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

A patient starting niacin (nicotinic acid) complains of flushing and warmth after doses. Which advice may reduce this?

  1. ADouble the dose to build tolerance faster
  2. BTake the niacin with a hot drink so that it dissolves and acts faster
  3. CTake aspirin 30 minutes before the niacin, if the prescriber agrees
  4. DTake it on an empty stomach in a hot bath
2.PharmacologyHard

A patient who takes propranolol has anaphylaxis and does not respond to repeated adrenaline doses. Which drug may help?

  1. AOral cetirizine alone
  2. BNaloxone
  3. CMore propranolol
  4. DGlucagon
3.Dosage calculationsMedium
22 kg10 mg/kgD = ? mg

A patient weighs 22 kg and is prescribed 10 mg/kg as a single dose. Find the dose D in mg.

22 kg10 mg/kg
D = mg
4.Dosage calculationsHard
24 kg100 cmBSA = √(h·w/3600)175 mg/m²D = ? mg

A patient is 100 cm tall and weighs 24 kg. The prescription is 175 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.

100 cm24 kg175 mg/m²
D = mg
5.Clinical pharmacokineticsMedium
VCss​ = 10 mg/LR = ? mg/hCL = 0.04 L/kg/h51 kg

Practice exercise (made-up values, not clinical guidance). A 51 kg patient receives a theophylline infusion. The clearance is 0.04 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 10 mg/L?

51 kgCL = 0.04 L/kg/hCss = 10 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
VCss,avg​ = ?450 mg · q8hCL = 0.04 L/kg/h91 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). A 91 kg patient takes oral aminophylline (S = 0.8, F = 1) every 8 h. The theophylline clearance is 0.04 L/kg/h. Each dose is 450 mg of aminophylline. Find the average steady-state level Css,avg.

CL = 0.04 L/kg/hτ = 8 hS = 0.8F = 191 kgD = 450 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: C · Take aspirin 30 minutes before the niacin, if the prescriber agrees

Why this is the answer

Niacin causes prostaglandin-mediated vasodilation and flushing. Aspirin beforehand, taking it with food and avoiding hot drinks and alcohol reduce this effect.

Answer

C · Take aspirin 30 minutes before the niacin, if the prescriber agrees
2.Pharmacology

Answer: D · Glucagon

Why this is the answer

Beta blockers can make anaphylaxis more severe and resistant to adrenaline. Glucagon acts through its own receptor to increase heart rate and contractility, bypassing the blocked beta receptors.

Answer

D · Glucagon
3.Dosage calculations

Answer: D = 220 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

10·22 = 220 mg

Answer

D = 220 mg
4.Dosage calculations

Answer: D = 142.9 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 = √(100·24/3600) = √0.6667 = 0.8165 m²

Dose

D = 175·0.8165 = 142.9 mg

Answer

D = 142.9 mg
5.Clinical pharmacokinetics

Answer: R = 20.4 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 = 0.04·51 = 2.04 L/h

Infusion rate

R = 2.04·10 = 20.4 mg/h

Answer

R = 20.4 mg/h
6.Clinical pharmacokinetics

Answer: Css,avg = 12.36 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 = 0.04·91 = 3.64 L/h

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 0.8·1·450/(3.64·8) = 12.36 mg/L

Answer

Css,avg = 12.36 mg/L

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