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

What should the nurse teach a patient starting nitrofurantoin?

  1. AStop it as soon as the burning settles
  2. BExpect blue urine, which shows that the drug is working well
  3. CTake it on an empty stomach with an antacid
  4. DTake it with food, and the urine may turn dark yellow or brown
2.PharmacologyHard

On admission, a patient's home medicine list includes warfarin for atrial fibrillation, but warfarin is not on the admission orders. What should the nurse do?

  1. AClarify the omission with the prescriber (medication reconciliation)
  2. BAssume the omission is intended and do nothing
  3. CGive the patient's own warfarin brought from home without an order
  4. DTell the patient to stop warfarin permanently
3.Dosage calculationsMedium
60 kg2 mg/kgD = ? mg

A patient weighs 60 kg and is prescribed 2 mg/kg as a single dose. Find the dose D in mg.

60 kg2 mg/kg
D = mg
4.Dosage calculationsHard
120 mg/5 mLV = ? mL

A child weighing 14 kg is prescribed 20 mg/kg per dose of an oral suspension that contains 120 mg in 5 mL. What volume V do you give? Round to one decimal place.

14 kg20 mg/kg120 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
0.1110100t (h)C (mg/L)2 h9 mg/L8 h1.1 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 9 mg/L at 2 h and 1.1 mg/L at 8 h. Assume first-order elimination. Find the elimination rate constant k.

C1 = 9 mg/L (2 h)C2 = 1.1 mg/L (8 h)
k = h⁻¹
6.Clinical pharmacokineticsHard
Vd = 0.7 L/kg4.5 → 15 mg/LLD = ? mg54 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). A 54 kg patient has a phenytoin level of 4.5 mg/L; the target is 15 mg/L. The drug is given intravenously as phenytoin sodium (S = 0.92), and the volume of distribution is 0.7 L/kg. What extra loading dose LD raises the level to the target?

54 kgVd = 0.7 L/kgC = 4.5 → 15 mg/LS = 0.92
LD = mg

3Solutions

1.Pharmacology

Answer: D · Take it with food, and the urine may turn dark yellow or brown

Why this is the answer

Nitrofurantoin is taken with food to reduce nausea and can harmlessly darken the urine. The full course is completed, and cough, breathlessness or numbness should be reported.

Answer

D · Take it with food, and the urine may turn dark yellow or brown
2.Pharmacology

Answer: A · Clarify the omission with the prescriber (medication reconciliation)

Why this is the answer

Medication reconciliation compares the patient's home medicines with current orders to find omissions, duplications and errors. The nurse raises the difference with the prescriber, who decides whether to continue, hold or change the drug.

Answer

A · Clarify the omission with the prescriber (medication reconciliation)
3.Dosage calculations

Answer: D = 120 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

2·60 = 120 mg

Answer

D = 120 mg
4.Dosage calculations

Answer: V = 11.7 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

20·14 = 280 mg

Volume

V = (280/120)·5 = 11.67 ≈ 11.7 mL

Answer

V = 11.7 mL
5.Clinical pharmacokinetics

Answer: k = 0.3503 h⁻¹

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(9/1.1)/6 = 2.102/6 = 0.3503 h⁻¹

Answer

k = 0.3503 h⁻¹
6.Clinical pharmacokinetics

Answer: LD = 431.4 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 = 0.7·54 = 37.8 L

Rise needed

15 − 4.5 = 10.5 mg/L

Loading dose

LD = 37.8·10.5/(0.92·1) = 431.4 mg

Answer

LD = 431.4 mg

In practice the dose is rounded to a convenient amount.

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