Abstract
This study was designed 1) to examine the effects of blood-brain barrier (BBB) permeability [quantified as permeability-surface area product (PS)], unbound fraction in plasma (fu,plasma), and brain tissue (fu,brain) on the time to reach equilibrium between brain and plasma and 2) to investigate the drug discovery strategies to design and select compounds that can rapidly penetrate the BBB and distribute to the site of action. The pharmacokinetics of seven model compounds: caffeine, CP-141938 [methoxy-3-[(2-phenyl-piperadinyl-3-amino)-methyl]-phenyl-N-methyl-methane-sulfonamide], fluoxetine, NFPS [N[3-(4′-fluorophenyl)-3-(4′-phenylphenoxy)propyl]sarcosine], propranolol, theobromine, and theophylline in rat brain and plasma after subcutaneous administration were studied. The in vivo log PS and log fu,brain calculated using a physiologically based pharmacokinetic model correlates with in situ log PS (R2 = 0.83) and in vitro log fu,brain (R2 = 0.69), where the in situ PS and in vitro fu,brain was determined using in situ brain perfusion and equilibrium dialysis using brain homogenate, respectively. The time to achieve brain equilibrium can be quantitated with a proposed parameter, intrinsic brain equilibrium half-life [t1/2eq,in = Vbln2/(PS · fu,brain)], where Vb is the physiological volume of brain. The in vivo log t1/2eq,in does not correlate with in situ log PS (R2 < 0.01) but correlates inversely with log(PS · fu,brain) (R2 = 0.85). The present study demonstrates that rapid brain equilibration requires a combination of high BBB permeability and low brain tissue binding. A high BBB permeability alone cannot guarantee a rapid equilibration. The strategy to select compounds with rapid brain equilibration in drug discovery should identify compounds with high BBB permeability and low nonspecific binding in brain tissue.
The blood-brain barrier (BBB) consists of a continuous layer of endothelial cells joined by tight junctions at the cerebral vasculature. It represents a physical and enzymatic barrier to restrict and regulate the penetration of compounds into and out of the brain and maintain the homeostasis of the brain microenvironment. Brain penetration is essential for compounds where the site of action is within the central nervous system (CNS), whereas BBB penetration needs to be minimized for compounds that target peripheral sites to reduce potential CNS-related side effects. Therefore, it is critical during the drug discovery phase to design and select compounds having appropriate brain penetration properties for drug targets that reside within and outside the CNS (Chen et al., 2003a; Golden and Pollack, 2003).
The kinetics of brain penetration consists of the extent of brain equilibrium and the time to achieve brain equilibrium. The extent of brain equilibrium is often quantified by brain-plasma partition coefficient (Kp), the ratio of total brain concentration and plasma concentration at steady state. This parameter depends upon drug binding in plasma and brain tissue, the uptake and efflux transporters at BBB, metabolism in the brain, and the bulk flow of cerebrospinal fluid (Hammarlund-Udenaes et al., 1997). If active transporters, brain metabolism and the bulk flow of cerebrospinal fluid do not contribute significantly to brain drug disposition, the free drug concentration in brain is equal to the free drug concentration in plasma, and the Kp is equal to the ratio of unbound fraction in plasma and unbound fraction in brain at equilibrium. Theoretically, the ratio of unbound brain concentration and unbound plasma concentration at steady state, Kp,free, is a better parameter to quantitate the extent of brain equilibrium (Tunblad et al., 2003). This parameter is not dependent upon plasma and brain tissue binding. In drug discovery, it is important to identify CNS-targeted compounds with Kp,free of unity by screening out substrates of efflux transporters. Extensive screening efforts have been made in the drug discovery phase to identify the substrates of known efflux transporters, such as P-glycoprotein (Adachi et al., 2001; Polli et al., 2001; Chen et al., 2003b; Lin and Yamazaki, 2003).
