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

When should a patient take a once-daily proton pump inhibitor such as omeprazole?

  1. AAbout 30–60 minutes before the first meal of the day
  2. BWith a glass of milk at bedtime, when acid output is highest
  3. CStraight after a large evening meal
  4. DOnly when heartburn is severe
2.PharmacologyHard

A patient with severe liver cirrhosis needs a benzodiazepine for alcohol withdrawal. Why is lorazepam often chosen instead of diazepam?

  1. ALorazepam is cleared by simple conjugation and has no active metabolites
  2. BLorazepam does not cause sedation in liver disease
  3. CLorazepam is a stronger anticonvulsant than all other benzodiazepines
  4. DLorazepam is excreted unchanged in the urine without any metabolism
3.Dosage calculationsMedium
024681010 mL

A child weighing 16 kg is prescribed 15 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?

16 kg15 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
100 mg/5 mLV = ? mL

A child weighing 18 kg is prescribed 20 mg/kg per dose of an oral suspension that contains 100 mg in 5 mL. What volume V do you give?

18 kg20 mg/kg100 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)1 h7 mg/L5 h2.8 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 7 mg/L at 1 h and 2.8 mg/L at 5 h. Assume first-order elimination. Find the half-life t½.

C1 = 7 mg/L (1 h)C2 = 2.8 mg/L (5 h)
t½ = h
6.Clinical pharmacokineticsHard
94 kg61 · womanSCr 2.8 mg/dLfe​ = 0.7D = ? mcg

Practice exercise (made-up values, not clinical guidance). A 61-year-old woman weighs 94 kg and has a serum creatinine of 2.8 mg/dL (248 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual digoxin dose is 250 mcg for a creatinine clearance of 120 mL/min, and a fraction fe = 0.7 of the drug is excreted unchanged by the kidneys. Using the Dettli dose fraction Q = 1 − fe·(1 − CrCl/normal CrCl), find the adjusted dose D. Round to the nearest whole number.

61 years94 kgwomanSCr = 2.8 mg/dL250 mcgfe = 0.7CrCl normal 120 mL/min
D = mcg

3Solutions

1.Pharmacology

Answer: A · About 30–60 minutes before the first meal of the day

Why this is the answer

Proton pump inhibitors block pumps that are active, so they work best when taken before breakfast. Food then activates the pumps when the drug level is high.

Answer

A · About 30–60 minutes before the first meal of the day
2.Pharmacology

Answer: A · Lorazepam is cleared by simple conjugation and has no active metabolites

Why this is the answer

Diazepam is metabolised by CYP enzymes into long-acting active metabolites, which accumulate in liver failure. Lorazepam, oxazepam and temazepam are glucuronidated, a process better preserved in liver disease.

Answer

A · Lorazepam is cleared by simple conjugation and has no active metabolites
3.Dosage calculations

Answer: V = 9.6 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 = 15·16 = 240 mg

Volume

V = 240/25 = 9.6 mL

On the syringe

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

Answer

V = 9.6 mL
4.Dosage calculations

Answer: V = 18 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

20·18 = 360 mg

Volume

V = (360/100)·5 = 18 mL

Answer

V = 18 mL
5.Clinical pharmacokinetics

Answer: t½ = 3.026 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.

Elimination rate constant

k = ln(7/2.8)/4 = 0.9163/4 = 0.2291 h⁻¹

Half-life

t½ = 0.693/0.2291 = 3.026 h

Answer

t½ = 3.026 h
6.Clinical pharmacokinetics

Answer: D = 121 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.

Creatinine clearance (Cockcroft–Gault)

CrCl = (140 − 61)·94/(72·2.8)·0.85 = 31.31 mL/min

Dose fraction (Dettli)

Q = 1 − 0.7·(1 − 31.31/120) = 0.4826

Adjusted dose

D = 0.4826·250 = 120.7 ≈ 121 mcg

Answer

D = 121 mcg

In practice the dose is rounded to a convenient amount and checked against the product information.

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