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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