Although the extent of brain penetration or achievement of high free brain concentration is the most critical property, the time to reach brain equilibrium is another important perspective of the kinetics of brain penetration. In CNS drug discovery, it is often desirable to identify compounds that can quickly penetrate into brain thereby the unbound drug concentration at the targeted site in brain tissue can reach plasma unbound concentration quickly after administration. The property of quick brain penetration can be gauged by the time to reach brain equilibrium. Therefore, a short time to achieve brain equilibrium is a surrogate for a rapid achievement of active brain concentration. Rapid CNS penetration becomes essential for the compounds used for many diseases such as hypnosis (Hardman et al., 2001), status epilepsy (Li et al., 2000), and stroke (Adams and Leira, 1998). Empirical approaches to identify compounds with quick brain penetration during the discovery phase include screens to identify compounds with high BBB permeability (Di et al., 2003; Liu et al., 2004). In addition to BBB permeability, it has been implied in the literature that the time of brain equilibrium also depends upon the partition coefficient (Hammarlund-Udenaes et al., 1997). No study has been conducted to evaluate systematically the factors that determine the time to reach brain equilibrium.
The present study was designed to evaluate the effects of BBB permeability, plasma protein binding, and brain tissue binding on the time to reach brain equilibrium. The application of the results from the present study on strategies to select rapid brain penetration compounds in drug discovery is also discussed.
Materials and Methods
Chemicals. Caffeine, fluoxetine, propranolol, theobromine, and theophylline were obtained from Sigma-Aldrich (St. Louis, MO). N[3-(4′-Fluorophenyl)-3-(4′-phenylphenoxy)propyl]sarcosine (NFPS) and methoxy-3-[(2-phenyl-piperadinyl-3-amino)-methyl]-phenyl-N-methyl-methane-sulfonamide (CP-141938) were synthesized at Pfizer Global Research and Development Laboratories (Groton, CT) with purity greater than 98%. All other chemicals used in the experiments were of the highest available grade.
Animal Experiments. Male Sprague-Dawley rats (250-280 g) were obtained from Charles River Laboratories (Raleigh, NC). They were housed at controlled temperature and humidity in an alternating 12-h light/dark cycle with free access to food and water. Rats received caffeine (10 mg/kg), CP-141938 (5 mg/kg), fluoxetine (10 mg/kg), NFPS (10 mg/kg), propranolol (5 mg/kg), theobromine (10 mg/kg), or theophylline (10 mg/kg) subcutaneously. The doses were prepared in 0.9% saline and delivered in a volume of 2 ml/kg. Blood samples were collected in heparin-treated tubes at a designated time between 10 min and 24 h postdose via cardiac puncture. After centrifugation (3000 rpm, 10 min) of the blood, plasma was isolated. Brain tissue was harvested and rinsed with saline immediately after collection. The plasma and brain samples were stored at -20°C prior to analysis.
Protein Binding. The unbound fraction in plasma and brain homogenate was determined using a 96-well equilibrium dialysis method reported previously (Kalvass and Maurer, 2002). Briefly, fresh Sprague-Dawley rat plasma and brain tissue was obtained on the day of the study. Brain tissue was homogenized in 2 volumes (w/v) of 100 mM sodium phosphate buffer. Plasma, brain homogenate, and phosphate buffer (for equilibrium controls) were spiked with a compound (500 ng/ml), and 150 μl of these matrices were added to the dialysis apparatus. The receiver side contained 150 μl of phosphate buffer. The 96-well equilibrium dialysis apparatus was maintained on a shaking device in an incubator at 37°C for 5 h. Ten microliters of plasma or brain homogenate and 50 μl of buffer were taken from the apparatus and added to high-performance liquid chromatography (HPLC) vials containing 100 μl of acetonitrile. The samples were then vortexed, centrifuged, and the supernatant was stored at -20°C prior to analysis. The unbound fractions determined from diluted brain tissue homogenates were corrected to yield an estimate of unbound fraction in the intact brain tissue using a previously published method (Kalvass and Maurer, 2002).
