Development of a Physiologically-Based Pharmacokinetic Model of the Rat Central Nervous System

Central nervous system (CNS) drug disposition is dictated by a drug’s physicochemical properties and its ability to permeate physiological barriers. The blood–brain barrier (BBB), blood-cerebrospinal fluid barrier and centrally located drug transporter proteins influence drug disposition within the central nervous system. Attainment of adequate brain-to-plasma and cerebrospinal fluid-to-plasma partitioning is important in determining the efficacy of centrally acting therapeutics. We have developed a physiologically-based pharmacokinetic model of the rat CNS which incorporates brain interstitial fluid (ISF), choroidal epithelial and total cerebrospinal fluid (CSF) compartments and accurately predicts CNS pharmacokinetics. The model yielded reasonable predictions of unbound brain-to-plasma partition ratio (Kpuu,brain) and CSF:plasma ratio (CSF:Plasmau) using a series of in vitro permeability and unbound fraction parameters. When using in vitro permeability data obtained from L-mdr1a cells to estimate rat in vivo permeability, the model successfully predicted, to within 4-fold, Kpuu,brain and CSF:Plasmau for 81.5% of compounds simulated. The model presented allows for simultaneous simulation and analysis of both brain biophase and CSF to accurately predict CNS pharmacokinetics from preclinical drug parameters routinely available during discovery and development pathways.


Introduction
Quantification of central nervous system (CNS) drug levels in brain interstitial fluid (ISF) and cerebrospinal fluid (CSF) is often achieved by complex in vivo experimental procedures, such as microdialysis. This technique has the inherent advantage of directly measuring the concentration of unbound drug in the accessible brain biophase under non-steady state and steady-state conditions [1,2], reflecting both drug influx and efflux processes acting within the CNS. To be able to quantify the brain pharmacokinetics of a compound of interest, microdialysis offers the advantage of multiple time-point sampling within the same animal, although the procedure leads to local tissue damage around the site of probe insertion [3,4] and is an experimental procedure often limited to lower-species, although neuroimaging techniques, such as positron emission tomography, have been utilised in both lower-and higher-species to quantify temporal drug concentrations in brain [5]. Microdialysis and PET (positron emission tomography) are often considered the "gold-standard" for assessing (regional) brain disposition of drugs, but can be limiting due to their technical and experimental complexity, which may hinder widespread use in pre-clinical studies.
The ability to determine the relationship between systemic exposure and CNS drug disposition is an important focus for pharmaceutical industry and drug development programs. Typically, pre-clinical measurement of drug partitioning between the CNS (brain tissue and CSF components) and plasma to yield total brain-to-plasma concentration ratio, Kp brain is conducted in rodents and Kp brain is then converted to the unbound concentration ratio (Kp uu,brain ) by multiplication with plasma unbound drug fraction (fu p ) (Equation (1) C, total concentration; C u , unbound concentration; V u , unbound brain volume of distribution) [6]. The steady-state unbound brain-to-plasma ratio (Kp uu,brain ) (Equation (2)) or steady-state cerebrospinal fluid-to-plasma concentration ratios (CSF u :Plasma u and CSF:Plasma u ) (Equations (3) and (4) respectively) are routinely used to represent CNS disposition of pharmacologically active drugs within the CNS. Kp brain = C brain C plasma and Kp uu,brain = Kp brain Vu brain × fu p (1) Kp uu,brain = C u brain × dt  (4) Kp uu,brain and CSF u :Plasma u values less than 1 typically indicate restricted entry into the brain or CSF-compartments, predominantly a result of efflux or uptake transport proteins respectively, whereas values greater than 1 indicate unrestricted entry into the brain or CSF, facilitated by active transport. Values close to unity indicate predominantly passive transport of drug.
A major factor in successful delivery of drugs to the CNS is circumvention of physiological barriers. The ATP-binding Cassette (ABC) efflux transporters P-glycoprotein [7], breast cancer resistance protein (BCRP) and several multidrug resistance-associated proteins (MRPs) are expressed at the BBB (blood-brain barrier) [7][8][9][10]. Mdr1 knockout studies in mice reveal that P-glycoprotein significantly influences CNS disposition of both non-CNS targeted and CNS targeted therapeutics including amitriptyline, nortriptyline [11], olanzipine [12], buspirone, chlorpromazine, fluvoxamine, risperidone, zolpidem [13] and fexofenadine [14]. Similar reports of altered brain penetration of imatinib [15], oseltamivir [16] and genistein [17] have been reported in breast cancer resistance protein knockout mice. In addition to BBB-associated ABC transporters influencing CNS drug disposition, expression of highly restrictive tight junction complexes at the BBB (the transcellular electrical resistance is reported to be between 1000 and 1800 Ω cm 2 [18][19][20]) results in only limited passive diffusion of hydrophilic, low molecular weight (<400 Da) compounds [21] across the BBB into the CNS.
The blood-cerebrospinal fluid barrier (BCSFB) also can regulate entry of compounds into the CNS [22] and is an important consideration when describing CNS drug disposition. The BCSFB is located next to the choroidal epithelium, a continuous single layer of polarized epithelial-like cells, possessing tight junctions [23], which line the surface of the choroid plexuses. There are important physiological differences between the BBB and BCSFB. In vitro measurements suggest the transcellular electrical resistance of the BCSFB is approximately 10-to 15-fold less than that of the BBB, at 80-100 Ω cm 2 [18][19][20]. Unlike the BBB, the choroidal epithelium possesses extensive microvilli and studies suggest the total surface area of the choroid plexuses may be 10-fold greater than previous estimates, placing the surface area within a similar order of magnitude to that of the BBB [24][25][26][27][28], and resulting in in vivo BCSFB clearance measurements, per gram of brain, which may be similar to or greater than that at the BBB [29]. However, both P-glycoprotein [30,31] and BCRP [31] have been reported to be expressed at the apical plasma membrane of the choroidal epithelium, and have the potential to transport drugs from the choroidal epithelium into the ventricular CSF. It is therefore important that the differential transport directionalities at the BBB and BCSFB sites are taken into consideration when attempting to predict drug disposition within the CNS.
Efflux transporter proteins at the BBB will therefore limit penetration of compounds into the brain and impact on CNS disposition, whereas efflux transports at the BCSFB will act to potentially enhance the accumulation of compounds in the CSF. Consequently, for highly effluxed drugs there is often a discrepancy between the effects of efflux at the BBB (influencing Kp uu,brain ) and the BCSFB (influencing CSF u :Plasma u ) [32][33][34].
Clearly, the measurement of brain unbound concentrations would provide a better indicator for assessing CNS disposition, but microdialysis is not an option routinely employed, pre-clinically. However, determination of the extent of non-specific brain tissue binding (fu brain ), using brain slice and brain homogenate methods, is utilised to drive forward an understanding of overall brain drug penetration. Thus, an understanding of the role of drug transporter proteins at both the BBB and BCSFB coupled with knowledge of brain tissue binding is crucial in order to more effectively predict CNS drug disposition (Kp uu,brain and CSF u :Plasma u ) and facilitate early pharmacokinetic predictions and selection of compounds for further development [13,35].

