Pharmacokinetics II

General Principles of Drug Therapy

Integrated Scientific and Clinical Pharmacology

Pharmacokinetics II Applying Basic Principles to Clinical Medicine Marc Imhotep Cray, M.D. BMS / CK-CS Teacher

http://www.imhotepvirtualmedsch.com/

General Principles of Drug Therapy

Topics Outline       

Basic Concepts PK Compartment Models Desired Drug Level Drug Factors Affecting Pharmacokinetics Drug Clearance Patient-Specific Variables  Determination of Loading Dose  Determination of Maintenance Dose 2

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Applying the PK Principles to Clinical Medicine This lecture will cover principles and equations applied to determine dosing regimens for patients.

3

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

BASIC CONCEPTS

4

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Drug Pathway

5

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Course of a drug and its metabolites after oral administration

6

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Pharmacokinetics PK describes changes in plasma drug concentration (Cp) over time (T) It is most ideal to determine amount of drug that reaches its site of action as a function of time after administration Usually impractical or not feasible Therefore Cp is measured

Amount of drug in tissues is generally related to plasma concentration 7

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Clinical pharmacokinetics Clinical pharmacokinetics is about all factors that determine Cp and its time- course, i.e. it is about variability These various factors are introduced through course of the following sequence

8

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Important PK abbreviations Abbreviation

Definition

t1/2

the half-life of elimination

Vd

Volume of distribution

Cl

Clearance

AUC

Area under the curve

F

Fractional oral availability

Fu

fraction excreted unchanged

PB

Protein Binding

Tmax

Time to maximum concentration

Cmax

Peak concentration (Concentration maximum) 9

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Important PK abbreviations (2) Abbreviation ss Cp Cpt Cpo Cpss Ab e ln k

Definition Steady state Plasma concentration Plasma concentration at time = t Plasma concentration at time = o Plasma concentration at steady state Amount in body The natural logarithm (value = 2.7183) log to the base e the rate constant of elimination 10

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Therapeutic Considerations When Selecting Drug Dosage Dose Bioavailability (F) Route of administration (PO, IV, etc.)

Plasma concentration of drug reported by lab. (Cp) Desired steady-state plasma concentration of drug (Cpss)

Drug interactions

Volume of distribution (Vd)

Time interval between doses (Ď„)

Clearance (Cl)

Plasma level of drug initially (Co) Marc Imhotep Cray, M.D.

Half-life (t½)

11

General Principles of Drug Therapy

Aim of drug therapy Constant IV infusion

Aim of drug therapy is to achieve efficacy without toxicity involves achieving a plasma concentration (Cp) that is above minimal effective concentration (MEC), but Main determinants of Cpss below minimal toxic ďƒ˜dose concentration (MTC) ďƒ˜clearance (Cl) Marc Imhotep Cray, M.D.

12

General Principles of Drug Therapy

Drug at site of action

Cp

From a dosing point of view concentration of drug at site of action (target) is most important Practically difficult to measure Under steady-state (ss) conditions plasma concentration (Cp) is in equilibrium with concentration at sites of action (assuming a one compartment-model) In clinical practice Cp measured

13

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Mammillary Pharmacokinetic Model Most common pharmacokinetic model An empirical model = does not explain actual mechanisms by which drug is absorbed, distributed, and eliminated from body It is a compartmental model= groups of tissues that have similar blood flow and drug affinity are represented by a single compartment Thus, a compartment is not a real anatomic region within body 14

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Mammillary Pharmacokinetic Model (2) Uniform drug distribution is assumed within each compartment, and first-order rate equations are used to describe transport of drug into and out of the compartment

Since drug can enter and leave body, model is characterized as an “open� model

15

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Distribution and Elimination(1) IV Bolus Dose One-compartment model

Input (dose)

Drug in body

Output (elimination)

In model body is considered as a single container (one compartment) where drug is instantaneously and uniformly distributed Marc Imhotep Cray, M.D.

