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

How does glyceryl trinitrate (GTN) relieve angina?

  1. AIt increases the force of contraction so the heart pumps blood more efficiently
  2. BIt dissolves the clot in the coronary artery
  3. CIt releases nitric oxide, mainly dilating veins and reducing cardiac workload
  4. DIt blocks beta-1 receptors and slows the heart
2.PharmacologyHard

Beta-lactam antibiotics show time-dependent killing. What does this mean for administration?

  1. AA single very large daily dose works best
  2. BDoses should be given only when the patient has a fever
  3. CDoses should be given on time at evenly spaced intervals
  4. DDoses can be given at any time as long as the daily total is right
3.Dosage calculationsMedium
1:1000ampouleV = ? mL

An ampoule of epinephrine (adrenaline) is labelled 1:1000 (1 mg/mL). The prescription is 0.5 mg IM for anaphylaxis. What volume V do you draw up?

1:10000.5 mg
V = mL
4.Dosage calculationsHard
250 mg/5 mLV = ? mL

A child weighing 10 kg is prescribed 5 mg/kg per dose of an oral suspension that contains 250 mg in 5 mL. What volume V do you give?

10 kg5 mg/kg250 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)C₀ = 8 mg/Lt½ = 2.5 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 170 mg of tobramycin. The level back-extrapolated to time zero is 8 mg/L and the half-life is 2.5 h. Find the volume of distribution Vd.

D = 170 mgC₀ = 8 mg/Lt½ = 2.5 h
Vd = L
6.Clinical pharmacokineticsHard
Vd = 0.25 L/kg0.5 → 7 mg/LD = ? mg83 kg

Practice exercise (made-up values, not clinical guidance). An 83 kg patient on regular tobramycin doses is at steady state. The target is a peak of 7 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.25 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?

83 kgVd = 0.25 L/kgCpeak = 7 mg/LCtrough = 0.5 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: C · It releases nitric oxide, mainly dilating veins and reducing cardiac workload

Why this is the answer

GTN is converted to nitric oxide, which relaxes vascular smooth muscle through cGMP. Venodilation lowers preload, so the heart works less and needs less oxygen.

Answer

C · It releases nitric oxide, mainly dilating veins and reducing cardiac workload
2.Pharmacology

Answer: C · Doses should be given on time at evenly spaced intervals

Why this is the answer

For beta-lactams, efficacy depends on the time the drug level stays above the minimum inhibitory concentration. Evenly spaced, on-time doses, or extended infusions, support this.

Answer

C · Doses should be given on time at evenly spaced intervals
3.Dosage calculations

Answer: V = 0.5 mL

Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.

Concentration

1:1000 = 1 g/1000 mL = 1 mg/mL

Volume

V = 0.5/1 = 0.5 mL

Answer

V = 0.5 mL

US labels now state mg/mL (1 mg/mL = 1:1000; 0.1 mg/mL = 1:10 000). Never give 1 mg/mL epinephrine IV push.

4.Dosage calculations

Answer: V = 1 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

5·10 = 50 mg

Volume

V = (50/250)·5 = 1 mL

Answer

V = 1 mL
5.Clinical pharmacokinetics

Answer: Vd = 21.25 L

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 = 170/8 = 21.25 L

Answer

Vd = 21.25 L
6.Clinical pharmacokinetics

Answer: D = 134.9 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 = 0.25·83 = 20.75 L

Dose

D = 20.75·(7 − 0.5) = 134.9 mg

Answer

D = 134.9 mg

In practice the dose is rounded to a convenient amount.

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