Sample Analysis. The brain tissues were homogenized in 3 volumes (w/v) of water. Twenty microliters of plasma or brain homogenate, 20 μl of dimethyl sulfoxide, and 200 μl of acetonitrile were mixed in silanized 96-well glass tubes. For the protein binding samples, 10 μl of plasma or brain homogenate samples were mixed with 50 μl of control buffer, and 50 μl of buffer samples were mixed with 10 μl of control brain homogenate or control plasma to yield an identical matrix between buffer and nonbuffer samples. The samples were then mixed with 100 μl of acetonitrile and 50 μl of methanol water mixture (50:50, v/v) in 96-well glass tubes. After centrifugation at 3000 rpm for 5 min, the supernatant was analyzed by HPLC-tandem mass spectrometry methods.
The HPLC-tandem mass spectrometry system consisted of either a Shimadzu ternary pump (Shimadzu LC-10A; Shimadzu, Kyoto, Japan) or an Agilent quaternary pump HPLC system (Hewlett Packard, Palo Alto, CA), an autosampler, and a PE Sciex API 3000 or 4000 (PerkinElmer Sciex Instruments, Foster City, CA) mass spectrometer with a turbo ion spray interface (PerkinElmer Sciex Instruments, Thornhill, ON, Canada). A 10-μl aliquot of each sample was injected onto a HPLC column. CP-141938 was run on a Phenomenex Synergi Polar column (50 × 4.6 mm, 4 μm; Phenomenex, Torrance, CA) isocratically at 75% acetonitrile and 25% 5 mM ammonium acetate containing 0.01% formic acid and 0.1% isopropranol with a flow rate of 1 ml/min for 4 min. Propranolol, fluoxetine, and NFPS were run on a Phenomenex Primesphere C18 HC column (30 × 2.0 mm, 5 μm; Phenomenex) using a gradient pump program beginning at 5 to 10% acetonitrile and 90 to 95% aqueous 5 to 20 mM ammonium acetate containing 0.1% isopropranol with a flow rate of 0.4 ml/min. The acetonitrile increased linearly from 10 to 90% from 1.0 to 1.2 min and then maintained at 90% from 1.2 to 4.0 min. The system returned to the initial conditions in a single step and was allowed to equilibrate for 1 min. Caffeine, theobromine, and theophylline were run on a Phenomenex Luna Phenyl Hexyl column (50 × 4.6 mm, 5 μm; Phenomenex) isocratically at 20% acetonitrile and 80% 5 mM ammonium acetate containing 0.1% formic acid and 0.1% isopropranol for 5 min at a flow rate of 1 ml/min. All analytes were eluted between 1 and 4 min.
The compounds were monitored using the following mass transitions: CP-141938, 404.3→160.0 (declustering potential 51 V; collision energy 29 V); propranolol, 260.2→116.3 (36 V; 27 V); fluoxetine, 310.1→148.1 (26 V; 13 V); NFPS, 394.2→102.2 (26 V; 21 V); caffeine, 195.2→138.1 (41 V; 27 V); theobromine, 181.1→138.1 (46 V; 25 V); and theophylline, 181.1→123.1 (46 V; 23 V). The low limit of quantitation for the plasma samples of caffeine, CP-141938, fluoxetine, NFPS, propranolol, theobromine, and theophylline was 10, 1, 2.5, 1, 2, 50, and 50 ng/ml, respectively. The low limit of quantitation for the brain samples was 40, 4, 10, 4, 5, 200, and 200 ng/ml, respectively. The relative accuracy was between 80 and 120%. The contribution of residual blood in the brain tissue to the brain concentration was corrected by subtracting 3.7% of the plasma concentration from the corresponding brain concentration (Khor et al., 1991).
