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?

ABowel sounds and appetite
BDeep tendon reflexes, respiratory rate and urine output
CTemperature and skin colour only
DBlood glucose, pupil size and pupil reaction to light

2.PharmacologyHard

Carboprost is a prostaglandin used for postpartum haemorrhage. In which woman should it be avoided?

AA woman with iron deficiency anaemia
BA woman who had a vaginal birth
CA woman with asthma
DA woman who is breastfeeding

3.Dosage calculationsMedium

A patient weighs 15 kg. The prescribed dose is 7.5 mg/kg per day, given in 4 equal doses. How many milligrams D are given per dose?

15 kg7.5 mg/kg/day4× per day

D = mg

4.Dosage calculationsHard

An infusion contains 50000 units of a drug in 250 mL. The prescription is 2000 units per hour. At what rate R do you set the pump, in mL/h?

50000 units/250 mL2000 units/h

R = mL/h

5.Clinical pharmacokineticsMedium

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 90 mg of gentamicin. The level back-extrapolated to time zero is 7 mg/L and the half-life is 2 h. Find the clearance CL in L/h.

D = 90 mgC₀ = 7 mg/Lt½ = 2 h

CL = L/h

6.Clinical pharmacokineticsHard

Practice exercise (made-up values, not clinical guidance). A theophylline infusion runs at 24 mg/h with no loading dose. The patient's clearance is 2 L/h and the half-life is 9 h. What is the level C after 26 h?

R = 24 mg/hCL = 2 L/ht½ = 9 ht = 26 h

C = mg/L

3Solutions

1.Pharmacology

Answer: B · 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

B · Deep tendon reflexes, respiratory rate and urine output

2.Pharmacology

Answer: C · A woman with asthma

Why this is the answer

Carboprost is a PGF2-alpha analogue that can cause bronchospasm. Oxytocin is first-line, and carboprost is avoided in asthma.

Answer

C · A woman with asthma

3.Dosage calculations

Answer: D = 28.13 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

7.5·15 = 112.5 mg

Per dose

D = 112.5/4 = 28.13 mg

Answer

D = 28.13 mg

4.Dosage calculations

Answer: R = 10 mL/h

Concentration

50000/250 = 200 units/mL

Pump rate

R = 2000/200 = 10 mL/h

Answer

R = 10 mL/h

5.Clinical pharmacokinetics

Answer: CL = 4.456 L/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.

Volume of distribution

Vd = 90/7 = 12.86 L

Rate constant

k = 0.693/2 = 0.3466 h⁻¹

Clearance

CL = 0.3466·12.86 = 4.456 L/h

Answer

CL = 4.456 L/h

6.Clinical pharmacokinetics

Answer: C = 10.38 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 = 24/2 = 12 mg/L

Rate constant

k = 0.693/9 = 0.07702 h⁻¹

Level after the given time

C = 12·(1 − e^{−0.07702·26}) = 10.38 mg/L

Answer

C = 10.38 mg/L

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