Case studies of in vitro/in vivo and in vivo/in vivo predictions of pharmacokinetic parameters and clinical doses

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1 Version Case studies of in vitro/in vivo and in vivo/in vivo predictions of pharmacokinetic parameters and clinical doses PKPD Section DMPK & BAC AstraZeneca R&D Södertälje Sweden

2 PK/PD AstraZeneca R&D Södertälje, Sweden SYMBOLS AND THEIR DEFINITIONS...4 INTRODUCTION...6 ACKNOWLEDGEMENTS...7 CASE 1 - IN VITRO/IN VIVO EXTRAPOLATION GOALS MATERIALS AND METHODS IN VITRO SYSTEMS CONCENTRATION-TIME DATA EQUATIONS DATA ANALYSIS RESULTS AND DISCUSSION PRESENTATION OF DATA SIMULTANEOUS NONLINEAR REGRESSION - SNLR AREA-UNDER-THE-CURVE SUMMARY OF SNLR AND AUC ANALYSES CONCLUSIONS AND POINTS TO CONSIDER REFERENCES...16 CASE 2 - IN VIVO/IN VIVO EXTRAPOLATION GOALS MATERIALS AND METHODS INTRAVENOUS DATA ORAL DATA EQUATIONS DATA ANALYSIS RESULTS AND DISCUSSION RESULTS FROM INTRAVENOUS STUDIES RESULTS FROM ORAL STUDIES CONCLUSIONS AND POINTS TO CONSIDER REFERENCES...26 CASE 3 - IN VIVO/IN VIVO EXTRAPOLATION GOALS MATERIALS AND METHODS EXPERIMENTAL BACKGROUND CONCENTRATION-TIME DATA EQUATIONS DATA ANALYSIS

3 A practical guide to scaling in vitro and in vivo data 3. RESULTS AND DISCUSSION CONCLUSIONS AND POINTS TO CONSIDER...31 CASE 4 - IN VIVO/IN VIVO EXTRAPOLATION GOALS MATERIALS AND METHODS EXPERIMENTAL BACKGROUND CONCENTRATION-TIME DATA EQUATIONS DATA ANALYSIS RESULTS AND DISCUSSION CONCLUSIONS AND POINTS TO CONSIDER REFERENCES...37 GENERAL POINTS TO CONSIDER...38 APPENDIX 1.1 CASE STUDY APPENDIX 1.2 WINNONLIN COMMAND FILE FOR CASE STUDY APPENDIX 2.1 APPENDIX 2.2 CASE STUDY 2 - INTRAVENOUS DATA...45 CASE STUDY 2 - ORAL DATA...48 APPENDIX 3. CASE STUDY APPENDIX 4. CASE STUDY

4 PK/PD AstraZeneca R&D Södertälje, Sweden Symbols and their definitions Symbol Definition Unit a Allometric coefficient for CL arbitrary units Amount Amount of substrate in the incubation medium mol AUC Area under the plasma concentration-time curve nm. min, µm. min b Allometric exponents for CL BW Body weight g, kg C Plasma concentration nm, µm c Allometric coefficient for V arbitrary units C E Effective concentration range nm, µm CL, CL u Clearance, unbound clearance ml/min or L/h CL animal Clearance for a particular species ml/min or L/h CL b Blood clearance ml/min or L/h CL/F Oral clearance ml/min or L/h CL H Hepatic clearance ml/min or L/h CL H,b Hepatic blood clearance ml/min or L/h CL H,p Hepatic plasma clearance ml/min or L/h CL int Intrinsic clearance ml/min or L/h CL int, in vitro In vitro intrinsic clearance ml/min or L/h CL int, in vivo In vivo intrinsic clearance ml/min or L/h CL p Plasma clearance ml/min or L/h CV% Coefficient of variation, relative standard deviation % d Allometric exponents for V E H Hepatic extraction ratio F F H f u Bioavailability Availability across the liver Unbound fraction in plasma K m Michaelis -Menten constant µm K p Blood-to-plasma concentration ratio n, [P], K a Number of binding sites, protein concentration, affinity constant t 1/2 Effective half-life min or h t 1/2λZ Terminal half-life min or h Q H Hepatic blood flow L/h V Volume of distribution, unbound volume of distribution ml or L V/F Volume of distribution over bioavailability ml or L V ss, V uss Volume of distribution at steady state, unbound volume ml or L V max Maximum rate of metabolism µmol/ min V max Maximum rate of metabolism based on concentration µm/min V medium Volume of the in vitro incubation medium ml or L 4

5 A practical guide to scaling in vitro and in vivo data Symbol Definition CD Candidate drug FTIM First time in man g gram h Hour HED Human equivalent dose kg kilogra m mg milligram µg microgram L Liter LI Lead identification LO Lead optimization ml milliliter µl microlitre min minute mol mole mmol millimol MRSD Maximum Recommended Safe Dose µmol micromole M molar or mol per litre mm millimolar µm micromolar MMP milligram microsomal protein No. Number PN Prenomination PBPK Physiologically based pharmacokinetic models SNLR Simultaneous nonlinear regression analysis 5

