Abstract
The tissue distribution kinetics of i.v. Cyclosporine A (CyA) was investigated extensively in rats. The concentration-to-time data of 11 organs were analyzed separately using local physiologically based pharmacokinetic models, involving nonlinear plasma-to-blood cell distribution, membrane-permeability-limited plasma-to-tissue distribution and either linear or nonlinear tissue binding. Two global physiologically based pharmacokinetic models were then evaluated, each comprising arterial and venous pools together with the 11 organs, adopting either of the two local models. Both global models successfully described the blood and tissue distribution kinetics of CyA. In nonlinear model, the estimated dissociation constants (Kd) for the intracellular saturable binding ranged 0.2 to 60 ng/ml among the organs, which are comparable with values reported for cyclophilin-CyA binding in vitro. The predicted human pharmacokinetic profile using the physiologically based pharmacokinetic models, after scale-up of physiological parameters from rat to human, generally agreed with the observations following i.v. and oral administration, with moderate discrepancies due presumably to uncharacterized species differences and/or the effect of i.v. vehicle on the CyA binding in plasma. Nevertheless, the models allow reasonable prediction of drug exposure at the biological target, i.e., intracellular, unbound CyA, which may differ among various organs according to the local physiological elements, e.g., tissue cellular membrane permeability. As well as helping optimize the CyA regimen in patients, who are likely to exhibit a variety of physiological and pathological conditions, the modeling suggests possible insights into the known grafted-organ specific efficacy of CyA.
The use of CyA needs careful therapeutic monitoring to prevent graft loss and side-effects, such as nephrotoxicity. In clinics, CyA concentration at trough is measured routinely and the dose to patients is controlled so that the trough concentration is maintained within an empirically safe range. Although various factors have been identified (White, 1981;Lindholm, 1991) which affect the blood concentration-time profiles of CyA, the task still remains to fully characterize its PK and to establish mechanistically the relationship between blood concentration and drug action (both efficacy and toxicity). Such knowledge seems of particular importance when a dose setting is sought for new formulations of CyA which may differ from the conventional regimen in PK profiles. PBPK modeling offers a means of achieving these objectives, because it provides a kinetic link between blood and various tissue concentrations.
Bernareggi and Rowland (1991) demonstrated the usefulness of PBPK modeling of CyA using tissue size, blood flow data and steady-state tissue-to-blood concentration measurements. They first developed a PBPK model for rats assuming each organ acted as a well-stirred compartment and then scaled-up the model to describe the plasma pharmacokinetics of CyA in humans. They also pointed out that nonlinear plasma-to-blood cell uptake of the drug is an important kinetic determinant in both rats and humans. More recently, Kawai et al. (1994) proposed a PBPK model to describe both blood and tissue kinetics of a cyclosporine derivative, SDZ IMM 125. Their approach extended the model development procedure of Bernareggi and Rowland (1991) by taking into account the anatomical subcompartments of organ/tissues;i.e., vascular, interstitial and intracellular spaces. Drug transfer among these subcompartments was limited to varying extents by membrane permeability. Furthermore, their PBPK model upon scale-up provided valuable insight into the observed time- and dose-dependent kinetics of SDZ IMM 125 in human and also helped to characterize interindividual variation in human pharmacokinetics.
In our study, blood and tissue kinetics of CyA were extensively investigated after acute dose administration to rats to establish a sound and quantitative link between blood and target (tissue) exposures by means of a PBPK model. The model was then scaled-up to predict drug exposure at local sites of action in humans, facilitating a better understanding of the relationship between efficacy and the blood PK profile.
Methods
In Vivo Experiments
Chemicals.
CyA and monoclonal antibody RIA for CyA (Sandimmun-kit; Ball et al., 1988) were supplied by Sandoz Pharma Ltd., Basel Switzerland. Commercially available CyA for intravenous administration (Sandimmun) was used directly for in vivo study in rats. Other chemicals were of analytical grade.
Animal experiment.
Male Sprague Dawley rats (256 ± 14 g) were divided into 13 time groups (two or three rats per group) for terminal tissue sampling at 2, 4, 8, 15, 30 min, 1, 2, 4, 8, 12, 16, 24 and 32 hr after completing drug administration. Intravenous CyA (5.9 mg/kg) was given to all rats as a 2-min infusion via a jugular vein cannular and blood was collected via a carotid arterial cannular. For animals in the time groups between 2 min and 1 hr only terminal blood was collected, and for those between 2 and 32 hr serial blood samples were taken at 15, 30 min, 1, 2, 6, 12, 16 and 24 hr or until the time of terminal sampling. The rats were killed by decapitation and 11 organs were dissected out and homogenized; lung, heart, kidney, bone, muscle, spleen, liver, gut, skin, fat and thymus.
Analysis of CyA.
Blood and tissue homogenates were analyzed for unchanged CyA by a previously established monoclonal antibody RIA (Bernareggi and Rowland, 1991). The coefficient of variation of the assay in fresh tissue homogenate was less than 10% and the limit of quantification was 50 ng/g tissue. The specificity of the method has been verified by a comparison with a specific HPLC assay (Guptaet al., 1987).
Models
Local (organ) PBPK models.
