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

How should a patient take oral alendronate?

  1. AWith milk at bedtime, then lying down straight away to aid absorption
  2. BWith plain water on an empty stomach, staying upright for 30 minutes
  3. CCrushed into yoghurt with calcium supplements
  4. DWith breakfast and coffee to protect the stomach
2.PharmacologyHard

A patient with myasthenia gravis took extra pyridostigmine doses. She now has increasing weakness, heavy salivation, sweating, small pupils and diarrhoea. What is the most likely cause?

  1. ACholinergic crisis from too much anticholinesterase drug
  2. BAn allergic reaction to pyridostigmine
  3. CA stroke unrelated to the medication
  4. DMyasthenic crisis from too little anticholinesterase drug
3.Dosage calculationsMedium
024681010 mL

A child weighing 20 kg is prescribed 7.5 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?

20 kg7.5 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 1200 units of a drug that comes as 5000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

1200 units5000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 0.8 mcg/LLD = ? mcg100 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 100 kg patient is to be loaded with digoxin tablets to reach a level of 0.8 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.

100 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
t (h)C (mg/L)Css​4 hC = ?

Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 125 mg/h with no loading dose. The patient's clearance is 5 L/h and the half-life is 8 h. What is the level C after 4 h?

R = 125 mg/hCL = 5 L/ht½ = 8 ht = 4 h
C = mg/L

3Solutions

1.Pharmacology

Answer: B · With plain water on an empty stomach, staying upright for 30 minutes

Why this is the answer

Alendronate is taken first thing in the morning with water only, before food or other drugs. Staying upright reduces the risk of oesophageal ulceration, and food or calcium blocks its absorption.

Answer

B · With plain water on an empty stomach, staying upright for 30 minutes
2.Pharmacology

Answer: A · Cholinergic crisis from too much anticholinesterase drug

Why this is the answer

Excess acetylcholine causes muscarinic signs (salivation, sweating, miosis, diarrhoea) and depolarising weakness. In myasthenic crisis, weakness occurs without these cholinergic signs; both can cause respiratory failure.

Answer

A · Cholinergic crisis from too much anticholinesterase drug
3.Dosage calculations

Answer: V = 3 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.

Dose from body weight

D = 7.5·20 = 150 mg

Volume

V = 150/50 = 3 mL

On the syringe

On this 10 mL syringe every small line is 0.2 mL.

Answer

V = 3 mL
4.Dosage calculations

Answer: V = 0.24 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.

Volume

V = 1200/5000 = 0.24 mL

On the syringe

On this 1 mL syringe every small line is 0.01 mL.

Answer

V = 0.24 mL
5.Clinical pharmacokinetics

Answer: LD = 800 mcg

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.

Volume of distribution

Vd = 7·100 = 700 L

Amount of active drug needed

Vd·C = 700·0.8 = 560 mcg

Loading dose

LD = 560/(1·0.7) = 800 mcg

Answer

LD = 800 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: C = 7.322 mg/L

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.

Steady-state level

Css = 125/5 = 25 mg/L

Rate constant

k = 0.693/8 = 0.08664 h⁻¹

Level after the given time

C = 25·(1 − e−0.08664·4) = 7.322 mg/L

Answer

C = 7.322 mg/L

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