6 PK/PD AstraZeneca R&D Södertälje, Sweden Introduction Scaling from in vitro and in vivo data has become common practice within the pharmaceutical industry. It is now performed during all preclinical phases, from early lead optimization (LO) to candidate drug (CD) selection and compilation of the IND dossier. Let us then ask ourselves why do we want to scale? What are the practical reasons for this? The primary clinical reasons for scaling data from animals to man are to obtain an appropriate clinical dose; the plasma concentration-time profile for assessment of the efficacy interval and safety margin; and/or the response-time course (onset, intensity, and duration of action). Most often scaling involves the use of allometric principles, which relates a physiological variable (e.g., clearance) to a measurable size such as body weight. A less frequently used allometric approach involves the application of physiologically based pharmacokinetic (PBPK) models. This version of our document does not cover PBPK models but will in the future. It focuses instead on scaling in vitro or in vivo parameters by means of simple allometry. Scaling is also performed for preclinical decision-making purposes, in that the compound or compound series with the best predicted characteristics (such as lowest cost of goods, most convenient formulation, highest safety margin, etc.) in man may be more highly ranked. From a clinical point of view, scaling is done for prediction of the human equivalent dose (HED). The HED estimate is then used to estimate the maximum recommended safe dose (MRSD) in man. The latter is often calculated as HED/25 or HED/10 or something less. However, as soon as sufficient data are available from the lowest clinical dose panel, then that will guide any further increase in dose for the next panel(s). Success of predicting the right first time in man (FTIM) dose varies between compound classes and therapeutic areas, with an increased predictability with application of multiple sources of in vivo data. So far, investigators have limited themselves primarily to extrapolating pharmacokinetic parameters such as clearance, volume of distribution, halflife, and bioavailability across the liver. This is still often hampered by predictions from a single species (e.g., the rat) or inconclusive in vitro enzyme kinetics (e.g., a single-point approach coupled with standardized correction factors for amount of protein, etc.). What is generally neglected when scaling pharmacokinetic data is to estimating the variability in the prediction or the predicted range. This variability, which can be substantial, originates primarily from the uncertainty of the effective (target) concentration range, variability in the measured preclinical parameters, variability in the allometric exponent (b), and variability in the man-to-beast body weight ratio. Questions related to the success of scaling a certain parameter include what do we have to do when the predicted human dose interval has low precision? Alternatively, how do we discriminate between a precise versus and an imprecise prediction? How does the clinic deal with an imprecise prediction? In light of the precision of the determinants (EC 50, CL animal, body weight ratio man-to-animal, allometric exponent b, etc.) of the scaled clinical dose, we still know very little about the predicted distribution of the dose. Monte- Carlo simulations indicate that this distribution is highly skewed towards higher doses. Besides the scaling of pharmacokinetic parameters, we believe that more effort will be invested in scaling pharmacodynamic parameters such as potency (EC 50 /IC 50 ), efficacy, 6

7 A practical guide to scaling in vitro and in vivo data and turnover (k in, k out ) of response. We are convinced that good pharmacodynamic properties may often save a compound with less than optimal pharmacokinetics. One typical example of this is omeprazole, with a human plasma half-life of less than an hour, whereas the half-life of response is in the range of hours. Another example is Seroquel (quetiapine), which in spite of its pharmacokinetic properties (high CL, relatively short t 1/2, and active metabolites) is being investigated for a convenient dosing schedule in man. Both Prilosec (omeprazole, inhibition of turnover of acid secretion) and Seroquel (neuroleptic) have unique pharmacodynamic properties in that the rate-limiting step is the slower turnover of response (acid-secreting or antipsychotic improvement) rather than the plasma kinetics, which is comparatively rapid in terms of short plasma halflives. The PK/PD section at AstraZeneca R&D Södertälje organized a one-day workshop in 2002, which was followed up by a joint meeting with preclinical DMPK and Experimental Medicine in Mölndal in January 2003, for the purpose of sharing, updating, and documenting scaling practice. Primarily two types of recommendation evolved from the meeting: one advocating simultaneous nonlinear regression (SNLR) of several sources of data and the other providing the scaled human parameters with a prediction interval. The ambition was also to start collecting and compiling case studies. This report documents some of these efforts. It is meant to be a quick reference for kineticists, pharmacologists, toxicologists, preclinical/clinical project leaders, and others interested in practicing the scaling of pharmacokinetic and pharmacodynamic data to man. If you should find errors in data, equations, or the analysis (or even grammatical flaws) when reading this, please do not hesitate to let us know by contacting Johan.Gabrielsson@AstraZeneca.com. You may also give us your suggestions about the format. We hope to keep this document alive and we will therefore constantly update the material with new case studies as this scientific area develops within and outside of AstraZeneca. Södertälje, December 2, 2003 Acknowledgements We would particularly like to thank colleagues at DMPK & BAC, Research DMPK, and Carina Stenfors, Bioscience, AstraZeneca R&D Södertälje, Ulf Bredberg, AstraZeneca R&D Mölndal, and Carl-Johan Johansson, AstraZeneca R&D Lund, for their support during the experimental work, fruitful scientific discussions, and/or constructive criticism of this document. The compilation of data and figures by Carl von Essén is also appreciated. 7

8 PK/PD AstraZeneca R&D Södertälje, Sweden Case 1 - In vitro/in vivo extrapolation 1. Goals To calculate CL int from in vitro data based on microsomes and hepatocytes To contrast the simultaneous nonlinear regression (SNLR) approach with the traditional area under the concentration curve (AUC) approach To compare and scale in vitro and in vivo data for each species to man To simulate extrapolated CL int and CL H as a function of concentration 2. Materials and Methods 2.1 In vitro systems Data for compound X were obtained from in vitro incubations of pooled liver microsomes and hepatocytes (fresh or cryopreserved) from different species at 1, 10, and 20 µmol/l. The experimental data for the in vitro systems are summarized in Table 1. Table 1. In vitro test system (hepatocytes and microsomes), species, substrate concentration, incubation volume, number of cells per incubation, and milligram microsomal protein (MMP) per gram liver for mouse, rat, rabbit, dog, and man. In vitro test system Species Substrate concentration (µm) Incubation volume (µl) Hepatocytes Rat No. of cells per incubation MMP per gram liver (mg/g) Dog Man Rat Rabbit Dog Man Microsomes Mouse Rat 50 Rabbit 50 Dog 50 Man Mouse Rat 50 Rabbit 50 Dog 50 Man Mouse Rat 50 Dog 50 Man

