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

In which patient is bupropion contraindicated?

  1. AA patient who wants to stop smoking
  2. BA patient with seasonal allergies
  3. CA patient with a seizure disorder or an eating disorder
  4. DA patient with high blood cholesterol and a family history of it
2.PharmacologyHard

A nurse calculates a child's dose and finds it is ten times higher than the usual range in the drug reference. What should the nurse do?

  1. AGive the dose, because the prescriber is responsible for the order
  2. BWithhold it, recheck the calculation and clarify with the prescriber
  3. CGive half the dose as a compromise
  4. DGive one tenth of the dose without telling anyone
3.Dosage calculationsMedium
60 kg10 mg/kgD = ? mg

A patient weighs 60 kg and is prescribed 10 mg/kg as a single dose. Find the dose D in mg.

60 kg10 mg/kg
D = mg
4.Dosage calculationsHard
77 kg163 cmBSA = √(h·w/3600)60 mg/m²D = ? mg

A patient is 163 cm tall and weighs 77 kg. The prescription is 60 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.

163 cm77 kg60 mg/m²
D = mg
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 0.8 mcg/LLD = ? mcg68 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 68 kg patient is to be loaded with digoxin tablets to reach a level of 0.8 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.

68 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
VCss,avg​ = 20 mg/LD = ? mg · q12hCL = 6 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 6 L/h. What dose D in mg gives an average steady-state level of 20 mg/L?

CL = 6 L/hτ = 12 hS = 1F = 1Css,avg = 20 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: C · A patient with a seizure disorder or an eating disorder

Why this is the answer

Bupropion increases the risk of seizures, especially with bulimia or anorexia, where electrolyte disturbances are common. It is used for depression and as a smoking cessation aid.

Answer

C · A patient with a seizure disorder or an eating disorder
2.Pharmacology

Answer: B · Withhold it, recheck the calculation and clarify with the prescriber

Why this is the answer

Doses outside the safe range must be questioned before administration. The nurse holds the dose, rechecks the weight and calculation and contacts the prescriber or pharmacist.

Answer

B · Withhold it, recheck the calculation and clarify with the prescriber
3.Dosage calculations

Answer: D = 600 mg

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

10·60 = 600 mg

Answer

D = 600 mg
4.Dosage calculations

Answer: D = 112 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).

Body surface area

BSA = √(163·77/3600) = √3.486 = 1.867 m²

Dose

D = 60·1.867 = 112 mg

Answer

D = 112 mg
5.Clinical pharmacokinetics

Answer: LD = 544 mcg

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 = 7·68 = 476 L

Amount of active drug needed

Vd·C = 476·0.8 = 380.8 mcg

Loading dose

LD = 380.8/(1·0.7) = 544 mcg

Answer

LD = 544 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: D = 1440 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) = 20·6·12/(1·1) = 1440 mg

Answer

D = 1440 mg

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