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 assessments are most important during a magnesium sulfate infusion?

ATemperature and skin colour only
BBlood glucose, pupil size and pupil reaction to light
CDeep tendon reflexes, respiratory rate and urine output
DBowel sounds and appetite

2.PharmacologyHard

A patient on rifampicin, isoniazid, pyrazinamide and ethambutol develops a painful swollen big toe. Which drug is most likely responsible?

ARifampicin
BPyrazinamide
CIsoniazid
DEthambutol

3.Dosage calculationsMedium

A patient weighs 25 kg. The prescribed dose is 7.5 mg/kg per day, given in 4 equal doses. How many milligrams D are given per dose?

25 kg7.5 mg/kg/day4× per day

D = mg

4.Dosage calculationsHard

A child weighing 28 kg is prescribed 10 mg/kg per dose of an oral suspension that contains 250 mg in 5 mL. What volume V do you give?

28 kg10 mg/kg250 mg/5 mL

V = mL

5.Clinical pharmacokineticsMedium

Practice exercise (made-up values, not clinical guidance). An 80 kg patient receives a theophylline infusion. The clearance is 0.04 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 10 mg/L?

80 kgCL = 0.04 L/kg/hC_ss = 10 mg/L

R = mg/h

6.Clinical pharmacokineticsHard

Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 80 mg/h with no loading dose. The patient's clearance is 4 L/h and the half-life is 6 h. What is the level C after 7 h?

R = 80 mg/hCL = 4 L/ht½ = 6 ht = 7 h

C = mg/L

3Solutions

1.Pharmacology

Answer: C · Deep tendon reflexes, respiratory rate and urine output

Why this is the answer

Loss of reflexes is an early sign of magnesium toxicity, followed by respiratory depression and cardiac arrest. Low urine output allows magnesium to accumulate.

Answer

C · Deep tendon reflexes, respiratory rate and urine output

2.Pharmacology

Answer: B · Pyrazinamide

Why this is the answer

Pyrazinamide reduces uric acid excretion and can cause hyperuricaemia and gout. It is also hepatotoxic, like isoniazid and rifampicin.

Answer

B · Pyrazinamide

3.Dosage calculations

Answer: D = 46.88 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.

Total per day

7.5·25 = 187.5 mg

Per dose

D = 187.5/4 = 46.88 mg

Answer

D = 46.88 mg

4.Dosage calculations

Answer: V = 5.6 mL

Dose from weight

10·28 = 280 mg

Volume

V = (280/250)·5 = 5.6 mL

Answer

V = 5.6 mL

5.Clinical pharmacokinetics

Answer: R = 32 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

CL = 0.04·80 = 3.2 L/h

Infusion rate

R = 3.2·10 = 32 mg/h

Answer

R = 32 mg/h

6.Clinical pharmacokinetics

Answer: C = 11.09 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.

Steady-state level

C_ss = 80/4 = 20 mg/L

Rate constant

k = 0.693/6 = 0.1155 h⁻¹

Level after the given time

C = 20·(1 − e^−0.1155·7) = 11.09 mg/L

Answer

C = 11.09 mg/L

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