9 A practical guide to scaling in vitro and in vivo data The data were obtained from in vitro incubations of different concentrations, with liver microsomes (pooled) and hepatocytes (cryopreserved or fresh) from mouse, rat, rabbit, dog, and man (Appendix 1.1). Intravenous plasma concentration-time data were obtained from the Sprague Dawley rat, guinea pig, beagle dog, and cynomolgus monkey. 2.2 Concentration-time data The in vitro concentration-time data are summarized in Figure 1. The underlying concentration-time data are tabulated in Appendix Concentration (µm) 10 1 Mouse Rabbit Rat Human Dog Concentration (µm) 10 1 Dog Human Rat Time (min) Time (min) Figure 1. Semilogarithmic plot of substrate (compound X) concentration versus time obtained from microsomes (left: mouse, rat, rabbit, dog, and man) and hepatocytes (right: rat, rabbit, dog, and man). See Appendix 1.1 for raw data. 2.3 Equations The single enzyme model determines the decline of the substrate concentration (C), and has previously been shown to be the best model to describe the decline in substrate concentration. This model was used for the simultaneous non-linear regression SNLR 1 approach, which involves fitting several concentration-time courses simultaneously. dc dt V max = C (1:1) K + C m See Appendix 1.2 for the WinNonlin command file source code of the model, initial parameter estimates, constants, and experimental data.the maximum rate of metabolism (V max ) is then derived from Equation 1:2, where V medium denotes the incubation volume. V max = V V (1:2) max medium The maximum in vitro intrinsic clearance ( CL according to Equation 1:3 V int,invitro ) is then determined by V max and K m max CL int,invitro = (1:3) Km 1 Gabrielsson & Weiner [1994, 1997, 2000], Kakkar et al [1999]. 9

10 PK/PD AstraZeneca R&D Södertälje, Sweden The in vitro intrinsic clearance may also be calculated by means of the area under the concentration curve (AUC) approach (Equation 1:4). The initial amount of substrate in the incubation medium (Amount) is divided by the total area under the substrate concentrationtime curve (AUC). Amount CLint, invitro = (1:4) AUC The in vitro intrinsic clearance, derived from the microsomal system, is then scaled to the in vivo intrinsic clearance (Cl int, in vivo ) by means of the data from Table 1 and Equation 1:5. CL int, in vivo mg microsomal protein = CLint,in vitro g total liver (1:5) g liver The in vitro intrinsic clearance, derived from the hepatocyte system, is scaled to the in vivo intrinsic clearance by means of Equation 1:6 and the data from Tables 1 and 2. CL int, in vivo 6 10 hepatocytes = CLint,in vitro g total liver (1:6) g liver Hepatic blood clearance CL H, b, is then calculated from Equation 1:7. Since the unbound fraction of compound X in plasma (f u ) is greater than 0.4 and similar across the different species it is not taken into account for the calculation of the hepatic blood clearance (organ), CL H, b. CL H,b Q Q H u int,invivo = (1:7) H f CL + f CL u int,invivo Hepatic plasma clearance (CL H, p ) is then calculated from Equation 1:8 taking the blood-toplasma concentration ratio (K p ) into account. CL H,p = CL K (1:8) H,b p Human plasma clearance (CL p ) can also be predicted from allometric plots (Figure 4), using CL p b = a BW (1:9) where the parameters a and b are obtained by plotting the logarithm of clearance versus the logarithm of body weight. ln CLp = ln a + b ln BW (1:10) The resulting regression line has a slope b and an intercept a of the abscissa for a body weight equal to 1 kg. 10

11 A practical guide to scaling in vitro and in vivo data 2.4 Data analysis Data (see Appendix 1.1) were analyzed by means of WinNonlin Pro 3.1, using the simultaneous non-linear regression SNLR approach (2). See Appendix 1.2 for the WinNonlin command file source code. For compound X, a single enzyme model based on Equation 1:1 was used. The AUC method was used in situations of sparse data. Table 2 contains information about commonly used liver weights, hepatic blood flows, body weights, number of hepatocytes, microsomes per gram liver, and blood-to-plasma concentration ratios of compound X for mouse, rat, rabbit, dog, and man. Table 2. Species, liver weight, hepatic blood flow (Q H ), body weight (BW), number of hepatocyte cells per gram liver, milligram microsomal protein (MMP) per gram liver, and blood-to-plasma concentration ratios (K p ) for mouse, rat, rabbit, dog, and man, respectively. Species Liver weight (g) Q H (ml/min) BW (kg) No. of hepatocytes* per gram liver MMP per gram liver (mg/g) Mouse ** Rat Rabbit ** Dog Human (20-77) * No of hepatocytes ** Mean value of K p in rat, dog, and man 3. Results and Discussion 3.1 Presentation of data Figure 2 shows the observed and model-predicted concentration-time data for compound X in two incubations of rabbit microsomes. K p dc dt V = k V max = ' max m V C + C ' max V medium Figure 2. Semi-logarithmic plot of observed ( ) and model predicted (---) concentration-time data of compound X in incubations with rabbit microsomes. The initial concentrations were 1 and 10 µm. Note the non-linear nature of compound X. The model predictions are based on Equation 1: Time (min) Figure 3 shows the observed and model-predicted concentration-time data for compound X in three incubations of human microsomes. 2 von Bahr et al 1980, Bäärnhielm et al 1986, Powis et al 1988, Shaw et al

