evaluating Potential Tissue Drug Distribution in Toxicology Studies from Readily...

RESEARCH ARTICLE – Pharmacokinetics, Pharmacodynamics and Drug Transport and Metabolism

An Algorithm for Evaluating potential Tissue Drug Distributionin Toxicology Studies from Readily Available PharmacokineticParameters

PATRICK POULIN,1 DONNA M. DAMBACH,2 DYLAN H. HARTLEY,3 KEVIN FORD,2 FRANK-PETER THEIL,4 ERIC HARSTAD,2

JASON HALLADAY,5 EDNA CHOO,5 JASON BOGGS,5 BIANCA M. LIEDERER,5 BRIAN DEAN,5 DOLORES DIAZ2

1Consultant, Quebec city, Quebec, Canada2Safety Assessment, Genentech Inc., South San Francisco, California, 940803Array Biopharma, Boulder, Colorado4UCB Pharma, Brussels, Belgium5Drug Metabolism and Pharmacokinetics, Genentech Inc., South San Francisco, California, 94080

Received 4 June 2013; revised 21 June 2013; 25 June 2013; accepted 27 June 2013

Published online 22 July 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jps.23670

ABSTRACT: Having an understanding of drug tissue accumulation can be informative in the assessment of target organ toxicities; however,obtaining tissue drug levels from toxicology studies by bioanalytical methods is labor-intensive and infrequently performed. Additionally,there are no described methods for predicting tissue drug distribution for the experimental conditions in toxicology studies, which typicallyinclude non-steady-state conditions and very high exposures that may saturate several processes. The aim was the development of analgorithm to provide semiquantitative and quantitative estimates of tissue-to-plasma concentration ratios (Kp) for several tissues fromreadily available parameters of pharmacokinetics (PK) such as volume of distribution (Vd) and clearance of each drug, without performingtissue measurement in vivo. The computational approach is specific for the oral route of administration and non-steady-state conditionsand was applied for a dataset of 29 Genentech small molecules such as neutral compounds as well as weak and strong organic bases. Themaximum success rate in predicting Kp values within 2.5-fold error of observed Kp values was 82% at low doses (<100 mg/kg) in preclinicalspecies. Prediction accuracy was relatively lower with saturation at high doses (≥100 mg/kg); however, an approach to perform low-to-highdose extrapolations of Kp values was presented and applied successfully in most cases. An approach for the interspecies scaling was alsoapplied successfully. Finally, the proposed algorithm was used in a case study and successfully predicted differential tissue distribution oftwo small-molecule MET kinase inhibitors, which had different toxicity profiles in mice. This newly developed algorithm can be used topredict the partition coefficients Kp for small molecules in toxicology studies, which can be leveraged to optimize the PK drivers of tissuedistribution in an attempt to decrease drug tissue level, and improve safety margins. C© 2013 Wiley Periodicals, Inc. and the AmericanPharmacists Association J Pharm Sci 102:3816–3829, 2013Keywords: ADME; DMPK; disposition; distribution; partition coefficients; pharmacokinetics; tissue distribution; toxicology; volume ofdistribution; safety assessment

INTRODUCTION

The distribution of drugs into tissues, that is, tissue accumu-lation, is a recognized contributor to drug toxicity1,2; however,evaluation of tissue drug partitioning under in vivo conditionis not routinely performed in toxicology studies, partly becauseit is resource-intensive. This issue can also be approachedwith physiologically based pharmacokinetics (PK) modeling,where the impacts of dosing regimen on tissue distribution can

Abbreviations used: AUC, area under the curve; BM, bone marrow; Clog P,log n-octanol–water ratio calculated; CpKa, ionization constant calculated; Eh,hepatic extraction ratio; CL, clearance; fup, fraction unbound in plasma; fut,fraction unbound in tissue; fucells, unbound fraction in intracellular water; Gen,Genentech; F, bioavailability; 8, elimination rate constant; Ka, absorption rateconstant; Kp, tissue-to-plasma concentration ratio; NCA, noncompartmentalanalyses; pKa, ionization constant; PO, per os; REP, erythrocyte-to-plasmaratio; Vd, volume of distribution; Vz, volume of distribution of the terminalphase.

Correspondence to: Patrick Poulin (Telephone: +418-802-3985; Fax: +650-742-5234; E-mail: [email protected])

Journal of Pharmaceutical Sciences, Vol. 102, 3816–3829 (2013)C© 2013 Wiley Periodicals, Inc. and the American Pharmacists Association

be predicted from description of its controlling processes, al-though this could be a data-intensive approach. Alternatively,it can be of interest to verify whether tissues can be treatedas well-stirred compartments, and the influences of altered de-livery through changes in blood flow can be neglected.3–13 Thispremise assumes that the same physicochemical mechanismsare present in each tissue, and hence, relationships among drugtissue partitioning can be developed, comparably to a physio-logical approach. The challenge is that, being more empirical,the well-stirred compartment model may not totally accountfor the processes that determine the relationship of simple PKobservations to tissue-specific and regimen-specific drug con-centrations; processes such as nonlinear metabolism, satura-tion of binding, and non-steady-state distributions that dependon the dosing regimens and the interaction among uptake, re-distribution, and tissue-specific clearance processes. Despitethese limitations, consistent patterns of relative partitioninginto various tissues can be identified that can allow reasonableestimate with less intensive data collection, for which the inputparameters are readily available.3–18

3816 Poulin et al., JOURNAL OF PHARMACEUTICAL SCIENCES 102:3816–3829, 2013

RESEARCH ARTICLE – Pharmacokinetics, Pharmacodynamics and Drug Transport and Metabolism 3817

Theoretical Background

The endpoint is the estimation of values of tissue–plasma ra-tios (Kp), which are the parameters commonly used to esti-mate the degree to which a drug accumulate across tissues.For steady-state conditions after continuous intravenous infu-sions, consistent patterns of relative partitioning into varioustissues were made by relaying some in vitro physicochemicalproperties of drugs to tissue composition data to predict the Kp

values by considering the binding to tissue lipids and plasmaproteins14–18; therefore, the predicted Kp values linearly corre-lated across tissues.3,9 However, these in vitro-based calculationmodels did not cover the exposure conditions observed in toxi-cology studies such as oral route of absorption and non-steady-state conditions, and performed less accurately compared withmodels derived from in vivo data.14,18 Alternatively, the in vivoKp data may also be used to develop consistent patterns ofrelative tissue distribution into various tissues for any expo-sure condition. Moreover, several authors demonstrated thatdrug tissue partitioning, and, thus, the in vivo Kp values, cor-related across tissues for several drugs.3–7 Specifically, muscleKp values correlate with Kp values of other tissues (e.g., brain,lung, liver, heart, skin, intestine, and red blood cells; r2 mostlyin the range of 0.60–1), irrespective of the chemical nature ofthe drug and exposure conditions. The established correlationmethods enable the prediction of Kp values in various tissuesunder in vivo conditions on the basis of a known muscle Kp

value. The linearity of the correlations between the Kp valuesof several tissues suggests that, as expected, the biological fea-tures related to the binding of drugs to lipids and/or proteins arecommon among tissues.3–7 Recently, the principle of the correla-tion model has been successfully extended to further examplesin veterinary, oncology, and PK studies either for steady-stateand non-steady-state conditions for various routes of adminis-tration (i.e., intravenous, oral, or intraperitoneal).8–10 Moreover,the analyses of Jansson et al.8 and Edginton and Yun11 incor-porated descriptors of drug properties such as lipophilicity incoming up with their Kp estimates.