An organ model was proposed in our former work on a cyclosporine derivative, SDZ IMM 125 (Kawaiet al., 1994), which assumed not only “membrane-transport-limited” tissue distribution (Dedrick et al., 1973) but also an intracellular interaction component (fig.1). This model describes the intracellular interaction by slow exchange of cell-internalized drug with a “deep” binding compartment operating under linear conditions and characterized by first-order rate constants (kass and kdis). Although the model both successfully described the PK of SDZ IMM 125 in rat and predicted PK in human, the physiological or biological meaning of the tissue model assumption was left unclear. Our study uses an alternative tissue model, which assumes a rapidly equilibrating but saturable intracellular binding (NL model) to replace the “deep” binding compartment of the first linear model (LD model), and compares the two. The associated rate equations for these two models are described in the .
Two physiologically based pharmacokinetic (PBPK) models proposed for cyclosporine A (CyA) in each organ. Both models have in common a transport barrier at the cell membrane but differ in the intracellular distribution of CyA. The liner-deep-pool (LD) model assumes the existence of a slowly interacting intracellular pool with the first-order rate constants, kass and kdis, whereas the nonlinear (NL) model assumes spontaneous intracellular distribution with saturable binding characterized by a dissociation constant (KD,TC) and a capacity (Bt). The intrinsic clearance term, CLint,H only applies to the liver. A bidirectional arrow denotes instantaneous equilibrium, and a single directional arrow denotes a non-instantaneous equilibration process. RBC is the blood cell compartment in the capillary and ISF is the interstitial space. Other assumptions, terms and mass balance for each model are described in the .
Blood distribution.
Unbound fraction of CyA in plasma (fuP) was previously measured (Bernareggi and Rowland, 1991) and the reported value (0.06) was used as a concentration-independent parameter in all the models. The blood cell uptake of CyA, in contrast, is saturable and concentration dependent. The dissociation constant (KD,BC; 0.185 μg/ml) and capacity (nPT; 4.64 μg-equivalent/ml) of the blood cell binding site, measured earlier in vitro (Kawai and Lemaire, 1993), were used. Plasma and blood cell compartments in arterial and blood pool as well as tissue capillaries are modeled independently (fig. 1 and) with a permeability-surface area product (PSBC) accounting for drug exchange between them.
Interstitial drug distribution.
The method of calculating interstitial drug binding, developed previously for SDZ IMM 125 (Kawaiet al., 1994), was applied to CyA (). In brief, drug exchange between capillary plasma and interstitial fluid is assumed to occur only with unbound drug and to be instantaneous; drug partition between them is determined by the unbound fractions, i.e., fuP and fuI for plasma and interstitial spaces, respectively. In plasma, CyA interacts almost exclusively with lipoproteins (Urien et al., 1990) and the same was assumed to occur in tissue interstitium, the values of fuI in individual organs, therefore, was calculated from the respective interstitial lipoprotein concentrations (Sloop et al., 1987), assuming that both affinity and capacity of CyA binding per unit concentration of protein are independent of protein concentration. The calculated value of fuI was 0.06 for the liver and spleen, 0.17 for skin, and 0.09 for the other organs.
Clearance.
It was assumed that the liver is the only organ of elimination (Bernareggi and Rowland, 1991). Hepatic clearance (CLH) was therefore identical to systemic blood clearance (CLb) and calculated by dividing the intravenous dose by the AUCblood (infinite value; see “Data Analysis”). Intrinsic clearance (CLintH) was then calculated assuming the “well-stirred” hepatic distribution model and concentration-independent clearance (Pang and Rowland, 1977):
Data Analysis
Estimation of kinetic distribution parameters and development of PBPK models.
The number of kinetic parameters were estimated by fitting the local PBPK (LD and NL) models to the individual organ tissue concentration-time data. The parameters to be estimated are the permeability-surface area product of tissue cellular membrane (PSTC), the intracellular unbound fraction (fuT), the association and dissociation rate constants for slow intracellular interaction (kass and kdis, respectively) for LD model, whereas they are PSTC, fuT, dissociation constant (KD,TC) and capacity (Bt; μg-equivalents/g) of the saturable intracellular binding site for the NL model. The data analysis procedure used is essentially identical to that used for the analysis of SDZ IMM 125 pharmacokinetics (Kawai et al., 1994) and includes stepwise processes as follows:
1) Concentration-time profiles in arterial plasma and blood cells (CP,A and CBC,A) were generated using the arterial blood measurements and values of fuP, KD,BC, nPT and Hct, measured in a formerin vitro study (Kawai and Lemaire, 1993).
2) Using CP,A and CBC,A as input functions, model equations () were fit to the tissue concentration-time data of each organ, except the liver and lung, to estimate PSTC, fuT (both models), kass and kdis (LD) or KD,TC and Bt (NL). Drug distribution to heart tissue is assumed to occur predominantly with blood in the coronary arterial capillary bed: direct delivery of drug from ventricular blood was neglected, given the large difference in the tissue surface areas which are in contact with these two blood streams.
3) Liver data were similarly analyzed to estimate the distribution parameters except that the input functions (CBC,H,in and CP,H,in) were obtained from predicted venous outputs from spleen (sp) and gut (gu), derived by substituting the respective parameters estimated in procedure (2) into the appropriate model, as inputs into the portal vein together with arterial measurements (CP,A and CBC,A) as input from the hepatic artery (ha). That is,
4) Lung data were analyzed with the calculated mixed venous plasma and blood cell returns as the input functions (CBC,pul,in and Cp,pul,in), given by:
5) Using the parameter values estimated above, a global PBPK model can be developed for each of LD and NL models that describes drug mass balance in the entire body (according to equations EA11-EA23, Appendix). This global model was fit simultaneously to the concentration-time data in arterial blood, lung and liver to re-estimate the clearance and distribution parameters in the liver; i.e., CLint,H, fuT (both models), kass, kdis (LD), Bt and KD,TC (NL).
