1521-009X/42/6/983–989$25.00 DRUG METABOLISM AND DISPOSITION Copyright ª 2014 by The American Society for Pharmacology and Experimental Therapeutics

http://dx.doi.org/10.1124/dmd.113.056606 Drug Metab Dispos 42:983–989, June 2014

Quantitative Investigation of the Brain-to-Cerebrospinal Fluid Unbound Drug Concentration Ratio under Steady-State Conditions in Rats Using a Pharmacokinetic Model and Scaling Factors for Active Efflux Transporters Hiroshi Kodaira, Hiroyuki Kusuhara, Eiichi Fuse, Junko Ushiki, and Yuichi Sugiyama Graduate School of Pharmaceutical Sciences, the University of Tokyo, Tokyo (H.Ko., H.Ku.); Pharmacokinetic Research Laboratories, Research Division, Kyowa Hakko Kirin Co., Ltd., Shizuoka (H.Ko., E.F., J.U.); and Sugiyama Laboratory, RIKEN Innovation Center, RIKEN Research Cluster for Innovation, RIKEN (Y.S.), Kanagawa, Japan Received December 19, 2013; accepted March 13, 2014

A pharmacokinetic model was constructed to explain the difference in brain- and cerebrospinal fluid (CSF)-to-plasma and brainto-CSF unbound drug concentration ratios (Kp,uu,brain, Kp,uu,CSF, and Kp,uu,CSF/brain, respectively) of drugs under steady-state conditions in rats. The passive permeability across the blood-brain barrier (BBB), PS1, was predicted by two methods using log(D/molecular weight0.5) for PS1(1) or the partition coefficient in octanol/water at pH 7.4 (LogD), topologic van der Waals polar surface area, and van der Waals surface area of the basic atoms for PS1(2). The coefficients of each parameter were determined using previously reported in situ rat BBB permeability. Active transport of drugs by P-glycoprotein (P-gp) and breast cancer resistance protein (Bcrp) measured in P-gp- and Bcrp-overexpressing cells was extrapolated to in vivo by introducing scaling factors. Brain- and CSF-to-

plasma unbound concentration ratios (Kp,uu,brain and Kp,uu,CSF, respectively) of 19 compounds, including P-gp and Bcrp substrates (daidzein, dantrolene, flavopiridol, genistein, loperamide, quinidine, and verapamil), were simultaneously fitted to the equations in a three-compartment model comprising blood, brain, and CSF compartments. The calculated Kp,uu,brain and Kp,uu,CSF of 17 compounds were within a factor of three of experimental values. Kp,uu,CSF values of genistein and loperamide were outliers of the prediction, and Kp,uu,brain of dantrolene also became an outlier when PS1(2) was used. Kp,uu,CSF/brain of the 19 compounds was within a factor of three of experimental values. In conclusion, the Kp,uu,CSF/brain of drugs, including P-gp and Bcrp substrates, could be successfully explained by a kinetic model using scaling factors combined with in vitro evaluation of P-gp and Bcrp activities.

Introduction

brain barrier (BBB). The BBB, which is formed by endothelial cells, limits the rapid and free exchange of drugs between the CNS and blood because of the highly developed tight junctions between adjacent endothelial cells (de Lange and Danhof, 2002; Abbott, 2004) and also of the active efflux mediated by P-glycoprotein (P-gp/MDR1/ABCB1), breast cancer resistance protein (Bcrp/ABCG2), and multidrug resistance-associated protein 4 (MRP4/ABCC4) (Schinkel, 1999; Leggas et al., 2004; Belinsky et al., 2007; Enokizono et al., 2007, 2008; Ose et al., 2009). In fact, the Cbrain of drugs, and consequently the Cu,brain, is inversely correlated with the activity of P-gp (Kikuchi et al., 2013). Drug concentration in the cerebrospinal fluid (CSF) (Cu,CSF) has been considered as a surrogate of Cu,brain because the ependymal layer between CSF and CNS has been considered to allow the free exchange of drugs (Lin, 2008; Liu X et al., 2009). CSF is produced by the choroid plexus in the ventricles, slowly turns over by bulk flow with poor mixing, and is finally absorbed into the venous blood. The choroid plexus is referred to as the blood-CSF barrier (BCSFB) because of its highly developed tight junctions between epithelial cells

For drugs acting in the central nervous system (CNS), it is assumed that an unbound drug in the brain (Cu,brain) is available to interact with the target site in the CNS. Estimating or measuring the Cu,brain of new chemical entities is a critical issue in drug discovery and development to allow understanding of the relationship between drug exposure and CNS effects. However, direct measurement of Cu,brain is not practicable, particularly in nonhuman primates and humans, because of its invasiveness, and thus there are great efforts to identify a surrogate. It is accepted that the unbound drug concentration in plasma (Cu,p) is not necessarily a surrogate of Cu,brain (Kalvass and Maurer, 2002; Maurer et al., 2005; Liu et al., 2009; Watson et al., 2009) because of the blood-

This study was supported by the Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research (S) [Grant 24229002], and Scientific Research (B) [Grant 23390034]. dx.doi.org/10.1124/dmd.113.056606.