Brain PBPK Model. A hybrid brain PBPK model was constructed based upon a previously published whole-body PBPK model (Peng et al., 2001). The brain consists of two compartments, i.e., brain intravascular and extravascular compartments (Fig. 1A). This model was based upon the following assumptions: 1) only the unbound drug in vascular space is available to cross the BBB, and the unbound and bound compound equilibrates instantaneously within each compartment; 2) no transporter contributes significantly to the brain disposition, consequently, the uptake and efflux clearance is equal to PS, the product of BBB permeability-surface area product representing the distribution clearance across BBB via passive diffusion; and 3) cerebrospinal fluid does not significantly impact on the brain drug disposition (Wang et al., 1997).
The plasma of the hybrid PBPK model consists of one compartment for all compounds except fluoxetine. The plasma of fluoxetine consists of a central compartment and a peripheral compartment. It is assumed that the elimination only occurs in the central compartment.
For caffeine, CP-141938, NFPS, theobromine, and theophylline their mass balance rate equation for the central compartment consisting of rapid perfusion organs is: where Vp (ml/kg) is distribution volume of central compartment, Ca (ng/ml) is the concentration in central compartment, ka (h-1) is absorption rate constant, Xdose (ng/kg) is the dose administered, Clp (ml/h/kg) is systemic clearance, Q (ml/h/kg) is cerebral blood flow, and Civ (ng/ml) is concentration in the intravascular space in brain. For propranolol: For fluoxetine: where Cld (ml/h/kg) is distribution clearance between the central and peripheral compartment and Csp (ng/ml) is concentration in the peripheral compartment. The initial conditions for eqs. 1, 2, 3, and 4 is Ca = 0, Xdose = dose, Ca = dose/Vp,Ca = dose/Vp, respectively.
Its mass balance rate equation for the peripheral compartment consisting of slow perfusion organs is: where Vsp (ml/kg) is distribution volume of the peripheral compartment.
The mass balance rate equation for brain intravascular compartment is: where Viv (ml/kg) is the physiological volume of intravascular space in brain, fu,plasma is unbound fraction in plasma determined using equilibrium dialysis, Cex (ng/ml) is concentration in extravascular space, and Kp is equilibrium brain/plasma partitioning coefficient: Kp = (fu,plasma/fu,brain). fu,brain is the unbound fraction in brain tissue.
The mass balance rate equation for brain extravascular compartment is: where Vev (ml/kg) is physiological volume of extravascular space. The initial conditions for eqs. 5, 6, and 7 is Csp = 0, Civ = 0, and Cev = 0, respectively.
The Q, Vev, and Viv was assumed to be 312 ml/h/kg, 6.56 ml/kg, and 0.24 ml/kg, respectively (Peng et al., 2001). The pharmacokinetic parameters for the plasma (ka, Vp, Vsp, Clp, and Cld) were estimated by fitting eqs. 1, 2, 3, 4, 5 to the observed plasma concentrations in Fig. 2, and the pharmacokinetic parameters for the brain (PS, Kp, and fu,brain) were estimated by fitting eqs. 6 and 7 to brain concentrations using the nonlinear least-squares regression program WinNonlin (version 3.2; Pharsight Corporation, Mountain View, CA). The goodness-of-fit were assessed based on Akaike's Information Criterion (Akaike, 1976), the degree of colinearity of parameters, the degree of bias in residual error, the standard error of parameter estimates, and visual inspection of the generated curves relative to the data. A weighting scheme of 1/YPredicted was used for all fitting procedures (Liu et al., 1999).
Plasma terminal elimination rate constants (kel) for all compounds except fluoxetine were determined from Clp/Vp, where the Clp and Vp were calculated from the PBPK model. The kel of fluoxetine was estimated from eq. 8, based on a standard two-compartment open model with elimination from the central compartment, assuming the mass balance in brain is negligible: where k12 is the rate constant from central (plasma) compartment to peripheral compartment, k21 is the rate constant from peripheral compartment to central compartment, and k10 is the elimination rate constant from plasma compartment (Gibaldi and Perrier, 1982). By definition, k12 = Cld/Vp, k21 = Cld/Vsp, and k10 = Clp/Vp.