The application of such correlation models in toxicology waslimited because the Kp value for muscle used as input param-eter in the correlation equations is not commonly generated.To overcome this difficulty, Jansson et al.8 proposed to combinethe correlation equations with the overall volume of distribu-tion (Vd) measured in vivo, which is a readily available param-eter because it can be estimated from the measured plasmaconcentration–time profiles by using noncompartmental anal-yses (NCA)12 as part of routine PK studies in drug discovery.This will yield quantitative estimates of Kp values for severaltissues based on in vivo Vd values, without conducting any tis-sue measurement in vivo. In addition, in the early stages of drugdiscovery, it could be of interest to predict whether a drug haslow or high potential for tissue accumulation, and to be ableto rank-order drugs based on this potential. In other words,when drugs have similar Vd values, the additional informa-tion on clearance (CL) may help to rank-order drugs; therefore,when plasma concentration over time is increased because ofa lower CL effect, the tissue distribution should also increase,and inversely, under non-steady-state conditions.13 Therefore,our hypothesis was that semiquantitative (rough) estimates ofKp values under non-steady-state conditions in toxicology stud-ies could also be made by including CL effects in addition to

Vd. The CL data are also routinely generated in drug discoveryusing NCA analyses.12

In the work described herein, an algorithm was provided forevaluation of tissue drug distribution from readily availablePK parameters by combining semiquantitative and quantita-tive estimates of Kp values for common target organs identifiedin toxicological studies, thus avoiding the need to measure ac-tual drug levels in tissues. This algorithm expands from thecurrent correlation models used in the PK studies, as it wasapplied for wide dose ranges that include high doses, and anapproach to perform low-to-high doses extrapolations of Kp val-ues is presented in addition to an interspecies extrapolationapproach. The current computational approach is specific forthe oral route of administration under non-steady-state con-ditions. Finally, the utility of the proposed algorithm in drugdiscovery was also challenged in a case study to predict dif-ferential tissue distribution of two small molecule MET kinaseinhibitors from their in vivo Vd and CL values. Accordingly, Diazet al.1 recently reported that minimal structural changes low-ering ionization constant (pKa) for one small molecule MET ki-nase inhibitor compared to another caused significant changesin Vd (decreased) and CL (increased), which resulted in loweredtissue distribution and reduced toxicity profiles in mice. Over-all, this provides a novel tool for toxicologists to guess tissuedrug partitioning in the interpretation of toxicological data.

METHODS

Figures 1, 2, 3 illustrate the overall algorithm for tissue dis-tribution model development and predictive assessment strat-egy to conduct semiquantitative and quantitative assessmentsin a stepwise fashion. Test set of compounds is presented inTable 1.

Figure 1. Illustration of the overall model development and predic-tion assessment strategy for the development of a novel semiquanti-tative and quantitative algorithm to estimate tissue drug distribution(Kp).

DOI 10.1002/jps.23670 Poulin et al., JOURNAL OF PHARMACEUTICAL SCIENCES 102:3816–3829, 2013

3818 RESEARCH ARTICLE – Pharmacokinetics, Pharmacodynamics and Drug Transport and Metabolism

Figure 2. Pharmacokinetics parameters used to define “GeneralRules” for qualitatively evaluating potential tissue drug accumulationas explained in the Methods section. LBF refers to the liver blood flowrate.

Modeling Assumptions

We hypothesized that the existing correlation models used toestimate Kp values of drugs from readily available PK parame-ters are also applicable for the exposure conditions observed intoxicology studies (i.e., oral or intraperitoneal route and non-steady-state conditions) because they were successfully appliedirrespective of the exposure conditions and chemical nature ofthe drug.3–11 Prediction of tissue distribution of drugs at thewhole organ level was made assuming total tissue dose is re-lated to toxicity. The liver was assumed to be the main organfor elimination. To compute the residual amount of drug inthe body, the appropriate Vd is the one computed by the intra-venous route. As non-steady-state conditions were observed inthis study (i.e., pseudo-equilibrium conditions only), the Vd ofthe terminal phase (Vz) was used instead.12 When Vz is com-puted after extravascular drug administration (e.g., oral gav-age), the most appropriate parameter to use is Vz/F (where F isthe bioavailability), instead of Vz. The same principle appliesto the CL. Distribution is typically fast, whereas the absorp-tion and CL can be slow. Therefore, to predict the Kp valuesobserved here after oral gavage, we assumed that when Ka (theabsorption rate constant) is greater than 8 (the elimination rateconstant), the final phase is governed by the elimination pro-cess, and, therefore, the Vd computed by the intravenous routecan be used.13 This assumption is likely to apply here becausethe current dataset comprised low-to-medium CL compoundsin rats in most cases (Table 1). Therefore, the Vd refers to Vz inthis study. As data on Vd (Vz) were readily available comparedwith Vd/F, the available data were challenged first in this studyfor the current dataset.

Estimation of Vd and CL In Vivo

Noncompartmental analyses were performed to estimate Vd

(Vz) and CL at the given standard intravenous dose (1 mg/kg)as part of our routine PK studies, and were performed onall plasma concentration–time profiles observed after intra-venous administration (1 min–24 h) to derive Vd (Vz). Modelsimulation provided the area under the concentration–timecurve (AUC) and area under the first moment curve by in-

tegrating the model-predicted arterial concentration and themodel-predicted arterial concentration multiplied by time. Allnoncompartmental parameters were derived from these values(Vz = dose/(AUC0–infinity × 8z) (CL = dose/AUC).12

Test Compounds and Animal Studies

A total of 29 Genentech compounds (Gen 1–29), for which tis-sue drug levels in preclinical species were obtained in toxicologystudies, were used to develop the model (Table 1). The chem-ical structures of these compounds were diverse and includedcharged (bases) and uncharged (neutral) molecules at physio-logical pH as characterized by the ionization constant calcu-lated (CpKa). For these drugs, the observed value of plasmaprotein binding ranged from 39% to 99.9%, lipophilicity (logn-octanol–water ratio calculated, Clog P) values ranged from0.30 to 9.0, animal Vd values ranged from 0.12 to 12 L/kg, andCL values ranged from 0.45 to 126 mL/(min kg). We do nothave data for compounds with carboxylic acid functionalitiesin our studies, and therefore, this class of compounds was notinvestigated here. The diverse drug datasets are compiled inTables 2, 3, 4, according to the different model developmentsteps described in Figure 1.

Test compounds were administered to Sprague–Dawley rats,CD-1 mice, or Beagle dogs by oral gavage once a day (rangingfrom 1 to 15 days depending on the study), with doses rangingfrom 0.5 to 600 mg/kg body weight, as part of routine toxicologystudies. Animals were sacrificed at 24 h after the last dose, andpooled venous plasma and tissues were collected and frozen at−80◦C prior to drug level analyses. Drug plasma and tissueconcentrations were determined by Liquid Chromatography-tandem Mass Spectrometry (LC–MS/MS). For tissue analy-sis, samples were homogenized in water or phosphate-bufferedsaline prior to protein precipitation with acetonitrile, followedby LC–MS/MS analysis. The tissues analysed for drug con-centration were heart, kidney, liver, lung, muscle, BM (bonemarrow; femoral), and plasma. Because of the nature of thetoxicology studies, 24 h postdosing time points at the terminalphase were available for each drug, with the exception of threedrugs (Gen 10, 14, and 15) that were given only as single doses,and for which 4 h postdosing time points were available as theelimination phase was likely to be reached. The measured Kp

value for each one of the drug was obtained by dividing thedrug concentration measured in tissue by the drug concentra-tion measured in pooled venous plasma. Up to four animals pertime point were used (i.e., for each time point, a maximum offour Kp values were available). The analyses were done fromthe mean Kp values. The latter was deemed necessary as we ob-served some variability across animal Kp values. The low andhigh dose ranges were defined separately as it was observed formost drugs that their Kp values significantly changed at dosesover 100 mg/kg, approximately, compared with lower doses.

PK Parameters Used to Define “General Rules” for QualitativelyEvaluating Potential Tissue Drug Accumulation

In drug discovery, it is of interest to predict the potential tissueaccumulation for a particular drug when comparing drugs withsimilar Vd values under non-steady-state conditions. Therefore,the additional information on CL could be of relevance. For thepurposes of defining “General Rules”, for the semiquantitativeevaluation of potential tissue drug accumulation from readilyavailable PK parameters, the in vivo Kp values from various

Poulin et al., JOURNAL OF PHARMACEUTICAL SCIENCES 102:3816–3829, 2013 DOI 10.1002/jps.23670


Figure 3. (a) Correlation equations of Method 1 used for quantitatively predicting Kp values based on Eqs. 1 and 2 as explained in the Methodssection. The second equation for BM and liver (indicated by *) was obtained in this study as explained in the Methods section. Adrenals valuesrepresent the average between medulla and cortex. An equation for brain was not available for strong bases in Richter et al.7; alternatively, itwas obtained from Bjorkman.6 An equation for gut was not available; therefore, the equation from another splanchic organ (spleen) was usedinstead. Correlation equations for strong and weak bases (or neutrals) were considered separately, however, the equations used for weak basesalso apply to acids based on Richter et al.7 nd, not determined. (b) Correlation equations of Method 2 used for quantitatively predicting Kp valuesbased on Eq. 3 from Edginton and Yun,11 as explained in the Methods section.

tissues were classified according to the magnitude (i.e., low,medium, or high) of Vd and CL values observed in rats for thecurrent dataset of drugs as illustrated in Figure 2. This way,we verified whether the measured values of Vd and CL couldindicate the degree to which a drug accumulated in tissues.Drugs tested at 100 mg/kg or at a lower dose were used for thisexercise (Table 2).

