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 patient take oral alendronate?

  1. AWith plain water on an empty stomach, staying upright for 30 minutes
  2. BWith breakfast and coffee to protect the stomach
  3. CWith milk at bedtime, then lying down straight away to aid absorption
  4. DCrushed into yoghurt with calcium supplements
2.PharmacologyHard

A drug has a half-life of 6 hours. Its plasma level is 80 mg/L. Assuming first-order elimination and no further doses, what is the level after 18 hours?

  1. A10 mg/L
  2. B26.7 mg/L
  3. C20 mg/L
  4. D40 mg/L
3.Dosage calculationsMedium
12 kg30 mg/kgD = ? mg

A patient weighs 12 kg and is prescribed 30 mg/kg as a single dose. Find the dose D in mg.

12 kg30 mg/kg
D = mg
4.Dosage calculationsHard
40k units250 mL? mL/h1200 units/h

An infusion contains 40000 units of a drug in 250 mL. The prescription is 1200 units per hour. At what rate R do you set the pump, in mL/h?

40000 units/250 mL1200 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)C₀ = 6 mg/Lt½ = 2.5 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 120 mg of tobramycin. The level back-extrapolated to time zero is 6 mg/L and the half-life is 2.5 h. Find the clearance CL in L/h.

D = 120 mgC₀ = 6 mg/Lt½ = 2.5 h
CL = L/h
6.Clinical pharmacokineticsHard
VCss,avg​ = 10 mg/LD = ? mg · q12hCL = 0.05 L/kg/h85 kg · S = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). An 85 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.05 L/kg/h. What dose D in mg gives an average steady-state level of 10 mg/L?

CL = 0.05 L/kg/hτ = 12 hS = 1F = 185 kgCss,avg = 10 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: A · With plain water on an empty stomach, staying upright for 30 minutes

Why this is the answer

Alendronate is taken first thing in the morning with water only, before food or other drugs. Staying upright reduces the risk of oesophageal ulceration, and food or calcium blocks its absorption.

Answer

A · With plain water on an empty stomach, staying upright for 30 minutes
2.Pharmacology

Answer: A · 10 mg/L

Why this is the answer

18 hours is three half-lives. The level halves three times: 80 → 40 → 20 → 10 mg/L.

Answer

A · 10 mg/L
3.Dosage calculations

Answer: D = 360 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

30·12 = 360 mg

Answer

D = 360 mg
4.Dosage calculations

Answer: R = 7.5 mL/h

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.

Concentration

40000/250 = 160 units/mL

Pump rate

R = 1200/160 = 7.5 mL/h

Answer

R = 7.5 mL/h
5.Clinical pharmacokinetics

Answer: CL = 5.545 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 = 120/6 = 20 L

Rate constant

k = 0.693/2.5 = 0.2773 h⁻¹

Clearance

CL = 0.2773·20 = 5.545 L/h

Answer

CL = 5.545 L/h
6.Clinical pharmacokinetics

Answer: D = 510 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.

Clearance

CL = 0.05·85 = 4.25 L/h

Dose

D = Css,avg·CL·τ/(S·F) = 10·4.25·12/(1·1) = 510 mg

Answer

D = 510 mg

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