Quantitative investigation of the brain-to-cerebrospinal fluid unbound drug. concentration ratio under steady-state conditions in rats using a

Transcription

1 DMD Fast This article Forward. has not been Published copyedited on and March formatted. 8, The 04 final version as doi:0.4/dmd may differ from this version. 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, Ph.D., Eiichi Fuse, Ph.D., Junko Ushiki, and Yuichi Sugiyama, Ph.D. Graduate School of Pharmaceutical Sciences, the University of Tokyo, Tokyo, Japan (H.Ko, H.Ku); Pharmacokinetic Research Laboratories, Research Division, Kyowa Hakko Kirin Co., Ltd., Shizuoka, Japan (H.Ko, E.F., J.U.) Sugiyama Laboratory, RIKEN Innovation Center, RIKEN Research Cluster for Innovation, RIKEN, Japan (Y.S.) Copyright 04 by the American Society for Pharmacology and Experimental Therapeutics.

2 Running title: Pharmacokinetic model for drug disposition in the brain Corresponding author: Yuichi Sugiyama, Ph.D. Sugiyama Laboratory, RIKEN Innovation Center, RIKEN Research Cluster for Innovation, RIKEN, -6 Suehiro-cho, Tsurumi-ku, Yokohama-shi, Kanagawa , Japan. Number of text pages (including references): 4 Number of tables: 3 Number of figures: Number of references: 36 Number of words in the abstract: 3 Number of words in the introduction: 65 Number of words in the discussion: 94 Abbreviations: CNS, central nervous system; BBB, blood-brain barrier; BCSFB, blood-cerebrospinal fluid barrier; CSF, cerebrospinal fluid; C CSF, total drug concentration in cerebrospinal fluid; C brain, total drug concentration in brain; C u,p, unbound drug concentration in plasma; C u,brain, unbound drug concentration in brain; C u,csf, unbound drug concentration in cerebrospinal fluid; K p,uu,brain, brain-to-plasma unbound drug concentration ratio; K p,uu,csf, cerebrospinal fluid-to-plasma unbound drug concentration ratio; K p,uu,csf/brain, cerebrospinal fluid-to-brain unbound drug concentration ratio; Mdr, multidrug resistance protein; P-gp, P-glycoprotein; Bcrp, breast cancer resistance protein

3 Abstract A pharmacokinetic model was constructed to explain the difference in brain- and CSF-to-plasma, and brain-to-csf unbound drug concentration ratios (K p,uu,brain, K p,uu,csf, and K p,uu,csf/brain, respectively) of drugs under steady-state conditions in rats. The passive permeability across the blood brain barrier (BBB),, was predicted by two methods using log(d/molecular weight 0.5 ) for () or LogD, TA, and vsa_base for (). The coefficients of each parameter were determined using previously reported in situ rat BBB permeability. Active transport of drugs by P-gp and 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 (K p,uu,brain and K p,uu,csf, respectively) of 9 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 K p,uu,brain and K p,uu,csf of 7 compounds were within a factor of three of experimental values. K p,uu,csf of genistein and loperamide were outliers of the prediction, and K p,uu,brain of dantrolene also became an outlier when () was used. K p,uu,csf/brain of the 9 compounds was within a factor of three of experimental values. In conclusion, the K p,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. 3

4 Introduction For drugs acting in the central nervous system (CNS), it is assumed that an unbound drug in the brain (C u,brain ) is available to interact with the target site in the CNS. Estimating or measuring C u,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 C u,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 (C u,p ) is not necessarily a surrogate of C u,brain (Kalvass et al., 00; Maurer et al., 005; Liu et al., 009; Watson et al., 009) because of the blood 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, 00; Abbott, 004), and also of the active efflux mediated by P-glycoprotein (P-gp/MDR/ABCB), breast cancer resistance protein (BCRP/ABCG), and multidrug resistance-associated protein 4 (MRP4/ABCC4) (Schinkel, 999; Leggas et al., 004; Belinsky et al., 007; Enokizono et al., 007; Enokizono et al., 008; Ose et al., 009). In fact, the C brain of drugs, and consequently the C u,brain, is inversely correlated with the activity of P-gp (Kikuchi et al., 03). Drug concentration in the cerebrospinal fluid (CSF) (C u,csf ) has been considered as a surrogate of C u,brain because the ependymal layer between CSF and CNS has been considered to allow the free exchange of drugs (Lin, 008; Liu X et al., 009). 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 (Abbott, 005). Expression of P-gp and Bcrp was 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 brush border membrane for Bcrp (Rao et al., 999; Zhuang et al., 006; Gazzin et al., 008). 4