Model Development
A whole-body PBPK model was constructed in Matlab (version 8.1). The model consisted of the following compartments: lung, bone, brain vascular space (V), brain extravascular space (EV), cerebrospinal fluid (CSF), choroid plexus (CP), heart, kidney, liver, muscle, adipose, skin, pancreas, gut, spleen, and arterial and venous blood ( Figure 1). All tissue compartments were considered well stirred (perfusion limited) except for CNS-related compartments ( Figure 1). Mouse and rat tissue volumes and perfusion rates were sourced from literature sources [58] (Table 1) with drug tissue partition coefficients calculated from the tissue-composition-based approach [59,60] using LogP and pKa parameters predicted using ChemAxon (http://www.chemaxon.com) or obtained from the literature (see Supplementary Information). Where absent in the literature, blood flow was scaled based on an allometric function (weight 3/4 ), and tissue volumes scaled to body weight [61,62], assuming a mouse body weight of 30 g and rat body weight of 250 g [58] (see Supplementary Information).  [58]; b taken from Brown et al. [58] or blood flow scaled to the 0.75 of body weight and tissue volumes scaled to body weight (bold) [61,62]; c assuming hepatic artery flow is 2% (mouse) and 2.1% (rat) of cardiac output [58]; d assuming portal vein flow is 14.1% (mouse) and 15.3% (rat) of cardiac output [58]; e fractional volume of brain intravascular fluid, 0.014; Fractional volume of brain interstitial space, 0.188 [63], assuming brain weight of 1.8 g in rats and 0.36 g in mice [64]; f average of values reported from Eyal et al. [65] and Stange et al. [66]; g taken from Jay et al. [67]; h Brain IVS: brain intravascular space; i taken from Abbott et al. [68]; and j assuming choroid plexus (CP) weight is 0.2% of brain weight [69].
The CNS was comprised of brain IVS (intravascular space), brain ISF and CSF compartments. A rate-limited permeability barrier between the IVS and ISF and IVS and CSF represented the BBB and BCSFB respectively, and was incorporated into the model as passive bi-directional clearance terms (CL passive ) and active efflux terms (CL active ) modeling both passive and active flux of compounds across each permeability barrier ( Figure 1). Bulk flow of ISF was incorporated within the model to represent the flow of unbound brain ISF drug to CSF. Unbound drug fractions in plasma (fu p ), brain ISF (fu b ) and cerebrospinal fluid (fu CSF ) were incorporated into the plasma, brain and CSF compartments respectively.
Well-stirred organs were described by the following equation: where C is the concentration of drug, Q t is the tissue perfusion rate, C art is the arterial drug input, V t is the volume of tissue compartment and Kp t is the partition coefficient of the tissue compartment. The removal of drugs from the eliminating organs (liver and kidney) was described by additional clearance terms (hepatic clearance: CL H and renal clearance: CL R ). Hepatic clearance was predicted from in vivo data (human blood or plasma clearance: CL b or CL p) or in vitro data (in vitro intrinsic metabolic clearance: CL int, in vitro ) and renal clearance was calculated using a GFR (glomerular filtration rate) correction approach [70].
When using CL b or CL p as an input, the in vivo intrinsic clearance (CL int, in vivo ) was calculated (Equation (6)) by, if necessary, correcting for the blood:plasma ratio (R b ) (Equation (7)) (or, where not available, by assuming R b = 1 for basic drugs and R b = 0.55 for neutral and acidic drugs), and scaled using an allometric function of body weight (weight 3/4 ) to yield a species-specific CL int, in vivo .
When using the in vitro intrinsic metabolic clearance (CL int, in vitro ) as input, an in vivo intrinsic clearance (CL int, in vivo ) term was calculated by scaling CL int, in vitro accounting for microsomal recovery (microsomal protein content (rat: 45 milligrams protein per gram of liver [71] or hepatocellularity 130 × 10 6 cells per gram of liver) [72,73] and rat or mouse liver weight (40 grams per kilogram body weight [58] and 88 grams per kilogram body weight [71] respectively. The unbound hepatic plasma clearance was then calculated using a well-stirred liver model (Equation (8)), where hepatic blood flow (Q h ) was assumed to be 55 mL min −1 kg −1 (rats) and 90 mL min −1 kg −1 (mice) [71].
For compounds which are cleared renally, unbound renal clearance (CL R ) was predicted using the GFR approach described by Lin [71] and by assuming a rat/human GFR ratio of 4.8 and a mouse/human GFR ratio of 6.6 (Mouse GFR = 12 mL/min/kg [74]), corrected for rat fu plasma .
Permeability rate-limited transport across the BBB was described by Equations (9) where Q t is tissue perfusion rate, V ev is extra-vascular volume, V v is the vascular volume, CL passive is the passive clearance across the BBB (subscript denotes either luminal-to-abluminal or abluminal-to-luminal flux), fu p is free drug fraction in plasma and fu b is free drug fraction in brain. Permeability rate-limited transport across the BCSFB was described by Equations (11) and (12 where Q t is the perfusion rate, V cp is choroid plexus cellular volume, V CSF is the CSF volume, CL passive is the passive clearance across the BCSFB (subscript denotes either basolaterial-to-apical (BA) or apical-to-basolaterial (AB) flux), fu b is free drug fraction in brain, fu p is free drug fraction in plasma, fu CSF is free drug fraction in CSF and C ev is the concentration in the brain extravascular compartment.

