Pharmacokinetics – a practical application of calculus

1. Pharmacokinetics – a practical application of calculus April 6, 2009 Elena Ho

2. Bayer Aspirin In 1897, Felix Hoffman, a research chemist employed by the "Farbenfabrikin vorm. Freidr. Bayer and Co." synthesized acetylsalicylic acid. On February 1, 1899, Aspirin® was registered as a trademark. On March 6th of the same year, this drug was registered with the Imperial Patent Office in Berlin. Aspirin quickly become popularworldwide, and remains an important drug today. (Interestingly, it was not until 1971 that Sir John Vane discovered the mechanism of action of aspirin, a feat that earned him the 1981 Nobel Prize for Medicine.)

3. The Bayer Group is a global enterprise with companies in almost every country. The map shows some of the principal sites. The Bayer Group is a global enterprise with companies in almost every country. The map shows some of the principal sites. The Bayer Group is a global enterprise with companies in almost every country. The map shows some of the principal sites.

4. Business operations : • Bayer HealthCaremakes an important contribution to human and animal health with its innovative products and by researching new therapeutic approaches. The subgroup has four operating divisions: Bayer Schering Pharma* (prescription medicines), Consumer Care (over-the-counter medicines and nutritional supplements), Medical Care (blood glucose monitoring systems and contrast injection systems), Animal Health (veterinary medicines and grooming products) • Bayer CropScienceis a world leader in the areas of crop protection, pest control, seeds and plant biotechnology. As a partner in the production of high-quality food, feed and fiber, the company offers comprehensive solutions for modern, sustainable agriculture and non-agricultural applications. • Bayer MaterialScienceis one of the world’s leading manufacturers of polymers and high-quality plastics. Apart from its polycarbonates and polyurethanes, this company’s offering also includes innovative developments in the fields of coatings, adhesives, insulating materials and sealants. Principal customers are the automotive and construction industries, the electrical/electronics sector and manufacturers of sports and leisure articles, packaging and medical equipment.

5. Products • The Bayer Group markets some 5,000 products. Best-sellers include: • in the health care field: Yasmin®/YAZ®/Yasminelle®, Betaferon®/Betaseron®, Kogenate®, Adalat®, Avalox®/Avelox® • in the nutrition field: Confidor®/Gaucho®/Admire®/Merit®, Flint®/Stratego®/Sphere® • in the field of high-tech materials: Makrolon®, Baydur®, Bayflex® Footwear, Desmodur®/Desmophen®

6. Workforce • On December 31, 2007, the Bayer Group had 106,200 employees worldwide (2006: 106,000). North America accounted for 16,800 of these employees, while 18,900 were based in Asia-Pacific, 14,300 in Latin America/Africa/Middle East and 56,200 in Europe. In Germany we had 39,100 employees, who made up 36.8 percent of the Group workforce. • 106,200 employees worldwide (as of December 31, 2007), including:56,200 in Europe16,800 in North America18,900 in Asia-Pacific14,300 in Latin America/Africa/Middle East

7. Bayer is seeking exceptional college students for summer internships at the Berkeley site. Help us spread the word. • Visit website for details... • http://www.bayerjobfair.com/interns Application deadline is March 15, 2009.

12. CNS Penetration Protein Binding Tissue Binding Metabolic Stability Renal Excretion Biliary Excretion Permea-bility Efflux Aqueous Solubility Dosing Regimen How much ? How often ? Oral bio-availability Half-life Absorption Clearance Volume of Distribution

13. Typical Study Tools

14. Barriers between Dose and Target Kerns & Li 2003, DDT 8:316-323

15. Interesting facts about a human body • Absorbing surface area of skin: 1.73 m2 • Absorbing surface area of the lung: 70 m2 • Absorbing surface area of GI tract: ~200m2 (1/2 basketball court) • Small intestine is ~2” around, 22’ long • Total length of capillaries is ~ 37,000 miles

16. Compartment models A compartment is an entity which can be described by a definite volume and a concentration (of drug) Concentration Dose V Dose (mg) = C (ug/ml) x V (ml) V = Dose/Concentration One compartment model: the drug enters the body, distributes instantly between blood and other body fluid or tissues.

17. Model • One compartment • Two compartment • Three compartment Hydrodynamic analogy Drug in Drug in Drug out Drug out __________________________ Drug in central tissue Drug out ____________________________ Drug in Tissue 1 central Drug in Tissue 2 Tissue 1 central Tissue 2 Drug out Drug out Drug recycle

18. The human body is a multimillion compartment model considering drug concentration in different organelles, cells, or tissues We have access to only two types of body fluid – blood and urine We will begin with the simplest model

19. Single dose, IV, one compartment : dose of drug introduced rapidly and completely and quickly distributes into its homogenous volume of distribution. Drug is then eliminated by metabolism and excretion. Then : dA/dt = - kel A where kel = ke + km rearrange to : dA/A = - kel dt Integrate: ∫A0 dA/A = - kel ∫ t0 dt Gives: ln A |A0= - kel t |t0 or ln A – ln A0 = - kel . t – t0 A t A t This yields the familiar exponential or logarithmic expressions A = A0 e – Kel t C = C0 e – Kel t log C = log C0 – kel . t /2.3 Kel = 2.3/t . log C/C0 C0 - Kel/2.3 log C time