ABBREVIATIONS: AFE, average fold error; CNS, central nervous system; BBB, blood-brain barrier; Bcrp, breast cancer resistance protein; BCSFB, blood-cerebrospinal fluid barrier; CFR, corrected flux ratio; CSF, cerebrospinal fluid; CCSF, total drug concentration in cerebrospinal fluid; Cbrain, total drug concentration in brain; Cu,p, unbound drug concentration in plasma; Cu,brain, unbound drug concentration in brain; Cu,CSF, unbound drug concentration in cerebrospinal fluid; Kp,uu,brain, brain-to-plasma unbound drug concentration ratio; Kp,uu,CSF, cerebrospinal fluid-to-plasma unbound drug concentration ratio; Kp,uu,CSF/brain, cerebrospinal fluid-to-brain unbound drug concentration ratio; LogD, the partition coefficient in octanol/water at pH 7.4; Mdr, multidrug resistance protein; MW, molecular weight; P-gp, P-glycoprotein; TPSA, topologic van der Waals polar surface area; vsa_base, van der Waals surface area of the basic atoms. 983

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ABSTRACT

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Kodaira et al.

(Abbott, 2005). Expression levels of P-gp and Bcrp were also detected in the choroid epithelial cells; however, their localization in these cells is suggested to be cytoplasmic or subapical for P-gp and in the brushborder membrane for Bcrp (Rao et al., 1999; Zhuang et al., 2006; Gazzin et al., 2008). Because of the lack of P-gp and Bcrp in the blood-facing plasma membrane of the choroid epithelial cells, their substrates should easily penetrate into the CSF. Indeed, we reported that the Cu,CSF of P-gp and Bcrp substrates exceeds the Cu,brain in rodents, and defects in P-gp and Bcrp expression diminished this concentration difference for P-gp and Bcrp substrates, respectively (Kodaira et al., 2011). Recently, a group of drugs were found to undergo active efflux at the BBB mediated by both P-gp and Bcrp (Oostendorp et al., 2009; Kusuhara and Sugiyama, 2009; Kodaira et al., 2010). Simultaneous defects in P-gp and Bcrp expression are necessary to completely eliminate the concentration difference of such dual substrates (Kodaira et al., 2011). Thus, active efflux at the BBB affects the estimation of Cu,brain using Cu,CSF. In addition, the Cu,CSF of drugs is determined by multiple parameters, passive permeability across the BBB and BCSFB, CSF bulk flow rate, and diffusion across the ependymal layer. For quantitative interpretation of the relationship between Cu,brain and Cu,CSF, these factors must also be considered. The purpose of the present study was to develop a pharmacokinetic model to describe the CSF- and brain-to-plasma and CSF-to-brain unbound concentration ratios (Kp,uu,brain, Kp,uu,CSF, and Kp,uu,CSF/brain, respectively) in rats of 19 drugs, including P-gp and Bcrp substrates, which we had determined previously under steady-state conditions (Kodaira et al., 2011). A nonlinear least-squares method was used to simultaneously fit the equations representing Kp,uu,brain and Kp,uu,CSF of drugs, including P-gp and Bcrp substrates to the observed data. We could reasonably well explain the observed Kp,uu,brain and Kp,uu,CSF for 17 compounds and the observed Kp,uu,CSF/brain for 19 compounds in rats using the fitted parameters.

Prediction of the BBB Passive Permeability by In Silico Structure Descriptors. BBB passive permeabilities of 19 compounds were calculated using in silico models. Based on reports by Murakami et al. (2000) and Liu et al. (2004), a linear regression of reported logPS1 against log(D/MW0.5) or threestructure descriptors [logD, topologic van der Waals polar surface area (TPSA), and van der Waals surface area of the basic atoms (vsa_base)] for non-P-gp and non-Bcrp substrates was used in this study. PS1 is the passive permeability clearance at the BBB (ml/s per gram), MW is the molecular weight, LogD is the partition coefficient in octanol/water at pH 7.4, TPSA is the topologic van der Waals polar surface area, and vsa_base is the van der Waals surface area of the basic atoms (Ertl et al., 2000). The coefficients of equations in two linear regression models were calculated by regression analysis of the reported BBB permeability of non-P-gp and non-Bcrp substrate compounds (Table 1). The PS values observed at the BBB (observed PS1) in rats were obtained by Liu et al. (2004) and Summerfield et al. (2007). Physicochemical parameters, logD, and TPSA for the test compounds were obtained using ACD/PhysChem Suite (version 12; ACD/Laboratories, Toronto, Canada), and vsa_base was obtained using MOE 2010 (Chemical Computing Group, Montreal, QC, Canada). The PS1 calculated by using log (D/MW0.5) or three-structure descriptors was expressed as PS1(1) and PS1(2), which were corrected for brain weight per body weight in rats (1.8 g/0.25 kg) (Davies and Morris, 1993). Mass-Balance Differential Equations. A three-compartment model comprising the blood, brain interstitial, and CSF compartments is shown in Fig. 1. The mass-balance equations for each compartment are shown in eq. 1, eq. 2, and eq. 3: Blood: V1 ×

dfblood × Cblood   ¼ 2 ðPS1 þ PS3 Þ × fblood × Cblood   dt 2   CL × f blood × CBlood   þ   kinf þ   ðPS1   þ   PS4 Þ × fu;brain × Cbrain   þ   ðPS3   þ   CLbulk  flow Þ × fu;CSF × CCSF ð1Þ