5 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 C u,csf of P-gp and Bcrp substrates exceeds the C u,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., 0). Recently, a group of drugs were found to undergo active efflux at the BBB mediated by both P-gp and Bcrp (Oostendorp et al., 009; Kusuhara and Sugiyama, 009; Kodaira et al., 00). Simultaneous defects in P-gp and Bcrp expression are necessary to completely eliminate the concentration difference of such dual substrates (Kodaira et al., 0). Thus, active efflux at the BBB affects the estimation of C u,brain using C u,csf. In addition, the C u,csf of drugs is also 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 C u,brain and C u,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 (K p,uu,brain, K p,uu,csf, and K p,uu,csf/brain, respectively) in rats of 9 drugs including P-gp and Bcrp substrates, which we had determined previously under steady-state conditions (Kodaira et al., 0). A nonlinear least squares method was used to simultaneously fit the equations representing K p,uu,brain and K p,uu,csf of drugs including P-gp and Bcrp substrates to the observed data. We could reasonably well explain the observed K p,uu,brain and K p,uu,csf for 7 compounds and the observed K p,uu,csf/brain for 9 compounds in rats using the fitted parameters. 5

6 Materials and methods Drug selection and animal data The unbound concentration in the brain, CSF, and plasma was calculated as the product of unbound fraction and total concentration. K p,uu,brain and K p,uu,csf represent the C u,brain and C u,csf divided by the C u,p, whereas K p,uu,csf/brain represents the C u,brain divided by the C u,csf. These values were all based on our previous report (Kodaira et al., 0). Of 5 compounds, 9 were selected for further analysis: benzylpenicillin, cephalexin, and cimetidine were excluded because they are substrates of organic anion transporter 3 and peptide transporter ; sulpiride was excluded because of its low K p,uu,brain and K p,uu,csf in rats (0.0 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. Prediction of the BBB passive permeability by in silico structure descriptors BBB passive permeabilities of 9 compounds were calculated using in silico models. Based on reports by Murakami et al. (000) and Liu et al. (004), a linear regression of reported log against log(d/mw 0.5 ) or three-structure descriptors (logd, TA, and vsa_base) for non-p-gp and non-bcrp substrates was employed in this study. are the passive permeability clearances at the BBB (ml/s/g), MW is the molecular weight, LogD is the partition coefficient in octanol/water at ph 7.4, TA is the topological van der Waals polar surface area, and vsa_base is the van der Waals surface area of the basic atoms (Ertl et al., 000). 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 ). The values observed at the BBB (observed ) in rats were obtained by Liu et al. (004) and Summerfield et al. (007). Physicochemical parameters, logd, and TA for the test compounds were obtained using ACD/PhysChem Suite (version, ACD/Labs, Toronto, 6

7 Canada), and vsa_base was obtained using MOE 00 (Chemical Computing Group, Montreal, QB, Canada). The calculated by using log(d/mw 0.5 ) or three-structure descriptors were expressed as () and (), which were corrected for brain weight per body weight in rats (.8 g/0.5 kg) (Davies and Morris, 993). Mass balance differential equations A three-compartment model, comprising the blood, brain interstitial, and CSF compartments, is shown in Figure. The mass balance equations for each compartment are as follows: Blood: df V Brain: V df blood C dt blood = ( + ) + 3 f blood C blood CL f blood C Blood + k ( + 4 ) f u, brain C brain + ( 3 + CLbulk flow ) f u, CSF CCSF inf () ( ) fu,brain Cbrain + fu,csf CCSF u,brain brain = fblood Cblood () CSF: V df dt C ( + + CLbulk flow) fu,csf CCSF u,csf CSF 3 = 3 fblood Cblood + fu,brain Cbrain 3 (3) dt C The parameters are summarized in Table. CL and k inf represent the total body clearance and infusion rate, respectively. Under steady-state conditions, K p,uu,brain and K p,uu,csf are given by: K p,uu,brain = f u,brain f p = + C C 4 brain p = CLbulk + 3 f f u,brain blood flow C C + brain blood CLbulk flow ( CL + + CL ) + bulk flow bulk flow (4) 7

