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

Which type of diuretic acts on the thick ascending limb of the loop of Henle?

  1. APotassium-sparing diuretics
  2. BOsmotic diuretics
  3. CLoop diuretics such as furosemide
  4. DThiazide diuretics
2.PharmacologyHard

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

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

A child weighing 13 kg is prescribed 4 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?

13 kg4 mg/kg10 mg/mL
V = mL
4.Dosage calculationsHard
50%stockV₁ = ? mL

You must prepare 250 mL of a 5% (w/v) solution from a 50% (w/v) stock solution. What volume of stock V₁ do you need?

C₁ = 50%C₂ = 5%V₂ = 250 mL
V₁ = mL
5.Clinical pharmacokineticsMedium
10100t (h)C (mg/L)1 h35 mg/L13 h15.2 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 35 mg/L at 1 h and 15.2 mg/L at 13 h. Assume first-order elimination. Find the half-life t½.

C1 = 35 mg/L (1 h)C2 = 15.2 mg/L (13 h)
t½ = h
6.Clinical pharmacokineticsHard
VCss,avg​ = 20 mg/LD = ? mg · q12hCL = 3 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 3 L/h. What dose D in mg gives an average steady-state level of 20 mg/L?

CL = 3 L/hτ = 12 hS = 1F = 1Css,avg = 20 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: C · Loop diuretics such as furosemide

Why this is the answer

Loop diuretics block the Na⁺/K⁺/2Cl⁻ cotransporter in the thick ascending limb and are the most powerful diuretics.

Answer

C · Loop diuretics such as furosemide
2.Pharmacology

Answer: D · 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

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

Answer: V = 5.2 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 = 4·13 = 52 mg

Volume

V = 52/10 = 5.2 mL

On the syringe

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

Answer

V = 5.2 mL
4.Dosage calculations

Answer: V₁ = 25 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 = 5·250/50 = 25 mL

Answer

V₁ = 25 mL
5.Clinical pharmacokinetics

Answer: t½ = 9.973 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.

Elimination rate constant

k = ln(35/15.2)/12 = 0.8341/12 = 0.0695 h⁻¹

Half-life

t½ = 0.693/0.0695 = 9.973 h

Answer

t½ = 9.973 h
6.Clinical pharmacokinetics

Answer: D = 720 mg

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.

Dose

D = Css,avg·CL·τ/(S·F) = 20·3·12/(1·1) = 720 mg

Answer

D = 720 mg

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