Brain: V2 ×

dfu;brain × Cbrain   ¼   PS1 × fblood × Cblood   dt 2   ðPS1   þ   PS2   þ   PS4 Þ × fu;brain × Cbrain   þ   PS2 × fu;CSF × CCSF

Materials and Methods Drug Selection and Animal Data. The unbound concentrations in the brain, CSF, and plasma were calculated as the product of unbound fraction and total concentration. Kp,uu,brain and Kp,uu,CSF represent the Cu,brain and Cu,CSF divided by the Cu,p, whereas Kp,uu,CSF/brain represents the Cu,brain divided by the Cu,CSF. All these values were based on our previous report (Kodaira et al., 2011). Of 25 compounds, 19 were selected for further analysis: benzylpenicillin, cephalexin, and cimetidine were excluded because they are substrates of organic anion transporter 3 and peptide transporter 2; sulpiride was excluded because of its low Kp,uu,brain and Kp,uu,CSF in rats (0.02 and 0.05, respectively); and fleroxacin and pefloxacin, which are a Bcrp-specific substrate and a dual substrate of P-gp and Bcrp, respectively, were excluded because of the uncertain involvement of Bcrp on their brain distribution in vivo.

fu;brain × Cbrain fu;brain × Cbrain Kp;uu;brain   ¼   ¼ ¼  fp × Cp fblood   × Cblood

fu;CSF × CCSF fu;CSF × CCSF ¼   ¼  Kp;uu;CSF   ¼   fp × Cp fblood × Cblood

CSF: V3 ×

dfu;CSF × CCSF   ¼  PS3 × fblood × Cblood   þ   PS2 × fu;brain × Cbrain   dt   2   PS2   þ   PS3   þ   CLbulk  flow × fu;CSF × CCSF ð3Þ

The parameters are summarized in Table 2. CL and kinf represent the total body clearance and infusion rate, respectively. Under steady-state conditions, Kp,uu,brain and Kp,uu,CSF are given by eq. 4 and eq. 5: The drug concentration in arterial blood could be assumed to be the same as that in brain capillary blood because of the negligible extraction rate in the

1þ 1þ 

PS4 PS1

ð2Þ

þ

CLbulk  flow PS3

CLbulk  flow PS3

PS2 2 þ PS PS1 þ PS3 þ

PS

2 2 þ PS PS1 þ PS3

ðPS2 × CLbulk  flow   þ  PS2 × PS4   þ  ​ PS4 × CLbulk  flow Þ

ð4Þ

PS1 × PS3

PS

PS2 4 2 1 þ PS PS1 þ PS1 þ PS3 ðPS2 × CLbulkflow   þ  PS2 × PS4   þ  ​ PS4 × CLbulkflow Þ CLbulkflow PS2 PS2 4 1 þ PS PS1 þ PS3 þ PS1 þ PS3 þ PS1 × PS3

ð5Þ

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Pharmacokinetic Model for Drug Disposition in the Brain TABLE 1

Physicochemical parameters to predict passive blood-brain barrier (BBB) permeability and in vitro transport activities of (breast cancer resistance protein (Bcrp) and P-glycoprotein (P-gp) for 19 compounds Molecular weight (MW), the partition coefficient in octanol/water at pH 7.4 (LogD) at pH 7.4, and topologic van der Waals polar surface area (TPSA) of test compounds were obtained using ACD/ PhysChem Suite (version 12, ACD/Laboratories, Toronto, Canada). The van der Waals surface area of the basic (vsa_base) was obtained using MOE 2010 (Chemical Computing Group, Montreal, QC, Canada). The calculation of the PS1(1) and PS1(2) of test compounds is described in Materials and Methods. Corrected flux ratio (CFR), which represents the ratio of transcellular transport in transporter-expressing and control cells, was obtained from a previous study (Kodaira et al., 2011). CFRs that showed statistical significance were included in the calculation; otherwise, CFR was regarded as 1. PS2, PS3, and PS4 were calculated using fitted parameters. Physicochemical Parameters

Clearance (ml/min per kg)

Compound MW cLogD pH 7.4

Antipyrine Buspirone Caffeine Carbamazepine Citalopram Daidzein Dantrolene Diazepam Flavopiridol Genistein Loperamide Midazolam Phenytoin Quinidine Risperidone Sertraline Thiopental Verapamil Zolpidem

188 386 194 236 324 254 314 285 402 270 477 326 252 324 410 306 242 455 307

0.441 1.19 20.628 1.90 1.35 2.11 1.43 2.80 0.678 1.93 3.63 3.78 2.52 0.947 1.86 3.04 2.99 2.46 2.97

