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

Why are benzodiazepines used with great caution in older people?

  1. AThey cause severe high blood pressure in older people
  2. BThey raise the risk of confusion, falls and fractures
  3. CThey cause permanent hearing loss in older people
  4. DThey are not absorbed from the gut after age 65
2.PharmacologyHard

Which pair of adverse effects is characteristic of long-term amiodarone treatment?

  1. AOtotoxicity and nephrotoxicity
  2. BGum overgrowth and excess hair growth
  3. CThyroid dysfunction and pulmonary fibrosis
  4. DDry cough and angioedema
3.Dosage calculationsMedium
024681010 mL

A child weighing 6 kg is prescribed 15 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?

6 kg15 mg/kg10 mg/mL
V = mL
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 1100 units of a drug that comes as 5000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

1100 units5000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 10 mg/LR = ? mg/hCL = 0.035 L/kg/h73 kg

Practice exercise (made-up values, not clinical guidance). A 73 kg patient receives a theophylline infusion. The clearance is 0.035 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 10 mg/L?

73 kgCL = 0.035 L/kg/hCss = 10 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
77 kg50 · manSCr 1.6 mg/dLCrCl → D = ? mg

Practice exercise (made-up values, not clinical guidance). A 50-year-old man weighs 77 kg and has a serum creatinine of 1.6 mg/dL (141 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual cefazolin dose is 1000 mg every 8 h for a creatinine clearance of 100 mL/min. Keeping the interval, the dose is reduced in proportion to the creatinine clearance. Find the adjusted dose D. Round to the nearest whole number.

50 years77 kgmanSCr = 1.6 mg/dL1000 mg q8hCrCl normal 100 mL/min
D = mg

3Solutions

1.Pharmacology

Answer: B · They raise the risk of confusion, falls and fractures

Why this is the answer

Older people are more sensitive to benzodiazepines and often eliminate them more slowly. Sedation, unsteadiness and confusion raise the risk of falls and fractures.

Answer

B · They raise the risk of confusion, falls and fractures
2.Pharmacology

Answer: C · Thyroid dysfunction and pulmonary fibrosis

Why this is the answer

Amiodarone is iodine-rich and accumulates in tissues, causing hypo- or hyperthyroidism, pulmonary fibrosis, liver injury, photosensitivity and corneal deposits. The other pairs fit aminoglycosides, phenytoin and ACE inhibitors.

Answer

C · Thyroid dysfunction and pulmonary fibrosis
3.Dosage calculations

Answer: V = 9 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 = 15·6 = 90 mg

Volume

V = 90/10 = 9 mL

On the syringe

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

Answer

V = 9 mL
4.Dosage calculations

Answer: V = 0.22 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 = 1100/5000 = 0.22 mL

On the syringe

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

Answer

V = 0.22 mL
5.Clinical pharmacokinetics

Answer: R = 25.55 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 = 0.035·73 = 2.555 L/h

Infusion rate

R = 2.555·10 = 25.55 mg/h

Answer

R = 25.55 mg/h
6.Clinical pharmacokinetics

Answer: D = 602 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.

Creatinine clearance (Cockcroft–Gault)

CrCl = (140 − 50)·77/(72·1.6) = 60.16 mL/min

Adjusted dose

D = 1000·60.16/100 = 601.6 ≈ 602 mg

Answer

D = 602 mg

In practice the dose is rounded to a convenient amount and checked against the product information.

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