Pharmacology: cram pack

Formula sheets, the key method steps for every topic and 6 practice problems, with full solutions at the back.

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1Formulas and methods

Dosage calculations

Dose from strength
volume = dose / strength
Weight-based dose
dose = mg/kg × body weight
Tablets
number = dose / tablet strength
Units
1 g = 1000 mg, 1 mg = 1000 mcg

Method

  1. Convert the ordered dose and the stock strength to the same unit.
  2. Use desired over have times quantity: (D/H) × Q.
  3. For weight-based doses, multiply by the weight in kg first, then divide the daily dose by the number of doses.
  4. Estimate first and check that the answer is reasonable.

Clinical pharmacokinetics

Rate constant and half-life
k = ln 2/t½ = 0.693/t½
First-order decay
C = C₀·e−kt = C₀·(1/2)t/t½
Two levels
k = ln(C₁/C₂)/Δt
Volume and clearance
Vd = dose/C₀, CL = k·Vd
Loading dose
LD = Vd·C/(S·F)
Maintenance rate
R = CL·Css/(S·F)
Average steady state
Css,avg = S·F·D/(CL·τ)
Steady state
1 − (1/2)ⁿ after n half-lives; ≈ 97% after 5
Infusion
C = (R/CL)(1 − e−kt)
Interval and dose from peak and trough
τ = ln(Cpeak/Ctrough)/k, D = Vd·(Cpeak − Ctrough)
Cockcroft–Gault
CrCl = (140 − age) × kg/(72 × SCr mg/dL), × 0.85 for women
Renal adjustment
dose × CrCl/normal; Dettli Q = 1 − fe·(1 − CrCl/normal)

Method

  1. Convert the half-life to a rate constant: k = 0.693/t½.
  2. Turn per-kg values into totals: Vd (L) = L/kg × weight, CL (L/h) = L/kg/h × weight.
  3. Pick the relation: C = C₀·e−kt, LD = Vd·C/(S·F), maintenance rate = CL·Css/(S·F), τ = ln(Cpeak/Ctrough)/k.
  4. For kidney function, estimate CrCl with Cockcroft–Gault first, then scale the dose or the interval.
  5. Check the result: levels fall by half every half-life, and steady state takes about five half-lives.

2Practice problems

1.PharmacologyMedium

Which side effects are most common when starting gabapentin?

  1. AHair loss and weight loss
  2. BInsomnia and agitation
  3. CDrowsiness and dizziness
  4. DCough and runny nose
2.PharmacologyHard

Why may omeprazole be avoided in a patient taking clopidogrel?

  1. AIt increases clopidogrel absorption from the gut and causes bleeding
  2. BIt speeds up kidney excretion of clopidogrel
  3. CIt binds clopidogrel in the stomach and makes it insoluble
  4. DIt inhibits CYP2C19, so less clopidogrel is converted to its active form
3.Dosage calculationsMedium
1:1000ampouleV = ? mL

An ampoule of epinephrine (adrenaline) is labelled 1:1000 (1 mg/mL). The prescription is 0.3 mg IM for anaphylaxis. What volume V do you draw up?

1:10000.3 mg
V = mL
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 190 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

190 units1000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)1 h6 mg/L5 h2 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of tobramycin, the level is 6 mg/L at 1 h and 2 mg/L at 5 h. Assume first-order elimination. Find the half-life t½.

C1 = 6 mg/L (1 h)C2 = 2 mg/L (5 h)
t½ = h
6.Clinical pharmacokineticsHard
t (h)C (mg/L)Css​t = ?95%

Practice exercise (made-up values, not clinical guidance). A theophylline infusion is started without a loading dose. The half-life in this patient is 9 h. How long t does it take to reach 95% of the steady-state level?

t½ = 9 h95% Css
t = h

3Solutions

1.Pharmacology

Answer: C · Drowsiness and dizziness

Why this is the answer

Gabapentin and pregabalin commonly cause sedation, dizziness and unsteadiness, which raise the risk of falls. They also increase sedation when combined with opioids.

Answer

C · Drowsiness and dizziness
2.Pharmacology

Answer: D · It inhibits CYP2C19, so less clopidogrel is converted to its active form

Why this is the answer

Clopidogrel must be activated by liver enzymes, mainly CYP2C19. Omeprazole inhibits this enzyme and can reduce its antiplatelet effect, so another acid suppressant may be chosen.

Answer

D · It inhibits CYP2C19, so less clopidogrel is converted to its active form
3.Dosage calculations

Answer: V = 0.3 mL

Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.

Concentration

1:1000 = 1 g/1000 mL = 1 mg/mL

Volume

V = 0.3/1 = 0.3 mL

Answer

V = 0.3 mL

US labels now state mg/mL (1 mg/mL = 1:1000; 0.1 mg/mL = 1:10 000). Never give 1 mg/mL epinephrine IV push.

4.Dosage calculations

Answer: V = 0.19 mL

Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.

Volume

V = 190/1000 = 0.19 mL

On the syringe

On this 1 mL syringe every small line is 0.01 mL.

Answer

V = 0.19 mL
5.Clinical pharmacokinetics

Answer: t½ = 2.524 h

Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × Css. A loading dose is LD = Vd × C/(S × F), with S the salt factor (fraction of active drug in the salt) and F the bioavailability (1 for IV). From two levels, k = ln(C₁/C₂)/Δt; for an IV bolus Vd = dose/C₀ and CL = k × Vd. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.

Elimination rate constant

k = ln(6/2)/4 = 1.099/4 = 0.2747 h⁻¹

Half-life

t½ = 0.693/0.2747 = 2.524 h

Answer

t½ = 2.524 h
6.Clinical pharmacokinetics

Answer: t = 38.9 h

Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(Cpeak/Ctrough)/k and the dose that restores the peak is Vd × (Cpeak − Ctrough). The average steady-state level is Css,avg = S·F·dose/(CL·τ). An infusion rises as C = (R/CL)(1 − e−kt). For a drug cleared by the kidneys, the dose is scaled with the creatinine clearance. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.

Rate constant

k = 0.693/9 = 0.07702 h⁻¹

Time to the given fraction of steady state

t = −ln(1 − 0.95)/0.07702 = 2.996/0.07702 = 38.9 h

Answer

t = 38.9 h

That is 4.322 half-lives.

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