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 receptor do beta blockers such as metoprolol mainly block?

  1. AAlpha-1 receptors in blood vessels
  2. BMuscarinic receptors in the heart
  3. CBeta-3 receptors in fat tissue
  4. DBeta-1 adrenergic receptors in the heart
2.PharmacologyHard

A patient on stable warfarin is prescribed a course of metronidazole. What is the likely effect, and what should the nurse expect?

  1. AThe INR stays the same, as these drugs do not interact
  2. BThe INR rises, so closer INR monitoring is needed
  3. CMetronidazole replaces warfarin, so warfarin is stopped
  4. DThe INR falls, so the risk of clotting increases
3.Dosage calculationsMedium
024681010 mL

A child weighing 6 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?

6 kg10 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
120 mg/5 mLV = ? mL

A child weighing 18 kg is prescribed 20 mg/kg per dose of an oral suspension that contains 120 mg in 5 mL. What volume V do you give?

18 kg20 mg/kg120 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)C₀ = 8 mg/Lt½ = 3 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 130 mg of gentamicin. The level back-extrapolated to time zero is 8 mg/L and the half-life is 3 h. Find the clearance CL in L/h.

D = 130 mgC₀ = 8 mg/Lt½ = 3 h
CL = L/h
6.Clinical pharmacokineticsHard
Vd = 0.3 L/kg0.5 → 8 mg/LD = ? mg95 kg

Practice exercise (made-up values, not clinical guidance). A 95 kg patient on regular gentamicin doses is at steady state. The target is a peak of 8 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.3 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?

95 kgVd = 0.3 L/kgCpeak = 8 mg/LCtrough = 0.5 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: D · Beta-1 adrenergic receptors in the heart

Why this is the answer

Cardioselective beta blockers block beta-1 receptors, lowering heart rate, contractility and renin release.

Answer

D · Beta-1 adrenergic receptors in the heart
2.Pharmacology

Answer: B · The INR rises, so closer INR monitoring is needed

Why this is the answer

Metronidazole inhibits the metabolism of warfarin (mainly via CYP2C9), so warfarin levels and the INR rise. The bleeding risk increases, and the INR is checked more often during and after the course.

Answer

B · The INR rises, so closer INR monitoring is needed
3.Dosage calculations

Answer: V = 1.2 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 = 10·6 = 60 mg

Volume

V = 60/50 = 1.2 mL

On the syringe

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

Answer

V = 1.2 mL
4.Dosage calculations

Answer: V = 15 mL

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.

Dose from weight

20·18 = 360 mg

Volume

V = (360/120)·5 = 15 mL

Answer

V = 15 mL
5.Clinical pharmacokinetics

Answer: CL = 3.755 L/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.

Volume of distribution

Vd = 130/8 = 16.25 L

Rate constant

k = 0.693/3 = 0.231 h⁻¹

Clearance

CL = 0.231·16.25 = 3.755 L/h

Answer

CL = 3.755 L/h
6.Clinical pharmacokinetics

Answer: D = 213.8 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.

Volume of distribution

Vd = 0.3·95 = 28.5 L

Dose

D = 28.5·(8 − 0.5) = 213.8 mg

Answer

D = 213.8 mg

In practice the dose is rounded to a convenient amount.

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