Relationship between Brain and Plasma Concentrations. To obtain an explicit expression to describe the brain-to-plasma concentration ratio (BP) time course, the brain PBPK model was simplified by removing the cerebral blood flow from the model under the assumption that BBB permeability is the rate-limiting step for brain penetration (Fig. 1B) (Hammarlund-Udenaes et al., 1997). Since brain tissue weight is less than 1% of body weight in rats (Brown et al., 1997), the amount of drug in brain tissue is much less than that in the rest of the body. Therefore, the impact of efflux of drug from brain on plasma concentration can be considered negligible. After a compound is administrated by an intravenous bolus injection, the mass balance rate equation for plasma can be described as: The mass balance rate equation for brain tissue can be described as: where Vb (ml/kg) is the volume of brain tissue and Cb (ng/ml) is concentration in the brain compartment.
Integration of the rate equations yield plasma and brain concentration-time equations: Let kel = (Clp/Vp) and kout = (PS · fu,brain/Vb), where kel and kout is the plasma elimination rate constant in and the brain elimination rate constant, respectively.
BP can be obtained from eqs. 11 and 12: According to eq. 13, compounds can be separated into two classes. For class I compounds, their kout is less than kel. Their BP increases over time after a single dose and cannot reach a plateau. Their brain terminal t1/2 is longer than the plasma t1/2. For class II compounds, their kout is greater than kel. Their BP increases initially and then reaches a plateau, and the terminal t1/2 of the brain concentration is equal to the plasma t1/2. From eq. 13, the equilibration time can be quantified with a parameter, equilibration half-life (t1/2eq), which is defined as the time to reach 50% of BP at equilibrium. It can be calculated by the following formula: If the plasma concentration maintains constant by an intravenous bolus loading dose and a constant intravenous infusion maintaining dose, the Cp will be constant (Patlak and Pettigrew, 1976). The following equation can be obtained from eq. 10: From eq. 15, the equilibration time can be quantified with another parameter, intrinsic equilibration half-life (t1/2eq,in), which is defined as the time to reach 50% of BP at equilibrium. It can be calculated by the following formula:
Results
The PS values of caffeine, CP-141938, fluoxetine, NFPS, propranolol, theobromine, and theophylline determined previously using the in situ rat brain perfusion method are presented in Table 1 (Liu et al., 2004). The unbound fractions in rat plasma (fu,plasma) and brain homogenate (fu,brain) measured by an equilibrium dialysis method are also presented in Table 1. The determined unbound fraction in rat plasma is consistent with the values reported in the literature (Bonati et al., 1984; Chauvelot-Moachon et al., 1988; Yasuhara and Levy, 1988; Shum and Jusko, 1989; Caccia et al., 1990). We observed an inverse relationship between permeability and the nonspecific binding in brain homogenate for some of the model compounds. Fluoxetine and propranolol have high PS and low fu,brain. CP-141948, theobromine, and theophylline have low PS and high fu,brain.
Determination of PBPK Parameters. The dose-normalized plasma and brain concentrations and the corresponding BP time course of the seven compounds are presented in Fig. 2. The absorption of caffeine, CP-141938, NFPS, theobromine, and theophylline was best described by a first-order kinetics process. Fluoxetine and propranolol were treated as an intravenous bolus administration due to their rapid absorption. The heterogeneous way of treating the absorption process was only used to describe the plasma concentration-time profiles and should have no impact on the calculation of parameters related to brain drug disposition. The in vivo fu,brain was calculated from fu,plasma/Kp. Brain elimination rate constant (kout) was determined from PS · fu,brain/Vb, where the PS and fu,brain were calculated from the PBPK model and Vb is the physiological volume of rat brain, 6.56 ml/kg b.wt. (Peng et al., 2001). Plasma elimination rate constants (kel) for all compounds except fluoxetine were determined from Clp/Vp, where the Clp and Vp were calculated from the PBPK model. The terminal kel of fluoxetine was estimated from Clp, Cld, Vp, and Vsp using eq. 8. All the pharmacokinetic parameters are shown in Tables 2 and 3. Large variability of the estimated PS values for caffeine and theobromine was observed. This is likely due to the lack of data points before plasma and brain reached equilibrium (Fig. 2). The PBPK model was able to describe the BP values for all the data except the last time point (7 h) for CP-141938 (Fig. 2).