Steady-state tissue distribution parameters.
To compare the present dynamic data with previous tissue measurement in rats under steady-state conditions (Bernareggi and Rowland, 1991), the tissue partition coefficient, Kp, was also estimated from the tissue-to-blood ratios of AUC (Gallo et al., 1987) using finite AUC values up to 32 hr.
Calculation of AUC.
The finite AUC values (AUC32h) were calculated by the linear trapezoidal method from initiation of the i.v. infusion to 32 hr after the end of infusion, as follows. For blood, the concentration was assumed to increase in proportion to time, from zero (at the initiation of infusion) to the maximum concentration at the end of infusion, which was extrapolated using the first two blood measurements (2 and 4 min after infusion) assuming a mono-exponential decay during this period. For tissues, the concentration was assumed to increase also in proportion to time from zero (at the initiation of infusion) to the first measured concentration at 2 min after end of infusion. The infinite AUC was calculated only for blood (AUCblood), by adding the AUC32h to the extrapolated area after the last measurement (32 hr), assuming a mono-exponential decay;i.e., the terminal slope (kel) was estimated by a linear regression of the blood measurements from 4 to 32 hr post-dose and the last measured blood concentration was divided by the kel.
Software and statistics.
The model equations were described in ACSL language for simulation, and data fitting was performed using the program SimuSolv (The Dow Chemical Company, Midland, MI).
When needed, the Akaike Information Criteria (AIC; Akaike, 1976) was used to compare the acceptability of models, the preferred one being the one resulting in the smallest value of AIC.
A normally distributed error model was assumed in all the optimization procedures, i.e., γ was set to 2 (power term to the standard deviation of the error in the measurements).
Animal Scale-Up
The PBPK models developed for rat were scaled-up to human according to the method developed previously (Kawai et al., 1994). In brief, the model parameters set for rat were replaced by those for man, as follows. Physiological values (organ volume and blood flow rate) were taken from the literature; values for a 70-kg man were corrected for the average body weight of the subjects who participated in the clinical study of reference data, assuming body-weight-proportional changes in those parameters. Blood and tissue distribution parameters, fuP, KD,BC, nPT, fuI, fuT, kass, kdis, KD,TC and Bt, were assumed to be identical in mammals, per unit volume of organs. PSTC for various organs of human were predicted from the measurement in rat by use of an allometric equation
For predicting human PK after oral administration, a bioavailability (0.47) and an absorption rate constant (0.91 hr−1) had been estimated from Novartis internal data with a microemulsion formulation of CyA (Mueller et al., 1994) and these parameters were used as they are in the human model. However, a lag time before onset of the first-order absorption was necessary to mimic the delay in the absorption phase observed in the patient data; tlag of 0.3 hr was arbitrarily adopted.
Human PK data, kindly supplied by Dr. S. Gupta (single i.v. data in healthy subjects; Gupta et al., 1990) and Dr. J. Kovarik (multiple oral data in kidney transplant patients; Mueller et al., 1994), had been previously published.
Results
The concentrations of CyA in arterial blood and various organ/tissues measured in our study are shown below together with PBPK model simulations. After a 2-min i.v. infusion, the disposition kinetics of CyA in arterial blood showed a multiexponential decay, with a terminal half-life of 9.2 hr. The area under the arterial blood concentration-time curve (AUCblood) from time 0 to 32 hr postdose was 32.4 μg · hr/ml, and 35.1 μg · hr/ml when estimated to infinite time. Blood clearance was 168 ml/hr/kg. The value of CLint,H, calculated using equations 1 and 2a(fuB = 0.048; assuming linear conditions), was 3490 ml/hr/kg.
Tissue concentration-time profiles varied considerably among organs and the magnitude of distribution in individual organs was characterized by the area under the tissue concentration-time curve (AUC32h: table 1). The AUC ratio, tissuevs. blood (both 0–32 hr values), varied from 1.8 (muscle) to 11.6 (liver) and was in good agreement with the respective Kp (tissue-to-blood concentration ratio) value obtained previously in rats at steady state (Bernareggi and Rowland, 1991). The tissue distribution kinetics was also compared among the organs by plotting the tissue-to-blood concentration ratio, i.e., apparent Kp or Kp,app, against the time after dose (fig.2). The Kp,app-time profiles can be classified into three groups. For lung, kidney and liver (fig. 2A), Kp,app values were relatively constant immediately after the dose for the first 10 hr and then progressively increased afterward. Those of heart, muscle, bone, spleen and gut (fig. 2B) initially increased for the first few hours reaching a temporary plateau before further increasing as for the first group. The last group, i.e., skin, fat and thymus (fig. 2C), showed almost linear increases of Kp,app with time throughout the 32 hr. These differences in the tissue distribution reflect differences in blood perfusion rate, tissue membrane penetration or both.
Summary of blood and tissue distribution kinetic parameters in various organs; AUC from time zero to 32 hr and Kp values calculated by a AUC method (Gallo et al., 1987)
Tissue-to-blood CyA concentration ratios, Kp,app, in various organs with time in rat after drug administration. A) lung (•), kidney (□) and liver (▵); B) heart (◊), bone (▪), spleen (○), gut (⧫) and muscle (▵); C) skin (•), fat (∗) and thymus (+).
