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 assessments are most important during a magnesium sulfate infusion?

  1. ADeep tendon reflexes, respiratory rate and urine output
  2. BBlood glucose, pupil size and pupil reaction to light
  3. CTemperature and skin colour only
  4. DBowel sounds and appetite
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. BSevere hypertension from the combination
  3. CAdditive sedation and respiratory depression
  4. DMethadone causes diazepam to be excreted very quickly
3.Dosage calculationsMedium
024681010 mL

A child weighing 10 kg is prescribed 10 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?

10 kg10 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
120 mg/5 mLV = ? mL

A child weighing 24 kg is prescribed 20 mg/kg per dose of an oral suspension that contains 120 mg in 5 mL. What volume V do you give?

24 kg20 mg/kg120 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
10100t (h)C (mg/L)1 h40 mg/L17 h15.9 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 40 mg/L at 1 h and 15.9 mg/L at 17 h. Assume first-order elimination. Find the elimination rate constant k.

C1 = 40 mg/L (1 h)C2 = 15.9 mg/L (17 h)
k = h⁻¹
6.Clinical pharmacokineticsHard
Vd = 7 L/kg0.4 → 0.8 mcg/LLD = ? mcg55 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 55 kg patient has a digoxin level of 0.4 mcg/L; the target is 0.8 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?

55 kgVd = 7 L/kgC = 0.4 → 0.8 mcg/LF = 0.7
LD = mcg

3Solutions

1.Pharmacology

Answer: A · Deep tendon reflexes, respiratory rate and urine output

Why this is the answer

Loss of reflexes is an early sign of magnesium toxicity, followed by respiratory depression and cardiac arrest. Low urine output allows magnesium to accumulate.

Answer

A · Deep tendon reflexes, respiratory rate and urine output
2.Pharmacology

Answer: C · 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

C · Additive sedation and respiratory depression
3.Dosage calculations

Answer: V = 2 mL

Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.

Dose from body weight

D = 10·10 = 100 mg

Volume

V = 100/50 = 2 mL

On the syringe

On this 10 mL syringe every small line is 0.2 mL.

Answer

V = 2 mL
4.Dosage calculations

Answer: V = 20 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

20·24 = 480 mg

Volume

V = (480/120)·5 = 20 mL

Answer

V = 20 mL
5.Clinical pharmacokinetics

Answer: k = 0.05766 h⁻¹

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.

Elimination rate constant

k = ln(40/15.9)/16 = 0.9226/16 = 0.05766 h⁻¹

Answer

k = 0.05766 h⁻¹
6.Clinical pharmacokinetics

Answer: LD = 220 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 = 7·55 = 385 L

Rise needed

0.8 − 0.4 = 0.4 mcg/L

Loading dose

LD = 385·0.4/(1·0.7) = 220 mcg

Answer

LD = 220 mcg

In practice the dose is rounded to a convenient amount.

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