Before Drug Administration

After Drug Administration

16

General Principles of Drug Therapy

Distribution and Elimination(2) One-compartment model features‌

Note: Co is used to calculate Vd for drugs that obey a one-compartment model

Vd =

Amount of drug in body Ab (mg)

drugM.D. concentration Marc Plasma Imhotep Cray,

Cp (mg/L)

Drug distribute instantaneously after IV administration of a single dose A semilog plot of Cp versus time will be linear Drug elimination is first order ( constant fraction of drug is eliminated per unit time) Slope of semilog plot is = -k, where k is rate constant of elimination and has units of time Intercept on y axis is Co 17

General Principles of Drug Therapy

Distribution and Elimination(3) One-compartment model features ‌cont.

The plasma drug concentration (Ct) relative to t initial concentration (C0) at any time (t) after administration is given by ln Cpt = ln Cp0 – kt The relationship of plasma concentrations at any two points in time is given by ln Cp2 = ln Cp1 - k (t2 - t1)

18

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Distribution and Elimination(4) IV Bolus Dose Two-compartment model “A more common model for distribution and elimination of drugs�

Kout Kin Central compartment (plasma)

Peripheral compartment Before Drug Marc Imhotep Cray, M.D. Administration

Immediately After Drug Administration

After Drug Distribution Equilibrium

19

General Principles of Drug Therapy

Distribution and Elimination(5) IV Bolus Dose Two-compartment model features…

Body is a central compartment with rapid mixing and a peripheral compartment with slower distribution Central compartment is uniformly mixed very shortly after drug administration, whereas it takes some time for peripheral compartment to reach “pseudo-equilibrium”

Marc Imhotep Cray, M.D.

Cp decrease very rapidly b/c drug is being elim. from body and also drug is exiting plasma space as it distributes to other tissues and fluid compartments

General Principles of Drug Therapy

Distribution and Elimination(6) IV Bolus Dose Two-compartment model features ‌cont.

After distribution, a linear decrease in log drug concentration is observed if elim. phase is first order Curve is less steep in elim. phase because there is no longer a net decrease in plasma levels of drug due to distribution to tissues being completed Co obtained by extrapolation of elim. phase is used to calculate Vd, and elim. rate constant, k, is obtained from the slope of elim. phase 21

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Most important PK parameters Remember: Pharmacokinetics involves movement of drug into, within and out the body Most important PK parameters from a dosing point of view are: clearance (Cl), volume of distribution(Vd) half-life of elimination (t1/2 )  Cl determines maintenance dose (MD)  Vd determines loading dose (LD)  t1/2 determines dose interval (τ=tao) Marc Imhotep Cray, M.D.

22

General Principles of Drug Therapy

Achieving Cpss Multiple dosing regimens attain steady-state plasma concentrations

Key points: (1) a new dose is administered once every t½, (2) 50% of preceding peak plasma concentration is eliminated each t½ (3) Cpss is attained after 4 to 5 t½, regardless of whether drug was given by constant IV infusion or by repeated intermittent doses

Marc Imhotep Cray, M.D.

23

General Principles of Drug Therapy

Essential PK equation Infusion rate (k0) k0= Cl × Css Loading dose (LD) LD = (Vd × Cpss)/(F); for our purposes, F is usually 1 Maintenance dose (MD) MD=(Cl × Cpss × τ)/(F), where τ (tao) is the dosing interval

Marc Imhotep Cray, M.D.

Clearance (Cl) Cl = K × Vd, where K is the elimination constant Volume of distribution (Vd) Vd = (LD)/(Css) Half-life (t1/2) t1/2 = (0.693)/(K) or (0.693 × Vd)/(Cl)

General Principles of Drug Therapy

Loading dose In order to achieve rapid effect (e.g. treating status epilepticus with phenytoin) it is important to get Cp up to effect zone as soon as possible achieved with a loading dose

IV injection followed by a constant infusion

Factor determining loading dose is volume of distribution (Vd) Marc Imhotep Cray, M.D.

