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

Benzathine benzylpenicillin (penicillin G benzathine) is ordered. Which route is correct?

  1. ADeep intramuscular only
  2. BIntravenous infusion over 30 minutes
  3. CSubcutaneous in the abdomen
  4. DIntravenous push
2.PharmacologyHard

A breastfeeding mother needs a mild analgesic. Which drug is generally considered compatible with breastfeeding?

  1. ACodeine (as co-codamol)
  2. BAspirin
  3. CParacetamol (acetaminophen)
  4. DPethidine (meperidine)
3.Dosage calculationsMedium
90 kg10 mg/kg/day4× per dayD = ? mg

A patient weighs 90 kg. The prescribed dose is 10 mg/kg per day, given in 4 equal doses. How many milligrams D are given per dose?

90 kg10 mg/kg/day4× per day
D = mg
4.Dosage calculationsHard
125 mg/5 mLV = ? mL

A child weighing 16 kg is prescribed 20 mg/kg per dose of an oral suspension that contains 125 mg in 5 mL. What volume V do you give?

16 kg20 mg/kg125 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 20 mg/LR = ? mg/hCL = 3.5 L/h

Practice exercise (made-up values, not clinical guidance). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 3.5 L/h. What infusion rate R in mg/h gives a steady-state level of 20 mg/L?

CL = 3.5 L/hCss = 20 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
VCss,avg​ = 20 mg/LD = ? mg · q12hCL = 3 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 3 L/h. What dose D in mg gives an average steady-state level of 20 mg/L?

CL = 3 L/hτ = 12 hS = 1F = 1Css,avg = 20 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: A · Deep intramuscular only

Why this is the answer

Benzathine penicillin is a depot suspension given deep IM. Accidental intravenous injection can cause cardiorespiratory arrest and death.

Answer

A · Deep intramuscular only
2.Pharmacology

Answer: C · Paracetamol (acetaminophen)

Why this is the answer

Paracetamol passes into milk in small amounts and is widely regarded as safe. Codeine can cause dangerous opioid levels in babies of ultra-rapid metaboliser mothers, aspirin carries a Reye's risk and pethidine's metabolite accumulates in infants.

Answer

C · Paracetamol (acetaminophen)
3.Dosage calculations

Answer: D = 225 mg

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.

Total per day

10·90 = 900 mg

Per dose

D = 900/4 = 225 mg

Answer

D = 225 mg
4.Dosage calculations

Answer: V = 12.8 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

20·16 = 320 mg

Volume

V = (320/125)·5 = 12.8 mL

Answer

V = 12.8 mL
5.Clinical pharmacokinetics

Answer: R = 70 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.

Infusion rate

R = 3.5·20 = 70 mg/h

Answer

R = 70 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) = 20·3·12/(1·1) = 720 mg

Answer

D = 720 mg

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