8 K p, uu, CSF = f u, CSF f p = + C C 4 p CSF = CL + f f bulkflow 3 u, CSF blood C C + CSF blood ( CL + + CL ) + bulkflow bulkflow (5) 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 brain under steady-state conditions. Assuming that the passive permeability at the BCSFB is proportional to that at the BBB, 3 was substituted for : = A (6) 3 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, 984). Therefore, was assumed to be inversely proportional to the one-half power of the molecular weight: D = (7) MW where D is the fitting parameter. 4 is expressed using in vitro P-gp and Bcrp transport activities as follows: [ B ( CFRP gp ) + C ( CFRBcrp )] = (8) 4 where B and C represent the scaling factor for extrapolation of in vitro P-gp- and Bcrp-mediated efflux activities to the corresponding in vivo parameters. CFR represents the ratio of the basal-to-apical and apical-to-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., 0). CFR that showed statistical significance were included in the calculation, otherwise CFR was regarded as. By substituting equations (6), (7), and (8) into equations (4) and (5), we obtained the following: 8

9 K K CL + bulkflow A + ( + A) MW p,uu,brain = (9) CLbulkflow A D( + A) CLbulkflow A D A D X CLbulkflow A X + X MW MW MW D ( + A) D + X + MW p,uu,csf = (0) CLbulkflow A D( + A) CLbulkflow A D A D X CLbulkflow A X + X MW MW MW X = B CFR + C CFR P gp Bcrp where A to D are fitting parameters. The equations (9) and (0) were simultaneously fitted to the observed data (K p,uu,brain and K p,uu,csf ) of 9 compounds in rats using a nonlinear least squares method (WinNonlin, version 5.. Pharsight) to obtain parameters A to D. K p,uu,csf/brain values of 9 compounds were calculated by dividing calculated K p,uu,csf by calculated K p,uu,brain. Evaluation of predictive performance Predictive accuracy was assessed by comparing the predicted versus observed values of K p,uu,brain, K p,uu,csf, and K p,uu,csf/brain. Therefore, the predictive accuracy of each passive permeability was characterized 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: AFE predicted K p,uu,i LOG observed K p,uu,i = 0 n, where n represents the size of the data set. In addition, the resulting absolute average fold error (AAFE), which takes the absolute of plus and minus data and quantifies the magnitude of difference from the true value, was also assessed: AAFE predicted K p,uu,i LOG observed K p,uu,i = 0 n. 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 -fold 9

10 error and 3-fold error, are presented for each method. Precision was assessed based on the root mean squared error (RMSE) as follows: RMSE predicted K p, uu, i LOG observed K p, uu, i =. n 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 ± SEM. All statistical calculations were performed using SAS software (version 9; SAS Institute, Cary, NC). 0

11 Results In vitro and in vivo parameters of 9 compounds The K p,uu,brain, K p,uu,csf, and K p,uu,csf/brain of the 9 compounds ranged from to.9, from to.35, and from 0.39 to 4.6, respectively. The K p,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 -fold greater than their K p,uu,brain (i.e., K p,uu,csf/brain >). A linear regression analysis of the log values of the non-p-gp and non-bcrp substrates in present study yielded two linear equations that contain the descriptors described in Materials and methods. 0.5 log () = 0.8 log(d/ MW ).86 (R = 0.50) log () = 0.3 logd TA vas_ base.76 (R = 0.77) The passive permeability clearances at the BBB ( () and ()) for 9 compounds, which were calculated by two equations, ranged from.84 to 7. ml/min/kg and from.80 to 3.6 ml/min/kg, respectively (Table ). () showed a positive correlation with (), although the absolute value of () was somewhat greater than that of (). With the exception of some outliers, both () and () were comparable with the observed BBB permeability; () overestimated the BBB permeability of phenytoin and quinidine, and underestimated that of sertraline, whereas () overestimated the BBB permeability of quinidine. Determination of the parameters A D to describe K p,uu,brain and K p,uu,csf of the test compounds Simultaneous fitting of K p,uu,brain and K p,uu,csf of the 9 compounds with obtained by two methods was performed to obtain the parameters A D. The resulting fitted parameters A, B, C, and D were 760 ± 630 (CV: 35.6%), 7.49 ±.68 (CV:.4%),.8 ± 3.6 (CV: 8.%), and ± 0.00 (CV: 5.7%), respectively, when () was used, and 060 ± 30 (CV:

