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 type of diuretic acts on the thick ascending limb of the loop of Henle?

  1. ALoop diuretics such as furosemide
  2. BThiazide diuretics
  3. COsmotic diuretics
  4. DPotassium-sparing diuretics
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 excreted unchanged in the urine without any metabolism
  4. DLorazepam is a stronger anticonvulsant than all other benzodiazepines
3.Dosage calculationsMedium
024681010 mL

A child weighing 24 kg is prescribed 15 mg/kg of a drug. The stock solution contains 40 mg/mL. Draw up the dose: what volume V do you give?

24 kg15 mg/kg40 mg/mL
V = mL
4.Dosage calculationsHard
40k units500 mL? mL/h1000 units/h

An infusion contains 40000 units of a drug in 500 mL. The prescription is 1000 units per hour. At what rate R do you set the pump, in mL/h?

40000 units/500 mL1000 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
VCss​ = 4 mg/LR = ? mg/minCL = 750 mL/min

Practice exercise (made-up values, not clinical guidance). A patient has a lidocaine clearance of 750 mL/min. What infusion rate R in mg/min keeps the steady-state level at 4 mg/L?

CL = 750 mL/minCss = 4 mg/L
R = mg/min
6.Clinical pharmacokineticsHard
VCss,avg​ = ?200 mg · q8hCL = 0.04 L/kg/h75 kg · S = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A 75 kg patient takes oral theophylline (F = 1) every 8 h. The clearance is 0.04 L/kg/h. Each dose is 200 mg of theophylline. Find the average steady-state level Css,avg.

CL = 0.04 L/kg/hτ = 8 hS = 1F = 175 kgD = 200 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: A · Loop diuretics such as furosemide

Why this is the answer

Loop diuretics block the Na⁺/K⁺/2Cl⁻ cotransporter in the thick ascending limb and are the most powerful diuretics.

Answer

A · Loop diuretics such as furosemide
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 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 = 15·24 = 360 mg

Volume

V = 360/40 = 9 mL

On the syringe

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

Answer

V = 9 mL
4.Dosage calculations

Answer: R = 12.5 mL/h

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

40000/500 = 80 units/mL

Pump rate

R = 1000/80 = 12.5 mL/h

Answer

R = 12.5 mL/h
5.Clinical pharmacokinetics

Answer: R = 3 mg/min

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 in L/min

750 mL/min = 0.75 L/min

Infusion rate

R = 0.75·4 = 3 mg/min

Answer

R = 3 mg/min
6.Clinical pharmacokinetics

Answer: Css,avg = 8.333 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 = 0.04·75 = 3 L/h

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 1·1·200/(3·8) = 8.333 mg/L

Answer

Css,avg = 8.333 mg/L

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