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

While giving medicines, a patient says, "That pill looks different from the one I usually take." What should the nurse do?

  1. AStop and recheck the order and the medicine before giving it
  2. BGive the pill and check the chart afterwards
  3. CExplain that only the staff decide which medicines are given
  4. DReassure the patient and give the pill anyway
2.PharmacologyHard

Why is sildenafil contraindicated in a patient who uses nitrates for angina?

  1. ABoth raise cGMP in vascular smooth muscle and can cause severe hypotension
  2. BNitrates block the metabolism of sildenafil in the liver
  3. CSildenafil blocks the conversion of nitrates into nitric oxide in the vessels
  4. DThe combination causes dangerous hyperkalaemia
3.Dosage calculationsMedium
024681010 mL

A child weighing 23 kg is prescribed 20 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?

23 kg20 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
31 kg108 cmBSA = √(h·w/3600)100 mg/m²D = ? mg

A patient is 108 cm tall and weighs 31 kg. The prescription is 100 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.

108 cm31 kg100 mg/m²
D = mg
5.Clinical pharmacokineticsMedium
VCss​ = 12 mg/LR = ? mg/h · S = 0.8CL = 0.04 L/kg/h82 kg

Practice exercise (made-up values, not clinical guidance). An 82 kg patient is to receive an aminophylline infusion (salt factor S = 0.8: 80% of aminophylline is theophylline). The theophylline clearance is 0.04 L/kg/h. What aminophylline infusion rate R in mg/h gives a steady-state theophylline level of 12 mg/L?

82 kgCL = 0.04 L/kg/hCss = 12 mg/LS = 0.8
R = mg/h
6.Clinical pharmacokineticsHard
VCss,avg​ = ?300 mg · q12hCL = 0.04 L/kg/h67 kg · S = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A 67 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.04 L/kg/h. Each dose is 300 mg of theophylline. Find the average steady-state level Css,avg.

CL = 0.04 L/kg/hτ = 12 hS = 1F = 167 kgD = 300 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: A · Stop and recheck the order and the medicine before giving it

Why this is the answer

A patient's concern can reveal a wrong drug or wrong patient error. The nurse rechecks the order and product, and may call the pharmacy; a different brand or strength may explain the change.

Answer

A · Stop and recheck the order and the medicine before giving it
2.Pharmacology

Answer: A · Both raise cGMP in vascular smooth muscle and can cause severe hypotension

Why this is the answer

Nitrates increase cGMP production through nitric oxide and sildenafil blocks its breakdown by PDE5. Together they cause excessive vasodilation and a dangerous fall in blood pressure.

Answer

A · Both raise cGMP in vascular smooth muscle and can cause severe hypotension
3.Dosage calculations

Answer: V = 9.2 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 = 20·23 = 460 mg

Volume

V = 460/50 = 9.2 mL

On the syringe

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

Answer

V = 9.2 mL
4.Dosage calculations

Answer: D = 96.44 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).

Body surface area

BSA = √(108·31/3600) = √0.93 = 0.9644 m²

Dose

D = 100·0.9644 = 96.44 mg

Answer

D = 96.44 mg
5.Clinical pharmacokinetics

Answer: R = 49.2 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 = 0.04·82 = 3.28 L/h

Infusion rate

R = CL·Css/S = 3.28·12/0.8 = 49.2 mg/h

Answer

R = 49.2 mg/h
6.Clinical pharmacokinetics

Answer: Css,avg = 9.328 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.

Clearance

CL = 0.04·67 = 2.68 L/h

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 1·1·300/(2.68·12) = 9.328 mg/L

Answer

Css,avg = 9.328 mg/L

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