20. Biological half-life (T1/2) Consider again the rearranged expression dA/A = - kel dt Integrate between limits A and A/2 ∫A dA/A = - kel∫t0 dt Gives: ln A – ln (A/2) = kel t1/2 ln 2 = kel t1/2 = 0.693 Therefore: t1/2 = 0.693 / kel t/2 A/2

21. Area Under the Curve (AUC) The integral of drug blood level over time from zero to infinity and a measure of quantity of drug absorbed in the body Area = A o  ∞ Sum of all concentration from t0 to t∞ • Linear trapezoidal method: AUC t1t2 = Area of a trapezoid t1t2 • = (t2 – t1). (C2+ C1)/2 • ii) Log trapezoidal method: AUC t1t2 = (t2 – t1). (C2+ C1)/ln(C2/C1) • Lagrange method: cubic polynomial equation • Spline method: piecewise polynomials for curve-fitting

23. Linear and/or Log trapezoidal method T1, T2, T3, T4, T5, T6 T7 Advantages: Easy to use. Reliable for slow declining or ascending curves Disadvantages: error-prone for data points with a wide interval; over or under estimate the true AUC; log 0 is not defined; not good for multiexponential curve

24. ln 2 T = kel 1/2 Distribution Dose CL = Plasma Concentration Elimination AUC kel AUC(inf) Time CL V = kel dss In vivo Pharmacokinetics in Rodents Disposition kinetics: • single iv administration • repeated blood sampling • plasma concentration-time profile Volume of Distribution at steady-state: Plasma Half-life: Plasma Clearance: T1/2 = 0.693 x Vd/CL The clearance of compounds is evaluated in relation to the liver blood flow which is 60 and 90 mL/min/kg in rat and mouse, respectively. The volume of distribution should exceed that of total body water, i.e. 0.6-0.7 L/kg which indicates that the compound distributes freely into tissues.

25. Absorption GI Tract Stomach: Dissolution Stability at pH 1 Intestines: Dissolution Stability at pH 3-8 Permeability Metabolic stability Compound properties controlling absorption: • size MW • aqueous solubility Sw • lipophilicity logP • polarity PSA • ionization pKa • ...

26. Absorption Deriving Models of the Gastrointestinal Tract

27. Oral bioavailability: Barriers and In vitro Models Fraction ofdose absorbed: FA% Gut Lumen Portal Vein Gut Wall Oralbioavailability: Liver F% Oral Absorption limited by: Stability Solubility Permeability ATP-dependent Efflux Drug Metabolism Hepatocellular Uptake, Drug Metabolism and Biliary Excretion Gastric and Intestinal Juice Phys.-Chem. Descr. Caco-2 Intest. Microsomes Liver Microsomes Hepatocytes S9 mix, Cytosol In Vitro Models:

28. Cmax Absorption Distribution Elimination Plasma Concentration kel AUC(inf) Time Tmax D / AUC po po F = x 100% D / AUC iv iv In vivo Pharmacokinetics in Rodents Oral kinetics: • single po administration • repeated blood sampling • plasma concentration-time profile Max. plasma conc. andTime of max. pl. conc. Oral Bioavailability: Tmax Cmax There is no possibility to extrapolate the bioavailability in rodents to that in man. The sources of its limitation are oftenmore important than the actual value as this information may allow to study the corresponding mechanism using human invitro systems and to extrapolate the expected bioavailability .

29. Example of a pharmacokinetic study: single dose IV in the rat Study design Animal : Sprague-Dawley male rat, approximately 10 weeks old weighing ~250 g each (n=4) Compound : BAY xxxxxx supplied by AABBCC. Dissolve 0.7 mg in 10 ul of DMSO, bring it up to 1 mL with PBS. Dosing : each animal will receive a dose equivalent to 0.7 mg/kg. Time points: pre dose, 5 min, 30 min, 1, 2, 4, 7, 24, 28, 31 hours post dose Blood sample : collect 225 ul of blood in 25 ul of 5% Na Citrate at each time point. Centrifuge blood at 5000 g for 5 minutes. Separate the plasma and keep at -80ºC until analysis

30. SUMMARY OF RESULTS: Plasma concentration in ng/ml:

31. Rat plasma concentration was determined using ELISA immunoassay method:

32. Xxxxxx

33. Pharmacokinetic parameters: This compound represents a 2-compartment model. Elimination T1/2 = 6.8 hours Total plasma clearance = 135 ml/h/kg Vss = 1.03 L/kg Summary Remark This profile suggests a slow clearance compound with a moderate elimination half life. The volume of distribution at steady state is high, suggesting the compound distribution is beyond the plasma volume compartment

34. c in vitro CL in vivo CL t CL Vdss body weight Predicting Human PK • Direct Scalingof in vitro rate of metabolism to the CL in vivo • physiologically based • metabolic CL only •  first-pass effect •  oral bioavailability • Allometric Scalingof human PK based on animal data in vivo • empirical • total CL and Vss • requires mech. to be scalable •  t1/2

35. Research and development at Bayer HealthCare focus on identifying and developing new active substances to treat diseases with a high unmet medical need. Our job is to contribute to the understanding of our drug’s behavior and save lives one day Thank you