The blood and tissue measurements were then analyzed with local (LD and NL) organ models (fig. 1) adopting the stepwise procedure described in “Methods.” The arterial input functions (fig.3A) showed the concentration-dependent plasma/blood cell partition, with the plasma concentration exceeding the blood cell concentration during the first few hours and being lower thereafter. Also, these input functions differed among the various organs (fig. 3B); namely, the plasma concentration entering the lungs was highest during drug administration although that entering the liver was lowest. After drug administration, the order of plasma input concentrations was arterial blood>liver>lung. However, this difference was negligible within 0.5 hr postdose. For kidney, liver and lung, Kp,app values were constant for the initial period (fig. 2) due presumably to the high perfusion and high membrane permeabilities. Accordingly, “perfusion-limited” tissue distribution was assumed,i.e., no PS value was estimated for these organs. For the remaining organs, PS, fuT, kass and kdis were estimated for each organ by fitting individual organ data (table 2). Fitting quality or suitability of an organ model, was assessed using the sum of weighted residual squares (WRSS), maximized log-likelihood function (MLLF) and Akaike’s information criterion (AIC) as shown in table3. In general, LD and NL models achieved similar fitting quality (WRSS and MLLF), resulting in similar AIC values. An additional model, PS model, was also attempted in this model performance comparison. This model assumes no specific intracellular binding and, therefore, is identical to the other models when kass and Bt (LD and NL models, respectively) are set to zero. Data fit by the PS model was fairly good in the early postdose period while significant underestimation was observed beyond 10 h in most of the organs (results not shown). Comparison in the fitting quality parameters shown in table 3 suggests that the presence of specific intracellular binding is essential to describe the CyA tissue distribution.
Input functions developed for local PBPK model analysis in rat. A, CyA concentrations in arterial plasma (solid line) and blood cells (dotted line); B, CyA concentrations in arterial plasma (solid line), in the plasma entering the lung (dotted line) and liver (broken line). Despite an anatomical irrelevance, the plasma entering liver was regarded as the mixture of hepatic arterial and portal blood, the mixed venous return from gut and spleen, assuming no significant difference in drug delivery to liver tissue between hepatic arterial and portal blood perfusions.
Tissue distribution parameters estimated by a local PBPK model analysis assuming LD and NL models; a reference model (PS), which neglects specific intracellular binding was also attempted
Comparison of fitting quality between PS, LD, and NL models; maximized log-likelihood function (MLLF), weighted residual sum of squares (WRSS) and Akaike’s information criterion (AIC)3-a
Global PBPK models were subsequently developed assuming two organ models for all tissues, and then the models were fit simultaneously to blood, lung and liver data to finally estimate their tissue distribution parameters (table 4) as well as hepatic intrinsic clearance (CLint,H). The CLint,H was estimated as 2790 and 2720 ml/hr/kg with LD and NL models, respectively. Fitting quality (WRSS and MLLF) in this global model fit was slightly better with the NL model (0.74 and −51.0, respectively) than with the LD model (0.85 and −54.3). The CLint,H values were considerably smaller in the PBPK model analysis than estimated from the blood concentration-time data alone and conventional moment analysis (3490 ml/hr/kg) for two reasons. First, the blood unbound fraction (fuB) for the conventional method was calculated using equation 2a that assumes a concentration-independent blood distribution, although this is obviously not the case as indicated in figure 3A. Such a fuB value thus underestimated the true value, and caused an overestimation of CLint,H in equation 1. Second, calculation of the infinite AUCblood value needed to assume a log-linear terminal elimination phase, which might not practically be achieved for CyA in the experimental period (see PBPK simulation below). In this respect, the systemic clearance estimated from blood measurement alone might have yielded an overestimate of the true value by underestimating AUCblood.
Tissue distribution parameters for lung and liver estimated by fit using global PBPK models assuming “blood-flow-limited” tissue cellular drug uptake
Physiological parameters used in the PBPK model description for rat and human
Fractions of tissue vascular (Fvv) and interstitial spaces (Fvic) in various organs
Using global PBPK models based on local LD and NL organ models, arterial blood and various tissue concentrations were simulated, which are in good agreement with the experimental measurements (fig.4). No significant difference in the tissue data reproducibility was observed in general between the LD and NL model assumptions.
Measured and best fit predictions of CyA concentration in arterial blood and various organs/tissues in rat. Each plot and vertical bar represent the mean and standard deviation, respectively (data presented in table 1). Solid and dotted lines are the PBPK best fit predictions based on the parameters associated with the LD and NL model, respectively.