12 PK/PD AstraZeneca R&D Södertälje, Sweden Figure 3. Semi-logarithmic plot observed ( ) and model predicted (---) concentration-time data of compound X in incubations with human microsomes. The initial concentrations were 1, 10 and 20 µm. The model predictions are based on Equation 1: Time (min) The final estimates of maximum rate of metabolism in vitro, the Michaelis-Menten constant, in vivo intrinsic clearance, and their corresponding coefficients of variation for rabbit and man are summarized in Table 3. Table 3. In vitro test system, species, and the final estimates (±CV%) of maximum rate of metabolism in vitro (V max, in vitro ), the Michaelis-Menten constant (K m ), and in vivo intrinsic clearance (CL int, in vivo ) for rabbit and man. In vitro test system Species Microsomes Hepatocytes Rabbit Man Man V max, in vitro (µmol/min) K m (µm) Cl int, in vivo (ml/min) 5 10 ± ± ± ± ± ± ± ± ± Simultaneous nonlinear regression - SNLR The trail from the final parameter estimates by means of simultaneous non-linear regression SNLR, to human plasma clearance is demonstrated in Equations 1:11-1:17. Equation 1:11 gives the disposition of compound X in the hepatocyte system according to dc dt = C C µm/min µm = µm + µm µm min (1:11) where 0.06 and 20 represent V max and K m, respectively. V max is then obtained by multiplying V max by V medium in Equation 1:12. V 4 max = µm µmol L = (1:12) min min 6 This gives a V max of 6 10 µmol/min. The estimated values of V max and K m are inserted into Equation 1:3 to obtain CL int, in vitro. CL int,invitro 6 10 = 20 6 µmol/min L = (1:13) µm min 12

13 A practical guide to scaling in vitro and in vivo data CL int, in vitro is based on 10 5 cells in the incubation (Table 1), which gives a CL int, in vitro of L/min or 0.3 µl/min. The CL int, in vitro expressed as micro liters per minute per million cells, is given by 0.3 CL 5 10 µl/min 6 (cells/inc ubation) 6 int, invitro = 10 per 10 cells (1:14) which gives a CL int,invitro of 3 µl/min per 10 6 cells. The CL int, in vivo is then calculated by inserting the estimated CL int, in vitro, the number of hepatocytes per gram liver (Table 2), and the liver weight (Table 2) into Equation 1:6, CL int, in vivo 6 10 cells = µl/min g (1:15) g which gives a CL int, in vivo of µl/min or 540 ml/min. CL H, b is calculated from of CL int, in vivo and hepatic blood flow Q H, inserted into Equation 1:7, CL H, b = ml/min ml/min ml/min + ml/min ml = min (1:16) which gives a CL H,b of 394 ml/min. Hepatic plasma clearance (CL H, p ) is then calculated from of Equation 1:8 CL H, p = ml min (1:17) where 1.4 is the blood-to-plasma ratio (K p ) in Table 2 and Equation 1:8. This gives a CL H, p of 551 ml/min. 3.3 Area-under-the-curve An alternative approach to calculating CL int, in vitro is by means of Equation 1:4. The total amount of substrate (Amount) in the incubation, divided by the area under the substrate concentration-time curve (AUC), giving CL int,invitro = µmol µm min = L min (1:18) 7 which gives a CL int, in vitro of L/min or 0.19 µl/min based on 10 5 cells in the incubation (Table 1). CL int, in vitro expressed as µl/min per million cells is given by CL int, invitro µl/min 6 cells/incu bation 6 = 10 per 10 cells (1:19) which gives an CL int, in vitro of 1.9 µl/min per 10 6 cells. 13

14 PK/PD AstraZeneca R&D Södertälje, Sweden 3.4 Summary of SNLR and AUC analyses The results of the SNLR and AUC analyses using hepatocyte and microsomal data are summarized in Table 4. Table 4. Human hepatic blood clearance (CL H, b ), hepatic extraction ratio (E H ), and the Michaelis- Menten constant (K m ) predicted by means of the AUC and the SNLR methods using the hepatocyte and microsomal data. Method Hepatocytes Microsomes Target conc. (µm) CL H,b (L/min) E H K m (µm) CL H, b (L/min) AUC SNLR 0.39* * *Maximum CL H, b E H K m (µm) Figure 4 shows an allometric plot of superimposed in vitro and in vivo clearances for mouse, rat, rabbit, guinea pig, dog, minipig, cynomolgus monkey, and man against body weight. Note that the prediction interval has been superimposed upon data in order to give the reader a feeling for the uncertainty in the scaled values, rather than just giving the point estimate of, for example, clearance in man. The prediction interval stems from the total sample and not a regression as compared to the confidence interval (narrower) of the predicted regression line (mean). Clearance (ml/min) Hepatocytes Microsomes In vivo BW (kg) Prediction Interval Figure 4. Plasma clearance CL p plotted versus body weight for mouse, rat, guinea pig, dog, minipig, cynomolgus monkey, and man. Superimposed plasma clearance based on hepatocyte and microsomal data. The solid line and the dotted lines represent the regression line and the 95% prediction interval, respectively. The horizontal dashed lines correspond to the estimated clearance interval in man. This graph contains additional data not found in the raw data (Appendix 1.1). Figure 5 shows a simulation of human in vivo intrinsic clearance (CL int ) and organ clearance (CL H ) versus plasma concentration predicted from the data in Table 4. 14

15 A practical guide to scaling in vitro and in vivo data 1400 Clearance (ml/min) CL int - Hepatocytes CLH - Hepatocytes CL int - Microsomes CL H - Microsomes Figure 5. Simulated human intrinsic clearance (CL int ) and hepatic clearance (CL H ) plotted versus plasma concentrations. The blue horizontal bar represents the tentative therapeutic interval and the yellow-red bar the exposure range observed in safety studies Plasma conc. (µm) 4. Conclusions and points to consider The present analysis demonstrates the principles of the SNLR approach, which gave results similar to the more traditional AUC method. However, it is necessary to apply V max and K m when scaling nonlinear kinetics rather than a constant CL int value when K m is less than or similar to therapeutic concentrations. SNLR uses the whole dataset more efficiently than other approaches, but may not necessarily work for all designs, whereas the AUC method almost always gives a number. SNRL will probably be a more efficient and correct approach for compounds with a K m in the therapeutic range (Reference 3). The in vivo and in vitro scaled clearance values were superimposed when plotted against body weight in an allometric graph. The in vitro scaled data serve as guidance when in vivo data (e.g., in man) are lacking and /or inconsistent. The compound is expected to have a low to intermediate extraction ratio in man from hepatocyte and microsomal in vitro data. We would like to place a warn against the inappropriate use of amount of microsomal protein per gram liver (MMP). This value is cited with a range from about 20 to 77 units. One may easily convert a low clearance compound into a high clearance compound incorrectly, by using 50 or 77 rather than 20. Table 5 shows how the extraction ratios for low, intermediate, and high clearance compounds will change with a change in MMP. However, from a variability point of view, we recommend the user to do this exercise with his/her own data since MMP may vary between individuals. Table 5. Extraction ratios versus different values of conversion factor MMP (mg microsomal protein per gram liver) obtained from man MMP = 20 MMP = 50 MMP = 77 Low E H < Intermediate 0.3 < E H < High E H > The SNLR model was used for simulations of clearance and intrinsic clearance as a function of concentration in order to visualize in what concentration ranges one might expect nonlinear elimination. 15