Extrapolation of Passive Transport
Where apparent permeability (P app ) was reported in the absence and presence of transporter inhibitor, passive transport was assumed to be represented by the extent of inhibition. Where apparent permeability was reported in wild type and knock-out animals, passive transport was assumed to be the difference in apparent permeability. Passive bi-directional transport across the brain capillary was assumed to be represented by the apical-to-basolateral flux (P app,AB ) and basolateral-to-apical flux (P app,BA ) in the non-transfected LLC-PK1 cell line (by correcting for the insert surface area (0.33 cm 2 ) and expressed as cm/h), and extrapolated to in vivo CL passive for the luminal-to-abluminal (blood-to-brain) and abluminal-to-luminal (brain-to-blood) directions. Passive transport was effectively extrapolated to an in vivo passive clearance term based on correction for in vivo brain vascular endothelial surface area (SA), 150 cm 2 g brain −1 for rats [75] and 240 cm 2 g brain −1 for mice [44] and brain weight (rat: 0.57% of body weight; mouse: 1.6% of body weight [58]) yielding CL passive,LA (Equation (13)) or CL passive,AL (Equation (14)).
No studies have directly correlated drug permeability, in vitro or in vivo, at the BCSFB and the BBB. However, the in vivo permeability-surface area product (PS) of quinolone antibiotics at the choroid plexus [76,77] has been modeled in rats, and whilst based on pharmacokinetic modeling approaches, yielded similar in vivo permeabilities at the BBB (PS BBB ) and BCSFB (PS CSF ), when corrected for tissue weight. Furthermore the paracellular permeability of sucrose in monolayers of primary rat brain endothelial cells (average of 5 studies: 2-11 × 10 −6 cm/s [78][79][80][81][82], is similar to that reported in monolayers of primary rat choroid plexus cells (7 × 10 −6 cm/s [83]).
Due to the absence of either in vitro or in vivo choroidal epithelial permeability data for many compounds, passive flux across the BCSFB was extrapolated based on correcting for in vivo choroid plexus surface area (75 cm 2 in rats [27]) to yield an in vivo permeability clearance at the BCSFB (CL passive, BCSFB ) (Equation (15)): Bi-directional flux (CL passive, apical-to-basolaterial and CL passive, basolaterial-to-apical ) and active efflux at the BCSFB was parameterised using a similar approach to that detailed for the BBB.
When using in vivo reported CL passive to describe passive permeability at the BBB, CL passive at the BCSFB was scaled based on the BCSFB:BBB surface area.