TPSA

vsa_base

23.55 69.64 58.44 46.33 36.26 66.76 120.73 32.67 90.23 86.99 43.78 30.18 58.20 45.59 61.94 12.03 90.29 63.95 37.61

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.68 0.00 0.00 0.00

Observed PS1 (1) PS1

4.32a — 4.32a 6.91b 4.18b — — 14.2b — — — 19.6b 3.51b 0.172a 6.12b 31.6b — — —

4.45 5.70 2.84 8.02 6.21 8.72 6.43 11.5 4.59 8.05 15.6 17.2 10.4 5.24 7.53 12.7 12.7 9.58 12.3

CFR

PS2

PS3

PS4

PS1 (2)

PS2

PS3

0.0276 0.0193 0.0272 0.0247 0.0211 0.0238 0.0214 0.0225 0.0189 0.0231 0.0174 0.0210 0.0239 0.0211 0.0187 0.0217 0.0244 0.0178 0.0216

0.00253 0.00324 0.00161 0.00456 0.00353 0.00495 0.00365 0.00653 0.00261 0.00457 0.00886 0.00977 0.00591 0.00298 0.00428 0.00722 0.00722 0.00544 0.00699

0.00 0.00 0.00 0.00 0.0 89.3 65.8 0.00 157 113 619 0.0 0.0 204 95.9 0.0 0.00 172 0.0

5.91 3.64 2.58 6.32 6.30 4.93 1.80 10.0 2.31 3.45 10.7 13.7 6.30 4.89 4.94 31.6 4.43 5.68 9.77

0.0274 0.0191 0.0270 0.0245 0.0209 0.0236 0.0212 0.0223 0.0188 0.0229 0.0172 0.0208 0.0237 0.0209 0.0186 0.0215 0.0242 0.0176 0.0215

PS4

0.00558 0 0.00343 0 0.00243 0 0.00596 0 0.00594 0 0.00465 50.5 0.00170 18.4 0.00943 0 0.00218 78.8 0.00325 48. 6 0.0101 425 0.0129 0 0.00594 0 0.00461 190 0.00466 62.9 0.0298 0 0.00418 0 0.00536 102 0.00922 0

Bcrp P-gp

1.0 1.0 1.0 1.0 1.0 1.8 1.8 1.0 1.5 2.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 4.7 1.0 6.3 1.0 1.0 6.2 2.7 1.0 1.0 3.4 1.0

Substrate of P-gp and Bcrp

Nonsubstrate Nonsubstrate Nonsubstrate Nonsubstrate Nonsubstrate Bcrp Bcrp Nonsubstrate P-gp, Bcrp Bcrp P-gp Nonsubstrate Nonsubstrate P-gp P-gp Nonsubstrate Nonsubstrate P-gp Nonsubstrate

Bcrp, breast cancer resistance protein; P-gp, P-glycoprotein. a These PS values observed at the BBB (observed PS1) in rats were obtained by Liu et al. (2004). b These PS values obserbed at the BBB (observed PS1) were obtained by Summerfield et al. (2007).

     PS4 ¼ B × CFRP 2 gp 2 1   þ     C × CFRBcrp 2 1 × PS1 ;

brain under steady-state conditions. Assuming that the passive permeability at the BCSFB is proportional to that at the BBB, PS3 was substituted for PS1 in eq. 6: PS1   ¼   A × PS3 :

where B and C represent the scaling factor for extrapolation of in vitro P-gpand Bcrp-mediated efflux activities to the corresponding in vivo parameters. Corrected flux ratio (CFR) represents the ratio of the basal-to-apical and apicalto-basal transport across the monolayers of epithelial cells expressing either P-gp or Bcrp divided by the corresponding ratio in mock-vector transfected cells, as determined previously (Kodaira et al., 2011). CFR values that showed statistical significance were included in the calculation; otherwise, CFR was regarded as 1. By substituting eq. 6, eq. 7, and eq. 8 into eq. 4 and eq. 5, we obtained the following:

ð6Þ

Exchange across the ependymal surface occurs along with the concentration gradient by passive diffusion. The diffusion coefficient of each compound in water is inversely proportional to the one-half power of the molecular weight (Nugent and Jain, 1984). Therefore, PS2 was assumed to be inversely proportional to the one-half power of the molecular weight: D PS2   ¼   pffiffiffiffiffiffiffiffiffi; MW

ð7Þ

where A–D are fitting parameters. Equations 9 and 10 were simultaneously fitted to the observed data (Kp,uu,brain and Kp,uu,CSF) of 19 compounds in rats using a nonlinear least-squares method (WinNonlin, version 5.2.1; Pharsight Corporation, Mountain View, CA) to obtain parameters A–D. Kp,uu,CSF/brain

where D is the fitting parameter. PS4 is expressed using in vitro P-gp and Bcrp transport activities as follows:

Kp;uu;brain   ¼  

Kp;uu;CSF   ¼  

CLbulk​ flow × A × ð1þAÞ þ pDffiffiffiffiffiffi PS1 MW × PS1 CL flow × A × D Dð1þAÞ ×D×X ffiffiffiffiffiffi pffiffiffiffiffiffi þ pbulk​ þ pAffiffiffiffiffiffi MW × PS1 MW × PS1 2 MW × PS1



1þXþ

1þXþ

CLbulk​ flow × A PS1

CLbulk​ flow × A PS1

þ

ð8Þ

þ

CLbulk​ flow × A × X PS1

×D×X þ pAffiffiffiffiffiffi þ MW × PS

CLbulk​ flow × A × X PS1

× ð1þAÞ 1 þ X þ pDffiffiffiffiffiffi MW × PS

1

ffiffiffiffiffiffi þ pDð1þAÞ þ MW × PS 1

CLbulk​ flow × A × D pffiffiffiffiffiffi MW × PS1 2

    X  ¼   B × CFRP2gp 2 1   þ   C × CFRBcrp 2 1 ;

1

ð9Þ

ð10Þ

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Kodaira et al. Precision was assessed based on the root mean squared error, shown in eq. 13, as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 u  u u+ LOG predicted  Kp;uu;i observed  Kp;uu;i t RMSE  ¼   : n

ð13Þ

Fig. 1. Schematic diagram illustrating the three-compartment model. Cblood, Cbrain, CCSF, concentrations of drug in blood, brain, and cerebrospinal fluid (CSF); V1, V2, V3, volumes of the brain capillary lumen, brain, and ventricles; fblood, fu,brain, fu,CSF, unbound fraction in blood, brain, and CSF; PS1, PS product for passive permeability at the BBB; PS2, diffusion between brain and CSF; PS3, the PS product for passive permeability at blood-CSF barrier; PS4, the PS product for P-gp- and/or Bcrpmediated efflux from brain to blood; CLbulk flow, bulk flow rate of CSF; kinf, infusion rate; CL, total clearance of unbound drug.

To measure the degree to which the predicted and observed values are correlated, the correlation coefficient (r) was determined. The corresponding plots of predicted versus observed values are presented for each prediction method. Statistical Analysis. Values are all presented as mean 6 S.E.M. All statistical calculations were performed using SAS software (version 9; SAS Institute, Cary, NC).

values of 19 compounds were calculated by dividing calculated Kp,uu,CSF by calculated Kp,uu,brain. Evaluation of Predictive Performance. Predictive accuracy was assessed by comparing the predicted versus observed values of Kp,uu,brain, Kp,uu,CSF, and Kp,uu,CSF/brain. Therefore, the predictive accuracy of each passive permeability was characterized as shown in eq. 11 by using the average fold error (AFE), which gives a measure of the extent to which a particular method underpredicts or overpredicts the observed values:

Results

   predicted  Kp;uu;i   + LOG   observed  Kp;uu;i n ; AFE  ¼     10

ð11Þ

where n represents the size of the data set. In addition, the resulting absolute average fold error, which takes the absolute of plus and minus data and quantifies the magnitude of difference from the true value, was also assessed, as shown in eq. 12:   predicted  Kp;uu;i   + LOG observed  Kp;uu;i n : AAFE  ¼     10

In Vitro and In Vivo Parameters of 19 Compounds. The Kp,uu,brain, Kp,uu,CSF, and Kp,uu,CSF/brain of the 19 compounds ranged from 0.00886 to 2.19, from 0.0376 to 1.35, and from 0.139 to 4.16, respectively. The Kp,uu,CSF of P-gp substrates (loperamide, quinidine, and verapamil), Bcrp substrates (genistein, dantrolene, and daidzein), and a P-gp and Bcrp dual substrate (flavopiridol) were 2-fold greater than their Kp,uu,brain (i.e., Kp,uu,CSF/brain . 2). A linear regression analysis of the logPS1 values of the non-P-gp and non-BCRP substrates in present study yielded two linear equations (eq. 14 and eq. 15) that contain the descriptors described in Materials and Methods. logPS1 ð1Þ ¼   0:182   logðD=MW 0:5 Þ 2 1:86​         ð  R2 ¼ 0:50Þ ð14Þ logPS1 ð2Þ ¼   0:123  logD  2   0:00656   TPSA þ   0:0588  vas base  2 1:76  ðR2 ¼ 0:77Þ

ð12Þ

The specific fold error of the deviation between the predicted and observed values was also calculated. Therefore, the percentage and number of drugs with a deviation less than 2-fold error and 3-fold error are presented for each method.