16 PK/PD AstraZeneca R&D Södertälje, Sweden 5. References 1. von Bahr C, Groth CG, Jansson H, Lundgren G, Lind M, Glaumann H. Drug Metabolism in Human Liver in vitro: Establishment of a Human Liver Bank. Clinical Pharmacology and Therapeutics. 1980; 27(6); Bäärnhielm C, Dahlbäck H, Skånberg I. In vivo Pharmacokinetics of Felodipine Predicted from in vitro Studies in Rat, Dog and Man. Acta Pharmacologica et Toxicologica. 1986; 59(2); Gabrielsson J, Weiner D. Pharmacokinetic and Pharmacodynamic Data Analysis. Swedish Pharmaceutical Press. 1994, 1997, Kakkar T, Boxenbaum H and Mayersohn M. Estimation of K I in a Competitive Enzyme -Inhibition Model: Comparisons among Three Methods of Data Analysis. Drug Metabolism and Disposition. 1999; 27 (6); Kakkar T, Pak Y, Mayersohn. Evaluation of a Minimal Experimental Design for Determination of Enyzme Kinetic Parameters and Inhibition Mechanism. The Journal of Pharmacology and Experimental Therapeutics. 2000; 293 (3); Powis G. The Use of Human Liver for Foreign Compound Metabolism and Toxicity Studies. Drug Metabolism Reviews. 1989; 20(2-4); Shaw L, Lennard MS, Tucker GT, Bax NDS and Woods HF. Irreversible Binding and Metabolism of Propranolol by Human Liver Microsomes Relationship to Polymorphic Oxidation. Biochemical Pharmacology. 1987; 36(14);

17 A practical guide to scaling in vitro and in vivo data Case 2 - In vivo/in vivo extrapolation 1. Goals To analyze plasma concentration-time data for each species and assess the pharmacokinetic parameters CL and V ss To construct allometric plots of CL and V ss versus body weight (BW) of rat, marmoset, cynomolgus monkey, minipig, and dog To estimate allometric parameters a, b, c, and d in equations CL = a BW b V ss = c BW d To construct Dedrick plots and assess the superimposability of concentration-time data of different species. To predict the pharmacokinetics of compound X in man, based on data obtained in other species. 2. Materials and Methods The in vivo data were obtained from the rat, marmoset, cynomolgus monkey, minipig, and dog following both intravenous and oral administration of compound X (Appendices 2.1 and 2.2). 2.1 Intravenous data Table 1 summarizes the experimental background for the intravenously administered doses in the rat, marmoset, cynomolgus monkey, minipig, and dog. Table 1. Species, the intravenously administered bolus doses of the in vivo system, and the body weights (BW) of rat, marmoset, cynomolgus monkey, minipig, and dog. Species Dose (µmol/kg) BW (kg) Rat Marmoset Cynomolgus monkey Minipig Dog Figure 1 summarizes the concentration-time data after intravenous administration in the rat, marmoset, cynomolgus monkey, minipig, and dog. The different doses are found in Table 1 and the underlying concentration-time data are tabulated in Appendix

18 PK/PD AstraZeneca R&D Södertälje, Sweden 1000 Concentration (µm) Rat Marmoset Cynomolgus Minipig Dog Figure 1. Semi-logarithmic plot of concentration-time curves of rat, marmoset, cynomolgus monkey, minipig, and dog, following an intravenous dose of compound X. Table 1 contains dosing information for each species Time (h) 2.2 Oral data Table 2 summarizes the experimental background for the orally administered doses in the rat, marmoset, cynomolgus monkey, minipig, and dog. Table 2. Species, oral administration vehicle, dose and body weight (BW) of rat, marmoset, cynomolgus monkey, minipig, and dog. Species Vehicle Dose (µmol/kg) BW (kg) Rat 0.1M Meglumine M Meglumine M Meglumine % PVP in aq M Meglumine % PVP in aq Marmoset Water Water Cynomolgus monkey Water Water Minipig Water Water Dog 20% HP-β-CD M Meglumine % HP-β-CD M Meglumine Figure 2 summarizes the concentration-time data following oral administration to the rat, marmoset, cynomolgus monkey, minipig, and dog. The different doses are found in Table 2 and the underlying concentration-time data are tabulated in Appendix

19 A practical guide to scaling in vitro and in vivo data 1000 Concentration (µm) Rat Marmoset Cynomolgus Minipig Dog Figure 2. Semi-logarithmic plot of concentration-time curves of rat, marmoset, cynomolgus monkey, minipig, and dog, following an oral dose of compound X. Table 2 contains dosing information for each species Time (h) 2.3 Equations Equation 2:1 describes the relationship between body weight (BW) and Clearance (CL). CL b = a BW (2:1) where the parameters a and b are obtained by plotting the logarithm of clearance versus the logarithm of body weight. ln CL = ln a + b ln BW (2:2) The resulting regression line has a slope b and an intercept a of the abscissa for a body weight equal to 1 kg. The volume of distribution at steady state (V ss ) is obtained in a similar way by means from Equation 2:3. V ss d = c BW (2:3) The Dedrick plot uses normalized concentration-time data in order to enable comparison of species of different sizes. If the relationship between volume of distribution and body weight is directly proportional, (d=1), an elementary Dedrick plot may be used. The dose and body weight-normalized concentration for this plot is obtained from Equation 2:4 Concentration Normalized concentration = (2:4) Dose BW and body weight-normalized time is obtained from Equation 2:5. Time Normalized time = (2:5) 1 b BW 19