Extrapolation of Active Transport
Effective extrapolation of in vitro determined active transport data requires knowledge of cellular transporter expression within the in vitro system and within the target tissue to account for variations in transporter expression. To address this, Ball et al. [43] reported an approach that utilised either a relative activity factor (RAF) or a physiological scaling factor to relate activity/expression of transporters within in vitro systems to an in vivo metric. Furthermore, Hoffmeyer et al. [84] suggested that the transport activity of P-glycoprotein in human is dependent on the level of protein expression. Similarly, Shirasaka et al. [85] and Tachibana et al. [86] also demonstrated that P-glycoprotein transport activity in vivo was proportional to its protein expression levels in vitro. Given these findings we have assumed mdr1a activity is directly related to mdr1a protein expression level and the in vitro intrinsic transport activity of mdr1a (transport rate per mdr1a protein) is identical to that in vivo in rats. The availability of P-glycoprotein and BCRP efflux kinetics terms is limited for a vast number of compounds in the literature and hinders widespread utilisation of PBPK modeling to assess the brain distribution of drugs. In lieu of widespread and robust Michaelis-Menten kinetics parameters for transporter substrates, the active efflux component of drug transport was described by a corrected efflux ratio (ER) [55,87] (Equation (16)) derived from the ratio of the efflux ratio in mdr1-or BCRP-transfected cells and vector-transfected control cells.
To correct for the difference in protein abundance between in vitro cell lines and brain capillaries, an abundance-scaling factor (ASF) was incorporated to represent the ratio of in vivo-to-in vitro capillary abundance of transporter protein in cell lines (see Section 2.1.5) and either mice (P-glycoprotein; 14.1 fmol/μg protein or BCRP; 4.41 fmol/μg protein [56]) or rats (P-glycoprotein; 19.1 fmol/μg protein or BCRP; 4.95 fmol/μg protein [57]). For BCRP, in vitro abundance data were not available in the MDCK-II-BCRP cell line and therefore ASF was set as equal to 1. Subsequently active clearance was incorporated into the model as the product of the corrected in vivo efflux ratio and luminal-to-abluminal passive clearance (Equation (17)).
CL active = ER corrected × CL passive,LA × ASF (17) Active efflux at the BCSFB was modelled using a similar approach, with directionality of efflux transport being from the systemic circulation into the CSF. The proposed model incorporates active efflux for two widely investigated drug efflux transporters, P-glycoprotein and BCRP. Alternative transporter proteins with similar transport directionality could be paramatised within the model using in vitro passive and active permeability data for a specific transporter protein along with the protein abundance of the transporter(s).

Model Validation: Prediction of Temporal Brain and Plasma Concentrations in Rats
To validate the PBPK model the plasma and brain concentrations of the antibiotic norfloxacin were modeled and compared to in vivo measurements in rats. Norfloxacin plasma pharmacokinetics in rats, following an intravenous (IV) bolus of 150 mg kg −1 , has been described by a 2-compartment model [88]. For modeling purposes, the unbound fraction of norfloxacin in brain was assumed to be equal to 1. This approach can be rationalised since the unbound brain volume of distribution (V u,brain ) [89] for norfloxacin (0.98 ± 0.59 mL g brain −1 ), is similar to the brain water volume (0.8 mL g brain −1 ) [90] suggesting limited brain binding. Predicted norfloxacin brain ISF-and plasma concentration-time profiles were compared with in vivo norfloxacin brain ISF (determined using microdialysis) and plasma concentration-time profiles from 10 rats (pharmacokinetic data provided by Chenel et al. [88]).

Prediction of Kp uu,brain and CSF u :Plasma u in Rat
The rat CNS hybrid PBPK model was used to predict Kp uu,brain and CSF u :Plasma u . Permeation across the BBB and BCSFB was incorporated into the model using in vitro permeability determined in the L-mdr1a cell line, as reported by Uchida et al. [55] and detailed in Section 2.1.3. All compounds were simulated as intravenous bolus doses. Kp uu,brain and CSF u :Plasma u were predicted for a dataset of 25 compounds where in vitro permeability, fu plasma , fu brain , fu CSF , Kp uu,brain and CSF u :Plasma u had previously been reported in rats [53] (see Supplementary Information).

Prediction of Kp uu,brain for Actively Effluxed Compounds in Mice
In order to assess the utility of in vitro-derived cell culture permeability data to predict CNS drug disposition for actively effluxed compounds in mice, a whole body CNS PBPK model was parameterised with physiological tissue volumes and perfusion rates obtained from literature [91], with any absent data assumed to be equivalent to rats [59,60]. Permeation across the BBB and BCSFB was incorporated into the model using in vitro permeability determined in the L-mdr1a cell line, as reported by Uchida et al. [55] and the brain disposition of 11 P-glycoprotein substrates was modeled and predictions compared to reported Kp uu,brain in mice [55]. All compounds were simulated as intravenous bolus doses.

Sensitivity Analysis
To further explore the factors that influence the disposition of drugs into the brain biophase, a series of additional simulations were conducted exploring the impact of variation in CL passive (luminal-to-abluminal and abluminal-to-luminal were assumed equal), ER, fu plasma and fu brain on Kp uu,brain and CSF u :Plasma u utilising input parameters based on a model compound selected from the Kp uu,brain and CSF u :Plasma u predictions.

