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 topical corticosteroid cream usually be applied?

  1. AAs a thin layer to the affected area only, as directed
  2. BUnder a tight plastic dressing every night without advice
  3. COn broken, infected skin to speed healing
  4. DAs a thick layer over the whole body
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. BMetronidazole replaces warfarin, so warfarin is stopped
  3. CThe INR rises, so closer INR monitoring is needed
  4. DThe INR falls, so the risk of clotting increases
3.Dosage calculationsMedium
135 kgBSA = 2.2 m²100 mg/m²D = ? mg

A patient weighing 135 kg has a body surface area of 2.2 m². The prescription is 100 mg/m². Find the dose D in mg.

135 kgBSA = 2.2 m²100 mg/m²
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 2120 micrograms. The ampoule contains 4 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

2120 mcg4 mg/mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 0.7 L/kgC = 20 mg/LLD = ? mg84 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). An 84 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 20 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.

84 kgVd = 0.7 L/kgC = 20 mg/LS = 0.92
LD = mg
6.Clinical pharmacokineticsHard
86 kg59 · womanSCr 2.1 mg/dLCrCl → D = ? mg

Practice exercise (made-up values, not clinical guidance). A 59-year-old woman weighs 86 kg and has a serum creatinine of 2.1 mg/dL (186 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual vancomycin dose is 1000 mg every 12 h for a creatinine clearance of 100 mL/min. Keeping the interval, the dose is reduced in proportion to the creatinine clearance. Find the adjusted dose D. Round to the nearest whole number.

59 years86 kgwomanSCr = 2.1 mg/dL1000 mg q12hCrCl normal 100 mL/min
D = mg

3Solutions

1.Pharmacology

Answer: A · As a thin layer to the affected area only, as directed

Why this is the answer

Thin application to affected skin limits systemic absorption and skin atrophy. Occlusive dressings increase absorption and are used only when prescribed.

Answer

A · As a thin layer to the affected area only, as directed
2.Pharmacology

Answer: C · 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

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

Answer: D = 220 mg

Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).

Dose

D = 100·2.2 = 220 mg

Answer

D = 220 mg
4.Dosage calculations

Answer: V = 0.53 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

4 mg/mL = 4000 mcg/mL

Volume

V = 2120/4000 = 0.53 mL

Answer

V = 0.53 mL
5.Clinical pharmacokinetics

Answer: LD = 1278 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 = 0.7·84 = 58.8 L

Amount of active drug needed

Vd·C = 58.8·20 = 1176 mg

Loading dose

LD = 1176/(0.92·1) = 1278 mg

Answer

LD = 1278 mg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: D = 392 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.

Creatinine clearance (Cockcroft–Gault)

CrCl = (140 − 59)·86/(72·2.1)·0.85 = 39.16 mL/min

Adjusted dose

D = 1000·39.16/100 = 391.6 ≈ 392 mg

Answer

D = 392 mg

In practice the dose is rounded to a convenient amount and checked against the product information.

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