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 approach is usually recommended to prevent constipation in a patient on regular opioids?

  1. AA stimulant laxative such as senna, often with a stool softener
  2. BAn antidiarrhoeal drug at night to slow the gut
  3. CBulk-forming fibre alone, with fluid intake restricted
  4. DNo laxative until the patient has not opened the bowels for a week
2.PharmacologyHard

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

  1. ASevere hypertension from the combination
  2. BAdditive sedation and respiratory depression
  3. CDiazepam blocks the effect of methadone completely
  4. DMethadone causes diazepam to be excreted very quickly
3.Dosage calculationsMedium
80 kg10 mg/kgD = ? mg

A patient weighs 80 kg and is prescribed 10 mg/kg as a single dose. Find the dose D in mg.

80 kg10 mg/kg
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 310 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

310 units1000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 1 mcg/LLD = ? mcg63 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 63 kg patient is to be loaded with digoxin tablets to reach a level of 1 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.

63 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
Vd = 0.7 L/kg12 → 20 mg/LLD = ? mg96 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). A 96 kg patient has a phenytoin level of 12 mg/L; the target is 20 mg/L. The drug is given intravenously as phenytoin sodium (S = 0.92), and the volume of distribution is 0.7 L/kg. What extra loading dose LD raises the level to the target?

96 kgVd = 0.7 L/kgC = 12 → 20 mg/LS = 0.92
LD = mg

3Solutions

1.Pharmacology

Answer: A · A stimulant laxative such as senna, often with a stool softener

Why this is the answer

Opioid-induced constipation does not usually resolve with time, so a laxative is started with the opioid. Stimulant laxatives counter reduced motility; bulk-forming laxatives alone can worsen symptoms if fluid intake is low.

Answer

A · A stimulant laxative such as senna, often with a stool softener
2.Pharmacology

Answer: B · 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

B · Additive sedation and respiratory depression
3.Dosage calculations

Answer: D = 800 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

10·80 = 800 mg

Answer

D = 800 mg
4.Dosage calculations

Answer: V = 0.31 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.

Volume

V = 310/1000 = 0.31 mL

On the syringe

On this 1 mL syringe every small line is 0.01 mL.

Answer

V = 0.31 mL
5.Clinical pharmacokinetics

Answer: LD = 630 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 = 7·63 = 441 L

Amount of active drug needed

Vd·C = 441·1 = 441 mcg

Loading dose

LD = 441/(1·0.7) = 630 mcg

Answer

LD = 630 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: LD = 584.3 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 = 0.7·96 = 67.2 L

Rise needed

20 − 12 = 8 mg/L

Loading dose

LD = 67.2·8/(0.92·1) = 584.3 mg

Answer

LD = 584.3 mg

In practice the dose is rounded to a convenient amount.

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