Development of a Computation Method for QuantitativelyPredicting Kp

The “correlation model of distribution” was chosen as a valuableprediction method as introduced previously, and, hence, it waschallenged for more quantitative prediction of Kp values in tox-

icology studies based on the corresponding input Vd values ob-tained in vivo (Fig. 3). The correlation equations were built fromdata obtained in rat only, and, hence, they were used in thisstudy to enable prediction of Kp value in that species for sev-eral tissues. These equations were derived for diverse classesof compounds, but strongly basic drugs and weakly basic drugswere analyzed separately.6–8,11 The equations obtained for liverKp should already include some CL effect, in general, becausethe regression analyses were previously derived with in vivoKp data obtained for diverse drugs7,11; therefore, we have de-cided to not include any additional CL effect in predicting theliver Kp value in rats for a first look. In the present study, twospecific sets of correlation equations were evaluated based on



Table 1. Test Set of Genentech Compounds

Data Analysis Investigated

Compounds Class Clog P CpKa Vda CLa fup Prediction of Kp

in Rat; LowDose Range

Prediction of Kpin Rat; HighDose Range

InterspeciesScaling of Kp

Low-to-high DoseExtrapolation of

Kp

CaseStudy

Gen 1 N 5.3 – 2.1 40 0.005 XGen 2 N 2.5 – 2.9 19 nd X XGen 3 N 2.7 – 3.8 22 0.555 XGen 4 WB 0.96 5 2.7 39 0.331 X XGen 5 WB 0.89 5.1 3.7 30 0.079 XGen 6 WB 2.1 4.2 0.93 5.2 0.044 XGen 7 N 0.45 – 2.6 28 0.382 XGen 8 N 1.8 – 1.5 11 0.329 XGen 9 WB 1.7 5.3 4.9 126 0.319 X X XGen 10 N 3.9 – 0.26 2.2 0.021 XGen 11 WB 2.3 4.8 3.9 28 0.147 X X XGen 12 WB 1.7 4.2 0.85 5.3 0.019 XGen 13 SB 4.1 8.5 12 19 0.047 X XGen 14 SB 9 7.6 0.12 1.7 nd XGen 15 SB 9 7.6 1 2.8 0.0001 XGen 16 SB 3.9 7.1 6.1 64 0.109 XGen 17 WB 1.1 6.6 3.2 16 0.183 X XGen 18 SB 2.4 9.4 2.8 40 0.132 XGen 19 SB 2.4 7.6 4.24 36 0.07 X X XGen 20 WB 2.6 6.4 3.14 20 0.121 X X XGen 21 N 2.2 – 0.18 0.45 0.004 XGen 22 N 2.6 – 0.3 2.5 0.001 XGen 23 N 1.1 – 2.39 60 0.621 XGen 24 N 1.5 – 2.8 104 0.718 XGen 25 SB 2.3 7.9 12.4 36 0.046 X XGen 26 SB 3 7.9 5.06 32 0.077 X X XGen 27 WB 0.3 4.7 2.09 26.5 0.342 XGen 28b SB 4.3 7.45 3.6 16 0.012 XGen 29b WB 5.2 5.93 0.99 35 0.001 X

aVd in L/kg and CL in mL/(min kg) in rats. For compounds #28 and #29, data are presented for mice.bCompounds tested as case studies.N, neutrals; WB, weaker bases (pKa ≤ 6.6); SB, stronger bases (pKa > 6.6); Clog P, calculated log n-octanol–buffer ratio, CpKa, calculated ionization constant;

nd, not determined.

the recent literature; those from Richter et al.7 (Method 1; Fig.3a) and Edginton and Yun11 (Method 2; Fig. 3b). These two setsof equations were compared because they are not based on thesame correlation principle as described just below.

Method 1

We used the correlation equations of Richter et al.7 (Fig. 3a)because these equations were built on Kp data for several rattissues obtained under experimental conditions similar to thepresent study (i.e., oral gavage and intraperitoneal administra-tion and non-steady-state conditions). A simple linear regres-sion analysis was used to describe each correlation equationEq. 1:

Kptissue = m(Kpmuscle ) + b (1)

where: b = y-intercept; m = slope.The value for slope and intercept for each tissue is provided

in Figure 3a. However, as a proof of concept of these publishedcorrelation equations, a comparative assessment between thisstudy and Richter et al.7 was also performed. Therefore, thevalue of slope and intercept of the established linear regressionequations from Richter et al.7 for correlation between muscle

and liver as well as between muscle and BM were comparedwith our values obtained in this present study (Fig. 3a); for thisexercise, we were able to collect Kp data for muscle, liver, andBM for seven compounds. Overall, the established correlationequations from Richter et al.7 were used to enable the predictionof Kp value in various rat tissues on the basis of muscle Kp value,from which the latter is estimated below.

Estimation of the Input Muscle Kp Value

The muscle Kp value used as input in the correlation equationsof Richter et al.7 was predicted from readily available Vd esti-mates for each drug according to Jansson et al.8 (Fig. 3a). Thus,the Method 1 combines the correlation equations of Richteret al.7 and the approach of Jansson et al.8 for the estimationof muscle Kp value. According to Jansson et al.,8 it is well es-tablished that Vd is determined by the Kp values of nonadiposeand adipose tissues (Eq. 2:

Vd = Vp + Ve REP +∑

Vt Kp (2)

where V is the fractional tissue volume (L/kg) of tissues (t), ery-throcytes (e), and plasma (p), whereas REP is the erythrocyte–plasma ratio (assumed unity for the current drugs).



Table 2. Rat Dataset of Compounds for the Low and High Dose Ranges

Rat Data

Average of Observed Values

Drugs Vda CLa Route Dayb

TimePostdose (h) Dosea Liver Kp Lung Kp BM Kp Spleen Kp Muscle Kp Kidney Kp Heart Kp

Low Dose Range (<100 mg/kg)Gen 1 2.1 40 PO 4 24 20 20 5.7 3.4

40 18 3.7 2.9Gen 2 2.9 19 PO 4 24 75 6.6 1.8Gen 3 3.8 22 PO 4 24 6 4.0 1.8

15 2.4 1.2Gen 4 2.7 39 PO 8 24 50 25 5.1 7.8Gen 5 3.7 30 PO 8 24 20 14 2.5 1.5Gen 6 0.93 5.2 PO 8 24 10 2.1 1.0 0.37

30 2.8 0.94 0.34Gen 7 2.6 28 PO 7 24 10 22 2.3 1.1

30 14 2.1 1.0Gen 8 1.5 11 PO 8 24 1 5.8 0.62

3 4.2 0.58 0.48Gen 9 4.9 126 PO 7 24 50 15 1.3Gen 10 0.26 2.2 PO 1 24 20 7.6 2.3

60 4.1 1.0Gen 11 3.9 28 PO 4 24 10 8.0 1.5 1.4 3.2 2.2Gen 12 0.85 5.3 PO 8 24 20 4.7 1.4 1.4

50 4.3 1.2 1.3Gen 13 12 19 PO 8 24 10 20 37Gen 14 0.12 1.7 PO 1 4 30 3.7 0.58Gen 15 1 2.8 PO 1 4 50 8.9 2.4Gen 16 6.1 64 PO 6 24 50 34 10Gen 17 3.2 16 PO 7 24 10 10 1.8 1.2