The passive permeability clearances at the BBB [PS1(1) and PS1(2)] for 19 compounds, which were calculated by two equations, ranged from 2.84 to 17.2 ml/min per kilogram and from 1.80 to 31.6 ml/min per kilogram, respectively (Table 1). PS1(1) showed a positive

TABLE 2 List of parameters used to describe the disposition of test compounds in the brain and cerebrospinal fluid (CSF) Eqs. 1–3 were solved under steady-state conditions to obtain Kp,uu,brain (eq. 4) and Kp,uu, CSF (eq. 5). PS3 was substituted for PS1 divided by A. B and C were defined as the in vitro–in vivo scaling factors for P-glycoprotein (P-gp)- and breast cancer resistance protein (Bcrp)mediated efflux at the BBB. Parameters A–D were obtained by simultaneously fitting the observed Kp,uu,brain and Kp,uu,CSF of test compounds to eqs. 9 and 1 using a nonlinear least squares method (WinNonlin, version 5.2.1, Pharsight). Parameters

Concentration

Volume Clearance (ml/min per rat)

Unbound fraction Others Free parameters for fitting

Cblood Cbrain CCSF V1 V2 V3 PS1 PS2 PS3 PS4 CLbulk CL fblood fu,brain fu,CSF kinf A B C D

flow

ð15Þ

Concentration in the blood Concentration in the brain Concentration in the ventricles Distribution volume in the body Volume in the brain Ventricle volume Passive clearance in the BBB Clearance for exchange across the ependymal layer Passive clearance in the BCSFB Active efflux in the BBB Bulk flow rate (0.0029) (Suzuki et al., 1985) Total body clearance Unbound fraction in the blood Unbound fraction in the brain Unbound fraction in the CSF Infusion rate Ratio of PS1 to PS3 Scaling factor for P-gp Scaling factor for Bcrp Coefficient in eq. 7

BBB, blood-brain barrier; BCSFB, blood-cerebrospinal fluid barrier; CL, clearance; CSF, cerebrospinal fluid; V, volume.

Pharmacokinetic Model for Drug Disposition in the Brain correlation with PS1(2), although the absolute value of PS1(1) was somewhat greater than that of PS1(2). With the exception of some outliers, both PS1(1) and PS1(2) were comparable with the observed BBB permeability; PS1(1) overestimated the BBB permeability of phenytoin and quinidine and underestimated that of sertraline, whereas PS1(2) overestimated the BBB permeability of quinidine. Determination of the Parameters A–D to Describe Kp,uu,brain and Kp,uu,CSF of the Test Compounds. Simultaneous fitting of Kp,uu,brain and Kp,uu,CSF of the 19 compounds with PS1 obtained by two methods was performed to obtain the parameters A–D. The resulting fitted parameters A, B, C, and D were 1760 6 630 (CV: 35.6%), 7.49 6 1.68 (CV: 22.4%), 12.8 6 3.6 (CV: 28.1%), and 0.379 6 0.200 (CV: 52.7%), respectively, when PS1(1) was used and 1060 6 310 (CV: 37.9%), 7.48 6 1.73 (CV: 23.1%), 11.7 6 3.3 (CV: 28.4%), and 0.376 6 0.218 (CV: 58.1%), respectively, when PS1(2) was used. The method of calculation of PS1 had no marked effect on the fitted parameters B–D. Parameter A determined by PS1(1) was 1.7 times higher than that determined by PS1(2). The correlations between the predicted and observed Kp,uu values are shown in Fig. 2. Comparative assessment was conducted based on the number of compounds that fell within 2- to 3-fold error and on statistical indexes (Table 3). The numbers of compounds exhibiting an error less than 2-fold for Kp,uu,brain and Kp,uu,CSF were comparable regardless of PS1, whereas that for Kp,uu,CSF/brain with PS1(1) was higher than that with PS1(2). There were outliers: PS1(1) Kp,uu,CSF of genistein and loperamide (the observed and predicted values were 0.589 and 0.155 for genistein and 0.038 and 0.245 for loperamide, respectively); PS1(2) Kp,uu,brain of dantrolene (the observed and predicted values are 0.030 and 0.095, respectively), Kp,uu,CSF of genistein and loperamide (the observed and predicted values are 0.589 and 0.130 for genistein, and 0.038 and 0.271 for loperamide,

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respectively). Absolute average fold error and root mean squared error were slightly lower when PS1(1) was used for fitting (Table 3). Discussion In the present study, we aimed to demonstrate that a pharmacokinetic model comprising the three compartments—brain, CSF, and plasma—is able to explain the Kp,uu,brain and Kp,uu,CSF of drugs and their ratio, including those of P-gp and Bcrp substrates that undergo significant active efflux by P-gp and Bcrp at the BBB, by using scaling factors for P-gp and Bcrp. PS1 was calculated for 19 compounds using in silico structure descriptors (Table 1). Of the two methods tested, PS1(2) provided a better prediction than PS1(1). This was identical to the result of Liu et al. (2004), and PS1(2) could reproduce the actual BBB passive permeability for all tested drugs except quinidine. Because P-gp has limited penetration to the CNS across the BBB (Kusuhara et al., 1997), it is reasonable that quinidine was an outlier. In contrast to quinidine, both methods predicted similar or slightly lower passive permeability of risperidone, another P-gp substrate, compared with that observed. This finding is inconsistent with the observations that the brain penetration of risperidone at the BBB is also limited by P-gp (Doran et al., 2005) and that P-gp impacts on BBB permeability. Further studies are necessary to explain this discrepancy. Kp,uu,brain and Kp,uu,CSF, and consequently Kp,uu,brain/CSF, could be explained well using the fitted parameters. Only a small difference was found in the predictive performance of PS1(1) and PS1(2) (Table 3). This result may be partly because the Kp,uu,brain and Kp,uu,CSF determined under steady-state conditions were used for the calculations. When transcellular transport across the BBB occurs by passive diffusion, the Kp,uu,brain should be 1, irrespective of PS1 value. For Kp,uu,CSF, the difference between

