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

Ipratropium is a bronchodilator used in COPD. How does it work?

  1. AIt stimulates beta-2 adrenergic receptors in the airways
  2. BIt reduces inflammation like a corticosteroid
  3. CIt blocks muscarinic receptors in airway smooth muscle
  4. DIt blocks leukotriene receptors
2.PharmacologyHard

A woman has received a high-dose oxytocin infusion with large volumes of hypotonic fluid for many hours. She now has a headache, confusion and a low serum sodium. What is the most likely cause?

  1. ANormal tiredness after a long labour
  2. BExcessive salt in the infusion fluid
  3. CWater intoxication from the antidiuretic effect of oxytocin
  4. DAn allergic reaction to oxytocin causing brain swelling
3.Dosage calculationsMedium
60 kg30 mg/kg/day3× per dayD = ? mg

A patient weighs 60 kg. The prescribed dose is 30 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?

60 kg30 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
45 kg156 cmBSA = √(h·w/3600)250 mg/m²D = ? mg

A patient is 156 cm tall and weighs 45 kg. The prescription is 250 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.

156 cm45 kg250 mg/m²
D = mg
5.Clinical pharmacokineticsMedium
VCss​ = 12 mg/LR = ? mg/hCL = 0.03 L/kg/h63 kg

Practice exercise (made-up values, not clinical guidance). A 63 kg patient receives a theophylline infusion. The clearance is 0.03 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 12 mg/L?

63 kgCL = 0.03 L/kg/hCss = 12 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
0.1110t (h)C (mg/L)Cpeak​ = 8τ = ?Ctrough​ = 0.5

Practice exercise (made-up values, not clinical guidance). A patient's tobramycin half-life is 2.5 h. The target is a peak of 8 mg/L and a trough of 0.5 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.

t½ = 2.5 hCpeak = 8 mg/LCtrough = 0.5 mg/L
τ = h

3Solutions

1.Pharmacology

Answer: C · It blocks muscarinic receptors in airway smooth muscle

Why this is the answer

Ipratropium is an inhaled antimuscarinic. It blocks vagally mediated bronchoconstriction and mucus secretion, which is especially useful in COPD.

Answer

C · It blocks muscarinic receptors in airway smooth muscle
2.Pharmacology

Answer: C · Water intoxication from the antidiuretic effect of oxytocin

Why this is the answer

Oxytocin has antidiuretic activity at high doses. With large volumes of fluid this can cause water retention and dilutional hyponatraemia, so fluid balance and sodium are monitored.

Answer

C · Water intoxication from the antidiuretic effect of oxytocin
3.Dosage calculations

Answer: D = 600 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

30·60 = 1800 mg

Per dose

D = 1800/3 = 600 mg

Answer

D = 600 mg
4.Dosage calculations

Answer: D = 349.1 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 = √(156·45/3600) = √1.95 = 1.396 m²

Dose

D = 250·1.396 = 349.1 mg

Answer

D = 349.1 mg
5.Clinical pharmacokinetics

Answer: R = 22.68 mg/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.

Clearance

CL = 0.03·63 = 1.89 L/h

Infusion rate

R = 1.89·12 = 22.68 mg/h

Answer

R = 22.68 mg/h
6.Clinical pharmacokinetics

Answer: τ = 10 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 = 0.693/2.5 = 0.2773 h⁻¹

Dosing interval

τ = ln(8/0.5)/0.2773 = 2.773/0.2773 = 10 h

Answer

τ = 10 h

In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.

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