20 PK/PD AstraZeneca R&D Södertälje, Sweden A complex Dedrick plot must be used if V ss scales proportionately to BW to a factor (d) greater than 1 (unity). In this case, the dose and body weight-normalized concentration is obtained from Equation 2:6. Concentration Normalized concentration = (2:6) Dose d BW Hence, the body weight-normalized time is obtained from Equation 2:7. Time Normalized time = (2:7) d b BW Equation 2:8 is then used for prediction of the human dose range. Dose range man BW b man = CE CLanimal (2:8) BWanimal where (C E ) is the anticipated effective concentration range in man. 2.4 Data analysis Data were evaluated by means of noncompartmental analysis using a model for extra vascular input (Model 200) and intravenous infusion (Model 201) in WinNonlin 3.2. Mean (n= 3) plasma concentration versus time data were used for each dose group and species. 3. Results and Discussion Table 3 summarizes the clearance, the volume of distribution, oral clearance, and volume of distribution over bioavailability for the rat, marmoset, cynomolgus monkey, minipig, and dog, following intravenous and oral administration. 20

21 A practical guide to scaling in vitro and in vivo data Table 3. Species, dose, observed clearance (CL), and volume of distribution at steady state (V ss ) after intravenous administration and the observed oral clearance (CL/F) and volume of distribution over bioavailability (V/F) for rat, marmoset, cynomolgus monkey, minipig, and dog after oral administration. Intravenous dosing Oral dosing Species Dose (µmol/kg) CL (ml/min) V ss (L) Species Dose (µmol/kg) CL/F (ml/min) V/F (L) Rat Rat Marmoset Cynomolgus monkey Minipig Dog Marmoset Cynomolgus monkey Minipig Dog Results from intravenous studies Figure 3 shows clearance plotted versus body weight, following intravenous administration of compound X in the rat, marmoset, cynomolgus monkey, minipig, and dog Clearance (ml/min) CL = BW Body weight (kg) Rat Marmoset Cynomolgus Minipig Dog Regression 95% Prediction interval CL interval for man Figure 3. Logarithmic plot of clearance versus body weight of rat, marmoset, cynomolgus monkey, minipig, and dog, following intravenous administration. The solid line and the dotted lines represent the regression line and the 95% prediction interval, respectively. The horizontal dashed lines correspond to the estimated clearance interval in man. The regression equation is also inserted into the graph. The a (0.7941) and b (0.9985) parameters in Equation 2:1 are obtained by means of regressing data in Figure 3. Assuming a human body weight of 70 kg the expression for CL becomes 21

22 PK/PD AstraZeneca R&D Södertälje, Sweden CL = ml min (2:9) The corresponding value of CL is 55 ml/min. Figure 4 shows the volume of distribution at steady state plotted versus body weight, following intravenous administration of compound X in the rat, marmoset, cynomolgus monkey, minipig, and dog. Volume of distribution at steady state (L) Body weight (kg) V ss = BW Rat Marmoset Cynomologus Minipig Dog Regression 95% Prediction Interval V ss Interval for Man Figure 4. Logarithmic plot of volume of distribution at steady state versus body weight for rat, marmoset, cynomolgus monkey, minipig, and dog, following intravenous administration. The solid line and the dotted lines represent the regression line and the 95% prediction interval, respectively. The horizontal dashed lines correspond to the estimated volume of distribution interval in man. The regression equation is also inserted into the graph. The c ( ) and d (0.9209) parameters in Equation 2:3 are obtained by means of regressing data in Figure 4. Assuming a human body weight of 70 kg, the equation becomes V ss = L (2:10) The corresponding value of V ss is 23 L. The predicted daily dose range in man can then be estimated by inserting the actual value of C E (e.g., µg/ml), CL (55 ml/min), and b (0.9985) into Equation 2:8 Dose range man = 15 CL animal BW BW man animal mg day (2:11) The term converts minutes to days. Note that each of C E, CL animal, and b is associated with a certain amount of variability, which means that the variation of the final estimate of the daily dose range may be substantial. The predicted range in CL and V ss, and/or daily dose in man, is given by the prediction intervals in Figures 3 and 4. A semilogarithmic plot of dose and body weight-normalized concentration-time data for the rat, marmoset, cynomolgus monkey, minipig, and dog is shown in Figure 5. 22

23 A practical guide to scaling in vitro and in vivo data 100 Normalized concentration (kg/l) Rat Marmoset Cynomolgus Minipig Dog Figure 5. Semi-logarithmic, elementary Dedrick plot for rat, marmoset, cynomolgus monkey, minipig, and dog, following intravenous administration. Table 1 contains dosing information for each species Kallynochrons (h/kg (1-b) ) 3.2 Results from oral studies Figure 6 shows oral clearance (CL/F) plotted versus body weight for the rat, marmoset, cynomolgus monkey, minipig, and dog. Clearance/F (ml/min) CL/F= BW Rat Marmoset Cynomolgus Minipig Dog Regression 95% Prediction interval CL interval for Man Figure 6. Logarithmic plot of oral clearance versus body weight for rat, marmoset, cynomolgus monkey, minipig, and dog, following oral administration. The solid line and the dotted lines represent the regression line and the 95% prediction interval, respectively. The horizontal dashed lines correspond to the estimated oral clearance interval in man. The regression equation is also inserted into the graph. Body weight (kg) The a (0.6510) and b (1.6885) parameters in Equation 2:1 are obtained by regressing data in Figure 6. Assuming a human body weight of 70 kg, the expression for CL/F becomes CL / F = ml min (2:12) The corresponding value of CL/F is 849 ml/min. Figure 7 shows the volumes of distribution over bioavailability (V/F) plotted versus body weight for rat, marmoset, cynomolgus monkey, minipig, and dog. 23