Fig. 2. Comparison of predicted and observed Kp,uu (Kp,uu,brain, Kp,uu,CSF, Kp,uu,CSF/brain) of 19 compounds in rats. The predicted Kp,uu,brain and Kp,uu,CSF values were obtained by simultaneously fitting the observed Kp,uu,brain and Kp,uu,CSF of 19 compounds in rats to eqs. 9 and 10 using a nonlinear least-squares method (WinNonlin, version 5.2.1 Pharsight) for PS 1(1) (A) and PS1(2) (B). Predicted Kp,uu,CSF/brain values were calculated as K p,uu,CSF divided by Kp,uu,brain. Predicted values of K p,uu,brain, K p,uu,CSF, and Kp,uu,CSF/brain were compared with observed values, respectively. The solid line indicates unity. Dashed lines on either side of the unity line represent factors of 2- and 3-fold, respectively. 1, antipyrine; 2, buspirone; 3, caffeine; 4, carbamazepine; 5, citalopram; 6, daidzein; 7, dantrolene; 8, diazepam; 9, flavopiridol; 10, genistein; 11, loperamid; 12, midazolam; 13, phenytoin; 14, quinidine; 15, risperidone; 16, sertraline; 17, thiopental; 18, verapamil; 19, zolpidem.

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Kodaira et al. TABLE 3 Accuracy and precision of the prediction of Kp,uu,brain, Kp,uu,CSF, and Kp,uu,CSF/brain for 19 compounds in rats Specific fold error of deviation between the predicted and observed values was calculated. The percentage of compounds with a fold error of deviation less than 2 (% fold error #2) and 3 (% fold error #3) are presented for each PS1. The prediction accuracy and precision of each PS1 were characterized using the average fold error (AFE), absolute average fold error (AAFE), and root mean square error (RMSE). % # 2-fold

% # 3-fold

r2

Accuracy

Precision

Permeability

PS1 (1) PS1 (2)

Kp,uu,brain

Kp,uu,CSF

Kp,uu,CSF/brain

Kp,uu,brain

Kp,uu,CSF

Kp,uu,CSF/brain

Kp,uu,brain

Kp,uu,CSF

Kp,uu,CSF/brain

AFE

AAFE

RMSE

63% (12/19) 63% (12/19)

84% (16/19) 84% (16/19)

84% (16/19) 79% (15/19)

100% (19/19) 95% (18/19)

90% (17/19) 90% (17/19)

100% (19/19) 100% (19/19)

0.85

0.54

0.72

0.992

1.60

0.255

0.85

0.50

0.61

0.995

1.65

0.272

PS1(1) and PS1(2) could be compensated by parameter A, which represents the difference between the BBB and BCSFB in the clearance for passive transport. Assuming an equal passive permeability per unit surface area across the BBB and BCSFB, parameter A corresponds to the difference in the surface area for drug penetration from the blood circulation into the brain and CSF. The surface area of capillaries at the BBB is 5000-fold larger than that at the BCSFB (Pardridge et al., 1981; De Lange, 2004; Reichel, 2006). It was also reported that it is only 2- to 6-fold larger than the apical and basal surface areas, respectively, of the choroid plexus in rats (Keep and Jones, 1990). The fitted parameter A was of the same order of magnitude as the reported value (Pardridge et al., 1981; De Lange, 2004; Reichel, 2006). The method used for estimating PS1 barely affected the fitted parameters B, C, and D. To verify parameters B and C, scaling factors for P-gp- and Bcrp-mediated efflux, in vivo PSP-gp and PSBcrp of flavopiridol, the brain penetration of which is limited by both P-gp and Bcrp, were calculated using the in vitro CFR transport activities of P-gp and Bcrp, and fitted parameters B and C. In vivo PSP-gp was 4.3-fold higher than PSBcrp. This value is almost identical to the observed value (3.3) (Kodaira et al., 2010), which was calculated by comparing the Kp,brain of flavopiridol in P-gp(–/–), Bcrp(–/–), and P-gp/ Bcrp(–/–) mice. To explain why the Kp,uu,CSF of P-gp and Bcrp substrates was lower than that of nonsubstrate drugs (Fig. 2), despite the absence of P-gp and Bcrp in the blood-facing plasma membrane of the choroid epithelial cells (Rao et al., 1999; Zhuang et al., 2006; Gazzin et al., 2008), PS2 needs to be greater than PS3 and CLbulk flow, making a significant contribution of diffusion across the ependymal surface, followed by active efflux at the BBB to the clearance pathway from the CSF (Table 1). PS2 was on average 5-fold greater than PS3, ranging from 1.96 to 17 and from 0.72 to 12 when PS1(1) and PS1(2), respectively, were used. Therefore, Kp,uu,CSF does not decrease as much as Kp,uu,brain with an increase in the active efflux at the BBB. Indeed, the Kp,uu,CSF of P-gp and Bcrp substrates was larger than the Kp,uu,brain (Kodaira et al., 2011). The observation that the PS2 of most compounds was above their PS3 and CLbulk flow (Table 3) provides a rationale for using Kp,uu,CSF as a surrogate of Kp,uu,brain, although the magnitude of the overestimation of Kp,uu,brain increases with increasing active efflux clearance. Genistein and loperamide were outliers for the prediction of Kp,uu,CSF irrespective of PS1. Kp,uu,CSF of loperamide was overestimated, whereas that of genistein was underestimated. The Kp,uu,brain of loperamide was also overestimated, although it was within a 3-fold error (Fig. 2). Because eq. 4 and 5 were obtained under steady-state conditions, insufficient duration is one explanation for the overestimation. The observations that the uptake of loperamide by brain slices did not reach a plateau, even after an 8-hour incubation in vitro (Kodaira et al., 2011), also suggests that the brain and CSF concentrations of loperamide did not reach a plateau during a 120minute infusion. On the other hand, the reason for the underestimation of the Kp,uu,CSF of genistein is unclear. Defective expression of Bcrp

