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

An adult patient is due to receive digoxin. The apical pulse, counted for a full minute, is 52 beats per minute. What should the nurse do?

  1. AGive the dose with food to slow absorption
  2. BWithhold the dose and notify the prescriber
  3. CGive the dose and recheck the pulse in one hour
  4. DGive half the dose and document the pulse
2.PharmacologyHard

Some receptors show activity even without an agonist. How does an inverse agonist differ from a neutral antagonist at such receptors?

  1. AIt increases activity above the baseline
  2. BIt has no effect when given alone
  3. CIt destroys the receptor permanently
  4. DIt reduces activity below the baseline level
3.Dosage calculationsMedium
024681010 mL

A child weighing 6 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?

6 kg10 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
50k units250 mL? mL/h1200 units/h

An infusion contains 50000 units of a drug in 250 mL. The prescription is 1200 units per hour. At what rate R do you set the pump, in mL/h?

50000 units/250 mL1200 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)1 h10 mg/L5 h3.3 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 10 mg/L at 1 h and 3.3 mg/L at 5 h. Assume first-order elimination. Find the half-life t½.

C1 = 10 mg/L (1 h)C2 = 3.3 mg/L (5 h)
t½ = h
6.Clinical pharmacokineticsHard
Vd = 0.3 L/kg1 → 10 mg/LD = ? mg96 kg

Practice exercise (made-up values, not clinical guidance). A 96 kg patient on regular gentamicin doses is at steady state. The target is a peak of 10 mg/L and a trough of 1 mg/L, and the volume of distribution is 0.3 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?

96 kgVd = 0.3 L/kgCpeak = 10 mg/LCtrough = 1 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: B · Withhold the dose and notify the prescriber

Why this is the answer

Digoxin is usually withheld in adults if the apical pulse is below 60 per minute, and the prescriber is informed. Bradycardia may be an early sign of toxicity.

Answer

B · Withhold the dose and notify the prescriber
2.Pharmacology

Answer: D · It reduces activity below the baseline level

Why this is the answer

A neutral antagonist simply blocks agonists and leaves baseline activity unchanged. An inverse agonist stabilises the inactive receptor state, so constitutive activity falls below baseline.

Answer

D · It reduces activity below the baseline level
3.Dosage calculations

Answer: V = 1.2 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 = 10·6 = 60 mg

Volume

V = 60/50 = 1.2 mL

On the syringe

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

Answer

V = 1.2 mL
4.Dosage calculations

Answer: R = 6 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

50000/250 = 200 units/mL

Pump rate

R = 1200/200 = 6 mL/h

Answer

R = 6 mL/h
5.Clinical pharmacokinetics

Answer: t½ = 2.501 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(10/3.3)/4 = 1.109/4 = 0.2772 h⁻¹

Half-life

t½ = 0.693/0.2772 = 2.501 h

Answer

t½ = 2.501 h
6.Clinical pharmacokinetics

Answer: D = 259.2 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 = 0.3·96 = 28.8 L

Dose

D = 28.8·(10 − 1) = 259.2 mg

Answer

D = 259.2 mg

In practice the dose is rounded to a convenient amount.

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