Vd = Amount of drug in the body C0

25

General Principles of Drug Therapy

Oral dosing

Curve reflects accumulation and elimination, and intermittent administration 26

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Cp higher than desired

Cause/s: excessive dosage and(or) decreased Cl

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Cp higher than desired (2) Factors causing decreased Cl are: normal variation  saturable metabolism  genetic enzyme deficiency  renal failure  liver failure  old age very young age (neonate) enzyme inhibition 28

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Cp lower than desired Dose may be too low, or Cl too high: Factors causing increased Cl: poor absorption  high first-pass metabolism  genetic hypermetabolism  enzyme induction  non-compliance  normal variation 29

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Time to steady state

Determined by t1/2 of drug It takes 4-5 Ă— t1/2 to achieve >90% of steady state plasma concentration (Cpss) Marc Imhotep Cray, M.D.

30

General Principles of Drug Therapy

Time for drug elimination

Determined by t1/2 of drug It takes 4-5 Ă&#x2014; t1/2 for concentrations to reduce to <10% of the starting value Marc Imhotep Cray, M.D.

31

General Principles of Drug Therapy

Components of the line of steady state

Line of steady state is effectively made up of sum of line of assimilation and line of elimination i.e. net effect of input and output Marc Imhotep Cray, M.D.

32

General Principles of Drug Therapy

Drug Clearance (Cl)



Drug clearance (from plasma) is defined as: volume of plasma cleared of drug per unit time;

or



A constant relating rate of elimination to plasma concentration (Cp)  i.e. rate of elimination = Cl * Cp  Units: vol/time (e.g. L/h) 33

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Clearance (2)

 Clearance (Cl) is the single most important pharmacokinetic parameter

 Cl determines maintenance dose-rate, i.e. dose per unit time, required to maintain a plasma concentration

 Clearance does not apply to drugs with zero-order kinetics, but only to those with first-order (exponential) kinetics This applies to majority of drugs 34

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Clearance (3) Graph to right shows that rate of elimination (RE) is different at different concentration, i.e. it is driven by concentration rate of elimination Cp â&#x2C6;´rate of elimination (mg/h) = constant (L/h) * Cp (mg/L) 35

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Clearance (4) This ‘constant’ is clearance (Cl) and by deduction has units of volume/time (e.g. L/h) since units for rate of elimination are mg/h, and for concentration mg/L

i.e. rate of elimination = Cl * Cp

36

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Clearance (5) Thus, Cl is A constant relating rate of elimination to plasma concentration andď&#x192; Volume of plasma cleared of drug per unit time The equation can be rearranged as follows:

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Achievement of a constant steady state plasma drug concentration (CpSS)  In order to maintain a target Cp, drug must be administered at a rate equal to rate of elimination at that concentration, i.e. rate of administration = rate of elimination Since  rate of elimination = Cl * Cp, then  rate of administration = Cl * CpSS, or

Maintenance dose-rate = Cl * CpSS

General Principles of Drug Therapy

Maintenance dose-rate = Cl * CpSS

39

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Physiological relevance of drug clearance

ď&#x201A;§

Main organs responsible for drug clearance are liver (metabolism) and kidneys (removal of unchanged drug) ď&#x201A;§ Total body Cl is sum of all clearance processes, i.e.

40

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Determination of Cl



Plasma Cl is usually determined from area under plasma concentration vs time curve (AUC) after IV administration  AUC is determined using the ‘trapezoidal rule’ AUC = Area 1 + Area 2 + Area 3 + . . .

Area n, where each area is approximated by a trapezium 41

Marc Imhotep Cray, M.D.

General Principles of Drug Therapy

Area under the curve (AUC) The bigger the AUC, the smaller the Cl

After oral administration:

where F = oral availability 42

Marc Imhotep Cray, M.D.

Principles of Drug Therapy

NEXT Lecture , Pharmacokinetics-III including: • Volume of Distribution • The Half-Life • Oral Availability • Protein Binding • pH and Pharmacokinetics

43

General Principles of Drug Therapy

Companion learning tools:  MedPharm Guidebook: UNIT 1 General Principles of Pharmacology  eNotes: General Principles of Drug Action  For well illustrated video-summaries of the pharmacokinetic concepts covered in this series access the PK Concepts video mini-lectures folder  Doing the Math: To further understand the clinical use and application of PK access the Clinical Pharmacokinetics Case-based learning

Marc Imhotep Cray, M.D.

44