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 advice helps reduce the most common side effect of varenicline?

  1. ATake it with alcohol to reduce nausea
  2. BTake it on an empty stomach at bedtime with a little milk
  3. CTake double doses in the first week
  4. DTake it after food with a full glass of water
2.PharmacologyHard

A patient receiving a phenylephrine infusion has a rise in blood pressure and a fall in heart rate. What is the best explanation?

  1. APhenylephrine stimulates muscarinic receptors
  2. BPhenylephrine directly blocks beta-1 receptors in the heart's conduction system
  3. CAlpha-1 vasoconstriction raises blood pressure and causes reflex bradycardia
  4. DThe fall in heart rate shows phenylephrine toxicity of the AV node
3.Dosage calculationsMedium
024681010 mL

A child weighing 38 kg is prescribed 5 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?

38 kg5 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
125 mg/5 mLV = ? mL

A patient weighs 125.4 lb. The prescription is 2 mg/kg as a single dose, and the stock contains 125 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to one decimal place.

125.4 lb2 mg/kg125 mg/5 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 15 mg/LR = ? mg/hCL = 0.045 L/kg/h60 kg

Practice exercise (made-up values, not clinical guidance). A 60 kg patient receives a theophylline infusion. The clearance is 0.045 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 15 mg/L?

60 kgCL = 0.045 L/kg/hCss = 15 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
VCss,avg​ = 15 mg/LD = ? mg · q12hCL = 4 L/hS = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 4 L/h. What dose D in mg gives an average steady-state level of 15 mg/L?

CL = 4 L/hτ = 12 hS = 1F = 1Css,avg = 15 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: D · Take it after food with a full glass of water

Why this is the answer

Nausea is the most common adverse effect of varenicline and is reduced by taking it after food with water. Patients should also report changes in mood or behaviour.

Answer

D · Take it after food with a full glass of water
2.Pharmacology

Answer: C · Alpha-1 vasoconstriction raises blood pressure and causes reflex bradycardia

Why this is the answer

Phenylephrine is a pure alpha-1 agonist with little direct cardiac action. The higher blood pressure activates baroreceptors, which increase vagal tone and slow the heart.

Answer

C · Alpha-1 vasoconstriction raises blood pressure and causes reflex bradycardia
3.Dosage calculations

Answer: V = 3.8 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 = 5·38 = 190 mg

Volume

V = 190/50 = 3.8 mL

On the syringe

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

Answer

V = 3.8 mL
4.Dosage calculations

Answer: V = 4.6 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.

Weight in kg

125.4/2.2 = 57 kg

Dose

2·57 = 114 mg

Volume

V = (114/125)·5 = 4.56 ≈ 4.6 mL

Answer

V = 4.6 mL
5.Clinical pharmacokinetics

Answer: R = 40.5 mg/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.

Clearance

CL = 0.045·60 = 2.7 L/h

Infusion rate

R = 2.7·15 = 40.5 mg/h

Answer

R = 40.5 mg/h
6.Clinical pharmacokinetics

Answer: D = 720 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.

Dose

D = Css,avg·CL·τ/(S·F) = 15·4·12/(1·1) = 720 mg

Answer

D = 720 mg

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