30 6.9 2.0 1.1Gen 18 2.8 40 PO 7 24 6 3.2 2.1

20 2.9 2.6Gen 19 4.24 36 PO 8 24 10 20 16 2.9

30 16 12 2.7Gen 20 3.14 20 PO 14 24 75 19

High Dose Range (>100 mg/kg)Gen 2 2.9 19 PO 4 24 150 6.3 1.73Gen 4 2.7 39 PO 8 24 100 1.5 0.62 0.85Gen 9 4.9 126 PO 7 24 150 8.7 0.81Gen 11 3.9 28 PO 3 24 100 7.8 1.3 1.2

4 24 100 7.8 0.68 0.79Gen 13 12 19 PO 3 24 100 192 162Gen 17 6.1 64 PO 6 24 150 19 5.0

300 5.6Gen 19 4.24 36 PO 8 24 100 35 30 5.6Gen 20 3.14 20 PO 14 24 200 63Gen 21 0.18 0.45 PO 7 24 600 0.25 0.18Gen 22 0.3 2.5 PO 14 24 100 0.96

300 1.7600 1

Gen 23 2.39 60 PO 8 24 100 1.9500 1.7

Gen 24 2.8 104 PO 7 24 150 0.88Gen 25 12.4 36 PO 8 24 100 80 9.4 3.2

250 96 18 1.8500 108 22 8.0

Gen 26 5.06 32 PO 8 24 100 301 74 18300 204 75 8.3

aVd (L/kg), CL [mL/(min kg)], and dose (mg/kg).bNumber of days of exposure (one oral dose per day).nd, not determined; PO, per os.



Table 3. Rat Dataset of Compounds Used for the Low-to-High Dose Extrapolations

Maximal Deviation Between High and Low Dosesa for in vivo Kp and fup Values in Rats

Kp Liver Kp BM Kp Muscle fup PlasmaRoute Day Time

Postdose (h)Dose (L; low)

(H; high)Maximal Deviationb Maximal Deviationb Maximal Deviationb Maximal Deviationc

Gen 9 PO 7 24(L) 50 12 11 1

(H) 300 (L/H) (L/H)Gen 11 PO 4 24

(L) 10 1.5 1.4 1.3(H) 100 (L/H) (L/H)

Gen 19 PO 8 24(L) 10 1.8 1.9 1.8 1.6

(H) 100 (H/L) (H/L) (H/L)Gen 25 PO 8 24

(L) 100 2.3 2.5 1.4 1.8(H) 500 (H/L) (H/L) (H/L)

Gen 26 PO 8 24(L) 50 3.1 2.8 2.4 1.6

(H) 300 (H/L) (H/L) (H/L)

aExtrapolation across doses was made by using Eq. 4 from observed Kp data obtained from Table 2, whereas fup values were obtained in vitro at low and highdoses as mentioned in the Methods.

bMaximal deviation observed for rat Kp between the high and low doses as detailed in the Methods.cMaximal deviation observed for rat fup between the high and low doses as detailed in the Methods.PO, per os.

Table 4. Rat–Dog Dataset of Compounds Used for the Interspecies Scaling Exercise

Rat Data Scaling Factors Used in Eq. 5b Dog Data

Protein Binding Lipid Binding Clearance

Drugs ClassInput Vd

(L/kg)Rat KpValuesa

TissuesScaled

Scaling Factor 1;Ratio for fup

(fup,dog/fup,rat)c

Scaling Factor 2;Ratio for fut

(fut,rat/fut,dog)d

Scaling Factor 3;Ratio for Eh (1 −Ehdog/1 − Ehrat)e Predicted Kp

b Observed Kpf

Gen 20 WB 3.14 12.5 Liver 1.87 0.47 1.06 11.6 8.8Gen 26 SB 5.06 86 Liver 1.32 0.51 0.76 44 30Gen 27 WB 2.09 9.8 Liver 1.18 0.47 0.78 4.24 5.74

2.14 Lung 0.31 0.78 11.78 BM 0.73 1.53 1.241.75 Muscle 0.54 1.12 0.69

aPredicted in rats by using Vd in the correlation Method 1. For liver only, the observed Kp values were used for compound #26, as explained in the Methods.bThe scaling to dog consists of the product of the predicted Kp in rat and the scaling factors based on Eq. 5, as explained in the Methods.cData on fup in each species were obtained experimentally by using a dialysis equilibrium method.dData were estimated either from the ratio between dog and rat tissues of the total neutral lipids content for the weaker bases (#20 and #27) or the total acidic

phospholipids content for the stronger base (#26), as detailed in the Methods.eUsed for scaling liver Kp value only as explained in the Methods. Ehrat equals 0.31, 0.49, and 0.42 for compound #20, #26, and #27, respectively, whereas Ehdog

equals 0.27, 0.61, and 0.55 for these three compounds, respectively.fThe observed Kp values in dogs were determined 24 h postdosing at the end of the exposition as stated in the Methods. Dogs were exposed to drugs during

7 days at one oral dose per day; 15, 10, and 0.5 mg/kg for compounds #20, #26, and 27, respectively.WB; weaker bases (pKa ≤ 6.6), SB; stronger bases (pKa > 6.6).

The Jansson’s method consists of varying the muscle partition-ing value in Eq. 2 (and consequently the Kp value of all othertissues are calculated from the correlation equations of Richteret al.7) until the predicted Vd by using the Eq. 2 matches theobserved in vivo value (Fig. 3a). For the purpose of this study,the solver iterates until the predicted Vd is within 0.1% of thatobserved value. Data on tissue volumes for rats used in Eq. 2are presented in Table 7.

Method 2

The correlation-based prediction of Kp values was combined toimportant drug-specific parameters to develop a tissue-specificKp prediction algorithm based on measured Vd, lipophilicity

(log P), the degree of ionization, and/or fraction unbound inplasma (fup). Both Jansson et al.8 and Edginton and Yun11 pre-sented correlation equations, which include these readily avail-able drug-specific parameters. However, the correlation equa-tions from Edginton and Yun11 were more accurate as evaluatedin a recent comparative analysis11; therefore, these equationswere preferred in this study (Fig. 3b). These authors derivedtheir equations from Kp data obtained under steady-state con-ditions after intravenous administrations only; therefore, theseexperimental conditions are different from those investigatedin this present study. Because it has been reported that theseequations performed relatively well,11 they were also evalu-ated in this study assuming that the equations not vary sig-nificantly with the different experimental conditions. Thus, the



readily available drug-specific parameters were incorporatedin a stepwise multiple linear regression analysis to account forintertissue variation with the resulting structure11:

log Kp = A0 + A1B1 + A2B2 + A3B3 + A4B4 (3)

where A0, A1, A2, A3, and A4 are coefficients for each tissueand B1, B2, B3, and B4 are log Vd, log P, fup, and fraction ion-ized in tissue (fi), respectively. The values of these parametersare presented in Figure 3b. The fi was calculated by using thepKa of each drug and the intracellular pH of each tissue as in-put in Henderson–Hasselbalch equations as demonstrated byEdginton and Yun.11

Overall, the values of Kp predicted by the two methods werecompared with the observed in vivo Kp values for each drug. Thepredictions of Kp were made initially in rats for the lower doses(≤100 mg/kg) assuming linear PK. Additionally, the predictionsof Kp in rats were also extended to the higher doses (≥100mg/kg). The corresponding test sets of drugs are presented inTable 2.

Low-to-High Dose Extrapolations of Tissue Exposures

The input Vd used in the proposed algorithm was measured atlow doses only as part of our routine PK studies. Therefore, ifthe above correlation models are used, we expect lower predic-tive performances of the extent of tissue drug accumulation athigh doses compared with low doses because saturation pro-cesses may occur more frequently in plasma and/or tissues athigh doses. It needs to be a priori verified whether a given com-pound is likely to have predictions of Kp values influenced by thehigh doses typically used in toxicology studies. As no generalrule has been adopted in this area for the correlation model, toovercome this difficulty, we propose a simple approach to pre-dict by which factor (i.e., maximum fold error of deviation) thein vivo Kp values would change in a low-to-high dose extrapo-lation study.

