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

What does the clearance of a drug describe?

AThe amount of drug removed by one dialysis session
BThe time needed for the drug to disappear completely from the plasma
CThe volume of plasma cleared of the drug per unit of time
DThe fraction of the dose that is absorbed

2.PharmacologyHard

In adult cardiac arrest with shock-refractory ventricular fibrillation, which antiarrhythmic is commonly given?

ADigoxin
BVerapamil
CAmiodarone
DAdenosine

3.Dosage calculationsMedium

A patient weighing 29 kg has a body surface area of 1.05 m². The prescription is 135 mg/m². Find the dose D in mg.

29 kgBSA = 1.05 m²135 mg/m²

D = mg

4.Dosage calculationsHard

The prescription is 3680 micrograms. The ampoule contains 4 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

3680 mcg4 mg/mL

V = mL

5.Clinical pharmacokineticsMedium

Practice exercise (made-up values, not clinical guidance). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 55 mL/min. What infusion rate R in mg/h gives a steady-state level of 20 mg/L?

CL = 55 mL/minC_ss = 20 mg/L

R = mg/h

6.Clinical pharmacokineticsHard

Practice exercise (made-up values, not clinical guidance). A 57 kg patient on regular tobramycin doses is at steady state. The target is a peak of 7 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.3 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?

57 kgVd = 0.3 L/kgC_peak = 7 mg/LC_trough = 0.5 mg/L

D = mg

3Solutions

1.Pharmacology

Answer: C · The volume of plasma cleared of the drug per unit of time

Why this is the answer

Clearance is the volume of plasma from which the drug is removed per unit of time. Together with the dosing rate it determines the steady-state concentration.

Answer

C · The volume of plasma cleared of the drug per unit of time

2.Pharmacology

Answer: C · Amiodarone

Why this is the answer

Amiodarone is used for VF or pulseless VT that persists after shocks, with lidocaine as an alternative. Adenosine, digoxin and verapamil have no role in VF.

Answer

C · Amiodarone

3.Dosage calculations

Answer: D = 141.8 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).

Dose

D = 135·1.05 = 141.8 mg

Answer

D = 141.8 mg

4.Dosage calculations

Answer: V = 0.92 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.

Same units

4 mg/mL = 4000 mcg/mL

Volume

V = 3680/4000 = 0.92 mL

Answer

V = 0.92 mL

5.Clinical pharmacokinetics

Answer: R = 66 mg/h

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/h

55·60/1000 = 3.3 L/h

Infusion rate

R = 3.3·20 = 66 mg/h

Answer

R = 66 mg/h

6.Clinical pharmacokinetics

Answer: D = 111.1 mg

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.

Volume of distribution

Vd = 0.3·57 = 17.1 L

Dose

D = 17.1·(7 − 0.5) = 111.1 mg

Answer

D = 111.1 mg

In practice the dose is rounded to a convenient amount.

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