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 does sucralfate help a peptic ulcer heal?

  1. AIt neutralises acid by releasing bicarbonate
  2. BIt forms a protective coating over the ulcer base
  3. CIt blocks histamine H2 receptors in the stomach
  4. DIt kills Helicobacter pylori directly
2.PharmacologyHard

A patient with severe chronic hyponatraemia receives hypertonic saline. Why is the rate of correction strictly limited?

  1. ARaising sodium too fast can cause osmotic demyelination in the brain
  2. BHypertonic saline is toxic to the liver at high rates
  3. CRaising sodium too fast causes severe hypokalaemia and cardiac arrest
  4. DFast correction causes immediate kidney failure
3.Dosage calculationsMedium
024681010 mL

A child weighing 9 kg is prescribed 10 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?

9 kg10 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
25%stockV₁ = ? mL

You must prepare 500 mL of a 2.5% (w/v) solution from a 25% (w/v) stock solution. What volume of stock V₁ do you need?

C₁ = 25%C₂ = 2.5%V₂ = 500 mL
V₁ = mL
5.Clinical pharmacokineticsMedium
Vd = 0.7 L/kgC = 15 mg/LLD = ? mg59 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). A 59 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 15 mg/L. The volume of distribution is 0.7 L/kg and the salt factor is S = 0.92. Find the loading dose LD of phenytoin sodium in mg.

59 kgVd = 0.7 L/kgC = 15 mg/LS = 0.92
LD = mg
6.Clinical pharmacokineticsHard
VCss,avg​ = ?1000 mg · q12hCL = 4 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 4 L/h. Each dose is 1000 mg of vancomycin. Find the average steady-state level Css,avg.

CL = 4 L/hτ = 12 hS = 1F = 1D = 1000 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: B · It forms a protective coating over the ulcer base

Why this is the answer

Sucralfate forms a gel-like barrier that sticks to the ulcer and protects it from acid and pepsin. It is taken on an empty stomach and can reduce the absorption of other drugs taken at the same time.

Answer

B · It forms a protective coating over the ulcer base
2.Pharmacology

Answer: A · Raising sodium too fast can cause osmotic demyelination in the brain

Why this is the answer

In chronic hyponatraemia the brain adapts to low osmolality. Correcting sodium too rapidly shrinks brain cells and can cause osmotic demyelination (central pontine myelinolysis), so sodium is checked often.

Answer

A · Raising sodium too fast can cause osmotic demyelination in the brain
3.Dosage calculations

Answer: V = 1.8 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 = 10·9 = 90 mg

Volume

V = 90/50 = 1.8 mL

On the syringe

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

Answer

V = 1.8 mL
4.Dosage calculations

Answer: V₁ = 50 mL

Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.

Volume of stock

V₁ = 2.5·500/25 = 50 mL

Answer

V₁ = 50 mL
5.Clinical pharmacokinetics

Answer: LD = 673.4 mg

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 = 0.7·59 = 41.3 L

Amount of active drug needed

Vd·C = 41.3·15 = 619.5 mg

Loading dose

LD = 619.5/(0.92·1) = 673.4 mg

Answer

LD = 673.4 mg

In practice the dose is rounded to a convenient amount.

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) = 1·1·1000/(4·12) = 20.83 mg/L

Answer

Css,avg = 20.83 mg/L

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