Assessment of Prediction Accuracy
The predictability of individual compounds was assessed using a fold-error (FE) approach where: Predicted > Observed: Observed > Predicted: FE= observed predicted (19) Prediction accuracy was assessed by the average fold error (afe) approach (geometric mean error) (Equation (20)): Precision of prediction was assessed using root mean squared error (rmse) (Equation (21)) where n refers to the number of observations. 1 prediction observed The percentage of compounds within a 3-fold, 4-fold, 5-fold and >5-fold error was derived from predicted and observed values.

Results and Discussion
The availability of in vivo permeability measurements for candidate compounds undergoing pre-clinical assessment often remains a limiting factor for efficient and effective use of pharmacokinetic models attempting to model CNS drug disposition. Consequently, in vitro permeability data for passively and actively transported compounds are often used to extrapolate to in vivo permeability. Polli et al. [92] demonstrated a linear relationship between brain penetration (Kin) in rat in situ brain perfusion studies and apparent permeability in MDCK type-1 cells with a correlation coefficient of 0.86. A similar trend was reported between brain uptake index (BUI) and permeability across bovine brain endothelial cell cultures, with a correlation coefficient of 0.89 [50]. In more recent studies Uchida et al. [54] and Kodaira et al. [53] have demonstrated the utility of murine-mdr1a-expressing LLC-PK1 cells (L-mdr1a) to reconstruct Kp uu,brain and CSF u :Plasma u for a handful of P-glycoprotein substrates.
Our primary goal was to build upon existing approaches aimed at mechanistically predicting CNS drug disposition and examine the potential application of drug permeability data derived from L-mdr1a cells to predict Kp uu,brain in mice and both Kp uu,brain and CSF u :Plasma u in rats. Development of a PBPK model capable of predicting CNS drug disposition by extrapolation of in vitro-derived data may prove a valuable resource for rapid pre-clinical screening of candidate compounds during development.

Validation of the PBPK Model
To validate the PBPK model structure and the ability to predict both plasma and brain ISF temporal concentrations, we selected norfloxacin as a model compound and utilised published rat norfloxacin plasma data and brain pharmacokinetic data obtained by microdialysis [88].
Norfloxacin plasma ( Figure 2) and brain ( Figure 3) temporal concentration profiles were both predicted to be within the ranges observed in vivo. Simulation of brain ISF norfloxacin concentration-time profile using literature derived CL passive (value obtained from fitting to in vivo data) [76,77] in the absence of a P-glycoprotein/BCRP-type active efflux component yielded predictions in which the absorption and elimination phases were outside the range observed in vivo (Figure 3). Subsequent simulations using a CL passive 2-fold higher than the initial fitted value ( Table 2) and P-glycoprotein/BCRP-type active efflux processes (efflux ratio of 3) resulted in absorption and elimination phases within the range reported in 10 rats by Chenel et al. [88] (Figure 3).
Importantly, incorporation of an active efflux component (P-glycoprotein/BCRP type) within our simulations corrected the over-prediction in brain ISF drug concentrations and demonstrated the importance of an efflux clearance mechanism in governing norfloxacin CNS drug disposition. These findings are consistent with those of Chenel et al. [88] who demonstrated the influence of efflux clearance mechanisms on norfloxacin brain pharmacokinetics. The inclusion of a P-glycoprotein/BCRP type active efflux component within our norfloxacin simulations is supported by a recent report demonstrating norfloxacin to be a BCRP substrate [93].  Model predicted norfloxacin brain concentrations in rats. Crosses represent literature reported brain concentration determined in rats following an IV-bolus dose [88]. Closed circles represent model predicted norfloxacin brain concentrations in rats in the absence of efflux. Open circles represent model predicted norfloxacin brain concentrations in rats in the presence of efflux (efflux ratio = 3).

Prediction of Central Nervous System (CNS) Disposition Using L-mdr1a in Vitro Permeability Data
Recent studies report positive correlations between drug permeability assessed in the LLC-PK1 porcine kidney cell line transfected with murine mdr1 (to produce the L-mdr1a cell line) and in vivo brain distribution of P-glycoprotein substrates in rats and mice [53].
Furthermore, due to the similarity in the abundance of P-glycoprotein in L-mdr1a cells (15.2 fmol/μg protein) compared to the abundance in brain capillaries (Mouse: 14.1 fmol/μg protein [56]; rat: 19.1 fmol/μg protein [57]), we examined the use of L-mdr1a-derived in vitro permeability data in predicting CNS drug disposition.
In an attempt to examine the validity of the scaling approach to determine permeability clearance at the BBB, based on extrapolating in vitro permeability data, we obtained literature reported in situ brain permeability-surface area products (PS) for 16 compounds spanning over a 100-fold range of PS.
With  [96] in cultured kidney epithelial cells, and support the extrapolation approach.

