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

Combining an SSRI with which drug most increases the risk of serotonin syndrome?

  1. AOmeprazole
  2. BAmoxicillin
  3. CParacetamol
  4. DA monoamine oxidase inhibitor
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. BMyasthenic crisis from too little anticholinesterase drug
  3. CAn allergic reaction to pyridostigmine
  4. DA stroke unrelated to the medication
3.Dosage calculationsMedium
024681010 mL

A child weighing 12 kg is prescribed 7.5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?

12 kg7.5 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 660 micrograms. The ampoule contains 2 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

660 mcg2 mg/mL
V = mL
5.Clinical pharmacokineticsMedium
0.1110t (h)C (mg/L)2 h6 mg/L7 h1.1 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 6 mg/L at 2 h and 1.1 mg/L at 7 h. Assume first-order elimination. Find the elimination rate constant k.

C1 = 6 mg/L (2 h)C2 = 1.1 mg/L (7 h)
k = h⁻¹
6.Clinical pharmacokineticsHard
VCss,avg​ = ?1250 mg · q12hCL = 5 L/hS = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 5 L/h. Each dose is 1250 mg of vancomycin. Find the average steady-state level Css,avg.

CL = 5 L/hτ = 12 hS = 1F = 1D = 1250 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: D · A monoamine oxidase inhibitor

Why this is the answer

SSRIs block serotonin reuptake and MAO inhibitors block its breakdown. Together they can cause serotonin syndrome with agitation, hyperthermia, tremor and clonus.

Answer

D · A monoamine oxidase inhibitor
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 = 3.6 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 = 7.5·12 = 90 mg

Volume

V = 90/25 = 3.6 mL

On the syringe

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

Answer

V = 3.6 mL
4.Dosage calculations

Answer: V = 0.33 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

2 mg/mL = 2000 mcg/mL

Volume

V = 660/2000 = 0.33 mL

Answer

V = 0.33 mL
5.Clinical pharmacokinetics

Answer: k = 0.3393 h⁻¹

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.

Elimination rate constant

k = ln(6/1.1)/5 = 1.696/5 = 0.3393 h⁻¹

Answer

k = 0.3393 h⁻¹
6.Clinical pharmacokinetics

Answer: Css,avg = 20.83 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.

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 1·1·1250/(5·12) = 20.83 mg/L

Answer

Css,avg = 20.83 mg/L

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