pharmacokinetics 2 and drug dosing · pharmacokinetics 2 and drug dosing dr. shabbits...

PCTH 325

Pharmacokinetics 2 and Drug Dosing

Dr. Shabbitsjennifer.shabbits@ubc.ca

September 11, 2014

1. Describe the mechanisms of drug metabolism, the significance of enzyme induction & inhibition, and how the first-pass effect can influence dosing

2. Describe how drugs are excreted from the body and how pH can be manipulated to influence this process

3. Define and describe MTC, MEC and the therapeutic range

4. Describe, interpret and apply the C vs t equation and graph

5. Define and calculate t½, Cmax, tmax, fraction remaining and fraction eliminated

6. Describe the significance of steady state and how it can be achieved

7. Calculate loading and maintenance doses and describe how and when they are used

Learning objectives

Metabolism

the irreversible biotransformation of drug

• makes it more polar to ↑ renal (urinary) excretion

Occurs primarily in the liver via 2 (usually sequential) enzyme-catalyzed processes:

• Phase I oxidation/reduction/hydrolysis

• Phase II conjugation

Phase I: cytochrome P450 enzymes

A superfamily of related enzymes that add on or uncover small polar groups (–OH, –NH2, –COOH) to water solubility

P450 EnzymesParent Drug

Phase 1 Metabolite

P450 enzyme induction and inhibition

• some P450 enzymes can be induced or inhibited by other drugs, foods, pregnancy or disease

Induction: metabolic activity of enzymes [Drug] (ex: alcohol)

Inhibition: metabolic activity of enzymes [Drug] (ex: grapefruit juice)

Primary cause of drug interactions

Requires drug dosing to be increased or decreased

Phase II: conjugative enzymes

Mediated by various non-P450 liver enzymes• covalently add large, polar,

endogenous molecules to Phase I metabolite

• ensures that metabolite is ready for excretion

(glucuronide, glutathione, sulfate, acetate, amino acids etc)

phenytoin

p-OH-phenytoin

phenytoin-ether-glucuronide

Phase IP450

Phase II glucuronyl transferase

Drug metabolism

• usually inactivates the drug

• is required to activate prodrugs

CYP2D6

Metabolite + Receptor ≠ MR complex

Drug metabolism

• may be harmful if the metabolite(s) are toxic

Acetaminophen

CYP2E1

Toxic semiquinone

Induced by alcohol

Tylenol® =

First pass metabolism

Most drugs absorbed from the GI tract are delivered tothe liver before reaching the systemic circulation

Drug

IV

Oral

oral doses > iv doses to account for loss due to metabolism

Some drug is metabolised(lost)

Drug delivered to target receptors

Drug metabolism in the gut Some drugs undergo significant metabolism by bacterial enzymes in the gut (ex: digoxin)

What effect might a course of antibiotic therapy have in a person taking digoxin?

Excretion – kidney (renal excretion)

The irreversible loss of drug from the body Blood Proximal tubule

Afferent arteriole

Drug in blood

Efferent arteriole

Urine

1. Passive Glomerular Filtrationdiffusion of small drugs <20kDa

2. Active Tubular Secretiontransport systems for large drugs

3. Passive Tubular Reabsorption concentration gradient may drive uncharged drug back into blood *urine pH is key

Weak acid: HA ⇋ H+ + A-

B + H+⇋ BH+Weak base:

Absorbed or Excreted?

Changing urine pH to treat an overdose

increasing urine pH shifts equilibrium to promote excretion of weak acid drugs (ex: aspirin)

• iv sodium bicarbonate raises pH from 6-8

HA H+ + A- Ionized form is water soluble excreted in urine

*Remember: pH = [H+]

Changing urine pH to treat an overdose

How would you modify the urine pH to treat an overdose of a weak base drug?

B + H+ BH+

Changing urine pH to treat an overdose

urine pH shifts equilibrium to promote excretion of weak base drugs (ex: amphetamine)

•

Summary

Administration of agonist or antagonist

Drug binds receptor(s)

Response

Enteral, parenteral, inhaled, topical, etc. Unionized drug - pH

desired? side effect? TD50, ED50,

Steady state

Ionized drug - pH

Phase I, Phase II, prodrugs

Part 4: Drug Dosing

Designing drug dosing regimens

How much drug?• Magnitude of therapeutic (and toxic) effects depends on

drug dose

How often?• Magnitude of effect declines over time as drug levels

decrease

For how long?• Continuous drug use has a cost (economic, side effects,

toxicity)

Concentration – time relationships[D

rug]

in b

lood

Time

• follow and predict drug concentration in the body• blood is the reference → delivers drug to receptors

Administer drug

Take blood samples at

various times

Measure [drug]

Plot data

? iv ? non-iv

0 ∞

Concentration – time relationships[D

rug]

in b

lood

Time

• allow us to ‘visualize’ the ADME processes

∞0

Concentration – time relationships

• show us the magnitude & duration of the effect

[Dru

g] in

pla

sma

Time

MTC (minimum toxic conc.)