Prediction of Kp uu,brain for 11 Actively Transported Compounds in Mice
Using L-mdr1a-derived permeability data reported by Uchida et al. [55], the predicted Kp uu,brain for over 90% of P-glycoprotein substrates was within 4-fold of observed Kp uu,brain . The predicted Kp uu,brain for all compounds was within 5-fold of observed Kp uu,brain ( Figure 4A,B), with an overall afe and rmse of 0.7 and 0.23 respectively (Table 3).  Uchida et al. [55] successfully demonstrated that Kp brain (and Kp uu,brain ) could effectively be reconstructed though the integration of in vitro mdr1a transport activity and mdr1a protein expression levels in the brain capillaries and in mdr1a-transfected cell monolayers. Our model yielded reasonable predictions for passively transported and actively transported P-glycoprotein substrates and demonstrated the successful extrapolation of in vitro permeability data to yield an in vivo transfer clearance across the brain capillaries.
The basis of these predictions is quantitative calculation of the temporal drug concentrations in plasma and brain compartments. Whilst Uchida et al. [55] initially reconstructed Kp uu,brain , for the first time we have shown that, using a well-designed PBPK modeling approach, plasma and brain ISF temporal concentrations, and Kp uu,brain can be adequately predicted in mice for a range of P-glycoprotein substrates, using a simple set of physiochemical and pre-clinically determined parameters.

Prediction of Rat Kp uu,brain and CSF u :Plasma u
In an attempt to assess the utility of L-mdr1a-derived permeability data to predict cross-species CNS distribution, we utilised L-mdr1a permeability data from 25 compounds to predict in vivo CNS distribution (Kp uu,brain and CSF u :Plasma u ) in rat. Our reported model was capable of predicting rat brain disposition (Kp uu,brain ) for 81.5% of compounds simulated to within 4-fold of the reported Kp uu,brain (Table 3 and Figure 5). The predicted Kp uu,brain of quinidine was within 6.8-fold of observed Kp uu,brain , whilst that of loperamide within 7.4-fold. The overall afe and rmse were 1.19 and 0.43 respectively (Table 3).
Predicted Kp uu,brain , for compounds with observed Kp uu,brain less than 0.01 and greater than 1 deviated further from the line of unity ( Figure 5A and local regression (LOESS) plot in Supplementary Information Section 5) but were nevertheless predicted within 4-fold of the reported Kp uu,brain .
For flavopirodol and perfloxacin, the use of either MDCKII or LLC-PK1-derived cell permeability data did not significantly alter model predictions.
Kp brain for P-glycoprotein substrates ranges from 1 to 50 [97]. The Kp uu,brain of quindine and loperamide, typical P-glycoprotein substrates, were 7.4-fold over-predicted in our model. Recent reports have identified a 39.4-fold [55] to 44-fold [53] increase in Kp brain when comparing wild-type to knock-out mice for quinidine and 23.3-fold [55] for loperamide. For these highly effluxed compounds, the use of in vitro permeability data may not truly reflect the extent of in vivo efflux and therefore the use of knock-out-to-wild-type Kp brain (or Kp uu,brain ) could also be used as a surrogate metric for efflux. Such an approach improved model predictions of both loperamide (Kp uu,brain = 0.025) and quinidine (Kp uu,brain = 0.071) to within a 3-fold prediction window (see Supplementary Information Section 6). The rat CNS whole-body PBPK model was successful in predicting CSF u :Plasma u for 81.5% of compounds to within 4-fold of observed CSF u :Plasma u (Table 3 and Figure 6A,B), with CSF u :Plasma u of benzylpenicillin 5.8-fold over predicted. The overall afe and rmse were 0.8 and 0.32 respectively (Table 3).

