In silico Prediction of Bioavailability of Pharmaceutical Formulations Using Population Pharmacokinetic Model Simulation

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1 In silico Prediction of Bioavailability of Pharmaceutical Formulations Using Population Pharmacokinetic Model Simulation Uthpali Mannapperuma Mahidol University Department of Pharmacy, Faculty of Pharmacy, Mahidol University, Bangkok, Thailand. Krobtham Sathirakul Mahidol University Department of Pharmacy, Faculty of Pharmacy, Mahidol University, Bangkok, Thailand. Abstract- The purpose of this study was to construct a model to describe the Population pharmacokinetics (PopPK) of S(-)-carvedilol, utilizing STELLA software. PopPK studies and characterizes the intersubject variability (ISV) and interoccasion variability of the different parameters which affect a drug s absorption, distribution, metabolism and excretion. A drug s bioavailablity is defined as the rate and extent to which the active ingredient or active moiety is absorbed from a drug product and becomes available at the site of action. The drug carvedilol was used as a model drug for this study. A orally administered a controlled release dosage form s PopPK parameters were used to create a virtual population on different formulations of oral carvedilol. The virtual population was used to evaluate the affect of the oral absorption rate constant (k a ) as a factor affecting the drug bioequivalence (BE). BE assesses if two pharmaceutical formulations of the same drug product have similar BA. pharmacokinetic (PK) parameters. The PopPK parameters were obtained from a previous study of S(-)- carvedilol on healthy volunteers by Othman et al. The BE study assessed the effect of formulation, by increasing the overall absorption rate constant from 10-50% and decreasing it from 10-40%. The software WinNonlin was used to conduct a BE study. Microsoft Office Excel 2007 was used to compile the simulated data. The formulations demonstrated BE for all formulations with k a increase upto 50% and for a decrease upto 30%. But when k a was decreased to 40% there was no BE. This study reveals the use of STELLA software as an effective prediction tool of formulation effects. Keywords- Bioavailability, Population Pharmacokinetics, STELLA I. INTRODUCTION Pharmacokinetics (PK) can be defined as the science of the kinetics of drug absorption, distribution, and elimination (i.e, excretion and metabolism). Usually blood sampling is carried out in PK studies where the plasma drug concentration vs. time curve is generated, where its shape is determined by the drug, the dose and the route of drug administration. The in silico approach to PK analysis consists of the development of computer aided models which defined rate controlling processes and constants [1]. The United States Food and Drug Administrtion (US FDA) defines bio availability as the rate and extent to which the active ingredient or active moiety is 85.1

2 Uthpali Mannapperuma and Krobtham Sathirakul absorbed from a drug product and becomes available at the site of action. For drug products that are not intended to be absorbed into the bloodstream, bioavailability may be assessed by measurements intended to reflect the rate and extent to which the active ingredient or active moiety becomes available at the site of action [2]. The US FDA defines bioequivalence (BE) as the absence of a significant difference in the rate and extent to which the active ingredient or active moiety in pharmaceutical equivalents or pharmaceutical alternatives becomes available at the site of drug action when administered at the same molar dose under similar conditions in an appropriately designed study [2]. Therefore to assess BA and BE usually the drug s plasma concentration time profile is assessed to determine the exposure of the drug at the site of action [1]. For oral formulations of dugs US FDA suggests a non-replicate crossover study designs where a reference product and a test product is administered to volunteers. The PK parameters that assess peak exposure of the drug such as the maximum concentration of the drug in blood (C max ) along with the PK parameters that assess total exposure such as the Area Under the Curve (AUC) from zero to time t (AUC 0-t ), where t is the last time point with measurable concentration for individual formulation, AU C from time zero to time infinity (AUC 0- ) is reported [2]. The US FDA defines PopPK as the sum of the models, their parameter values, and the use of study designs and data analysis methods designed to elucidate PopPK and their parameter values. PopPK model inferences aim to estimate some or all components of variability that are affecting the PK parameters [3]. This variability can be the intersubject variability (ISV) or the interoccasion variability (IOV) [4]. The Biopharmaceutics Classification System (BCS) provides a frame work to assess a drugs in vivo performance by analyzing the in vitro parameters of drug solubility and permeability. The classification of a drug in a BCS class will determine whether it the rate limiting factor of drug absorption in the oral route is either its solubility or permeability. The BCS classes are defined as following: Class 1- high solubility-high permeability drugs Class 2- low solubility-high permeability drugs Class 3- high solubility-low permeability drugs Class 4- low solubility-low permeability drugs [5, 6] Carvedilol is an antihypertensive drug [7, 8]. It belongs to the BCS class II drug [9]. Carvedilol was used as a model drug to create a virtual population on various formulations of a controlled release form of the drug based on peviously described PopPK parameters and variables. II. METHODOLOGY The PopPK parameters from a previous study by Othman et al. of S- carvedilol on healthy volunteers on a controlled release formulaiton was used to create an in siloco model [10, 11] ISV and IOV were modeled by the method described by Karlsson et al. [4] as given in equations 1 and 2. Equation 3 was used to model the random effects. P i = TVP exp (η i ) (equation 1) P ij = TVP exp (η i +k ij ) (equation 2) ln Y obs = ln Y pred + ε (equation 3) In equation 1 the ISV is denoted for a pharmacokinetic parameter P i, where the letter i in the subscript refers to an individual or the i th subject. The proportional difference between the hypothetical true parameter estimate of the i th subject and the typical population parameter value (TVP) is given by η i. The parameter η i has a normal distribution with a mean of 0 and a variance Special Issue of the International Journal of the Computer, the Internet and Management, Vol. 19 No. SP1, June,