By definition the Kp corresponds to the ratio between thefraction unbound in plasma to that in tissue (i.e., Kp =fup/fut).3,12,19 It is generally assumed that only the free drugconcentration in plasma is available for drug tissue distribu-tion and elimination. Therefore, one would expect that a dose-dependent change in fup would also be seen in fut, which willresult in changes in Kp or total Vd with dose. Furthermore,fup is typically a more readily available parameter comparedwith fut. Consequently, if fup increases with doses, as expected,because of the saturation of binding to plasma proteins, thevalues of Kp (= fup/fut) of any compound, and of the overall Vd,would also increase proportionally assuming linear PK whenno relevant transporter effect occurs in vivo. The same is truefor the impact of plasma CL on the decay rate of the plasmaconcentration–time profiles, particularly for low-to-medium CLcompounds for which the elimination is not limited by tissueblood flow rate. Therefore, our assumption was that the maxi-mal deviation of the observed Kp values between the high andlow doses tested in toxicology studies could be guessed from themaximal deviation of the fup values determined in vitro at thesame low and high doses Eq. 4:

∣∣∣∣Kphighdose

Kplowdose

∣∣∣∣ =∣∣∣∣fuphighdose

fuplowdose

∣∣∣∣ (4)

The full drug dataset for this exercise is presented inTable 3. Five compounds (#9, #11, #19, #25, and #26) have therequired dataset (i.e., in vivo Kp and in vitro fup) at the low andhigh doses. The substrate concentration used in the in vitro ex-periments to estimate fup varied from 5 to 50 :M, which coversthe low and high plasma drug concentration observed in vivo inrats for these drugs. The value of fup was determined by usinga previously described equilibrium dialysis method.19

In the presence of relevant transporter effects in one or sev-eral tissues, the use of fup value in the above Eq. 4 would belimited.20–22 Alternatively, the fraction of unbound drug in tis-sue cells determined in vitro (fucells; i.e., relative to drug concen-tration in the intracellular water) could potentially be used.20

To demonstrate the potential limitation of Eq. 4, the low-to-high extrapolation of liver Kp value was assessed with a drugwith different properties; therefore, compound #9 shows un-expectedly high in vivo CL [i.e., 126 mL/(min kg)] in the lowdoses range, which may indicate the effect of additional trans-porter and/or extrahepatic effect, and, hence, the low-to-highdose extrapolation of liver Kp value would be inaccurate basedon fup values. For the purpose of this study, compound #9 wasassessed with Eq. 4 from the readily available fup values.

Interspecies Scaling of Kp Values

The algorithm and correlation models described above providedKp estimates in the rat only, and therefore, they cannot be usedfor scaling to dog in their current form. Alternatively, a simpleapproach was proposed to scale predicted Kp values from rat todog, also from readily available parameters. It is well knownthat binding to plasma proteins may vary across species. How-ever, a few studies have indicated that protein binding in tis-sues could be relatively similar across species23,24; conversely,other studies showed interspecies differences in the tissue lipidcontent, and, therefore, in the nonspecific binding to lipids.14–17

For the purpose of this study, we looked at the differences inbinding to plasma proteins and tissue lipids for noneliminatingorgan, and, in addition, the CL effect for eliminating organ. Theother processes potentially occurring in specific tissues were as-sumed to be common across species.

Noneliminating Organ

The scaling of Kp values from rat to dog assumes species differ-ences in both the fraction unbound in plasma (i.e., fup) (scalingfactor 1; SF1) and tissue (i.e., fut) (scaling factor 2; SF2) accord-ing to the following series of conventional equations Eq. 5 (Refs.17,23):

Kpdog = Kprat SF1 SF2 (5)

Kpdog = Kprat

[fupdog

fuprat

futrat

futdog

](6)

Kprat = fuprat

futrat

(7)

To apply the above equation, the Kp value in rat was pre-dicted with the correlation model 1 based on in vivo Vd valueof each drug studied in this exercise. In addition, the valueof fup in each species was experimentally determined in vitro,whereas fut was estimated as following. In estimating fut, it was



assumed that nonspecific binding to lipids was the main deter-minant of drug distribution into tissues.15–17 For small moleculedrugs, tissue distribution is typically driven by the binding tolipids and/or plasma proteins, whereas pharmacological targetbinding is generally of minor relevance given the typical lowlevel of target expression relative to drug concentration. In gen-eral, the passive uptake of lipophilic strong bases into tissues isgoverned by binding preferentially to the acidic phospholipids,whereas for lipophilic weak bases, binding to neutral lipids isthe major determinant of their uptake.15–17 Therefore, the ratioof fut between rat and dog was estimated either from the ra-tio between dog and rat tissues of the neutral lipids content forthe two weaker bases or the acidic phospholipids content for thestronger base. In this context, we also assumed that the bind-ing affinity constant to each class of lipids, which are present inboth the rat and dog tissues, is similar in each species. In gen-eral, the approach assumes that the greater the lipid content ina tissue, the lower the fut will be. The lipid content in adult ratand dog tissues was obtained from the literature.17,25,26 Lung,liver, muscle, and BM were considered for this exercise. Theratios of total neutral lipids content between dog and rat tis-sues are approximately 0.31 (lung), 0.54 (muscle), 0.47 (liver),and 0.73 (BM). For BM, the lipid content on a dry weight basiswas available and used for each species. For liver tissue, theratio between rat and dog of total acidic phospholipids contentis 0.51, which was used for the stronger basic drugs.

Eliminating Organ

The liver Kp value predicted in rat does not include any CLeffect for dog compared with rat, and hence, interspecies differ-ences in total CL should also be accounted for in the interspeciesscaling of liver Kp value. The CL effect can be taken into ac-count as CL in each species is a parameter readily availableas said. Therefore, species differences in the hepatic extractionratio (Eh), and therefore, in fraction of drug noncleared in liverwas estimated by adding a third scaling factor [SF3 = (1 −Ehdog)/(1 − Ehrat)] in the above Eq. 5 for liver Kp [where Eh wasestimated by the reported in vivo blood CL value divided by theliver blood flow rate; 31 mL/(min kg) in dog and 65 mL/(min kg)in rat].22,27,28

For only one drug tested in the interspecies scaling exercise(i.e., compound #26), the prediction of liver Kp value in the lowdose ranges failed because the observed in vivo value is muchsuperior (18 vs. 86); therefore, the in vivo value was preferredinstead of the value predicted with the correlation model 1.The reason is that this compound shows significant nonlinear-ities in liver Kp values between the low and high dose ranges(Table 2). The full dataset for interspecies scaling is presentedin Table 4. Two weaker basic compounds (#20 and #27) and onestronger basic compound (#26) provided a complete dataset forthis exercise for the low doses range. The Kp values predictedin dogs by using Eq. 5 were compared with the correspondingobserved values. Dogs were dosed once daily for 7 days at 15,10, and 0.5 mg/kg for compounds #20, #26, and 27, respectively.

Implementation of the Algorithm Equations

All calculations, including Kp predictions, low-to-high dose ex-trapolations, and interspecies scaling, were conducted using anExcel spreadsheet (Microsoft R© Office Excel R© 2010, MicrosoftCorporation, Redmond, Washington) to facilitate an automa-tion and batch processing.

Evaluation of Predictive Performance

The prediction accuracy was assessed by comparing predictedversus observed values of Kp using several statistical parame-ters. The statistical evaluation previously described by Poulinand Theil4 was used in the present study. Therefore, the follow-ing statistical parameters were calculated and are presentedfor each prediction method studied: average fold error (AFE),absolute average fold error, root-mean-squared error, and corre-lation coefficient (r). Furthermore, the concordance correlationcoefficient is presented, which evaluates the global degree towhich pairs of predicted and observed data fall on the line ofunity passing through the origin. Specific fold errors of devia-tion between the predicted and observed values (percent folderror ≤2, ≤2.5, ≤3, ≤4, and ≤10) were also calculated.

Case Study

The overall algorithm to determine semiquantitative and quan-titative estimates of Kp values (Fig. 1) was further tested in acase study to retrospectively predict liver and BM distributionof two small molecule MET kinase inhibitors (#28 and #29), forwhich structural changes resulted in lower tissue distribution,decreased toxicity, and improved safety margins.1 The aim wasto verify whether Gen #28 had greater tissue distribution inBM and liver compared with Gen #29, as it was expected basedon tissue drug measurements. A lead compound (#28) had in-termediate (medium), Vd (3.6 L/kg), and low CL [16 mL/(minkg)] in mice, which resulted in relatively high levels of drugin BM and liver, and toxicity in these tissues. In contrast, astructurally related backup compound (Gen #29) had a lowerVd (0.99 L/kg) and higher CL [36 mL/(min kg)], which resultedin lower compound distribution to the BM and liver, and littleor no toxicity compared with the parent compound.

