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 technique is correct when giving subcutaneous enoxaparin from a prefilled syringe?

  1. AExpel the air bubble from the syringe first, then inject into the deltoid muscle
  2. BInject into the abdomen away from the navel and do not rub the site afterwards
  3. CInject into a vein on the back of the hand
  4. DMassage the site well for one minute after the injection
2.PharmacologyHard

A woman has received a high-dose oxytocin infusion with large volumes of hypotonic fluid for many hours. She now has a headache, confusion and a low serum sodium. What is the most likely cause?

  1. AExcessive salt in the infusion fluid
  2. BNormal tiredness after a long labour
  3. CAn allergic reaction to oxytocin causing brain swelling
  4. DWater intoxication from the antidiuretic effect of oxytocin
3.Dosage calculationsMedium
60 kg5 mg/kgD = ? mg

A patient weighs 60 kg and is prescribed 5 mg/kg as a single dose. Find the dose D in mg.

60 kg5 mg/kg
D = mg
4.Dosage calculationsHard
50 mg/1 mLV = ? mL

A patient weighs 123.2 lb. The prescription is 15 mg/kg as a single dose, and the stock contains 50 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give?

123.2 lb15 mg/kg50 mg/1 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)2 h6 mg/L4 h3.4 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 6 mg/L at 2 h and 3.4 mg/L at 4 h. Assume first-order elimination. Find the half-life t½.

C1 = 6 mg/L (2 h)C2 = 3.4 mg/L (4 h)
t½ = h
6.Clinical pharmacokineticsHard
VCss,avg​ = ?500 mg · q8hCL = 0.05 L/kg/h82 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). An 82 kg patient takes oral aminophylline (S = 0.8, F = 1) every 8 h. The theophylline clearance is 0.05 L/kg/h. Each dose is 500 mg of aminophylline. Find the average steady-state level Css,avg.

CL = 0.05 L/kg/hτ = 8 hS = 0.8F = 182 kgD = 500 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: B · Inject into the abdomen away from the navel and do not rub the site afterwards

Why this is the answer

Enoxaparin is given deep subcutaneously, usually in the abdomen at least 5 cm from the umbilicus. The air bubble in the prefilled syringe is not expelled, and rubbing the site increases bruising.

Answer

B · Inject into the abdomen away from the navel and do not rub the site afterwards
2.Pharmacology

Answer: D · Water intoxication from the antidiuretic effect of oxytocin

Why this is the answer

Oxytocin has antidiuretic activity at high doses. With large volumes of fluid this can cause water retention and dilutional hyponatraemia, so fluid balance and sodium are monitored.

Answer

D · Water intoxication from the antidiuretic effect of oxytocin
3.Dosage calculations

Answer: D = 300 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

5·60 = 300 mg

Answer

D = 300 mg
4.Dosage calculations

Answer: V = 16.8 mL

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.

Weight in kg

123.2/2.2 = 56 kg

Dose

15·56 = 840 mg

Volume

V = (840/50)·1 = 16.8 mL

Answer

V = 16.8 mL
5.Clinical pharmacokinetics

Answer: t½ = 2.441 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.

Elimination rate constant

k = ln(6/3.4)/2 = 0.568/2 = 0.284 h⁻¹

Half-life

t½ = 0.693/0.284 = 2.441 h

Answer

t½ = 2.441 h
6.Clinical pharmacokinetics

Answer: Css,avg = 12.2 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 = 0.05·82 = 4.1 L/h

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 0.8·1·500/(4.1·8) = 12.2 mg/L

Answer

Css,avg = 12.2 mg/L

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