3 In silico Prediction of Bioavailability of Pharmaceutical Formulations Using Population Pharmacokinetic Model Simulation of ω 2 [12, 13]. Similarly Similarly IOV can be modeled by equation 2 where k ij is also distributed normally and has a variance of π 2. Here the parameter value of i th subject at j th occasion is denoted by P ij [12, 13]. For the simulation of final observed values of the pharmacokinetic parameters, the random effects must be taken to account. ε is the term used to predict the observations of the model as given in equation 3 where, Y obs is the observed plasma concentration and Y pred is the model-predicted plasma concentration. Here ε is sampled by a random effects model where, ε is also normally distributed with a mean of 0 and a variance of σ 2 [12, 13]. A two compartment model with a central compartment (C) and a peripheral compartment (P) was constructed using the Stella software (Figure 1) with reference to the available PK parameters such as clearance (CL), volume of central compartment (Vc), volume of peripheral compartment (Vp), intercompartment clearance (Q) and the first order absorption rate constant (ka) to be used in the fitting of the natural log (Ln) transformed concentrations of S-carvedilol in the central compartment (Cc). The η i was available for Vc. For this formulation the absorption rate constant (k a ) was divided in to three ka 1 (0-2hr), ka 2 (2-4hr) and ka 3 (>4hr) where both similar η i and similar k ij values. A single relative bioavailability factor (Frel1) was available for the CR dosage form with η i and k ij values. Parameter value inputs used in the Stella model are given in Table 1. Inter-individual variability for k a1 and k a2 was used to create 24 individuals (ω=0.946). Using the variance of ε (σ 2 =0.1), 30 possible replicates of the concentration time profile of the central compartment was generated for each of the individuals. The plasma concentration (Cc) was tabulated by STELLA for each individual and these data ware compiled in Microsoft EXCEL The k a values (k a1, k a2 and k a3 ) were increased to 10%, 20%, 30%, 40% and 50% (formulation number 1 to 5) and were decreased to 10%, 20%, 30% and 40% (formulation number 6 to 9) in order to generate 9 different virtual formulations (Table 1). The model was run for all total 48 individuals for each of the k a increases and the obs Cc was tabulated. BE statistics were carried out using the software WinNonlin for each of the simulated formulation effects of k a increase. The reference product for the BE study was simulated by using the point estimates form the previous model describing the population pharmacokinetics of 20mg carvedilol controlled release formulation by Othman et al. [10, 11] Fig. 1 The STELLA model for population pharmacokinetics of the controlled release formulation E= ε, TVP Ka1= TVP for Ka1, TVP Ka2= TVP for Ka2, TVP Ka3= TVP for Ka3, TVP Frel1 = TVP for Frel1, TVP Vc= TPV for Vc, n1 Vc= ηi for Vc, K Ka1= kij for Ka1, K Ka2= kij for Ka2, K Ka3= kij for Ka3, n1 Ka1= ηi for Ka1, n1 Ka2= ηi for Ka2, n1 Ka3= ηi for Ka3, n1 Frel1= ηi for Frel1, Log obs=log observed concentration of the Cc, obs Cc=observed concentration of Cc and obs Cc 1000=1000 obs Cc 85.3