Prediction of CyA kinetics in humans was made by scaling-up these global models from rat to human with the same procedures applied previously for a cyclosporine derivative (Kawai et al., 1994), except for the scale-up of CLint,H. Initially, the prediction of CLint,H for human was attempted by use of CLint,H measured in rats and rat-human difference in thein vitro metabolic activities (Vickers et al., 1992). However, this resulted in a CLint,H too low to reproduce the blood kinetics observed in humans. Though no clear reason was found, the systemic clearance presently measured in rats and that reported in healthy subjects (Gupta et al., 1990) as reference in the current analysis are somewhat smaller and larger, respectively, than those reported elsewhere (Sangalli et al., 1988). A strain difference in intrinsic clearance between the animals used for the present in vivo study and those used for the former in vitro studies, as well as potential difference in the metabolic activity between the human populations, are some possible reasons for the discrepancy. In addition, an assumption in our model is that liver is the only clearance organ for CyA so thatin vitro metabolic activity in liver only was compared between the species when the initial scale-up was attempted, whereas metabolic activity in kidney is relatively high in humans (Vickerset al., 1992). Such an extrahepatic clearance and species differences might also be relevant. A reasonable alternate was therefore adopted to predict intrinsic clearance for human; the CLint,H (9700 ml/hr/kg) was first calculated from CLH (dose/AUC) and fuB (0.048) in healthy subjects (equation 1), and then corrected for the inconsistency in CLint found in rats between the conventional moment method and PBPK model fit (−25% smaller by PBPK fit) within the similar concentration range to human, which finally resulted in 6900 ml/hr/kg (for healthy subjects). Predicted and measured venous blood concentration of CyA following a constant rate (4 mg/kg) i.v. infusion for 2.5 hr in healthy subjects (Gupta et al., 1990) are compared in figure5. Virtually no difference was observed in these predictions between LD and NL local model assumptions. The predicted blood profile was mostly within the range of 1 S.D. from the average of actual measurements (n = 8); however, a certain degree of overestimation is noted during and soon after stopping the i.v. infusion, as well as an underestimation in the distribution phase (2–10 hr postinfusion). Generally, the quality of the prediction was not as good as was achieved for SDZ IMM 125 (Kawaiet al., 1994). The hypothesis for scaling-up PSTC values of individual organs was considered to be one of the factors responsible for this discrepancy in human PK prediction. As shown in figure 5, a better predictability was noted when an alternative scaling hypothesis was adopted, that the PSTCper unit mass of an organ is identical across the species (i.e., the power function for allometric PSTCscaling is 1 instead of 0.67, in equation 8).
Measured and predicted blood concentrations of CyA during and after an intravenous infusion of CyA for 2.5 hr (4 mg/kg) to healthy volunteers. Each plot and vertical bar represent the average and standard deviation (n = 8), respectively (Gupta et al., 1990). The comparison is made separately with LD (left) and NL (right) organ model assumptions. The solid and dotted lines are predictions when the allometric power factor is set to 0.67 and 1, respectively (see text and “Methods,” equation 8).
For oral kinetics, only the NL model was assumed because of no practical difference found between the organ model assumptions as shown in the intravenous kinetics (fig. 5). The same PBPK model scale-up was used to simulate the CyA concentrations in blood and tissues in patients treated with a twice daily oral regimen (1.5 mg/kg), except that the CLint,H value in this patient population was further adjusted based on the global model fit to the blood data with the fixed bioavailability (0.47; see “Methods”), which resulted in a somewhat lower value (5000 ml/hr/kg) as compared to healthy subjects. The simulation indicates that a steady state in blood is achieved within approximately 3 days of multiple treatment, although the concentration in the peripheral organs, such as skin, is still increasing progressively during this period (fig.6). Assuming a steady-state after day-3, as shown in figure 6, the simulated blood concentration-time profile (simulation of the second dose of day 6) was very similar to the average profile observed in 18 renal transplant patients (fig.7) who had received a new microemulsion oral formulation of CyA for 4 wk (Mueller et al., 1994; Sandimmun Neoral). The maximum and trough blood concentrations, both measured and predicted, were 0.72 and 0.06 μg/ml, respectively. This Cmax/trough ratio of 10 or more, is significantly larger than that obtained with the conventional Sandimmun formulation. In the same simulation run, PBPK model prediction of the tissue concentrations in various organs (fig. 6), including representative graft-organs, such as kidney, heart and skin, were made. The difference observed in the local exposure-to-time profiles among these organs reflected their unique physiological feature regarding drug distribution. Namely, the highly perfused kidney, with high cell-membrane permeability, was exposed highly to CyA, although the cellular distribution to heart and skin are limited depending on their perfusion rates and membrane permeability (PSTC). Also predicted are the more “efficacy-relevant” concentrations, i.e., intracellular unbound drug concentrations (fig. 8), which demonstrate that physiological factors, such as PSTC, are important in determining the relationship between blood PK and local target exposures. Indeed, the relative magnitude in the “effective” concentration shown in figure 8 is consistent with the clinical experience, that trough blood level should be maintained in the order of kidney<heart<skin, to prevent rejection of these organs (Holtet al., 1994; Wallwork, 1986).
The PBPK model prediction of CyA kinetics in blood and various tissues during a multiple oral dose (1.5 mg/kg, b.i.d.) regimen in patients (CLint,H is set to 5 l/hr/kg). Blood (——), heart (.....), kidney (––––) and skin (.–.–.–).
Measured (□) and PBPK model predicted (solid line) blood concentrations in renal transplant patients. In the clinical study (Mueller et al., 1994), the average dose was 102 ± 18 [SD] mg, or 1.5 mg/kg, twice daily. Each plot and vertical bar represent average and standard deviation in 18 subjects on the last day of 2-wk treatment. The PBPK model prediction is made for the second dose of day 6 of a 12-hourly multiple dosing (see text and “Methods” for other conditions used to generate the simulation).
The PBPK-predicted locally effective (intracellular unbound) CyA concentrations in various organs of human on the second dose of day 6 in renal transplantation patients receiving a 1.5 mg/kg twice daily oral regimen. Dotted, broken and combined dotted/broken lines represent the predictions in heart, kidney and skin, respectively.