24 PK/PD AstraZeneca R&D Södertälje, Sweden V/F (L) V/F =1.331 BW Rat Marmoset Cynomolgus Minipig Dog Regression 95% Prediction interval V/F interval for man Figure 7. Logarithmic plot of volume of distribution over bioavailability versus body weight for rat, marmoset, cynomolgus monkey, minipig, and dog, weight following oral administration.. The solid line and the dotted lines represent the regression line and the 95% prediction interval, respectively. The horizontal dashed lines correspond to the estimated volume of distribution interval in man. The regression equation is also inserted into the graph. Body weight (kg) The c (1.331) and d (1.3899) parameters in Equation 2:3 are obtained by regressing data in Figure 7. Assuming a human body weight of 70 kg, V/F becomes V / F = L (2:13) The corresponding value of V/F is 488 L. A semi-logarithmic plot of dose and body weight-normalized concentration-time data for the rat, marmoset, cynomolgus monkey, minipig, and dog is shown in Figure Normalized concentration (kg/l) Rat Marmoset Cynomolgus Minipig Dog Figure 8. Semi-logarithmic, elementary Dedrick plot of normalized concentration-time data of rat, marmoset, cynomolgus monkey, minipig, and dog, following oral administration. Table 2 contains dosing information for each species Kallynochrons (h/kg (1-b) ) In this case direct proportionality does not exist between body weight and V/F and therefore a complex Dedrick plot is constructed. Figure 9 shows a semilogarithmic plot of dose and body weight-normalized concentration-time data for the rat, marmoset, cynomolgus monkey, minipig, and dog. 24

25 A practical guide to scaling in vitro and in vivo data 100 Normalized concentration (kg d /L) Rat Marmoset Cynomolgus Minipig Dog Figure 9. Semi-logarithmic, complex Dedrick plot of normalized concentration-time data of rat, marmoset, cynomolgus monkey, minipig, and dog, following oral administration. Table 2 contains dosing information for each species Kallynochrons (h/kg (d-b) ) A potential reason for the lack of scalability of this compound may be the extremely high (>99%) protein binding, variability in binding across different species and concentration dependent plasma protein binding. Binding is depicted in Figure 10 for a number of species f u = 1 C u 1 + n P t n P K t a dog man minipig rabbit rat Figure 10. Log-log plot of free fraction f u plotted versus unbound concentration C u. Data are from rat, rabbit, minipig, dog and man. Note the nonlinearity in data which makes assessment of mean CL or V ss values inconclusive. Inset is the relationship between f u and C u Unbound concentration (µmol/l) Scaling preclinical pharmacokinetic data to man will be cumbersome and the predicted human dose can be expected to be a little way off the actual observed dose in man. Disparate free fraction f u versus unbound plasma concentrations C u profiles (see Figure 10) will contribute to this. We believe this to be the case even if the human predictions are based on fixed unbound plasma concentrations across all species. 4. Conclusions and points to consider Plasma concentration-time data were analyzed for each species and the pharmacokinetic parameters CL and V ss were assessed. 25

26 PK/PD AstraZeneca R&D Södertälje, Sweden Allometric plots of CL and V ss versus body weight (BW) of the rat, marmoset, cynomolgus monkey, minipig, and dog were constructed. The prediction intervals of CL and V ss in man were wide. The allometric parameters a, b, c, and d for CL and V ss were estimated. The human dose could not be estimated with any confidence. This was partly due to the fact that we had to tackle an extremely high plasma protein binding in combination with highly nonlinear with large inter-species differences in plasma protein binding, which confounds predictions based on total plasma concentrations. Dedrick plots of concentration-time data for different species were constructed. 5. References 1. Iavarone L, Hoke J. F, Bottacini M, Barnaby R, Preston G. C. First Time in Human for GV196771: Interspecies Scaling Applied on Dose Selection. Journal of Clinical Pharmacology. 1999; 39;

27 A practical guide to scaling in vitro and in vivo data Case 3 - In vivo/in vivo extrapolation 1. Goals To analyze plasma concentration-time data for each species and assess the pharmacokinetic parameters CL and V ss To construct allometric plots of CL and V ss versus body weight (BW) of mouse, rat, marmoset, rabbit, dog, and man To estimate allometric parameters a, b, c, and d in equations CL = a BW b V ss = c BW d To predict the pharmacokinetics of compound X in man, based on data obtained in other species 2. Materials and Methods The in vivo data were obtained from mouse, rat, marmoset, rabbit, dog, and man, following intravenous administration by either bolus or constant rate infusion (Appendix 3). 2.1 Experimental background Table 1 summarizes the experimental background for mouse, rat, marmoset, rabbit, dog, and man. Table 1. The species, form of administration, dose, body weight (BW), and unbound fraction of compound X in plasma (f u ) for mouse, rat, marmoset, rabbit, dog, and man. Species Intravenous administration Dose (µmol/kg) BW (kg) Mouse Bolus Bolus Rat Bolus Constant infusion Constant infusion Marmoset Infusion Constant infusion Rabbit Constant infusion Dog Bolus Constant infusion Man Infusion * in vitro data. f u * 27

