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

Which common side effect is typical of ACE inhibitors?

  1. ABradycardia
  2. BHypoglycaemia
  3. CAnkle swelling caused by vasodilation
  4. DDry cough
2.PharmacologyHard

Why is adenosine used with caution in patients with asthma?

  1. AIt can cause bronchospasm
  2. BIt causes severe hypertension in asthma
  3. CIt reduces the effect of inhaled steroids
  4. DIt is broken down too slowly in asthma
3.Dosage calculationsMedium
13 kgBSA = 0.64 m²375 mg/m²D = ? mg

A patient weighing 13 kg has a body surface area of 0.64 m². The prescription is 375 mg/m². Find the dose D in mg.

13 kgBSA = 0.64 m²375 mg/m²
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 325 micrograms. The ampoule contains 0.5 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

325 mcg0.5 mg/mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 0.8 mcg/LLD = ? mcg69 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 69 kg patient is to be loaded with digoxin tablets to reach a level of 0.8 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.

69 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
t (h)C (mg/L)Css​t = ?90%

Practice exercise (made-up values, not clinical guidance). A theophylline infusion is started without a loading dose. The half-life in this patient is 8 h. How long t does it take to reach 90% of the steady-state level?

t½ = 8 h90% Css
t = h

3Solutions

1.Pharmacology

Answer: D · Dry cough

Why this is the answer

ACE also breaks down bradykinin. When it is inhibited, bradykinin accumulates in the airways and causes a persistent dry cough in some patients.

Answer

D · Dry cough
2.Pharmacology

Answer: A · It can cause bronchospasm

Why this is the answer

Adenosine can trigger bronchospasm in people with asthma or COPD. Other treatment options, such as verapamil, may be chosen.

Answer

A · It can cause bronchospasm
3.Dosage calculations

Answer: D = 240 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 = 375·0.64 = 240 mg

Answer

D = 240 mg
4.Dosage calculations

Answer: V = 0.65 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

0.5 mg/mL = 500 mcg/mL

Volume

V = 325/500 = 0.65 mL

Answer

V = 0.65 mL
5.Clinical pharmacokinetics

Answer: LD = 552 mcg

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.

Volume of distribution

Vd = 7·69 = 483 L

Amount of active drug needed

Vd·C = 483·0.8 = 386.4 mcg

Loading dose

LD = 386.4/(1·0.7) = 552 mcg

Answer

LD = 552 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: t = 26.58 h

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.

Rate constant

k = 0.693/8 = 0.08664 h⁻¹

Time to the given fraction of steady state

t = −ln(1 − 0.9)/0.08664 = 2.303/0.08664 = 26.58 h

Answer

t = 26.58 h

That is 3.322 half-lives.

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