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 do patients taking clozapine need regular blood counts?

  1. AIt often causes iron-deficiency anaemia
  2. BIt can cause agranulocytosis
  3. CIt changes the blood group
  4. DIt raises the platelet count dangerously
2.PharmacologyHard

A patient on disulfiram becomes flushed, nauseated and has palpitations after using a mouthwash. What is the most likely cause?

  1. ADisulfiram toxicity from taking too many tablets by mistake
  2. BAn allergy to mint flavouring in the mouthwash
  3. CAlcohol in the mouthwash caused a disulfiram–alcohol reaction
  4. DLow blood glucose from skipping breakfast
3.Dosage calculationsMedium
024681010 mL

A child weighing 28 kg is prescribed 2 mg/kg of a drug. The stock solution contains 40 mg/mL. Draw up the dose: what volume V do you give?

28 kg2 mg/kg40 mg/mL
V = mL
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 3550 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?

3550 units5000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 25 mg/LR = ? mg/hCL = 80 mL/min

Practice exercise (made-up values, not clinical guidance). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 80 mL/min. What infusion rate R in mg/h gives a steady-state level of 25 mg/L?

CL = 80 mL/minCss = 25 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
84 kg66 · womanSCr 1.8 mg/dLCrCl → τ = ? h

Practice exercise (made-up values, not clinical guidance). A 66-year-old woman weighs 84 kg and has a serum creatinine of 1.8 mg/dL (159 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 gentamicin regimen is 80 mg every 8 h for a creatinine clearance of 100 mL/min. Keeping the dose, the interval is lengthened in proportion to the fall in clearance. Find the new dosing interval τ. Round to one decimal place.

66 years84 kgwomanSCr = 1.8 mg/dL80 mg q8hCrCl normal 100 mL/min
τ = h

3Solutions

1.Pharmacology

Answer: B · It can cause agranulocytosis

Why this is the answer

Clozapine can cause severe neutropenia (agranulocytosis). Regular white cell and neutrophil counts allow treatment to be stopped before life-threatening infection occurs.

Answer

B · It can cause agranulocytosis
2.Pharmacology

Answer: C · Alcohol in the mouthwash caused a disulfiram–alcohol reaction

Why this is the answer

Disulfiram reactions can occur with small amounts of alcohol in mouthwash, cough syrups, sauces or aftershave. Patients are taught to check labels and avoid all alcohol-containing products.

Answer

C · Alcohol in the mouthwash caused a disulfiram–alcohol reaction
3.Dosage calculations

Answer: V = 1.4 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 = 2·28 = 56 mg

Volume

V = 56/40 = 1.4 mL

On the syringe

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

Answer

V = 1.4 mL
4.Dosage calculations

Answer: V = 0.71 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 = 3550/5000 = 0.71 mL

On the syringe

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

Answer

V = 0.71 mL
5.Clinical pharmacokinetics

Answer: R = 120 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 in L/h

80·60/1000 = 4.8 L/h

Infusion rate

R = 4.8·25 = 120 mg/h

Answer

R = 120 mg/h
6.Clinical pharmacokinetics

Answer: τ = 19.6 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.

Creatinine clearance (Cockcroft–Gault)

CrCl = (140 − 66)·84/(72·1.8)·0.85 = 40.77 mL/min

New interval

τ = 8·100/40.77 = 19.62 ≈ 19.6 h

Answer

τ = 19.6 h

In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.

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