Model Sensitivity Analysis
Several parameters, particularly passive clearance, active efflux, fu brain and fu plasma , have the potential to significantly impact CNS drug distribution by influencing drug clearance across the BBB and BCSFB. To further explore the relationship between drug clearance across the BBB and BCSFB and the extent of protein/tissue binding, risperidone was selected as a model candidate compound and the impact of variation in passive clearance, active efflux, fu brain and fu plasma on Kp uu,brain and CSF u :Plasma u was assessed.
3.3.1. Passive Clearance 3.3.1.1. Impact of Variation in fu plasma and fu brain on Kp uu,brain and CSF u :Plasma u Irrespective of whether the passive clearance (CL passive ) (i.e., passive permeability) of risperidone at the BBB and BCSFB was low (CL passive 0.34 mL/h) or high (64 mL/h), increasing fu plasma (from 0.001 to 1) resulted in a substantial increase in Kp uu,brain across the range of fu brain (0.001 to 1) simulated ( Figure 7A: transparent mesh indicates high permeability condition; coloured profile indicates low permeability condition).
Under conditions of both low and high CL passive , an increase in fu brain (from 0.001 to 1) was associated with a decrease in brain partitioning (Kp uu,brain ) of risperidone. This decrease was observed across the range of fu plasma (0.001 to 1) simulated ( Figure 7A: transparent mesh indicates high permeability condition; coloured profile indicates low permeability condition).
Overall, Kp uu,brain at high CL passive was greater than Kp uu,brain at low CL passive when fu brain < 0.1. Brain penetration is therefore influenced by the extent of plasma protein binding (fu plasma ) and the extent of drug binding within the brain (fu brain ). Whilst these observations are relatively intuitive, the importance of both fu plasma (and hence unbound drug concentration in plasma) and drug permeability across CNS barriers in influencing CNS drug disposition is clearly demonstrated for drugs that exhibit high non-specific binding to brain tissue (fu brain ). For drugs that are highly bound to brain, fu plasma drives entry of drug into the brain. Such drugs are retained within the bulk of the brain (bound-unbound cycling) creating a sink effect, and increasing BBB CL passive would enhance this sink effect further increasing Kp uu,brain [98][99][100].
The disposition of drug into the CSF was demonstrated to be sensitive to fu plasma , with increased CSF u :Plasma u associated with increasing fu plasma . This finding was apparent for both low and high CL passive conditions ( Figure 7B: transparent mesh indicates high permeability; coloured profile indicates low CL passive conditions). However, simulations were insensitive to any change in fu brain (0.001-1) ( Figure 7B). These simulations demonstrated no apparent relationship between the extent of fu brain and CSF u :Plasma u , suggesting fu brain alone does not significantly influence the unbound concentration of drug within the CSF. These findings support the notion that the extent of free drug in plasma is an important factor influencing drug penetration across the BCSFB into the CSF. Irrespective of the extent of plasma protein binding (fu plasma 0.01 (low) or 1 (high)), Kp uu,brain was insensitive to changes in CL passive at higher fu brain (fu brain > 0.1) ( Figure 7C: transparent mesh indicates high fu plasma ; coloured profile indicates low high fu plasma ). The sensitivity of Kp uu,brain to changes in CL passive increased as fu brain decreased (<0.1) ( Figure 7C).
As already established, fu plasma determines the unbound plasma drug concentration available to penetrate the BBB and BCSBF, where higher fu plasma results in an increase in the unbound drug concentration available to cross the BBB and BCSFB. Equally, drug binding in brain provides a driving force for retention of drug within the brain mass, which is evident by the increasing Kp uu,brain as fu brain decreases (irrespective of changes in CL passive ). However the important role fu brain plays in determining Kp uu,brain for highly brain-bound drugs (fu brain < 0.1) is particularly evident for lower permeability compounds (CL passive < 1); Kp uu,brain appeared not to change significantly when fu brain was between 0.001 and 0.1. However Kp uu,brain was reduced when fu brain was between 0.1 and 1 (these findings were observed with both high fu plasma and low high fu plasma conditions).

Impact of Variation in fu brain and Active Efflux on Kp uu,brain
Irrespective of the extent of plasma protein binding (fu plasma : 0.01 (low) or 1 (high)), Kp uu,brain was influenced by variations in both fu brain over the range studied (fu brain 0.001-1) and efflux ratio (2-100) ( Figure 7D: transparent mesh indicates high fu plasma ; coloured profile indicates low fu plasma ). Kp uu,brain increased as fu brain decreased from 1 to 0.001, with extensive brain accumulation (Kp uu,brain greater than 1) when fu plasma was high (fu plasma = 1) ( Figure 7D).
The increase in Kp uu,brain as fu brain decreases can be rationalised by considering that Kp uu,brain is largely driven by a combination of membrane permeability (passive and active) and drug free fraction in plasma and brain. Where permeability is low (<0.5 mL/h) the impact of variation in fu brain on Kp uu,brain is limited ( Figure 7C). When passive permeability increases (CL passive > 0.5 mL/h), and with increasing active efflux at the BBB ( Figure 7D), the extent of dug passive permeability may augment Kp uu,brain and counter the impact a reduction in fu brain would have on Kp uu,brain .

Impact of Variation in CL passive and Efflux Ratio on Kp uu,brain
The extent of non-specific binding of drug in brain (fu brain ) had a significant effect on the sensitivity of Kp uu,brain to CL passive and to active efflux (Figure 8). When drug was highly bound in brain ( Figure 8A: fu brain = 0.01 and fu plasma = 1), increasing the extent of drug efflux (efflux ratio 2-50) resulted in a progressive decrease in Kp uu,brain , which was more apparent at higher CL passive (>10 mL/h).
Interestingly, at lower CL passive (<1 mL/h), increasing the extent of active efflux had minimal effects on Kp uu,brain compared to higher CL passive (>1 mL/h). This effect was diminished when fu brain was high ( Figure 8B: fu brain = 1 and fu plasma = 1), since Kp uu,brain was not sensitive to changes in CL passive over a range of efflux ratios (2-50).

Figure 8.
Sensitively analysis of the whole-body PBPK model. The impact of variations in fu brain (A) low fu brain and (B) high fu brain , CL passive and efflux ratio on Kp uu,brain (see text for details). Fu brain governs the unbound drug concentration in brain and, in conjunction with the clearance of drug across the BBB, helps to regulate the rate and extent of CNS drug accumulation. With extensive non-specific drug binding in brain tissue ( Figure 8A), Kp uu,brain was higher than when fu brain is not a limiting factor ( Figure 8B). In the absence of an efflux effect the sensitivity of Kp uu,brain to fu brain , particularly at low CL passive (Figure 8A), may reflect enhancement of the sink effect as drug is readily able to cross the BBB and accumulate within the brain mass with a diminished abluminal-to-luminal clearance. As active efflux increases, this effect is diminished as efflux provides an additional driving force to rebalance the partition of drug between intravascular spaces and brain biophase.