28 PK/PD AstraZeneca R&D Södertälje, Sweden 2.2 Concentration-time data Figure 1 summarizes the concentration-time data after intravenous administration in the mouse, rat, and dog (preliminary plot, more data are forthcoming).the different doses are found in Table 1 and the underlying concentration-time data are tabulated in Appendix Concentration (µm) Mouse Rat Dog Time (h) Figure 1. Semi-logarithmic plot (preliminary) of concentration-time curves of mouse, rat, and dog, following an intravenous dose of compound X. Table 1 contains dosing information for each species. 2.3 Equations Equation 3:1 describes the relationship between body weight (BW) and Clearance (CL). CL b = a BW (3:1) where the parameters a and b are obtained by plotting the logarithm of clearance versus the logarithm of body weight. ln CL = ln a + b ln BW (3:2) The resulting regression line has a slope b and an intercept a of the abscissa for a body weight equal to 1 kg. The volume of distribution at steady state (V ss ) is obtained in a similar way from Equation 3:3. V ss d = c BW (3:3) The effective half-life (t 1/2 ) is obtained from Equation 3:4. t Vss = ln 2 (3:4) CL 1/ 2 28

29 A practical guide to scaling in vitro and in vivo data 2.4 Data analysis Data were evaluated by means of noncompartmental analysis using a model for extra vascular input (Model 200) and intravenous infusion (Model 201) in WinNonlin 3.2. Mean plasma concentration versus time data were used for each dose group and species. 3. Results and Discussion Table 2 summarizes the doses, clearance, volume of distribution at steady state, effective half-life, free fraction, unbound clearance, and unbound volume of distribution for mouse, rat, marmoset, rabbit, and dog. Table 2. The species, dose, observed clearance (CL), volume of distribution at steady state (V ss ) and effective half-life (t 1/2 ) for mouse, rat, marmoset, rabbit, and dog. Species Dose (µmol/kg) CL (ml/min) V ss (L) t 1/2 (min) f u CL u (ml/min) Mouse Rat Marmoset Rabbit Dog V uss (L) Figure 2 shows clearance plotted versus body weight, following intravenous administration of compound X in the mouse, rat, marmoset, rabbit, and dog Clearance (ml/min) 10 1 Mouse Rat Marmoset Rabbit Dog Regression 95% Prediction interval CL interval for Man 0.1 CL = BW Body weight (kg) Figure 2. Logarithmic plot of clearance versus body weight for mouse, rat, marmoset, rabbit, and dog. The solid line and the dotted lines represent the regression line and the 95% prediction interval, respectively. The horizontal dashed lines correspond to the estimated clearance interval in man. The regression equation is also inserted into the graph. 29

30 PK/PD AstraZeneca R&D Södertälje, Sweden The a (4.9768) and b (0.8097) parameters in Equation 3:1 are obtained by regressing data in Figure 1. Assuming a human body weight of 70 kg, the expression for CL becomes CL = ml min (3:5) The corresponding value of CL is 156 ml/min. Figure 3 shows the volume of distribution at steady state plotted versus body weight, following administration of compound X in the mouse, rat, marmoset, and dog. 100 Volume of Distribution at steady state (L) V ss = BW Mouse Rat Marmoset Dog Regression 95% prediction interval V ss interval for Man Body weight (kg) Figure 3. Logarithmic plot of volume of distribution at steady state versus body weight for mouse, rat, marmoset, and dog. The solid line and the dotted lines represent the regression line and the 95% prediction interval, respectively. The horizontal dashed lines correspond to the estimated volume of distribution interval in man. The regression equation is also inserted into the graph. The c (0.2321) and d (1.0103) parameters in Equation 3:3 are obtained by regressing data in Figure 3. Assuming a human body weight of 70 kg, the expression for V ss becomes V ss = L (3:6) The corresponding value of V ss is 17 L. The effective half-life is calculated from Equation 3: ml t 1 / 2 = ln 2 = min (3:7) 46 ml/min which gives a t 1/2 of 76 min. Figure 4 shows the effective half-life plotted versus body weight, following administration of compound X in the mouse, rat, marmoset, and dog. 30

31 A practical guide to scaling in vitro and in vivo data 1000 Half-life (min) Mouse Rat Marmoset Dog Regression 95% Prediction interval t 1/2 interval for Man Body weight (kg) Figure 4. Logarithmic plot of effective half-life versus body weight for mouse, rat, marmoset, and dog, following an intravenous administered dose of compound X. The solid line and the dotted lines represent the regression line and the 95% prediction interval, respectively. The horizontal dashed lines correspond to the estimated half-life interval in man. Greater accuracy may be achieved by plotting clearance and volume of distribution corrected for protein binding against body weight. This is done by dividing clearance and volume of distribution based on total plasma concentrations by the free fraction of compound X (f u ). However, the already high precision of the scaled clearance and volume terms was not dramatically improved by corrections with f u. 4. Conclusions and points to consider Plasma concentration-time data were analyzed for each species and the pharmacokinetic parameters CL and V ss were assessed. Allometric plots of CL and V ss versus body weight (BW) of the mouse, rat, marmoset, and dog were constructed. The prediction intervals of CL and V ss in man were narrow. The allometric parameters a, b, c, and d for CL and V ss were estimated. The human CL and V ss were estimated with high precision. 31

32 PK/PD AstraZeneca R&D Södertälje, Sweden Case 4 - In vivo/in vivo extrapolation 1. Goals To analyze plasma concentration-time data for each species and assess the pharmacokinetic parameters CL and V ss To construct allometric plots of CL and V ss versus body weight (BW) of the rat, guinea pig, monkey, and dog To estimate allometric parameters a, b, c, and d in equations CL = a BW b V ss = c BW d To predict the pharmacokinetics of compound X in humans, based on data obtained in other species 2. Materials and Methods The in vivo data for compound X were obtained from the rat, guinea pig, monkey, and dog, following intravenous bolus administration (Appendix 4). 2.1 Experimental background Table 1 summarizes the experimental background for the rat, guinea pig, monkey, and dog. Table 1. Species, animal number (No.), dose, and body weight (BW) of the rat, guinea pig, monkey, and dog. Species No. Dose (µmol/kg) BW (kg) Rat Guinea pig Monkey Dog Concentration-time data Figure 1 summarizes the concentration-time data after intravenous administration in the rat, guinea pig, monkey, and dog. The different doses are found in Table 1 and the underlying concentration-time data are tabulated in Appendix 4. 32