First, the magnitude of tissue distribution of each drug waspredicted based on their values of Vd and CL according toFigure 2 (i.e., low, medium, or high distribution). Second, theKp values in the target organs for toxicity (BM and liver) werepredicted using the correlation models based on the Vd of eachdrug (Fig. 3). The predicted Kp values for the target tissueswere compared with the corresponding Kp values observed invivo in mouse for each drug. As the observed Kp values forthese two compounds were not meaningfully affected by thedose range used of 100–600 mg/mg (for #28, one daily dose wasgiven for 8 days, whereas for #29, one daily dose was given for14 days), the average in vivo Kp values for each tissue were usedfor comparison with the predicted values in this exercise. Be-cause mouse data were used in the case study, it was assumedthat the proposed correlation model (equations) developed forpredicting Kp values in rat could also be applied to anotherrodent species (i.e., mouse) but by using the Vd observed inmouse as the sole input parameter; however, the physiologicaltissue volumes used in Eq. 2 were changed from rat to mouse(Table 7).

RESULTS

Qualitative General Rules for Evaluating Potential Tissue DrugDistribution

Table 5 shows that in vivo tissue Kp values for the current drugsincrease with increasing in vivo Vd and decrease with increas-ing impact of in vivo plasma CL; therefore, both parameters



Table 5. General Rules for Qualitatively Evaluating Potential Tissue Drug Accumulation Based on ReadilyAvailable PK Parameters for Non-Steady-State In Vivo Conditions as Illustrated in Figure 2

Rat Data

Magnitude of PK Parametersa

Scenarios Observed Vd Observed CL Expected Tissue Kp Observed Tissue Kpb

1 Low High Low Avg = 0.87Med = 0.24(n = 18)

2 Low Low Low–medium Avg = 1.2Med = 1.0(n = 85)

3 Medium High Low–medium Avg = 1.2Med = 1.0(n = 52)

4 Medium Medium Medium Avg = 10.1Med = 1.6(n = 244)

5 High High Medium Avg = 5.2Med = 4.1(n = 31)

6 High Low to medium High Avg = 101Med = 62(n = 23)

aCL observed in rat: low: ≤10% LBF; medium: 10% to 75% LBF; high: >75% LBF (LBF; liver blood flow rate) [CL in mL/(min kg)].Vd: low: ≤1 L/kg; medium: 1–5 L/kg; high: >5 L/kg.

bKp values of lungs, BM, and/or muscle were considered for the current drugs. For the purpose of this study, liver was excludedfor this exercise because of the potential interplay between distribution and metabolism. Kp values measured for the low dose range(≤100 mg/kg) were used for this exercise (Table 2).

Avg, average; Med, median.

must be considered together. For example, drugs with low Vd

and high CL showed low tissue distribution, and low Kp values,whereas drugs with high Vd and intermediate CL showed highKp values on average, which supports our hypothesis.

Comparative Assessment with Richter et al.7 for the CorrelationEquations

A high degree of correlation was obtained in this study betweenthe in vivo Kp values of muscle and liver and between muscleand BM (r2 is 0.83 and 0.78, respectively). Furthermore, for theliver, the obtained slope and intercept are very similar to thosefound in the previous work of Richter et al.7 (slope: 3.23 vs.3.37; intercept: 0.61 vs. 0.78). For BM, only the slope is similarbetween the two studies (slope: 0.98 vs. 0.57; intercept: 0.06 vs.0.92) (Fig. 3). These observations support the principle of cor-relation between tissues, and justify the use of the correlationequations of Richter et al.7 in the present study.

Quantitative Prediction of Kp Values

Two correlation methods were used to calculate Kp values inrats for the current drug dataset (Fig. 3), and some examples oflow-to-high dose extrapolations and interspesies scaling werealso investigated. The overall statistical summary in terms ofaccuracy, precision, and correlation is listed in Table 6. Thesubset performances are described below.

Low Dose Range for Rat

The correlation Method 1 showed comparable or superior pre-dictivity compared with the correlation Method 2 (Table 6);therefore, only the results of the correlation Method 1 werefully investigated. For all rat tissues studied (heart, kidney,

liver, lung, muscle, spleen, and BM), the maximum success ratein predicting the observed Kp values was 63%, 82%, and 87%of the compounds with predictions falling within 2.0-fold, 2.5-fold, and threefold error, respectively. In particular, for the tar-get organ BM, the prediction of partition coefficients showed asimilar success rate compared with other tissues. For the othertarget organ, the liver, the accuracy is superior especially forthe twofold error range. Few Kp values were incorrectly esti-mated by a factor of fourfold error or greater, as the predictionsfalling within a 4.0-fold error ranged from 94% to 100% acrossthe prediction scenarios and methods. In addition, the globalcoefficient of correlation was relatively close to unity (rangingfrom 0.71 to 0.79), but was lower for liver (ranging from 0.44 to0.53). At the lower dose ranges, a slight overprediction of the ratin vivo Kp values was observed for the Method 1 (AFE valuesranging from 1.13 to 1.25), whereas the Method 2 underesti-mated the Kp values (AFE values ranging from 0.58 to 0.80).Therefore, a robust degree of prediction accuracy was obtainedin this study for the low doses particularly for the correlationMethod 1.

High Doses Range for Rat

The prediction performance was generally inferior for thehigher doses (Table 6), which is expected considering thegreater potential for saturation processes at high doses. Forthe prediction Method 1, the higher doses produced predictedKp values with accuracy of 30% within 2.0-fold, 40% within2.5-fold, and 60% within threefold error compared with the val-ues observed in rat. In addition, it was demonstrated that thepredictive performance is significantly better for the high CLcompounds compared with low CL compounds for all statistical



Table 6. Statistical Analyses Relative to the Prediction of Kp Values in Rat Tissues for the Current Drug Dataset as Illustrated in Figure 3

Prediction of Kp Values

Tissues % ≤ 2.0-fold % ≤ 2.5-fold % ≤ 3-fold % ≤ 4-fold % ≤ 10-fold AFE AAFE RMSE r CCC

Low Dose Rangea

All Rat Tissuesb

Method 1 (n = 78) 63 82 87 97 100 1.25 1.86 0.32 0.73 0.79Method 2 (n = 73) 60 78 84 86 96 0.80 2.04 0.40 0.66 0.64Rat BMMethod 1 (n = 22) 59 82 86 96 100 1.13 1.93 0.33 0.74 0.71Method 2 (n = 20) 55 70 80 80 85 0.58 2.38 0.54 0.03 0.01Rat LiverMethod 1 (n = 20) 80 90 90 95 100 1.19 1.71 0.29 0.52 0.53Method 2 (n = 18) 56 67 72 94 100 0.67 2.06 0.36 0.49 0.44High Dose Rangea

All Rat Tissuesb

Method 1 (n = 45) 30 40 60 69 93 1.18 3.03 0.56 0.60 0.65Intermediate CL Drugsc

Method 1 (n = 37) 24 32 57 62 92 1.08 3.38 0.60 0.60 0.64High CL Drugsc

Method 1 (n = 8) 50 75 75 100 100 1.81 1.81 0.33 0.91 0.71

aTest set of drugs is presented in Table 2. Methods 1 and 2 are presented in Figure 3 and explained in the Methods.bHeart, kidney, liver, lung, muscle, spleen, and BM (low dose range) and muscle, liver, lung, and BM (high dose range).cCL observed in rat. Intermediate (low to medium): 0%–75% LBF; high: >75% LBF (LBF; liver blood flow rate).AFE, average fold error; AAFE, absolute average fold error; RMSE, root-mean-square error; r, correlation coefficient; CCC, global concordance correlation

coefficient; n, indicates the number of predictions.

parameters except AFE values, probably because of the lowlikelihood of saturating clearance (Table 6).