Discussion
Our study with CyA and our previous study with a cyclosporine derivative SDZ IMM 125 (Kawai et al., 1994) clearly demonstrate that drug transfer kinetics between different physiological compartments, e.g., interstitial and intracellular spaces, needs particular consideration, to fully characterize their delivery to biological targets. Through these studies, PBPK modeling has proved a useful tool to interpret simultaneously local (tissue) and systemic (blood) data, integrate different sets of data (e.g., in vitro—in vivo bridging), and scale PK data from one species to another (animal scale-up), by simply adjusting individual parameters for known interspecies differences.
Use of such models to evaluate the PK of CyA and its derivatives is particularly meaningful because of their nonlinear (concentration-dependent) blood distribution (Kawai and Lemaire, 1993), the impact of which cannot be assessed properly when only blood kinetic data are evaluated by conventional approaches; this PK factor is known to vary relatively widely across animal species as well as among human populations, e.g., healthy subjects and patients. After taking into account this factor, we encountered the additional complexity that tissues cannot be adequately described by a single homogeneous compartment. In the case of SDZ IMM 125 (Kawai et al., 1994), a very slow tissue distribution process could not be explained fully by “membrane-permeability-limited” drug transfer; this slow process was described by assuming a slowly interacting intracellular component. In addition to this linear tissue distribution (LD) model, we explored whether a saturable intracellular binding (NL) model could explain the slow decay in tissue concentration. Saturation of tissue CyA distribution has previously been observed (Bernareggi and Rowland, 1991) in some, although not all, organs of rat based on steady state in vivo tissue measurements at the end of a 7-day s.c. CyA infusion (2.7 and 14 mg/kg/day). The local (NL) PBPK model yielded estimated KD,TC values ranging between 0.0002 and 0.06 μg/g tissue across various organs. This finding suggests that the infusion rates used in the former in vivo study were too high (as the steady-state blood level was 0.5 μg/ml, corresponding to 0.024 μg/ml as unbound drug, even with the lower rate), and that additional studies over a wide dose range are necessary to fully characterize such saturable tissue binding. Notwithstanding, the KD,TC estimates in our study are of similar magnitude to the dissociation constant of the putative CyA receptor, cyclophilin, measured in vitro (0.01–0.03 μM or 0.012–0.036 μg/ml;Dalgarno et al., 1986; Ryffel, 1993). A contribution of such “target” protein to the apparently slow tissue distribution is therefore highly likely, considering also that cyclophilin is abundant in most of the organs and interacts with CyA with significantly higher affinity than other cytosolic proteins (Wuesniaux et al., 1988; Fahr, 1993); importantly, calculations indicate that the binding should be partly saturated at therapeutic doses in patients. In this respect, the NL organ model is potentially more advantageous than the LD model to describe the tissue distribution of CyA and to relate its PK to the immunosuppressive efficacy. However, the KD,TCestimates varied sufficiently widely among different organs to suggest the existence of additional specific binding sites (proteins) with different affinities or velocities of interaction (i.e., time-dependent binding, as assumed for the LD model). For example, recently, a multidrug-specific membrane transporter,P-glycoprotein, has been extensively studied and shown to be involved in CyA cellular disposition (Tamai and Safa, 1990). Clearly, further work is needed to fully elucidate all aspects of CyA tissue distribution. However, at this stage, we adopted both linear (LD) and nonlinear (NL) local tissue distribution models in our PBPK analysis, due to current lack of clear evidence to reject either of the associated assumptions.
Before the CyA data modeling, we noted an 8-fold higher lipophilicity (log P) and a 7-fold larger permeability of blood cell membrane for CyA than SDZ IMM 125 (Kawai and Lemaire, 1993). Accordingly, we expected membrane limited tissue distribution to be less significant with CyA. In fact, PSTC values of CyA were generally larger than those estimated for SDZ IMM 125, except for spleen. However, PSTC ratios, CyA to SDZ IMM 125, were not as large as the initially anticipated 7- to 8-fold, such that the net transfer clearance of CyA (i.e., product of PSTC and fuB) was still not high enough to assume “blood flow limited” drug distribution in many organs. The membrane “barrier” proved essential in the PBPK modeling of CyA tissue kinetics.
Plasma protein binding plays an important role in tissue distribution. While unbound fractions in blood for CyA and SDZ IMM 125 are quantitatively similar in the linear range (0.048 and 0.055, respectively, according to equation 2a), the relative contribution of the various factors responsible for binding are different. CyA has a much higher affinity for lipoproteins, LDL and HDL (Urien et al., 1990), than does SDZ IMM 125, due presumably to its higher lipophilicity. This association with lipoproteins seems to cause two complexities, as follows. In our modeling, the plasma unbound fraction (fuP) of CyA in rat was fixed to 0.06. However, this fuP might be an overestimate of the true value, taking into account that in the method used to estimate its value (ultracentrifugation), it is not experimentally easy to obtain completely lipoprotein-free “plasma water.” Indeed, a smaller fuP (0.02) was obtained using microdialysis (Yang and Elmquist, 1996). Another difficulty in the data interpretation is that lipoproteins are known to facilitate cellular uptake of lipids, and CyA is supposed to behave as a lipid (Luke et al., 1992). These limitations do not apply to SDZ IMM 125 because of its low affinity for lipoproteins. This difference in lipoprotein binding may explain, first, why the CyA:SDZ IMM 125 PSTC ratios do not correlate well with their lipophilicity ratio and, secondly, why prediction of CyA kinetics in human was not as successful as in the case of SDZ IMM 125. Furthermore, cremophor, a solubilizing agent in the intravenous CyA formulation used in our in vivo study, has recently been shown to decrease the clearance of a highly lipophilic anticancer drug, paclitaxel, by limiting its transfer from the blood to the elimination organs (Sparreboom et al., 1996). Collectively, these findings suggest that a laboratory technique, which accurately measures “tissue-membrane-available” drug concentration in plasma, is needed in order to permit accurate characterization of local tissue distribution.