Therapeutic Range

MEC (minimum effective conc.)

Cmax

tmax ∞0

The C vs t equation – iv administration

Ct = C0e-kt

e = base of the natural logarithm

Ct = drug conc at time ‘t’

C0 = drug conc at time ‘0’

k = first order elimination rate constant→ the fraction of drug eliminated per unit time

Con

cent

ratio

n

Time0 0

t

Ct

C0

Linearizing the C vs t equation

Exponential: Ct = C0e-kt

Loge (or ln): lnCt = -kt + lnC0

ln C

t

Time (t)

Y = mX + b

lnC0

Slope = -k

use these equations to predict drug concentration at various times

Application of k: half-life (t½ )

Sample Calculation:

The first order elimination rate constant for acetaminophen (Tylenol®) is 0.23 hr-1. What is its half-life?

Elimination half-life (t½): the time required for drug concentration to decrease by half

t½ = ln2 = 0.693k k

Note units

k: time-1

t½: time

# Elimination half-lives

% Drug Remaining

% Drug Eliminated

0 100 0

1 50 50

2 25 75

3 12.5 87.5

4 6.25 93.75

5 3.13 96.87

Used to estimate “drug washout” prior to surgery, following a drug overdose etc. ~5 half-lives for drug to be ‘completely’ eliminated

Application of t½: drug washout

Question…

A person presents to the ER following an overdose of Tylenol (t½ = 3 hrs). How long will it take for the drug to get out of his system

without any medical intervention?

Application of C vs t eqn: predicting [drug]

If the initial plasma concentration of Tylenol is 20 μg/ml, what will the plasma concentration be after 8 hours?

Use Ct = C0e-kt or lnCt = -k t + lnC0

Step 1: lnC8h = -kt + lnC0

Step 2:

Step 3:

Step 4:

Con

cent

ratio

n

Too brief

Time

Con

cent

ratio

n

Not even reached

Time

Drugs can be taken in single doses

Single drug dosing often puts drug concentration in the therapeutic range for too short a time, if at all

Drugs can be taken in multiple dosesPeak (max) & trough (min) concentrations fluctuatearound a prolonged steady state mean (Css)

Peaks

Troughs

Steady state occurs when the rate of drugadministration = the rate of drug elimination, whichtakes ~ 5 half-lives

Steady state concentration

Time

Con

cent

ratio

n

Css

Administration = Elimination(rate in = rate out)

Drug input

Drug output

Steady state can occur at ANY concentration. Thegoal is to have Css fall within the therapeutic range

Steady state concentration

Time

Con

cent

ratio

n

Css

The concentration is a function of:• drug dose• dosing interval

Getting to steady stateA proper dosing regimen will put Css in the therapeutic range. There are 2 approaches:1. Exponential approach: give small, repeat doses at

intervals ≈ the drug’s half-life (ex: 200 mg every 4 hr)

2. Give a loading dose followed by maintenance doses

# t½ Time (hr) Amount previous dose left (mg)

New Dose (mg)

Total amount in body (mg)

0 0 0 200 2001 4 100 200 3002 8 150 200 3503 12 175 200 3754 16 187.5 200 387.55 20 193.75 200 393.86 24 196.88 200 396.9

Loading dose (LD)

• A large dose of drug used to raise the plasma concentration to a therapeutic (target) level faster than with smaller repeat doses

LD = Ctarget x Vdwhere Ctarget = desired Css

Intermittent, non-iv administration

Maintenance dose (MD)• Smaller repeat doses are then used to maintain

the desired plasma concentration

• The MD replaces the drug that is eliminated by the body during the dosing interval ‘t’ (ie the time between doses)

MD = (fraction eliminated) x LD = (1-e-kt) x LD

Rearranging Ct = C0e-kt gives us the:

Fraction remaining (Ct/C0) = e-kt

Fraction eliminated = 1-e-kt

Practice problem

The target concentration of a drug to be given 3times a day is 35 mg/L. The Vd = 25 L andt1/2 = 12 h. What loading and maintenancedoses would be appropriate?

What is k?

Practice problem – cont’d

MD = (1-e-kt) x LD

What is t?

the technical dosing regimen would be:

the practical dosing regimen would be:

Therapeutic drug monitoring

• Provides individualized (patient-specific) dosing information

Give an initial dose based on expected, published averages

Measure the patient’s actualplasma concentration

Revise subsequent dosing

• Useful for drugs with narrow therapeutic range & special populations (ex: geriatrics, pregnancy, pediatrics)

Derivation of the half-life equation ~ FYI

lnCt = lnC0 -kt

ln(Ct/C0) = -kt

multiply through by -1

ln(C0/Ct) = kt

when t = t½ Ct = ½C0 or C0 = 2Ct

ln(2Ct/Ct) = kt½

ln2 = kt½

t½ = ln2/k = 0.693/k