4 Uthpali Mannapperuma and Krobtham Sathirakul TABLE I THE ABSORPTION RATE CONSTANT VALUES USED TO GENERATE VIRTUAL FORMULATIONS OF CONTROLLED RELEASE CARVEDILOL The mean values of the C max, and AUC from zero time to the last observable concentration (AUC last ), and the AUC from zero time to infinity (AUC INF obs ) was calculated by the software WinNonlin. The ratio between reference product values to the test product value were assessed for BE. The Ratio of the Ln(C max ), Ln(AUC last ) and Ln(AUC INF obs ) is the ratio between the reference product s PK parameter values to the new product s values. The regulatory range of BE was pre-determined 90% confidence interval of 80% to 125% of the ratio [2]. Therefore, at 40% k a decrease there is no BE between the reference product to the test product developed virtually (Table II). IV. CONCLUSIONS Virtual BE studies can be successfully carried out if well defined population pharmacokinetic variables for a drug are available. We can conclude that the rate of absorption will not affect the BE of this dosage form even if the absorption is increased up to 50% and decreased up to 30%. TABLE II BIOEQUIVALENCE ANALYSIS FOR THE FORMULATIONS WITH INCREASE OF k a III. RESULTS Ln(C max ), Ln(AUC last ) and Ln(AUC INF obs ) were analyzed with respect to the reference product and the nine new formulations. There ratio for all three parameters are close to 100% and the 90% confidence interval values fall within the regulatory limits when the k a is increased up to 40%. Therefore the new formulations with an increased k a still are within the limits of BE described by the regulators up to 40%. But at 50% k a increase the upper and lower limits of the 90% confidence interval of the ratio of Ln(C max ) is at and which is just close to the limits of BE set out by the regulators (Table II). Similarly, at 40% k a decrease the lower limit of the 90% confidence interval is at and the upper limit is at while the ratio of reference to test formulation C max lies at Special Issue of the International Journal of the Computer, the Internet and Management, Vol. 19 No. SP1, June,

5 In silico Prediction of Bioavailability of Pharmaceutical Formulations Using Population Pharmacokinetic Model Simulation TABLE III BIOEQUIVALENCE ANALYSIS FOR THE FORMULATIONS WITH DECREASE OF k a ACKNOWLEDGMENT This research was possible due to the financial support by the Thailand International Development Agency Scholarship for the M.Sc. in Pharmacy, awarded to the Faculty of Pharmacy, Mahidol University. REFERENCES [1] Shargel L, Wu-Pong S, and Yu ABC, Applied biopharmaceutics and pharmacokinetics, 5 ed. New York: McGraw Hill, [2] U.S. Department of Health and Human Services Food and Drug Administration Center for Drug Evaluation and Research (CDER), "Guidance for Industry: Bioavailability and Bioequivalence Studies for Orally Administered Drug Products - General Considerations. March 2003." [3] Food and Drug Administration, "Guidance for Industry: Population Pharmacokinetics," F. D. A. U.S. Department of Health and Human Services, Ed. Rockville, MD, [4] M. O. Karlsson and L. B. Sheiner, "The importance of modeling interoccasion variability in population pharmacokinetic analyses," J Pharmacokinet Pharmacodyn., vol. 21, pp , [5] L. X. Yu, G. L. Amidon, J. E. Polli, H. Zhao, M. U. Mehta, D. P. Conner, V. P. Shah, L. J. Lesko, M.-L. Chen, V. H. L. Lee, and A. S. Hussain, "Biopharmaceutics Classification System: The Scientific Basis for Biowaiver Extensions," Pharm. Res., vol. 19, pp , [6] G. L. Amidon, H. Lennernäs, V. P. Shah, and J. R. Crison, "A Theoretical Basis for a Biopharmaceutic Drug Classification: The Correlation of in vitro Drug Product Dissolution and in vivo Bioavailability," Pharm. Res., vol. 12, pp , [7] Sweetman SC, "Martindale: The Complete Drug Reference," 35 ed London: Pharmaceutical Press, [8] J. Cheng, K. Kamiya, and I. Kodama, "Carvedilol: Molecular and Cellular Basis for Its Multifaceted Therapeutic Potential," Cardiovasc Drug Rev., vol. 19, pp , [9] C.-Y. Wu and L. Z. Benet, "Predicting Drug Disposition via Application of BCS: Transport/Absorption/ Elimination Interplay and Development of a Biopharmaceutics Drug Disposition Classification System," Pharm. Res., vol. 22, pp , [10] A. Othman, D. Tenero, D. Boyle, N. Eddington, and M. Fossler, "Population pharmacokinetics of S( )-carvedilol in healthy volunteers after administration of the immediate-release (IR) and the new controlled-release (CR) dosage forms of the racemate," AAPS J., vol. 9, pp. E208-E218, [11] A. Othman, D. Tenero, D. Boyle, N. Eddington, and M. Fossler, "Corrigendum: Population pharmacokinetics of S(-)-carvedilol in healthy volunteers after administration of the immediaterelease (IR) and the new controlledrelease (CR) dosage forms of the racemate," AAPS J., vol. 9, pp. E326-E327, [12] H. C. Kimko and S. B. Duffull, "Simulation for Designing Clinical Trials: A Pharmacokinetic- Pharmacodynamic Modeling Perspective," in Drugs and the Pharmaceutical Sciences, J. Swarbrick, Ed. New York: Mercel Dekker, 2003, p [13] M. O. Karlsson and L. B. Sheiner, "The importance of modeling interoccasion variability in population pharmacokinetic analyses," J Pharmacokinet Pharmacodyn., vol. 21, pp ,