HOW DO I DESIGN AND ADJUST A DOSAGE REGIMEN?

1. HOW DO I DESIGN AND ADJUST A DOSAGE REGIMEN?

2. WHAT IS THE BEST WAY TO GAIN AN UNDERSTANDING OF HOW TO DESIGN AND ADJUST A DOSAGE REGIMEN? PHARMACOKINETICS

3. WHAT IS PHARMACOKINETICS? PHARMACOKINETICS is the study of the kinetics of drug absorption and disposition. ABSORPTION DISPOSITION ELIMINATION DISTRIBUTION EXCRETION METABOLISM

4. WHY BE CONCERNED ABOUT PHARMACOKINETICS AND DOSAGE REGIMENS? Pharmacokinetics and Dosage Regimens Determine: • How much drug is in the body at any given time • How long it takes to reach a constant level • of drug in the body during chronic • drug administration • How long it takes for the body to rid itself of • drug once intake of drug has stopped

5. WARNING!! THE STUDY OF PHARMACOKINETICS MAKES SOME PEOPLE ANXIOUS

6. BUT RELAX, Pharmacokinetics Can Be Made FRIENDLY

7. MAJOR CONCEPT #1 CONCEPT OF VOLUME OF DISTRIBUTION (VD) OF DRUGS (Stir) As a first approximation, the body behaves like a well-stirred beaker, i.e., chemicals are dispersed throughout the container (body) rather quickly.

8. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: DEFINITION OF VD Add DRUG to Beaker Obtain Sample Assay for [Drug] (Stir) Calculate Volume [Drug] = Amount Added  Volume of Beaker Volume of Beaker = Amount Added  [Drug]

9. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: DEFINITION OF VD Dose Body with DRUG Obtain Plasma Sample Assay for [D]P Calculate Volume (This volume is called VD) By DEFINITION: VD = A/[D]P (where A is amount of drug in body and [D]P is concentration of drug in plasma)

10. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: DEFINITION OF VD WARNING: VD is a calculated value that should not be taken literally as representing some real volume!!!!!! • VD is: • a calculated value, • a reproducible value, • a clinically useful value. VD is not a real volume with an independent existence. In this regard, the word “volume” is used in a metaphorical sense.

11. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: INTRODUCTION TO VD By DEFINITION: VD = A/[D]P Rearranging: A = VD x [D]P Suppose you want a certain desirable [D]p, call it [D]P(target) Substituting [D]P(target) for [D]P: Atarget = VD x [D]P(target) Where Atarget is the amount of drug in body required to achieve a given [D]P(target)

12. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: INTRODUCTION TO VD If patient has no drug in body to begin with, then can administer an amount (called “Loading Dose”) to achieve a given Atarget and [D]P(target) Since loading dose (LD) must provide Atarget amount of drug in body, and since not all of an administered dose may be absorbed: LD x B = Atarget or LD = Atarget/B or (VD x [D]P(target))/B Where B is “Bioavailability” ,i.e., fraction (ranging from 0 to 1) of administered dose absorbed into body

13. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: INTRODUCTION TO VD (KEY EQUATION #1) VD x [D]P(target) LD = B

14. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: INTRODUCTION TO VD LD = (VD x [D]P(target))/B VD and [D]P(target) and B are THE determinants of loading dose (LD)!! In other words, the amount of drug that must be given to achieve rapidly a target concentration of drug in the plasma is solely determined by VD, B and [D]P(target).

15. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: DETERMINANTS OF VD Distribution into Body Compartments Small VD vs Large VD Restriction of Drug to Limited Areas of Body Free Assess of Drug to Many Areas of Body

16. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: DETERMINANTS OF VD Tissue Binding  [D]P A  VD =  [D]P

17. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: DETERMINANTS OF VD Plasma Protein Binding A VD = [D]P [D]P

18. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: DETERMINANTS OF VD Distribution into Fat  [D]P A  VD =  [D]P

19. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: OBTAINING VD [D]P0 is [D]Pat time 0 and is obtained by extrapolation VD is usually easy to obtain! 1. Give bolus of drug. 2. Measure plasma levels over time. 3. Extrapolate to find plasma level at time 0. Decrease in [D]P dueto elimination Log [D]P Time (hrs) VD = Amount in body at time 0/[D]p0 = DoseIV /[D]P0

20. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: OBTAINING VD One- versus Two-Compartment Behavior (Time) Initial Restriction of Drug to Limited Areas of Body Slow Equilibration of Drug to Other Areas of Body

21. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: OBTAINING VD One- versus Two-Compartment Behavior y-axis is VD VD(final) One VD(initial) Two Time (hrs) 1-Compartment: VD(final) reached within minutes 2-Compartment: VD(final) reached only after noticeable delay

22. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: OBTAINING VD Two-Compartment Behavior [D]P0 is [D]Pat time 0 and is obtained by extrapolation  VD(initial) is easy to obtain for 2- compartment behavior! Log [D]P or Log Amount Body Slowly Equilibrating Tissues Plasma  Time (hrs) VD(initial) = VD() = Amount in body at time 0/[D]p0 = DoseIV /[D]P0

23. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: OBTAINING VD Two-Compartment Behavior  VD(final) is difficult to obtain for 2-compartment behavior! Log [D]P or Log Amount Body Slowly Equilibrating Tissues Plasma  Time (hrs) VD(final) = VD() = Amount in body at time t after distribution /[D]Ptime t after distribution Because of elimination, amount in body at time t after distribution DoseIV

24. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: OBTAINING VD Two-Compartment Behavior • NOTE THAT: • Obtaining VD() requires advanced training in pharmacokinetics • VD() and VD() have different uses (next slide) • May run across another term called VD(ss) • VD(ss) is somewhat less than VD() • For practical purposes VD(ss) and VD() can be interchanged

25. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: IMPORTANCE OF VD USEFUL FOR CALCULATING LOADING DOSE

26. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: IMPORTANCE OF VD Does the drug exhibit 1- or 2- compartment behavior? 1 2 (KEY EQUATION #1) VD x [D]P(target) V? x [D]P(target) LD = LD = B B Whether you use VD() and VD() depends on what trade-offs you are willing to make! Next slide

27. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: IMPORTANCE OF VD (example of 2-compartment drug; lidocaine) LD using VD(ß), followed by constant rate infusion [Lidocaine]P (g/ml) [D]P(target) Constant rate infusion without LD LD using VD(), followed by constant rate infusion Time (minutes) LD using VD() without constant rate infusion

28. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: IMPORTANCE OF VD (example of 2-compartment drug; lidocaine) Window of potentially toxic levels [Lidocaine]P (g/ml) [D]P(target) Window suboptimal levels Window of suboptimal levels Time (minutes) Suboptimal levels

29. CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS: EXAMPLE OF USING VD TO CALCULATE LD Pharmacokinetic Parameters forDigoxin: [D]P(target) = 1.5 µg/L VD = 580 L Oral Bioavailability = 0.7 Calculation of Oral LD For Digoxin: LD = (VD x [D]P(target))/B Oral LD = (580 L x 1.5 µg/L) /0.7 Oral LD = 1243 µg ~ 1.2mg

30. MAJOR CONCEPT #2 CONCEPT OF DRUG CLEARANCE (Cl) DRUG Think of drug clearance as removal of drug from body by body’s garbage disposal systems!

31. CONCEPT OF DRUG CLEARANCE (Cl): DEFINITION OF Cl By Definition: Rate of Drug Elimination Cl = [D]P Units of Cl: Amount/Time Volume = Amount/Volume Time

32. CONCEPT OF DRUG CLEARANCE: DEFINITION OF Cl Example: Rate of Drug Elimination = 10 mg/hr [D]P = 4 mg/L 10 mg/hr Cl = = 2.5 L/hr 4 mg/L

33. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Cl is usually constant over a wide range of [D]P Cl [D]P This is a consequence of the fact that most drugs are eliminated from body by 1st order kinetics (dA/dt = -k•A).

34. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Cl is a major determinant of [D]P at STEADY STATE ([D]PSS) INPUT STEADY STATE LEVEL (Kidney & Liver) OUTPUT

35. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Toxic Threshold [D]PSS (Therapeutic Window) Therapeutic Threshold [D]P (mg/L) Multiple Doses Single Dose Time (hrs) [D]PSS = [D]P at steady state

36. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl How does Cl influence [D]PSS? By Definition: Steady state is said to exist when: Rate of Drug Administration (R0) = Rate of Drug Elimination (Input = Output)

37. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl By definition of Cl: Rate of Drug Elimination Cl = (Eq A) [D]P Rearranging Eq A: (Eq B) Rate of Drug Elimination [D]P = Cl

38. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Applying Eq B to Steady State: (Eq C) Rate of Drug Elimination at Steady State [D]PSS = Cl By definition of steady state: (Eq D) R0 = Rate of Drug Elimination at Steady State

39. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Substituting Eq D into Eq C: (Eq E) R0 [D]PSS = Cl

40. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Additional definitions: Maintenance Dose (MD) = Amount of Drug Taken at Regular Intervals Dosing Interval (DI) = Time Between MDs Bioavailability (B) = Fraction of Administered Dose that is Absorbed into Systemic Circulation

41. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Recognizing that: Rate of Drug Administration (R0) = Amount of Drug Delivered to the Systemic Circulation Time Substituting Definitions of B, MD, and DI: (Eq F) B x MD R0 = DI

42. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Substituting Eq F into Eq E: B x MD [D]PSS = DI x Cl (KEY EQUATION #2)

43. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Key Equation #2 reveals that [D]PSS depends not on the absolute values of MD and DI, but on their ratio! B x MD [D]PSS = DI x Cl

44. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Toxic [D]P (mg/L) [D]PSS Therapuetic Time (hrs) Constant rate infusion of 672 mg per 24 hr 224 mg bolus every 8 hr 672 mg bolus every 24 hr [D]PSS is same for all three regimens

45. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Since [D]PSS is a major determinant of a) Therapeutic Response b) Toxicity Cl is important!!

46. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Rearranging Key Equation #2: (Eq G) [D]PSS x Cl MD/DI = B Since our goal is to provide[D]P(target), we let: [D]PSS = [D]P(target) (Eq H)

47. CONCEPT OF DRUG CLEARANCE: INTRODUCTION TO Cl Substituting Eq H into Eq G: (Key Equation #3) [D]P(target) x Cl MD/DI = B

48. CONCEPT OF DRUG CLEARANCE: DETERMINANTS of Cl Most drugs are cleared by the kidneys and/or liver, therefore: Rate of Elimination = Rate of Renal Elimination + Rate of Hepatic Elimination (Law of conservation of mass!)

49. CONCEPT OF DRUG CLEARANCE: DETERMINANTS of Cl Rate of Elimination/[D]P = Rate of Renal Elimination/[D]P + Rate of Hepatic Elimination/[D]P (Divide each term by [D]P)

50. CONCEPT OF DRUG CLEARANCE: DETERMINANTS of Cl Cl Rate of Elimination/[D]P = Rate of Renal Elimination/[D]P + Rate of Hepatic Elimination/[D]P ClR ClH (By definition of Cl, ClR & ClH)