Fig. 4. A two-compartment pharmacokinetic model.

Transcription

1 3.4 Pharmacokinetic (PK) modeling and simulations Noora Sjöstedt, Wilma Kiander, Heidi Kidron Introduction (Hanna Kortejärvi) Pharmacokinetic modeling and simulations can be performed with different types of models. Figures 4-6 present some typical examples. One of the simplest approaches is compartmental modeling (Fig. 4). In the case of two-compartment pharmacokinetic behavior, drug substance is distributed from blood and wellperfusedtissues to the peripheral tissues like fat, bone, and skin. The modeling scenario can be for example how differences in the drug absorption or elimination rate affect the drug concentration in the central and peripheral compartments. If we are interested in simulating drug concentrations in a certain tissue like the brain or adipose tissue, we can use physiologically-based pharmacokinetic (PBPK) models (Fig. 5). A simple PBPK model may include compartments for blood, brain, kidney and liver. Drug distribution to tissues is limited either by perfusion or permeability. Each organ can be further divided into sub-compartments. This is the case for example in the compartmental absorption and transit (CAT) model of Yu et al. (Int J Pharm 1996) and related models, where the gastrointestinal tract is divided into several compartments (Fig. 6). The use of a PBPK also allows for more complex models that may target subgroups of the population, such as pregnant women or children. Fig. 4. A two-compartment pharmacokinetic model. The selection of the model depends on the data we have, the scenario we are interested in simulating and the available modeling and simulation tools. We can start with simple empirical models and then continue to more challenging mechanistic models like the PBPK and CAT type of models. All types of PK models have to be tested or validated with test compounds having enough available in vivo data. There are many commercially available software for PK modeling and simulation. Phoenix WinNonlin (Certara) can be utilized for PK and PK/PD modeling and Phoenix NLME for population-based PK modeling. Simcyp (Certara) and Gastroplus (Simulations Plus, Inc.) are developed mainly for PBPK modeling and simulation of pharmacokinetics in different populations. 1

2 Fig. 5. A simple PBPK model. Picture from Fig. 6. The Simcyp Advanced drug absorption and metabolism (ADAM) model, which is an extension of the CAT model presented by Yu et al. (Int J Pharm 1996). Picture from The STELLA software (isee systems) used in this practical is a simple and easy to use software for modeling substance flows. Models are constructed using stocks, which in our case describe the amount of drug at a certain time point, flows, which describe the flux of the drug, and converters, which include the parameter values to describe drug flow. Drug flow typically follows first order kinetics, but also other types of kinetics such as zero order kinetics or Michaelis-Menten kinetics can be used. Conv erter Stock 1 Stock 2 Flow Fig. 7. Elements of the STELLA model. 2

3 3.4.2 Aim of the practical The STELLA software was already introduced and utilized in the Advanced Pharmacokinetics I practicals. Here you will learn to utilize STELLA for pharmacokinetic simulations of the absorption phase of drug substance or drug product. A drug substance as such has certain solubility, dissolution, and permeability properties and these can be modified by formulation in the final drug product. This is important, since these properties can have effect on drug input rate, concentrations in plasma and overall exposure. The specific aims of the practical are To learn how simulation can be utilized for the design of permeability experiments. To construct and utilize STELLA models to estimate what is the rate-limiting step in the absorption phase. To learn to construct and utilize the compartmental absorption and transit (CAT) model and combine drug substance and drug product properties together with the knowledge of physiology of the gastrointestinal tract. To realize how the data from different sources (QSAR in silico model, in vitro and in vivo) can be combined in a model Materials Parameter values for the simulations are obtained from experimental in vitro cell studies and from literature. If the students have not acquired experimental in vitro data, the data obtained within the group can be used. Use the following units in all tasks: cm, min, ml, μg Methods The practicals will start with a short demonstration of the STELLA simulation program. The lecturer will be available during hands-on sessions as agreed together with the students. Detailed instructions for basic use of STELLA have already been provided in the course Advanced Course in Pharmacokinetics I, practicals Modeling tasks 1. Design of the in vitro cell culture permeability experiment using a pharmacokinetic simulation model You are planning an experiment to measure the permeability of a test compound (paracetamol) across MDCKII cells. The permeability experiments are performed using Transwell inserts with a surface area of 1.12 cm 2. The volume of the test solution in the apical chamber is 0.5 ml and 1.5 ml in the basolateral chamber. Based on the preliminary experiments, the Papp value of paracetamol is cm/second. Problems 1) Construct a STELLA model to describe the transfer rate of paracetamol from the apical chamber to the basolateral chamber. Which equation should you use to describe the transfer rate? 3

