Pharmacology: cram pack

Formula sheets, the key method steps for every topic and 6 practice problems, with full solutions at the back.

New problemsBack to the course

In the print window, choose “Save as PDF” to keep a copy on your device.

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. BTake it on an empty stomach with an antacid
  3. CTake it with food, and the urine may turn dark yellow or brown
  4. DExpect blue urine, which shows that the drug is working well
2.PharmacologyHard

A patient taking warfarin asks for something for a headache. Which drug is usually the safest choice?

  1. AAspirin
  2. BIbuprofen, at the lowest dose
  3. CParacetamol (acetaminophen)
  4. DNaproxen
3.Dosage calculationsMedium
16 kgBSA = 0.81 m²20 mg/m²D = ? mg

A patient weighing 16 kg has a body surface area of 0.81 m². The prescription is 20 mg/m². Find the dose D in mg.

16 kgBSA = 0.81 m²20 mg/m²
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 540 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

540 units1000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 25 mg/LR = ? mg/hCL = 4.5 L/h

Practice exercise (made-up values, not clinical guidance). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 4.5 L/h. What infusion rate R in mg/h gives a steady-state level of 25 mg/L?

CL = 4.5 L/hCss = 25 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
Vd = 0.5 L/kg3.6 → 12 mg/LLD = ? mg83 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). An 83 kg patient has a theophylline level of 3.6 mg/L; the target is 12 mg/L. The drug is given intravenously as aminophylline (S = 0.8), and the volume of distribution is 0.5 L/kg. What extra loading dose LD raises the level to the target?

83 kgVd = 0.5 L/kgC = 3.6 → 12 mg/LS = 0.8
LD = mg

3Solutions

1.Pharmacology

Answer: C · 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

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

Answer: C · Paracetamol (acetaminophen)

Why this is the answer

NSAIDs and aspirin impair platelet function and can cause GI bleeding, which adds to warfarin's bleeding risk. Paracetamol is usually preferred, though regular high doses can raise the INR.

Answer

C · Paracetamol (acetaminophen)
3.Dosage calculations

Answer: D = 16.2 mg

Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).

Dose

D = 20·0.81 = 16.2 mg

Answer

D = 16.2 mg
4.Dosage calculations

Answer: V = 0.54 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.

Volume

V = 540/1000 = 0.54 mL

On the syringe

On this 1 mL syringe every small line is 0.01 mL.

Answer

V = 0.54 mL
5.Clinical pharmacokinetics

Answer: R = 112.5 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.

Infusion rate

R = 4.5·25 = 112.5 mg/h

Answer

R = 112.5 mg/h
6.Clinical pharmacokinetics

Answer: LD = 435.8 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 = 0.5·83 = 41.5 L

Rise needed

12 − 3.6 = 8.4 mg/L

Loading dose

LD = 41.5·8.4/(0.8·1) = 435.8 mg

Answer

LD = 435.8 mg

In practice the dose is rounded to a convenient amount.

ExamProblems · examproblems.com/courses/pharmacology