Given these limitations, we have attempted to assess the effect of tissue barriers on drug delivery to local targets, particularly in human after scaling up the rat PBPK model. Comparisons were made between kidney, heart and skin, each of which represents one of the three groups of organs classified by their tissue distribution-time profiles (fig. 2), and noting the high frequency of transplantation of these organs in clinics. After transplantation, patients are treated initially with relatively high oral CyA doses; the dose is then reduced stepwise to the minimum maintenance dose that avoids renal toxicity,i.e., the so-called “stable” condition. The target trough blood concentration starts from 0.3 to 0.4 μg/ml in the initial period and decreases to 0.1 μg/ml or higher in the stable condition, depending on which organ is transplanted. Generally, the kidney needs the lowest trough exposure, although heart and skin need increasingly higher exposure in this order. This clinical experience draws an interesting comparison with our predicted magnitude of the intracellular unbound drug concentration, the putatively efficacious species. In figures 6 to 8, use of a low dose for renal transplant patients (1.5 mg/kg) was evaluated assuming stable conditions, whereas patients’ physiological conditions during the transient period after surgery are usually unstable making model prediction problematic during this period. The intracellular unbound CyA in kidney well exceeds the Kd of cyclophilin (assuming the range of 0.012–0.036 μg/ml; Dalgarno et al., 1986; Ryffel, 1993) particularly at the peak concentration, although that in heart reaches only the middle of range, and that in skin falls short of the lowest value of Kd at all times. For heart transplantation, a 1.5- to 2-fold higher than renal transplantation oral dose appears necessary to achieve as effective CyA concentration (fig. 8). These simulations by our global PBPK model demonstrate that membrane transport can limit drug delivery to the local efficacy site, and may be relevant to the graft-maintenance exposure (or dose), which differs among organs to be transplanted (Holt et al., 1994;Wallwork, 1986).
However, the relevance of other factors to efficacy is obvious. In clinical practice, graft-maintenance of liver and lung needs relatively high CyA exposure; i.e., a trough concentration similar to (for liver) or even higher (for lung) than for heart transplantation, even under stable conditions. This fact can not fully be explained by PK factors and the model we proposed in our study, because liver and lung are highly perfused organs with high membrane permeabilities for CyA. Indeed, predicted intracellular unbound CyA concentrations for these organs (like those in fig. 8 for other organs) are similar to or even higher than those predicted for kidney by our global PBPK model (results not shown). One may postulate organ specific affinity of CyA binding to the receptor proteins, such as cyclophilin. There are several forms of cyclophilin reported to date, with different sizes and structures, some of which are organ-specifically distributed (Schneider et al., 1994). However, as yet, the biological roles of each of the subforms have not clearly been characterized. Specific localization of cyclophilins within an organ structure has also been reported (Ryffel et al., 1991) and may explain the organ specific sensitivities to CyA, while our model assumes the presence of a single homogeneous compartment within tissue cells for unbound CyA as the site of action. In addition, our tissue distribution model neglects the existence of any unidirectional drug transporter on the membrane, which causes a concentration gradient in unbound drug concentrations between blood and intra(tissue)cellular space even at steady state.
Our study characterized the local tissue distribution of CyA in various organs by performing an extensive in vivo kinetic experiment in rats and interpreting the data with PBPK models. This approach helped to discriminate critical physiological and biological factors affecting the local as well as global PK, including those to be further investigated, and also to assess the impact of these factors on drug delivery to the target, and thus efficacy. Modeling, in combination with animal scale-up, was shown to be invaluable, particularly for drugs, such as CyA, which need therapeutic PK monitoring and careful control of exposure, since successful medication requires a sound understanding of PK. For example, a positive correlation between CyA exposure and cholesterol level in blood led authors (von Ahsen et al., 1997) to recommend reducing the Sandimmun dose in hypercholesterolemic patients. This would be reasonable if the unbound drug fraction in the blood of these patients is similar to that in patients with typical cholesterol levels. But this is highly unlikely given that the unbound fraction in the plasma varies inversely with cholesterol. This factor can easily be explored using the PBPK model, as shown in figure 9, where the plasma unbound fraction (fuP) is varied by ±50% of the standard value (0.06). While blood exposure is predicted to vary with plasma protein binding, effective drug exposure to the kidney (and effect) should be virtually unaffected. Whether this occurs in practice requires experimental verification. An assumption in the PBPK model is that the only effect of plasma cholesterol is to alter the fraction of drug unbound there. If, as well as unbound drug, the lipoprotein-associated drug in plasma is also transferred directly through tissue membranes, our prediction may not mimic reality. A continuous effort is therefore needed to clarify such biological mechanisms and assess their impact on both local and systemic PK.
Predicted effect of altered plasma protein binding on, A, the mixed venous blood PK and B, local renal exposure of CyA in patients after the same dosing condition as in figures 8 and 9. In the simulation, plasma unbound fraction (fuP) was set to 0.03 (dotted line), 0.06 (solid line; the standard condition used in the other model simulation) and 0.09 (broken line).
