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

A patient wants to stop paroxetine suddenly. What should the nurse explain?

  1. AStopping suddenly causes the drug to work better for a while
  2. BStopping suddenly causes dangerous low blood sugar
  3. CIt can be stopped at any time, as antidepressants cause no withdrawal effects
  4. DIt can cause dizziness, "electric shock" feelings and irritability
2.PharmacologyHard

A patient on methadone is also prescribed diazepam for anxiety. What is the main safety concern?

  1. ADiazepam blocks the effect of methadone completely
  2. BMethadone causes diazepam to be excreted very quickly
  3. CSevere hypertension from the combination
  4. DAdditive sedation and respiratory depression
3.Dosage calculationsMedium
22 kg20 mg/kgD = ? mg

A patient weighs 22 kg and is prescribed 20 mg/kg as a single dose. Find the dose D in mg.

22 kg20 mg/kg
D = mg
4.Dosage calculationsHard
100 mg/5 mLV = ? mL

A child weighing 8 kg is prescribed 15 mg/kg per dose of an oral suspension that contains 100 mg in 5 mL. What volume V do you give?

8 kg15 mg/kg100 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 15 mg/LR = ? mg/hCL = 0.03 L/kg/h61 kg

Practice exercise (made-up values, not clinical guidance). A 61 kg patient receives a theophylline infusion. The clearance is 0.03 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 15 mg/L?

61 kgCL = 0.03 L/kg/hCss = 15 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
VCss,avg​ = ?400 mg · q8hCL = 0.04 L/kg/h82 kg · S = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). An 82 kg patient takes oral theophylline (F = 1) every 8 h. The clearance is 0.04 L/kg/h. Each dose is 400 mg of theophylline. Find the average steady-state level Css,avg.

CL = 0.04 L/kg/hτ = 8 hS = 1F = 182 kgD = 400 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: D · It can cause dizziness, "electric shock" feelings and irritability

Why this is the answer

Antidepressant discontinuation syndrome is common with short half-life drugs such as paroxetine and venlafaxine. The dose is tapered gradually under supervision.

Answer

D · It can cause dizziness, "electric shock" feelings and irritability
2.Pharmacology

Answer: D · Additive sedation and respiratory depression

Why this is the answer

Combining opioids with benzodiazepines greatly increases the risk of sedation, respiratory depression and death. If both are needed, the lowest doses are used and the patient is monitored closely.

Answer

D · Additive sedation and respiratory depression
3.Dosage calculations

Answer: D = 440 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

20·22 = 440 mg

Answer

D = 440 mg
4.Dosage calculations

Answer: V = 6 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

15·8 = 120 mg

Volume

V = (120/100)·5 = 6 mL

Answer

V = 6 mL
5.Clinical pharmacokinetics

Answer: R = 27.45 mg/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.

Clearance

CL = 0.03·61 = 1.83 L/h

Infusion rate

R = 1.83·15 = 27.45 mg/h

Answer

R = 27.45 mg/h
6.Clinical pharmacokinetics

Answer: Css,avg = 15.24 mg/L

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 = 0.04·82 = 3.28 L/h

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 1·1·400/(3.28·8) = 15.24 mg/L

Answer

Css,avg = 15.24 mg/L

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