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 patient should usually not use the combined oral contraceptive pill?

  1. AA 25-year-old woman with heavy periods
  2. BA 22-year-old non-smoker with acne
  3. CA 30-year-old non-smoker with no medical problems
  4. DA 38-year-old woman who smokes 20 cigarettes a day
2.PharmacologyHard

A patient with early aspirin (salicylate) overdose has tinnitus and is breathing fast. Which acid–base pattern is classic?

  1. ARespiratory acidosis with normal bicarbonate
  2. BPure metabolic alkalosis
  3. CRespiratory alkalosis followed by metabolic acidosis
  4. DMetabolic alkalosis followed by respiratory acidosis
3.Dosage calculationsMedium
117 kgBSA = 2.05 m²135 mg/m²D = ? mg

A patient weighing 117 kg has a body surface area of 2.05 m². The prescription is 135 mg/m². Find the dose D in mg.

117 kgBSA = 2.05 m²135 mg/m²
D = mg
4.Dosage calculationsHard
250 mg/5 mLV = ? mL

A child weighing 18 kg is prescribed 5 mg/kg per dose of an oral suspension that contains 250 mg in 5 mL. What volume V do you give?

18 kg5 mg/kg250 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)C₀ = 12 mg/Lt½ = 2 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 250 mg of tobramycin. The level back-extrapolated to time zero is 12 mg/L and the half-life is 2 h. Find the volume of distribution Vd.

D = 250 mgC₀ = 12 mg/Lt½ = 2 h
Vd = L
6.Clinical pharmacokineticsHard
Vd = 7 L/kg0.5 → 1 mcg/LLD = ? mcg67 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 67 kg patient has a digoxin level of 0.5 mcg/L; the target is 1 mcg/L. The volume of distribution is 7 L/kg and the tablets have F = 0.7. What extra loading dose LD raises the level to the target?

67 kgVd = 7 L/kgC = 0.5 → 1 mcg/LF = 0.7
LD = mcg

3Solutions

1.Pharmacology

Answer: D · A 38-year-old woman who smokes 20 cigarettes a day

Why this is the answer

Smoking over the age of 35 greatly increases the risk of myocardial infarction and stroke with combined hormonal contraception. Progestogen-only or non-hormonal methods are preferred.

Answer

D · A 38-year-old woman who smokes 20 cigarettes a day
2.Pharmacology

Answer: C · Respiratory alkalosis followed by metabolic acidosis

Why this is the answer

Salicylates stimulate breathing, causing respiratory alkalosis early. They then disturb cell metabolism, causing a metabolic acidosis with a raised anion gap. Adults often show a mixed picture.

Answer

C · Respiratory alkalosis followed by metabolic acidosis
3.Dosage calculations

Answer: D = 276.8 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 = 135·2.05 = 276.8 mg

Answer

D = 276.8 mg
4.Dosage calculations

Answer: V = 1.8 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

5·18 = 90 mg

Volume

V = (90/250)·5 = 1.8 mL

Answer

V = 1.8 mL
5.Clinical pharmacokinetics

Answer: Vd = 20.83 L

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 = 250/12 = 20.83 L

Answer

Vd = 20.83 L
6.Clinical pharmacokinetics

Answer: LD = 335 mcg

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 = 7·67 = 469 L

Rise needed

1 − 0.5 = 0.5 mcg/L

Loading dose

LD = 469·0.5/(1·0.7) = 335 mcg

Answer

LD = 335 mcg

In practice the dose is rounded to a convenient amount.

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