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 half the dose and document the pulse
  2. BGive the dose with food to slow absorption
  3. CGive the dose and recheck the pulse in one hour
  4. DWithhold the dose and notify the prescriber
2.PharmacologyHard

A baby born to a mother on methadone becomes irritable on day 2, with a high-pitched cry, tremors, sneezing and poor feeding. What is the most likely cause?

  1. AVitamin K deficiency bleeding
  2. BNormal newborn behaviour
  3. CNeonatal hypoglycaemia from maternal diabetes
  4. DNeonatal opioid withdrawal syndrome
3.Dosage calculationsMedium
80 kg7.5 mg/kgD = ? mg

A patient weighs 80 kg and is prescribed 7.5 mg/kg as a single dose. Find the dose D in mg.

80 kg7.5 mg/kg
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 1720 micrograms. The ampoule contains 4 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

1720 mcg4 mg/mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 12 mg/LR = ? mg/hCL = 0.05 L/kg/h66 kg

Practice exercise (made-up values, not clinical guidance). A 66 kg patient receives a theophylline infusion. The clearance is 0.05 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 12 mg/L?

66 kgCL = 0.05 L/kg/hCss = 12 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
VCss,avg​ = ?1000 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. Each dose is 1000 mg of vancomycin. Find the average steady-state level Css,avg.

CL = 4 L/hτ = 12 hS = 1F = 1D = 1000 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: D · 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

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

Answer: D · Neonatal opioid withdrawal syndrome

Why this is the answer

After birth the baby no longer receives opioid from the mother and develops withdrawal. Assessment uses a scoring tool, with non-drug care first and opioid treatment if signs are severe.

Answer

D · Neonatal opioid withdrawal syndrome
3.Dosage calculations

Answer: D = 600 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.

Dose

7.5·80 = 600 mg

Answer

D = 600 mg
4.Dosage calculations

Answer: V = 0.43 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.

Same units

4 mg/mL = 4000 mcg/mL

Volume

V = 1720/4000 = 0.43 mL

Answer

V = 0.43 mL
5.Clinical pharmacokinetics

Answer: R = 39.6 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 = 0.05·66 = 3.3 L/h

Infusion rate

R = 3.3·12 = 39.6 mg/h

Answer

R = 39.6 mg/h
6.Clinical pharmacokinetics

Answer: Css,avg = 20.83 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.

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 1·1·1000/(4·12) = 20.83 mg/L

Answer

Css,avg = 20.83 mg/L

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