12 37.9%), 7.48 ±.73 (CV: 3.%),.7 ± 3.3 (CV: 8.4%), and ± 0.8 (CV: 58.%), respectively, when () was used. The method of calculation of had no marked effect on the fitted parameters B to D. The parameter A determined by () was.7 times higher than that determined by (). The correlations between the predicted and observed K p,uu values are shown in Figure. Comparative assessment was conducted based on the number of compounds that fell within - to 3-fold error, and on statistical indexes (Table 3). The numbers of compounds exhibiting an error less than -fold for K p,uu,brain and K p,uu,csf were comparable regardless of, whereas that for K p,uu,csf/brain with () was higher than that with (). There were outliers: () K p,uu,csf of genistein and loperamide (the observed and predicted values were and 0.55 for genistein, and and 0.45 for loperamide, respectively); () K p,uu,brain of dantrolene (the observed and predicted values are and 0.095, respectively), K p,uu,csf of genistein and loperamide (the observed and predicted values are and 0.30 for genistein, and and 0.7 for loperamide, respectively). AAFE and RMSE were slightly lower when () was used for fitting (Table 3).

13 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 K p,uu,brain and K p,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. was calculated for 9 compounds using in silico structure descriptors (Table ). Of the two methods tested, () provided a better prediction than (). This was identical to the result of Liu et al.(004) and () 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., 997), 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 is inconsistent with the observations that the brain penetration of risperidone at the BBB is also limited by P-gp (Doran et al., 005), and that P-gp impacts on BBB permeability. Further studies are necessary to explain this discrepancy. K p,uu,brain and K p,uu,csf, and consequently K p,uu,brain/csf, could be explained well using the fitted parameters. There was only a small difference in the predictive performance of () and () (Table 3). This may be partly because the K p,uu,brain and K p,uu,csf determined under steady-state conditions were used for the calculations. When transcellular transport across the BBB occurs by passive diffusion, the K p,uu,brain should be, irrespective of value. For K p,uu,csf, the difference between () and () 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 5,000-fold larger than that at the BCSFB (De Lange, 004, Pardridge et al., 98, Reichel, 3

14 006). It was also reported that it is only - to 6-fold larger than the apical and basal surface areas, respectively, of the choroid plexus in rats (Keep and Jones, 990). The fitted parameter A was of the same order of magnitude as the reported value (De Lange, 004, Pardridge et al., 98, Reichel, 006). The method used for estimating 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 P-gp and Bcrp 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 P-gp was 4.3-fold higher than Bcrp. This is almost identical to the observed value (3.3, Kodaira et al., 00), which was calculated by comparing the K p,brain of flavopiridol in P-gp( / ), Bcrp( / ), and P-gp/Bcrp( / ) mice. To explain why the K p,uu,csf of P-gp and Bcrp substrates was lower than that of nonsubstrate drugs (Figure ), despite the absence of P-gp and Bcrp in the blood-facing plasma membrane of the choroid epithelial cells (Rao et al., 999; Zhuang et al., 006; Gazzin et al., 008), needs to be greater than 3 and CL bulk 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 ). was on average 5-fold greater than 3, ranging from.96 to 7, and from 0.7 to when () and (), respectively, were used. Therefore, K p,uu,csf does not decrease as much as K p,uu,brain with an increase in the active efflux at the BBB. Indeed, the K p,uu,csf of P-gp and Bcrp substrates was larger than the K p,uu,brain (Kodaira et al., 0). The observation that the of most compounds was above their 3 and CL bulk flow (Table 3) provides a rationale for using K p,uu,csf as a surrogate of K p,uu,brain, although the magnitude of the overestimation of K p,uu,brain increases with increasing active efflux clearance. Genistein and loperamide were outliers for the prediction of K p,uu,csf irrespective of : K p,uu,csf of loperamide was overestimated, whereas that of genistein was underestimated. The K p,uu,brain of loperamide was also overestimated, although it was within a 3-fold error (Figure ). Because equations (4) and (5) were obtained under steady-state conditions, insufficient 4

