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

Convert the ordered dose and the stock strength to the same unit.
Use desired over have times quantity: (D/H) × Q.
For weight-based doses, multiply by the weight in kg first, then divide the daily dose by the number of doses.
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·C_ss/(S·F)
Average steady state: C_ss,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(C_peak/C_trough)/k, D = Vd·(C_peak − C_trough)
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

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

2Practice problems

1.PharmacologyMedium

Which drug is used for torsades de pointes?

AIntravenous adenosine (rapid push)
BIntravenous magnesium sulfate
COral digoxin
DIntravenous verapamil

2.PharmacologyHard

Which finding most favours serotonin syndrome over neuroleptic malignant syndrome?

ARecent start of an antipsychotic drug
BSlow onset over days with lead-pipe rigidity
CA very high creatine kinase
DRapid onset with hyperreflexia and clonus

3.Dosage calculationsMedium

A patient weighs 15 kg and is prescribed 20 mg/kg as a single dose. Find the dose D in mg.

15 kg20 mg/kg

D = mg

4.Dosage calculationsHard

A patient is 161 cm tall and weighs 71 kg. The prescription is 135 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.

161 cm71 kg135 mg/m²

D = mg

5.Clinical pharmacokineticsMedium

Practice exercise (made-up values, not clinical guidance). A patient has a lidocaine clearance of 650 mL/min. What infusion rate R in mg/min keeps the steady-state level at 3 mg/L?

CL = 650 mL/minC_ss = 3 mg/L

R = mg/min

6.Clinical pharmacokineticsHard

Practice exercise (made-up values, not clinical guidance). An 87 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.05 L/kg/h. Each dose is 400 mg of theophylline. Find the average steady-state level C_ss,avg.

CL = 0.05 L/kg/hτ = 12 hS = 1F = 187 kgD = 400 mg

C_ss,avg = mg/L

3Solutions

1.Pharmacology

Answer: B · Intravenous magnesium sulfate

Why this is the answer

IV magnesium is first-line for torsades de pointes, even when serum magnesium is normal. QT-prolonging drugs are stopped and potassium is corrected.

Answer

B · Intravenous magnesium sulfate

2.Pharmacology

Answer: D · Rapid onset with hyperreflexia and clonus

Why this is the answer

Serotonin syndrome develops within hours of a serotonergic drug and causes clonus, hyperreflexia, agitation, dilated pupils and diarrhoea. NMS develops over days after a dopamine antagonist, with lead-pipe rigidity and slow reflexes.

Answer

D · Rapid onset with hyperreflexia and clonus

3.Dosage calculations

Answer: D = 300 mg

Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.

Dose

20·15 = 300 mg

Answer

D = 300 mg

4.Dosage calculations

Answer: D = 240.6 mg

Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).

Body surface area

BSA = √(161·71/3600) = √3.175 = 1.782 m²

Dose

D = 135·1.782 = 240.6 mg

Answer

D = 240.6 mg

5.Clinical pharmacokinetics

Answer: R = 1.95 mg/min

Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × C_ss. 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.

Clearance in L/min

650 mL/min = 0.65 L/min

Infusion rate

R = 0.65·3 = 1.95 mg/min

Answer

R = 1.95 mg/min

6.Clinical pharmacokinetics

Answer: C_ss,avg = 7.663 mg/L

Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(C_peak/C_trough)/k and the dose that restores the peak is Vd × (C_peak − C_trough). The average steady-state level is C_ss,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.

Clearance

CL = 0.05·87 = 4.35 L/h

Average steady-state level

C_ss,avg = S·F·D/(CL·τ) = 1·1·400/(4.35·12) = 7.663 mg/L

Answer

C_ss,avg = 7.663 mg/L

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