Acknowledgments
The authors thank Drs. S. Gupta, L. Benet, J. Kovarik and E. Mueller for providing the human PK data as well as clinical information. Comments and suggestions from Drs. R. Hof, J. Vonderscher and M. Lemaire are gratefully acknowledged.
Blood distribution.
The intracellular binding was characterized by a dissociation constant (KD,BC) and number of binding sites (nPT), assuming instantaneous interaction. These specific parameters are related to the blood cell concentration (CBC) as reported by Legg and Rowland (Legg and Rowland, 1988);
Drug exchange across the blood cell membrane was characterized by a permeability-surface area product (PSBC) assuming passive diffusion. Equations of drug flux between plasma and blood cells are (for the closed in vitro situation):
Binding to interstitial plasma protein.
The fraction of CyA unbound in interstitial fluids (fuI) in various organs was estimated adopting a previously established model for β-lactam antibiotics (Tsuji et al., 1985). Namely, the concentration of drug bound to a certain class of protein (Cb) is described by a binding isotherm using the number of available binding sites (N*), the dissociation constant (KD*) and unbound drug concentration (Cu) in the protein solution;
PBPK description of organ models.
An organ is divided into four (LD model) or three (NL model) tissue compartments with exchange of drug between them (fig. 1). The extracellular tissue space can be divided into 1) vascular blood cells and 2) the combined interstitial and tissue plasma spaces with drug assumed to be instantaneously equilibrating between them for both LD and NL models. As in plasma, drug in the interstitial fluid is both unbound and bound to lipoproteins. For the LD model, the tissue cell space is divided into two compartments, namely: 3) a rapidly interacting pool characterized by fuT and 4) a moderately slowly interacting pool with association and dissociation rate constants (kass and kdis, respectively). NL model is schematically similar to LD model, however, no transport barrier for intracellular CyA exists. Namely, a single cellular compartment is considered with two independent binding sites; both are rapidly interacting with intracellular unbound CyA, one with a concentration-linear coefficient (fuT) and the other with a dissociation constant (KD,TC) and a maximum number (Bt) of binding site. Elimination in both LD and NL models is assumed to occur only from the unbound pool of the intracellular space of the liver (via metabolism), characterized by intrinsic clearance, CLint,H. Intravenous drug administration is described by a zero-order rate (Riv) into the mixed venous return entering the lungs, while oral administration, described by a first-order absorption constant (ka), bioavailability (f) and oral dose (Dpo) occurs from compartment D0:
The rate equation for each compartment is;
a; Vascular blood cells
b; Combined plasma and interstitial fluid
c; Rapidly interacting tissue pool
LD model
NL Model
These equations apply to all organs but the liver, for which the rate of hepatic elimination (vHel) has to be subtracted from, and following oral administration ka · D0 (equation 10) added to, the right hand term, where;
The coefficients Fcv and Fci were derived from the model defining the combined plasma and interstitial fluid compartments (see above) and are calculated using fuP, fuI, VP and VI, thus;
Global PBPK model.
The global (whole body) model comprises 11 organs, each of which is characterized by a local model, either LD or NL (equations EA11-EA19) and appropriately connected to plasma and blood cells of the systemic arterial and venous pools (fig. FA1). Thus, for all organs except the liver and lungs, the input concentrations, Cp,in and CBC,in, are arterial plasma and blood cell concentrations (CP,A and CBC,A), respectively. For the liver, the input concentration corresponds to the concentration in the mixed blood entering this organ from the hepatic artery and the venous outputs from the spleen and gut; for the lungs the input concentration is that in the mixed venous return. The concentrations CP,A and CBC,A are defined by those in the pulmonary venous outflow and the plasma to blood cell exchange, namely;
Schematic representation of the global PBPK model used in our analysis. Note that drug distribution in each of the compartments (organs and blood pools) is modeled to anatomical details as shown in figure 1.
Volume of tissue vascular and interstitial spaces.
Volumes and blood flow rates for each organ or tissues, listed in (table AI), were obtained from the literature (Kawai et al., 1994). These values are given as for a 250-g rat and a 70-kg human, and were adjusted to the body weight of the subject to be simulated using the PBPK models, assuming that the parameters vary in proportion to body weight. Fractional volumes of tissue vascular (Fvv) and interstitial (Fvic) space are shown in table AII. Fvv values were measured in rats without bleeding (Tsuji et al., 1985; Khor and Mayersohn, 1991; Khor et al., 1991; Altman, 1961); Fvic was taken from the literature (Tsuji et al., 1983, 1985, 1990). Actual volumes of tissue vascular and interstitial spaces in an organ were obtained by multiplying these fractions by the volume of the organ (table AI).
Footnotes
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Send reprint requests to: Dr. Ryosei Kawai, Novartis Pharma AG, Drug Metabolism & Pharmacokinetics, K-136. 1.23, CH-4002 Basel, Switzerland.
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↵1 This work was supported in part by The Wellcome Trust.
- Abbreviations:
- CyA
- cyclosporine A
- PK
- pharmacokinetics
- PBPK
- physiologically-based pharmacokinetics
- LD
- a local PBPK model assuming linear intracellular binding with “deep pool”
- NL
- a local PBPK model assuming saturable intracellular binding
- PS
- permeability-surface area product
- WRSS
- sum of weighted residual squares
- MLLF
- maximized log-likelihood function
- AIC
- Akaike’s information criterion
- Received February 6, 1998.
- Accepted June 8, 1998.
- The American Society for Pharmacology and Experimental Therapeutics