Conclusions
With development of therapeutic drugs targeted to the CNS lagging behind development of drugs for other therapeutic areas there is an urgent requirement to better predict CNS drug disposition. The application of brain microdialysis and PET imaging techniques will provide a true quantitative understanding of the temporal (regional) brain concentrations, but the techniques and equipment needed for their applications in understanding CNS drug disposition is often a limiting factor to their widespread use.
To address this issue, we have developed a mechanistic, whole-body physiologically-based pharmacokinetic model incorporating both brain biophase (brain ISF) and cerebrospinal fluid compartments, which provided reasonable estimates of brain-to-plasma and CSF-to-plasma ratios using routinely determined experimental parameters (e.g., in vitro permeability, efflux ratio, fu plasma or fu blood and fu brain ). This model not only allows the simultaneous prediction of brain-to-plasma and CSF-to-plasma ratios and examination of the impact of drug permeability and blood flow on CNS drug disposition, but allows a quantitative prediction of unbound drug concentration within the CNS.
Despite the lack of availability of in vitro permeability data from representative in vitro choroid plexus cell models (such as the immortalised Z310 rat cell line [101]), the model adequately predicted CSF-to-plasma ratios for over 90% of the compounds simulated. The lack of predictive models currently capable of quantifying both brain biophase and CSF drug disposition significantly hinders the assessment of drug disposition within the CNS. Current methods utilising CSF drug kinetics as surrogates for brain drug kinetics remain controversial [95,102], with many studies disagreeing with the use of CSF as a surrogate for brain [103][104][105]. The physiological differences between the BCSFB and the BBB, advocate the viewpoint that CSF and BCSFB are distinct entities when compared to the BBB. In particular, since CSF drug concentrations do not accurately reflect brain drug concentrations for many actively transported compounds, it is essential that the brain and CSF be considered as separate entities within mechanistic models.
Clearly, in the context of the interactions of drug substrates with transporter proteins, the benefit of the proposed PBPK model would be to effectively incorporate the impact of temporal concentrations on transporter activity and the impact this would have on CNS pharmacokinetics.
The proposed model is capable of predicting temporal CNS drug concentrations, however due to the lack of routinely available transporter-specific Michaelis-Menten terms for drug substrates, the proposed approach of examining overall CNS disposition (Kp uu,brain and CSF u :Plasma u ) is a valid one. In addition, the complexity of modeling the kinetics of drug-transporter protein interaction, at a cellular level, is now recognised and could potentially be examined further within the proposed model if BBB and BCSFB cellular compartments were expanded towards a semi-systems biology based model [106]. It is prudent to note however, that such approaches would benefit from the use of microdialysis or PET imaging in combination with more elaborate semi-systems biology models, to aid in the development and validation of models.
The present study reports, for the first time, a PBPK CNS model that predicts Kp uu,brain and CSF:Plasma (bound and unbound) for compounds possessing diverse pharmacokinetic characteristics. Additionally, this study illustrates the potential use of in vitro L-mdr1a-derived permeability data to predict rat CNS drug disposition within an acceptable tolerance.

Acknowledgments
The authors would like to thank Brian Houston for his advice during the preparation of this manuscript.

Author Contributions
Conceived and designed the study: R.B. Performed the simulations: R.B. Analysed the data: R.B. and J.P. Provided in-vivo microdialysis data: M.C. Wrote the manuscript: R.B.

Conflicts of Interest
The authors declare no conflict of interest.  [88] is split between hepatic (85%) and renal (15%) clearance [109].   a Permeabilities in italics represent in vivo passive influx in mice and are used in conjunction with the equivalent in situ brain permeability (italics) for correlation purposes; and b values in italics represent in situ brain permeabilities in mice used for correlation purposes. Figure S1. Correlations and confidence interval plots of in situ brain perfusion and predictions of CL passive .    [53]; b unless otherwise indicated data was taken from Hallifax et al. [113], as either plasma clearance (denoted by: p) or microsomal clearance (denoted by: m); c unless otherwise indicated, intrinsic in vivo clearance was calculated based on a well stirrer liver model assuming average hepatic blood flow (Q H , 55 mL/min/kg). Blood clearance and unbound fraction in blood were determined using the blood:plasma ratio (R b ) or by assuming a value of 1 for basic and neutral drugs and 0.55 for acidic drugs; d taken from Blum et al. [137]; e calculated from Ronfield et al. [138]; and f taken from Bres et al. [139]; na: not applicable. Table S9. Renal clearance. Renal clearance in rats (CL R ) was calculated based on glomerular filtration rate (GFR) ratio approach as described by Lin [70].  Scavone et al. (1989 [140], 1997 [141]) and Thompson et al. [142]; b taken from Rumble et al. [143]; c taken from Birkett and Miners [144]; d taken from Brogard et al. [145]; e taken from Larson et al. [146]; f taken from Stuck et al. [147]; g taken from Setchell et al. [148]; h taken from Hughes, Ilett and Jellett [149] and Verme et al. [150]; and i taken from Bres and Bressolle [140].  S6. Simulated Kp uu,brain and CSF u :P u for Loperamide and Quinidine Figure S3. Kp uu,brain model predictions for loperamide and quinidine (highlighted in black) using an in vivo surrogate efflux ratio metric for highly effluxed transporter substrates.