Low-to-High Dose Extrapolations

The low-to-high dose extrapolation based on Eq. 4 was success-ful for four of the five compounds tested (#11, #19, #25, and#26) (Table 3). For Gen #9, however, the extrapolation was un-successful, with a maximum fold error of deviation of in vivoKp values of 11, whereas the maximum increase in fup wasonly twofold. Compound #9 is considered an outlier because itstissue disposition seems to be determined by transporter ef-fects compared with passive drug permeation, and therefore,changes in the fup values at low and high doses was not a goodindicator of low-to-high doses extrapolations of Kp values com-pared with the other drugs tested.

Interspecies Scaling from Rat to Dog

The interspecies scaling from rat to dog tissues by using Eq. 5for three compounds (#20, #26, and #27) produced predicted Kp

values within twofold error in all cases compared with observedvalues in dogs (Table 4).

Case Study

On the basis of the semiquantitative estimate algorithm pro-posed in this study (Fig. 2), Gen #28 [Vd: 3.6 L/kg; CL: 16mL/(min kg)] would be predicted to have a higher potentialfor accumulation in tissues compared with Gen #29 [Vd: 0.99L/kg; CL: 36 mL/(min kg)]. This was further supported by thepredicted Kp values in BM and liver for Gen #28 compared withGen #29 based on quantitative estimates from the two correla-tion methods used in this study (Fig. 3). For the BM, correlationMethod 1 predicted Kp values of 5.7 and 0.65 for Gen #28 andGen #29, respectively, whereas correlation Method 2 predictedKp values of 0.77 and 0.56, respectively. Therefore, each cor-relation method predicted higher drug accumulation in BM for

Gen #28 compared with Gen #29, which was expected; however,the Method 1 provided more accurate estimates of the in vivovalues because the observed Kp values in BM were 3.4 for Gen#28 and 0.7 for Gen #29, respectively.

For the liver, correlation Method 1 predicted Kp values of 12.3and 6.1 for Gen #28 and Gen #29, respectively, whereas correla-tion Method 2 predicted Kp values of 9.3 and 5.45, respectively.Again, each correlation method predicted higher drug accumu-lation in liver for Gen #28 compared with Gen #29; however,the Method 1 provided slightly more accurate estimates of thein vivo values because the observed Kp values in liver were 13.5for Gen #28 and 8.7 for Gen #29, respectively.

DISCUSSION

At early stage of drug discovery, readily available PK param-eters such as in vivo Vd and CL values can be useful to serveas the basis for reasonable predictions for tissue drug distribu-tion in toxicology studies that are conducted with longer dosingduration and higher dose levels compared with the PK studies.The main focus of this study was to provide an algorithm topredict tissue drug distribution that can be applied to drug ex-posures achieved in toxicology studies, by combining semiquan-titative and quantitative estimates of Kp values from readilyavailable PK parameters (Fig. 1). Notably, this study adds tothe existing body of knowledge by (1) offering a first attemptto explore the correlation models for prediction of Kp valuesin toxicology studies, (2) suggesting ways for refinement of thegeneric correlation model for interspecies scaling and low-to-high dose extrapolations of Kp, and (3) giving general rulesfor evaluating potential tissue drug distribution in toxicologystudies from readily available PK parameters. Therefore, thismethodology bears the potential to predict drug tissue parti-tioning in toxicological studies without performing tissue drugmeasurements in vivo. The present findings may have some



Table 7. Volumes of Tissues in Rat and Mouse Used in theCorrelation Model

Volumes (% of BW)a

Tissues Rat Mouse

Plasma 0.0407 0.030Adipose 0.04172 0.07Adrenals 0.00019 0.00048Bone marrow 0.06588 0.112Brain 0.0052 0.0165Gut + GITb 0.027 0.0422Heart 0.00432 0.005Kidneys 0.0073 0.0167Liver 0.037 0.0549Lungs 0.005 0.0073Muscle 0.54 0.40Pancreas 0.00376 0.0030Skin 0.17476 0.1653Spleen 0.002 0.0035Testes 0.00048 0.0076Thymus 0.00292 0.0018Thyroid 0.00005 0.00005Blood cells 0.0333 0.025

aData adapted from Brown et al.27 and Davies and Morris.28

bThe GIT was subdivided as follows: stomach and small as well as largeintestines.

important implications for the drug distribution studies and thetoxicology studies using the oral route of administration undernon-steady-state conditions. We have predicted tissue distribu-tion of drugs at the whole organ level assuming that total tissuedose is related to toxicity. However, we agree that the regionaldistribution within an organ could be different between twodrugs that have similar Vd values (e.g., a drug may distributemainly in lipids and another drug mainly in lysosomes). There-fore, the regional distribution will not be predictable when onlyrelying on Vd, without more specific correlation equations.

The proposed algorithm expands from the current correla-tion models used in the PK studies, as it can potentially beused for wide dose ranges that include high doses. The devel-opment of adapted prediction methods of tissue distribution fortoxicology studies, which use high doses of drug that can sat-urate protein binding, transport, and/or clearance processes,can potentially be useful in the interpretation and translationof toxicity findings and, in cases in which toxicity might berelated to tissue drug levels, in the potential improvement oftoxicity profiles for small molecules. To estimate drug tissuedistribution in toxicology studies, it becomes important to havean evaluation of the conditions under which good or poor pre-dictions of Kp might be expected (i.e., under what circumstancesthe algorithm might fail), how to handle the non-steady-statenature of the tissue distribution, the longer dosing duration,and the higher dose levels that are typical of toxicology studies.These aspects are discussed below.

Our data suggest that dose levels might have an impact onthe tissue exposures in toxicology studies. Moreover, the pre-diction accuracy was decreased with saturation at high doses;however, an equation to perform low-to-high dose extrapola-tions of Kp values is presented, and it was applied successfullyto four drugs (i.e., compounds #11, #19, #25, and #26), demon-strating the usefulness of the low-to-high dose extrapolationmethod based on in vitro fup values, and also allowing the iden-

tification of which drugs might be influenced by dose levels forthese predictions. Consequently, the present study represents afirst step toward the improvement of predictions of Kp values athigh doses by using the correlation models. However, for com-pound #9, a change of in vitro fup value with an increase in doseis not a good indicator of the low-to-high extrapolation effect onKp values in vivo (Table 3). For this compound, Kp values inliver and BM obtained at the lower dose (50 mg/kg) are approx-imately 11 times greater than at the higher dose (300 mg/kg),whereas fup did not significantly change from low to high doses(Table 3); therefore, the current assumption of a proportionalchange of Kp in vivo and fup in vitro from low to high doses as-suming linear PK is not correct for this compound. The currentobservation suggests that its Vd (Kp) may significantly decreaseat high doses leading to lower Kp values, and this effect is notcovered by fup. An explanation for this could be that compound#9 showed plasma CL in vivo, much greater than the liver bloodflow rate in rats [i.e., 126 mL/(min kg)] at low dose of 1 mg/kg,which may indicate the involvement of transporter and/or ex-trahepatic CL effect in addition to liver metabolism. It has beenshown that the Vd can increase more than 100-fold because ofthe contribution of transporter-mediated uptake,21 which sug-gests that the Vd in vivo might be mainly determined by theuptake CL. Consequently, if the uptake CL becomes saturatedat the higher oral dose evaluated in this toxicology study (e.g.,300 mg/kg in the case presented here), the Vd (and resultingKp) would be expected to decrease because of the decreased im-pact of CL. Because there is still some room for improvement, afull extrapolation method remains to be established in a morequantitative way; therefore, in vitro fup value in Eq. 4 could po-tentially be replaced by in vitro fucells value for better estimatesof substantial nonlinearities, but this has not been yet tested inthe absence of such data. Furthermore, the Vd and CL valuesthat are routinely measured in vivo at low doses in PK studiescould also be estimated at higher dose levels, and therefore, Kp

values at any dose could simply be derived by using Vd andCL values in the proposed algorithm. However, we agree thatadditional in vivo data need to be collected with this secondapproach.

