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

Patients taking metronidazole are usually advised to avoid:

  1. ASunlight
  2. BGrapefruit juice
  3. CAlcohol
  4. DDairy products
2.PharmacologyHard

A patient taking digoxin has nausea, yellow-green vision and a dangerous arrhythmia. Which specific treatment can bind the drug?

  1. ADigoxin immune Fab (antibody fragments)
  2. BFlumazenil
  3. CIntravenous vitamin K (phytomenadione) given slowly
  4. DProtamine sulfate
3.Dosage calculationsMedium
024681010 mL

A child weighing 12 kg is prescribed 15 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?

12 kg15 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
25%stockV₁ = ? mL

You must prepare 100 mL of a 0.5% (w/v) solution from a 25% (w/v) stock solution. What volume of stock V₁ do you need?

C₁ = 25%C₂ = 0.5%V₂ = 100 mL
V₁ = mL
5.Clinical pharmacokineticsMedium
0.1110t (h)C (mg/L)1 h6 mg/L11 h0.8 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 6 mg/L at 1 h and 0.8 mg/L at 11 h. Assume first-order elimination. Find the half-life t½.

C1 = 6 mg/L (1 h)C2 = 0.8 mg/L (11 h)
t½ = h
6.Clinical pharmacokineticsHard
t (h)C (mg/L)Css​10 hC = ?

Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 60 mg/h with no loading dose. The patient's clearance is 3 L/h and the half-life is 6 h. What is the level C after 10 h?

R = 60 mg/hCL = 3 L/ht½ = 6 ht = 10 h
C = mg/L

3Solutions

1.Pharmacology

Answer: C · Alcohol

Why this is the answer

Metronidazole can cause a disulfiram-like reaction with alcohol, with flushing, nausea and palpitations. Alcohol is avoided during treatment and for a short time after.

Answer

C · Alcohol
2.Pharmacology

Answer: A · Digoxin immune Fab (antibody fragments)

Why this is the answer

Digoxin immune Fab binds digoxin in the blood and makes it inactive. It is used for life-threatening toxicity, such as serious arrhythmias or severe hyperkalaemia.

Answer

A · Digoxin immune Fab (antibody fragments)
3.Dosage calculations

Answer: V = 3.6 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 = 15·12 = 180 mg

Volume

V = 180/50 = 3.6 mL

On the syringe

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

Answer

V = 3.6 mL
4.Dosage calculations

Answer: V₁ = 2 mL

Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.

Volume of stock

V₁ = 0.5·100/25 = 2 mL

Answer

V₁ = 2 mL
5.Clinical pharmacokinetics

Answer: t½ = 3.44 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(6/0.8)/10 = 2.015/10 = 0.2015 h⁻¹

Half-life

t½ = 0.693/0.2015 = 3.44 h

Answer

t½ = 3.44 h
6.Clinical pharmacokinetics

Answer: C = 13.7 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.

Steady-state level

Css = 60/3 = 20 mg/L

Rate constant

k = 0.693/6 = 0.1155 h⁻¹

Level after the given time

C = 20·(1 − e−0.1155·10) = 13.7 mg/L

Answer

C = 13.7 mg/L

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