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 drug is the antidote for an opioid overdose?

  1. AFlumazenil
  2. BAcetylcysteine
  3. CNaloxone
  4. DAtropine
2.PharmacologyHard

A patient taking digoxin has nausea, yellow-green vision and a dangerous arrhythmia. Which specific treatment can bind the drug?

  1. AProtamine sulfate
  2. BFlumazenil
  3. CIntravenous vitamin K (phytomenadione) given slowly
  4. DDigoxin immune Fab (antibody fragments)
3.Dosage calculationsMedium
2 g+ 9.2 mLV = ? mL

A vial contains 2 g of powder. The label says: add 9.2 mL of water for injection to give a total volume of 10 mL. The prescription is 240 mg. What volume V of the reconstituted solution do you give?

2 g+ 9.2 mL → 10 mL240 mg
V = mL
4.Dosage calculationsHard
120 mg/5 mLV = ? mL

A child weighing 24 kg is prescribed 5 mg/kg per dose of an oral suspension that contains 120 mg in 5 mL. What volume V do you give?

24 kg5 mg/kg120 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 0.7 L/kgC = 20 mg/LLD = ? mg96 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). A 96 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.

96 kgVd = 0.7 L/kgC = 20 mg/LS = 0.92
LD = mg
6.Clinical pharmacokineticsHard
Vd = 0.25 L/kg0.5 → 6 mg/LD = ? mg98 kg

Practice exercise (made-up values, not clinical guidance). A 98 kg patient on regular tobramycin doses is at steady state. The target is a peak of 6 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.25 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?

98 kgVd = 0.25 L/kgCpeak = 6 mg/LCtrough = 0.5 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: C · Naloxone

Why this is the answer

Naloxone reverses opioid-induced respiratory depression. Flumazenil reverses benzodiazepines, acetylcysteine treats paracetamol overdose and atropine treats bradycardia or organophosphate poisoning.

Answer

C · Naloxone
2.Pharmacology

Answer: D · Digoxin immune Fab (antibody fragments)

Why this is the answer

Digoxin immune Fab binds digoxin in the blood and makes it inactive. It is used for life-threatening toxicity, such as serious arrhythmias or severe hyperkalaemia.

Answer

D · Digoxin immune Fab (antibody fragments)
3.Dosage calculations

Answer: V = 1.2 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.

Concentration after mixing

2000 mg/10 mL = 200 mg/mL

Volume

V = 240/200 = 1.2 mL

Answer

V = 1.2 mL
4.Dosage calculations

Answer: V = 5 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

5·24 = 120 mg

Volume

V = (120/120)·5 = 5 mL

Answer

V = 5 mL
5.Clinical pharmacokinetics

Answer: LD = 1461 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 = 0.7·96 = 67.2 L

Amount of active drug needed

Vd·C = 67.2·20 = 1344 mg

Loading dose

LD = 1344/(0.92·1) = 1461 mg

Answer

LD = 1461 mg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: D = 134.8 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 = 0.25·98 = 24.5 L

Dose

D = 24.5·(6 − 0.5) = 134.8 mg

Answer

D = 134.8 mg

In practice the dose is rounded to a convenient amount.

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