For high CL compounds, the 8 is likely to be higher than Ka

after oral administrations; in which case the current assump-tion (i.e., 8< Ka) is not met (e.g., compound # 9). In other words,the terminal phase may be governed by the absorption rate (e.g.,first-pass effect; F) rather than by the disposition into tissuesfor such compound.13 Therefore, the algorithm depends on onemore assumption, which is to know the contribution of F com-pared with elimination. Similarly, one would expect flip-flop ki-netics at the higher doses where dose-limited absorption mightoccur potentially because of low solubility in the intestine. Theimplication is that the effect of F should also be considered insuch cases, and, therefore, Vd/F obtained from the oral admin-istration profiles should be used as the input parameter in theproposed algorithm instead of Vd for intravenous administra-tion to estimate Kp value particularly for high CL and/or lowsolubility compounds. The implication of Vd/F compared withVd was not investigated in this study because Vd/F data werenot reported; however, the current assumption (i.e., 8 < Ka) ap-pears to hold true in most cases in light of the current results,probably because most of the compounds have low-to-mediumCL and relatively rapid oral absorption. The observed Kp val-ues did not significantly differ over time (e.g., 2, 4, 8, and 24 h;maximum twofold error deviation) (not shown), which may also



explain why we obtained relatively accurate predictions of Kp

at 24 h postdosing in this study.Providing for drug availability to the target organ can be

optimized only if the relationship between drug distribution todifferent organs and drug dose and duration can be quantita-tively characterized. In this way, to deal with the non-steady-state nature of the tissue distribution, the effect of CL was alsoconsidered in the semiquantitative estimate of Kp values (Fig.2 and Table 5). This way, this semiquantitative approach wouldhelp in rapidly identifying the drug with the greatest potentialof tissue accumulation among drugs with similar Vd values.Furthermore, the predicted Kp values could also be scaled overtime by using traditional mono-exponential PK equations thatincorporate separately the effect of rate constants for elimina-tion (i.e., slope of the plasma concentration–time curve, decayrate) and oral absorption (or the F) to adjust the Kp values forthe dominating process.13

Some tissues showed better predictivity than others, and,therefore, complexities of specific tissues (e.g., impact of elimi-nation in liver or blood organ barrier in brain) create additionaluncertainties as to which compound properties will be most in-formative in predicting whether a compound might be toxicbecause of the high compound tissue levels (or the ability of acandidate drug to not achieve toxic concentrations). For liver Kp

value predictions at low doses, the accuracy is relatively highfor the current dataset (Table 6), which means that the correla-tion models generally covered the impact of elimination for thecurrent drugs. However, the compounds #3, #6, and #18 are out-liers because the observed in vivo Kp values were about threetimes lower than the predicted values for liver. Drugs showinghigh efflux ratios may demonstrate lower Kp values in vivo thanpredicted with the correlation models, and inversely, for highinflux ratios. Studies in Multidrug Resitance Madin-Darby Ca-nine Kidney (MDR1–MDCK) cells could potentially be usefulto confirm a relevant transporter effect.10 In such cases, thepredicted liver Kp values could be readjusted for any additionalrelevant CL effect; Kp would significantly decrease for effluxprocesses [i.e., Kp × (1 − Eh)], or significantly increase for influxprocesses [i.e., Kp/(1 − Eh)]. For brain Kp value predictions, thecorrelation models have not been tested with the current drugs;however, these models represent an interesting prediction ap-proach for this tissue. Alternatively, Lv et al.29 demonstratedthe value of an integrated PK-driven approach to identify po-tentially efficacious/toxic agents for brain tumor chemotherapyby the combined use of in silico, in vitro cytotoxicity, and in vitroabsorption, distribution, metabolism, and elimination profilingstudies. However, a limitation of this approach is the need foradditional brain tissue collection and labor-intensive bioana-lytical studies, particularly to estimate the essential bindingof drugs in brain tissue under in vitro conditions. Neverthe-less, we consider that a combination of this approach with thispresent study can provide a meaningful model for advancedcalculation of brain Kp values.

We also explored the interspecies differences in Kp values,which leads to the notion that scaling of Kp based on differencesin fup and fut, and in addition for liver, Eh, might be more accu-rate or scientifically justifiable as a way to scale distribution pa-rameters across species, which is a standard approach.14,17 Thisstrategy was successful in this study because relatively good es-timates of Kp values in dog were obtained for three structurallydiverse compounds (Table 4). Differences in fut across speciescould either be estimated from the corresponding differences in

the tissue lipid content as shown in this study,14–17 or experi-mentally determined in vitro by using tissue homogenates fromeach species.19,24,30,31 Furthermore, it could be assumed that thecorrelation equations depicted in Figure 3 are conserved acrossspecies, and therefore, predictions of Kp in any species can onlybe made by using the input Vd for the respective species.

The correlation Model 2 derived from Edginton and Yun11

underestimated the in vivo Kp values compared with the cor-relation model 1 based on the equations of Richter et al.7 (i.e.,lower AFE values were obtained) (Table 6). In other words, theequations of Edginton and Yun11 generally predicted lower Kp

values compared with those of Richter et al.,7 and the later pro-vided closer estimates of the current in vivo Kp values (Table 6).First, note that Edginton and Yun11 incorporated descriptors ofdrug properties in coming up with their Kp estimates; however,we have used calculated instead of measured properties (e.g.,Clog P and pKa), which could also be of statistical relevance.Second, the equations of Edginton and Yun11 were built forintravenous administration under steady-state conditions bycontrast to those of Richter et al.7 for the oral and intraperi-tonial routes of absorption under non-steady conditions, whichare conditions also covered in our toxicology studies. Accord-ingly, the similarity in the slope and intercept between thispresent study and Richter et al.7 for some correlation equa-tions confirms the validity of this model for the exposure condi-tions observed in our toxicology studies (Fig. 3a). Furthermore,it is well known that in vivo Kp values are relatively greaterunder non-steady-state conditions (i.e., pseudeo-equilibrium)compared with steady-state conditions7; therefore, this mightalso explain why the model of Richter et al.7 predicted higherKp values for non-steady-state conditions compared with theEdginton and Yun model for steady-state conditions.11 Whenexperimental condition, other than non-steady-state condition,are studied, the correlation model of Edginton and Yun11 andother models3,6,8,11 could potentially be used instead; therefore,the Vd for steady-state conditions should be used as input,in contrast to this study where the Vd of the terminal phase(Vz) is preferred as the input parameter for non-steady-stateconditions.12

Overall, the assessment of the algorithm was confined by theavailability of measured data in rodents and dogs for a set of29 structurally diverse compounds such as neutral, weak, andstrong basic drugs. We lack data on Kp predictions for smallmolecules with carboxylic acid functionalities; however, thecorrelation equations used for the neutrals and weaker basesshould also be applicable for the acids.7,8,11 The interspeciesscaling and low-to-high dose extrapolation of Kp values havenot been thoroughly evaluated for a wide range of drugs, andthe expansion of our current dataset could be useful. A largerdataset would also be helpful in confirming the generalizabil-ity of the extrapolation methods and algorithm. However, themethods combined in this study (i.e., correlation equations andextrapolations) have previously been successfully validated byother authors,3–11,14–17 which supports the proposed algorithm.

CONCLUSIONS

This study demonstrated the impact of both Vd and CL on theprediction of tissue drug accumulation in preclinical speciesin toxicology studies. The estimates of Kp values were af-fected by Vd, CL, interspecies scaling, and low-to-high dose



extrapolations. Consequently, we conclude that a combinationof this information can provide a meaningful testing tier to pre-dict tissue drug distribution for small molecules based on read-ily available PK parameters. The case study suggests that whentoxicity is driven by drug tissue concentrations, changes in thephysicochemical parameters and PK properties that drive tis-sue distribution resulted in decreased drug concentrations intissues, lower toxicity, and improved safety margins, which isin accordance with Diaz et al.1 and Mariappan et al.2 The re-sults may have implications for the greater availability of Kp

values for drugs in toxicology studies. However, despite all thecaveats, the newly developed algorithm can be used to predicttissue distribution for small molecules, which can be leveragedto interpret toxicity data in animals and to optimize the PKdrivers of tissue distribution in an attempt to decrease toxicity.

ACKNOWLEGMENTS

The authors would like to kindly offer their gratitude to theIn Vivo Studies Group at Genentech, South San Francisco, andto the Bioanalytical Group (DMPK) for their assistance andsupport in performing the animal studies and collecting thesamples used in this study. This work represents an initiativeundertaken in collaboration as a part of Dr. Poulin’s researchprogram that was supported by Genentech Inc.

REFERENCES

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