15 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 h incubation in vitro (Kodaira et al., 0) also suggests that the brain and CSF concentrations of loperamide did not reach a plateau during a 0 min infusion. On the other hand, the reason for the underestimation of the K p,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 K p,uu,brain and K p,uu,csf (Kodaira et al., 0). Bcrp-mediated efflux of genistein at the BBB may be overestimated for an unknown reason. The K p,uu,csf/brain values of the test compounds varied from 0.4 to., showing a 0-fold difference in the mouse (Kodaira et al., 0), 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. Once we have determined the in vitro transport activities of investigational substrates of P-gp and Bcrp, our approach will help the estimation of the K p,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 assure the predictability, in addition to the compounds of interest, it is strongly recommended to measure some P-gp- and Bcrp-specific substrates as positive controls in the cell lines used in the analysis, for correction of the CFR. The our approach will elucidate the relationship between C u,brain and C u,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 (PET) data or by using quantitative proteomics, an emerging technique for quantifying protein expression. This will in future improve the predictability of K p,uu,brain and K p,uu,csf even for P-gp and BCRP substrates, although,our approach will be needed to validate 5

16 K p,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 including active efflux transport at the BBB can reasonably describe the K p,uu,csf/brain of drugs, even including P-gp and Bcrp substrates, by introducing in vitro in vivo scaling factors for P-gp and Bcrp. 6

17 Authorship contributions Participated in research design: Hiroshi Kodaira, Hiroyuki Kusuhara, Yuichi Sugiyama Conducted experiments: Hiroshi Kodaira Performed data analysis: Hiroshi Kodaira, Hiroyuki Kusuhara, Yuichi Sugiyama Wrote or contributed to the writing of the manuscript: Hiroshi Kodaira, Hiroyuki Kusuhara, Eiichi Fuse, Junko Ushiki, Yuichi Sugiyama 7

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23 Footnote This study was supported by the Japan Society for the Promotion of Science; Grant-in-Aid for Scientific Research (S) [4900], and Scientific Research (B) [ ]. 3

24 Figure legends Figure Schematic diagram illustrating the three-compartment model C blood, C brain, C CSF : concentrations of drug in blood, brain, and cerebrospinal fluid (CSF); V, V, V 3 : volumes of the brain capillary lumen, brain, and ventricles; f blood, f u,brain, f u,csf : unbound fraction in blood, brain, and CSF; : product for passive permeability at blood brain barrier; : diffusion between brain and CSF; 3 : product for passive permeability at blood CSF barrier; 4 : product for P-gp- and/or Bcrp-mediated efflux from brain to blood; CL bulk flow : bulk flow rate of CSF; k inf : infusion rate; CL: total clearance of unbound drug. Figure Comparison of predicted and observed K p,uu (K p,uu,brain, K p,uu,csf, K p,uu,csf/brain ) of 9 compounds in rats The predicted K p,uu,brain and K p,uu,csf values were obtained by simultaneously fitting the observed K p,uu,brain and K p,uu,csf of 9 compounds in rats to equations (9) and (0) using a nonlinear least squares method (WinNonlin, version 5.. Pharsight) for () (A) and () (B). Predicted K p,uu,csf/brain values were calculated as K p,uu,csf divided by K p,uu,brain. Predicted values of K p,uu,brain, K p,uu,csf, and K p,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 - and 3-fold, respectively., antipyrine;, buspirone; 3, caffeine; 4, carbamazepine; 5, citalopram; 6, daidzein; 7, dantrolene; 8, diazepam; 9, flavopiridol; 0, genistein;, loperamid;, midazolam; 3, phenytoin; 4, quinidine; 5, risperidone; 6, sertraline; 7, thiopental; 8, verapamil; 9 zolpidem 4