Determination of Brain Equilibrium Half-Life. The observed brain equilibrium half-life (Obs. t1/2eq) was visually estimated from Fig. 2 as the time for BP to reach 50% of the BP at the plateau between 4 and 6 h (Table 3). The plasma and brain concentrations of caffeine, propranolol, theobromine, and theophylline had a similar terminal t1/2, and their BP reached a plateau in less than 0.2 h. Their Obs. t1/2eq was assigned as 0.1 h. For CP-141938 and fluoxetine, the plasma and brain concentrations showed a similar terminal t1/2, and the BP reached a plateau in approximately 2 h. Their Obs. t1/2eq was assigned as 1 h. The brain concentration of NFPS exhibited a longer t1/2, and their BP did not reach a plateau at 24 h. Its t1/2eq was assigned as greater than 24 h. The t1/2eq and t1/2eq,in values were obtained using eqs. 14 and 16, respectively (Table 3).
Correlation of Pharmacokinetic Parameters. The relationship of in vivo log PS and the in situ log PS is presented in Fig. 3A (correlation coefficient R2 = 0.83). The regression equation is in vivo log PS = 1.16(in situ log PS) - 0.15. The relationship of in vivo log fu,brain and in vitro log fu,brain determined from brain homogenate is presented in Fig. 3B (R2 = 0.69). The data points appear to be clustered on the extremes of the range; therefore, more data are needed to evaluate the correlation. The relationship of log fu,plasma and log fu,brain determined from brain homogenate is presented in Fig. 3C (R2 = 0.91). The relationship of log t1/2eq,in and log(PS · fu,brain) is shown in Fig. 4A (R2 = 0.85). The relationship of log t1/2eq,in and in situ log PS is presented in Fig. 4B (R2 < 0.01).
Simulation of the Time Course of Brain-to-Plasma Concentration Ratio. BP time course data were simulated using the brain PBPK model (eqs. 1, 2, 6, and 7) to assess the effect of PS, fu,plasma, and fu,brain on the time to equilibrium (Fig. 5). The pharmacokinetic parameters used for the simulation are presented in the figure legend. The simulations demonstrate that a decrease in PS (condition 1 versus 2) or fu,brain (condition 1 versus 3) prolongs the time to equilibrium. However, the time to equilibrium did not change when PS decreased and fu,brain increased or PS increased and fu,brain decreased as long as PS · fu,brain was kept constant (data not shown). Therefore, compounds having similar PS · fu,brain should exhibit similar time to equilibrium, although they may have a much different PS. The simulations demonstrated fu,plasma has no impact on the time to equilibrium (data not shown).
Discussion
There has been a notion that a compound with high BBB permeability will in turn lead to rapid brain penetration. It was also implied in the literature that partition coefficient may play a role in the time to reach brain equilibrium (Hammarlund-Udenaes et al., 1997). However, the exact contribution of BBB permeability, plasma binding, and brain tissue binding on the time to equilibrium has not been assessed systemically. Caffeine, CP-141938, fluoxetine, NFPS, propranolol, theobromine, and theophylline were selected as the model compounds because they displayed a marked difference in their BBB permeability (160-fold), unbound fraction in plasma (14-fold), and brain tissue (560-fold).