4 2) Simulate a 3 h permeability experiment using a 250 μm paracetamol solution and check the cumulative drug concentration in the acceptor compartment. 3) Which time points would you choose to take samples? Remember that sink conditions should be maintained during the experiment, i.e drug concentration in the receiver side should remain < 10% of the loading concentration in the donor side. 4) What are the drug concentrations in the chosen time points? 5) The detection limit of UPLC analysis for the test compound measurement is no more than 75 μm. Do you need to dilute your samples for analysis? After the permeability experiment: 6) Use your own results from the cell permeability experiment of paracetamol and simulate the transfer of paracetamol from the donor compartment to the acceptor compartment through the cell barrier. 7) Compare simulation results with experimental values. What could be the reasons for differences between results (simulated vs. measured amounts in the acceptor compartment)? 8) Transfer of a drug from the donor to the acceptor compartment can be defined using a clearance term. Based on the transfer rate equation (step 1 above), calculate the clearance for paracetamol in this case. 2. Modeling the rate limiting step in the absorption phase In addition to oral administration, paracetamol can be administered rectally as a suppository. Assume the surface area of the rectum to be 200 cm 2 and the volume of fluid 3 ml. Problems 1) Simulate the absorption of a 500 mg paracetamol suppository assuming that paracetamol dissolves from the test formulation with the dissolution rate constant Kd = 4 h -1 (rapid dissolution) and is absorbed at sink conditions. Use your own experimental Papp value of paracetamol in all simulations. The solubility of paracetamol is 20 mg/ml.* 2) In order to study the effect of solubility on overall absorption, perform simulations also with solubility values of 2, 200, and 2000 mg/ml. 3) Use the model to determine the value (or range) at which the solubility becomes the rate limiting step for drug entry into the blood circulation, assuming that the drug is absorbed across the mucous membrane of the rectum. * For a hint on which equation to use to describe the dissolution of the tablet, see Kortejärvi et al. (Eur J Pharm Sci 2007). 3. Modeling of absorption, distribution, and elimination with the compartmental absorption and transit (CAT) model Yu et al. (Int J Pharm 1996) analyzed the in vivo transit and distribution of solid and solution dosage forms in the intestine as a function of time using data from 400 subjects. Based on these results the mean intestinal transit time is 199 min and the best fit for the transit and distribution kinetics was a 7-5 compartment model. Thus in the CAT model, the gastrointestinal tract is divided into compartments so that the stomach forms one compartment, the intestine (approximate surface area 250 m2) is divided into 7 compartments and the 4

5 colon is one compartment. Drug compound moves in the intestine from one compartment to another with the velocity defined by the 1st order rate constant (Kt), it dissolves in each of the 9 compartments according to the dissolution rate constant (Kd) and is absorbed according to absorption rate constant (Ka). Absorption from stomach and colon is assumed to be negligible in this model. Different dosage forms (solution, multiple, or single unit formulation) are distributed and transferred through the intestine following the same kinetics, but gastric emptying is a formulation-dependent process. In the publication of Kortejärvi et al. (Eur J Pharm Sci. 2007), the gastric emptying of different dosage forms has been analyzed based on several studies and gastric emptying time and kinetics have been determined for each dosage form (Table 1 in the article). The absorption rate constant (Ka) of a compound can be predicted from its molecular structure using calculated physicochemical descriptors. Linnankoski et al. (J Med Chem 2006) used quantitative-structure activity relationship (QSAR) modeling and found a simple equation for the prediction of Ka: log Ka = (logd6.0) (PSA) Equation (1) where Ka is the absorption rate constant in units of h -1, Log D6.0 is the distribution coefficient at ph 6.0 and PSA is the polar surface area. The logd6.0 of paracetamol is 0.34 and its PSA is 49.33, when calculated with ACDlabs software. The i.v. kinetics of paracetamol follow a 2-compartmental model and Amer et al. (J Pharm Sci 1983) have calculated the following parameters for i.v. infusion: Vd = 9.94 l, K12=9.5 h -1, K21= 2.35 h -1 and K10= 2.11 h -1. Problems 1) Calculate the Ka value for paracetamol based on Equation 1 and the physicochemical descriptors of paracetamol. 2) Build a CAT model for paracetamol based on calculated Ka value. 3) Build a second CAT model and use your own experimental Papp value to describe absorption. 4) Using both models, simulate the plasma concentrations after intake of a 500 mg paracetamol multiple unit tablet. Assume that the dissolution rate constant of the rapidly acting formulations is rather fast and Kd is 1.9 h-1. Compare the results of the models with each other and discuss differences. 5) Compare the concentration curves to your own in vivo paracetamol data from the bioequivalence studies. Give reason for possible differences in results. 6) Perform simulations using the Ka-model and change the Kd value. Conclude whether paracetamol is sensitive to changes in the dissolution rate. Explain the reasons for that. How does this affect the bioequivalence of paracetamol formulations? Remember that the Sensi Specs function in STELLA can be used for performing comparative simulations with changes in a parameter value. 5

6 3.4.6 Results and Report Explain your simulations and results in a coherent report complete with introduction, methods and conclusions. Give answers to all the questions presented in the problems. Generate tables or figures, whenever they are informative. Remember to provide headings for tables and legends for figures. Copy the structure of each model and equations from STELLA to your report. In the final report of the practicals you can utilize the knowledge the pharmacokinetic simulations gave you. Also use the figures and tables where applicable References Ameer, B.; Divoll, M.; Abernethy, D. R.; Greenblatt, D. J.; Shargel, L. Absolute and relative bioavailability of oral acetaminophen preparations. J. Pharm. Sci. 1983, 72, Kortejärvi H., Urtti A., and Yliperttula M Pharmacokinetic simulation of biowaiver criteria: the effects of gastric emptying, dissolution and absorption and elimination rates Eur. J. Pharm. Sci 30(2): Linnankoski, J., Mäkela, J.M., Ranta, V.P., Urtti, A., Yliperttula, M., Computational prediction of oral drug absorption based on absorption rate constants in humans. J. Med. Chem. 49, Thiel-Demby VE, Humphreys JE, St. John Williams LA, Ellens HM, Shah N, Ayrton AD and Polli JW, Biopharmaceutics Classification System: Validation and Learnings of an in Vitro Permeability Assay. Mol. Pharm. 6(1): Yu et al., Compartmental transit and dispersion model analysis of small intestinal transit flow in humans. Int. J. Pharm. 140: ,