diminished the difference in the unbound concentration between the brain and CSF, indicating that active efflux by Bcrp at the BBB is the predominant mechanism producing the difference in the Kp,uu,brain and Kp,uu,CSF (Kodaira et al., 2011). Bcrp-mediated efflux of genistein at the BBB may be overestimated for an unknown reason. The Kp,uu,CSF/brain values of the test compounds varied from 0.24 to 2.2, showing a 10-fold difference in the mouse (Kodaira et al., 2011), which is mainly the result of the active efflux at the BBB. The present study demonstrated that in vitro to in vivo extrapolation of the active efflux at the BBB successfully predicted this parameter, even for a P-gp and Bcrp dual substrate, using a simple pharmacokinetic model and in silico prediction of PS1. Once we have determined the in vitro transport activities of investigational substrates of P-gp and Bcrp, our approach will help in the estimation of the Kp,uu,brain of these investigational drugs and inform the decision to use CSF concentration as a surrogate for drug development. It should be noted that the scaling factors determined in this study obviously depend on the cell lines that were used for the evaluation of P-gp and Bcrp activities. To ensure the predictability, in addition to the compounds of interest, it is strongly recommended that some P-gp- and Bcrp-specific substrates be measured as positive controls in the cell lines used in the analysis for correction of the CFR. The our approach will elucidate the relationship between Cu,brain and Cu, CSF in nonhuman primates and humans once we are able to determine the scaling factors for P-gp and Bcrp in humans by accumulating positron emission tomography data or by using quantitative proteomics, an emerging technique for quantifying protein expression. This will in the future improve the predictability of Kp,uu,brain and Kp,uu,CSF even for P-gp and BCRP substrates, although our approach will be needed to validate Kp,uu values calculated by the model in humans by comparing the calculated data with in vivo data determined by PET. In conclusion, a simple pharmacokinetic model that includes active efflux transport at the BBB can reasonably describe the Kp,uu,CSF/brain of drugs, even including P-gp and Bcrp substrates, by introducing in vitro and in vivo scaling factors for P-gp and Bcrp. Authorship Contributions Participated in research design: Kodaira, Kusuhara, Sugiyama. Conducted experiments: Kodaira. Performed data analysis: Kodaira, Kusuhara, Sugiyama. Wrote or contributed to the writing of the manuscript: Kodaira, Kusuhara, Fuse, Ushiki, Sugiyama. References Abbott NJ (2004) Evidence for bulk flow of brain interstitial fluid: significance for physiology and pathology. Neurochem Int 45:545–552. Abbott NJ (2005) Dynamics of CNS barriers: evolution, differentiation, and modulation. Cell Mol Neurobiol 25:5–23. Belinsky MG, Guo P, Lee K, Zhou F, Kotova E, Grinberg A, Westphal H, Shchaveleva I, KleinSzanto A, and Gallo JM, et al. (2007) Multidrug resistance protein 4 protects bone marrow, thymus, spleen, and intestine from nucleotide analogue-induced damage. Cancer Res 67: 262–268.

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Address correspondence to: Dr. Yuichi Sugiyama, Sugiyama Laboratory, RIKEN Innovation Center, RIKEN Research Cluster for Innovation, RIKEN, 1-6 Suehirocho, Tsurumi-ku, Yokohama-shi, Kanagawa 230-0045, Japan. E-mail: ychi. [email protected]

Quantitative investigation of the brain-to-cerebrospinal fluid unbound drug concentration ratio under steady-state conditions in rats using a pharmacokinetic model and scaling factors for active efflux transporters.

A pharmacokinetic model was constructed to explain the difference in brain- and cerebrospinal fluid (CSF)-to-plasma and brain-to-CSF unbound drug conc...
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