The present study demonstrates the utility of using a hybrid brain PBPK model to calculate kinetic parameters that are directly related to physiological processes (Gibaldi and Perrier, 1982). The hybrid brain PBPK model instead of a whole-body PBPK model was used in the present study because the objective of this work was to examine the effects of plasma binding, brain tissue binding, and BBB permeability on the brain equilibrium time. The brain PBPK model describes the observed brain and plasma concentration time course and BP time course data well, except the last data point for CP-141938 (Fig. 2). This may be due to an experimental variability or slow equilibrium compartments within brain tissue as suggested previously for another P-glycoprotein substrate (Chen and Pollack, 1998). The calculated in vivo log PS from the PBPK model correlates with the determined log PS using an in situ brain perfusion method (R2 = 0.83, Fig. 3A). This study is consistent with a previous study in which Takasato et al. (1984) showed that in vivo PS values of eight solvent-like compounds using pharmacokinetic analysis were consistent with the in situ PS values (Rapoport et al., 1979). In addition, the calculated in vivo log fu,brain from the PBPK model also correlates with the determined log fu,brain determined in brain homogenate (Fig. 3B, R2 = 0.69). However, the data points are clustered at the extremes of the range, and more studies are needed to evaluate the correlation.
The present study demonstrates theoretically and experimentally that the time to equilibrium is governed by the product of PS and fu,brain. The time to equilibrium can be assessed by the time to reach the plateau of BP-time profiles (Fig. 2) (Rapoport et al., 1982). According to eq. 13, compounds can be separated into two classes. For class I compounds, their kout is less than kel. Their BP increases over time after a single dose and cannot reach a plateau. Their brain terminal t1/2 is longer than the plasma t1/2. In this study, NFPS exhibited this profile (Fig. 2). Its kout (0.14 h-1) is less than its kel (0.21 h-1). Its BP kept increasing up to 24 h postdose, and its brain terminal t1/2 was longer than its plasma t1/2 (Fig. 2). For the class II compounds, their kout is greater than kel. Their BP increases initially and then reaches a plateau, and the terminal t1/2 of the brain concentration is equal to the plasma t1/2. The BP-time profile after a single dose is similar to the plasma concentration-time profile after an intravenous infusion (eq. 13) (Gibaldi and Perrier, 1982). Six of the seven compounds belong to the class II compounds. Their kout is greater than kel, and their BP increased after administration then reached a plateau approximately between 10 min and 2 h. Their brain and plasma t1/2 values were similar (Table 2; Fig. 2).
For class II compounds, the time to reach equilibrium can be quantified with brain equilibration half-life (t1/2eq), which is defined as the time for BP to reach 50% of its plateau level after single intravenous bolus dose. A similar approach has been used in literature to describe the rate of penetration into cerebrospinal fluid (Brodie et al., 1960). The t1/2eq calculated using eq. 14 is consistent with the visually observed t1/2eq (Obs. t1/2eq) from the BP-time profiles (Table 3). Because t1/2eq is only applicable to class II compounds, we propose using the intrinsic brain equilibrium half-life (t1/2eq,in) to describe the time to equilibrium. The t1/2eq,in is defined as the time for BP to reach 50% of its plateau level under the condition of constant plasma concentration (Patlak and Pettigrew, 1976). According to eq. 16, t1/2eq,in is inversely proportional to the product of PS and fu,brain. Compounds having the same PS · fu,brain should exhibit the same time to reach brain equilibrium. These predictions were in agreement with the simulated data.
The experimental results from this study also support that t1/2eq,in is determined by the product of PS and fu,brain. Log t1/2eq,in does not correlate with in situ log PS (R2 < 0.01), however, a correlation was observed between the in vivo log t1/2eq,in and log(PS · fu,brain) (R2 = 0.85, Fig. 4A). In our theoretical analyses, it was assumed that a transporter does not contribute significantly to brain drug disposition, nevertheless, it can be demonstrated that the effect will be the same if transporters do contribute to the disposition, in which case, the efflux clearance from brain to plasma instead of PS should be used.
There is an apparent inverse relationship of PS and fu,brain for some of the model compounds. CP-141938 and theobromine have a low PS but high fu,brain, fluoxetine and propranolol have a high PS but low fu,brain (Tables 1 and 2). This inverse relationship is expected because highly lipophilic compounds tend to have a high permeability to cross the BBB and high binding with brain tissue. In contrast, less lipophilic compounds tend to have a low permeability across the BBB and less binding to brain tissue. The inverse relationship between PS and fu,brain may provide a mechanistic explanation for the observation made by Hammarlund-Udenaes (1997) that compounds having much different BBB permeability are able to reach brain equilibrium quickly.