25 Table Physicochemical parameters to predict passive BBB permeability and in vitro transport activities of Bcrp and P-gp for 9 compounds MW, clogd at ph 7.4, and TA of test compounds were obtained using ACD/PhysChem Suite (version, ACD/Labs, Toronto, Canada). The vsa_base was obtained using MOE 00 (Chemical Computing Group, Montreal, QB, Canada). The values observed at the BBB (observed ) in rats were obtained by Liu et al. (004) (a) and Summerfield et al. (007) (b). The calculation of the () and () of test compounds is described in the Materials and methods section. 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., 0). CFRs that showed statistical significance were included in the calculation, otherwise CFR was regarded as., 3, and 4 were calculated using fitted parameters. Compound physicochemical parameters clearance (ml/min/kg) CFR MW clogd ph 7.4 TA vsa_base Observed () 3 4 () 3 4 Bcrp P-gp Substrate of P-gp and Bcrp Antipyrine a non-substrate Buspirone non-substrate Caffeine a non-substrate Carbamazepine b non-substrate Citalopram b non-substrate Daidzein Bcrp Dantrolene Bcrp Diazepam b non-substrate Flavopiridol P-gp, Bcrp Genistein Bcrp Loperamide P-gp Midazolam b non-substrate Phenytoin b non-substrate Quinidine a P-gp Risperidone b P-gp Sertraline b non-substrate Thiopental non-substrate Verapamil P-gp Zolpidem non-substrate DMD Fast Forward. Published on March 8, 04 as DOI: 0.4/dmd Downloaded from dmd.aspetjournals.org at ASPET Journals on November 6, 08

26 Table List of parameters used to describe the disposition of test compounds in the brain and CSF Equations () (3) were solved under steady-state conditions to obtain K p,uu,brain (equation 4) and K p,uu, CSF (equation 5). 3 was substituted for divided by A. B and C were defined as the in vitro in vivo scaling factors for P-gp- and Bcrp-mediated efflux at the BBB. Parameters A D were obtained by simultaneously fitting the observed K p,uu,brain and K p,uu,csf of test compounds to equations (9) and (0) using a nonlinear least squares method (WinNonlin, version 5.. Pharsight). Parameters concentration C blood concentration in the blood C brain concentration in the brain C CSF concentration in the ventricles volume V distribution volume in the body V volume in the brain V 3 ventricle volume clearance passive clearance in the BBB (ml/min/rat) clearance for exchange across the ependymal layer 3 passive clearance in the BCSFB 4 active efflux in the BBB CL bulk flow bulk flow rate (0.009, Suzuki et al., 985) CL Total body clearance unbound fraction f blood unbound fraction in the blood f u,brain unbound fraction in the brain f u,csf unbound fraction in the CSF others k inf infusion rate free parameters A ratio of to 3 for fitting B scaling factor for P-gp C scaling factor for Bcrp D coefficient in Eq. (7) 6

27 Table 3 Accuracy and precision of the prediction of K p,uu,brain, K p,uu,csf, and K p,uu,csf/brain for 9 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 two (% fold error ) and three (% fold error 3) are presented for each. The prediction accuracy and precision of each were characterized using the average fold error (AFE), absolute average fold error (AAFE), and root mean square error (RMSE). % -fold % 3-fold r Accuracy Precision Permeability K p,uu,brain K p,uu,csf K p,uu,csf/brain K p,uu,brain K p,uu,csf K p,uu,csf/brain K p,uu,brain K p,uu,csf K p,uu,csf/brain AFE AAFE RMSE 63% 84% 84% 00% 90% 00% () (/9) (6/9) (6/9) (9/9) (7/9) (9/9) 63% 84% 79% 95% 90% 00% () (/9) (6/9) (5/9) (8/9) (7/9) (9/9) DMD Fast Forward. Published on March 8, 04 as DOI: 0.4/dmd Downloaded from dmd.aspetjournals.org at ASPET Journals on November 6, 08

28 k inf Brain Blood CSF C brain V f u,brain C CSF V 3 f u,csf 4 3 CL bulk flow C blood V f blood wnloaded from dmd.aspetjournals.org at ASPET Journals on November 6, 08 CL Figure

29 (A) Observed value (B) K p,uu,brain K p,uu,csf K p,uu,csf/brain Predicted value Observed value Predicted value Observed value wnloaded from dmd.aspetjournals.org at ASPET Journals on November 6, Predicted value Observed value Observed value Observed value Predicted value Predicted value Predicted value Figure