The inverse relationship between PS and fu,brain suggests that to search for rapid brain penetration compounds in drug discovery, both PS and fu,brain or the product of PS and fu,brain should be considered. A lead compound should not be eliminated as a candidate compound with quick onset of action only because it shows low permeability. For example, theobromine is a low PS (23 ml/h/kg) and high fu,brain (0.61) compound, resulting in PS · fu,brain of 14 ml/h/kg. In contrast, fluoxetine is a high PS (619 ml/h/kg) and low fu,brain (0.00094) compound, resulting in PS · fu,brain of 0.6 ml/h/kg. As expected from the PS · fu,brain, but not from the PS, the observed t1/2eq,in for theobromine (∼0.1 h) was shorter than that of fluoxetine (∼1 h).
The theoretical analysis and PBPK simulation in this study demonstrate that plasma protein binding only determines the total brain drug concentration, not the equilibration time (eq. 16). Interestingly, log fu,plasma correlates with log fu,brain for the seven model compounds (R2 = 0.91, Fig. 3C). This apparent correlation is also supported by literature data. For a set of 18 compounds (Kalvass and Maurer, 2002), log fu,plasma correlates with log fu,brain after two outliers (compounds 4 and 8) were removed (R2 = 0.60). In addition, a good correlation was also observed for 32 compounds (R2 = 0.85) (Maurer et al., 2005). Hence, in theory, plasma protein binding per se is not related to the time to equilibrium and should not be considered as a criterion to select rapid brain equilibrium compounds in drug discovery. However, due to the empirical correlation between plasma binding and brain tissue binding, low plasma protein binding may be used as a surrogate.
Two approaches, namely a hybrid brain PBPK model and a two-compartmental brain model, have been employed in this study. The hybrid brain PBPK model approach was used to calculate in vivo fu,brain and PS values and to simulate brain and plasma data. The two-compartmental brain model is a simplified form of the hybrid brain PBPK model and was used to derive the explicit expression of the theoretical relationship. These two approaches are consistent with each other. For example, NFPS did not reach equilibrium up to 24 h postadministration. The PBPK model showed that its kel is greater than its kout. This observation is consistent with the prediction from the analyses of the two-compartmental model that equilibrium cannot be achieved if its kel is greater than kout. For the other six compounds, the PBPK model showed that the kel values are less than their kout. This observation is also consistent with the prediction from the analyses of the two-compartmental model that the equilibrium can be achieved if its kel is less than kout.
In summary, the present study demonstrates the utility of the PBPK model to calculate physiologically relevant pharmacokinetic parameters. We demonstrated that rapid brain equilibration requires a combination of high BBB permeability and low brain tissue binding. Importantly, high BBB permeability alone cannot guarantee a quick equilibration time. The strategy to select compounds with rapid brain penetration in drug discovery should identify those compounds with high PS and low nonspecific binding in brain tissue and plasma.
Footnotes
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Article, publication date, and citation information can be found at http://jpet.aspetjournals.org.
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doi:10.1124/jpet.104.079319.
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ABBREVIATIONS: BBB, blood-brain barrier; CNS, central nervous system; NFPS, N[3-(4′-fluorophenyl)-3-(4′-phenylphenoxy)propyl]sarcosine; CP-141938, methoxy-3-[(2-phenyl-piperadinyl-3-amino)-methyl]-phenyl-N-methyl-methane-sulfonamide; HPLC, high-performance liquid chromatography; PBPK, physiologically based pharmacokinetics; PS, permeability-surface area product; BP, brain-to-plasma concentration ratio.
- Received October 14, 2004.
- Accepted February 28, 2005.
- The American Society for Pharmacology and Experimental Therapeutics