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

Convert the ordered dose and the stock strength to the same unit.
Use desired over have times quantity: (D/H) × Q.
For weight-based doses, multiply by the weight in kg first, then divide the daily dose by the number of doses.
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·C_ss/(S·F)
Average steady state: C_ss,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(C_peak/C_trough)/k, D = Vd·(C_peak − C_trough)
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

Convert the half-life to a rate constant: k = 0.693/t½.
Turn per-kg values into totals: Vd (L) = L/kg × weight, CL (L/h) = L/kg/h × weight.
Pick the relation: C = C₀·e^−kt, LD = Vd·C/(S·F), maintenance rate = CL·Css/(S·F), τ = ln(Cpeak/Ctrough)/k.
For kidney function, estimate CrCl with Cockcroft–Gault first, then scale the dose or the interval.
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:

AAlcohol
BGrapefruit juice
CDairy products
DSunlight

2.PharmacologyHard

What is the main mechanism of action of proton pump inhibitors such as omeprazole?

AIrreversible inhibition of the H⁺/K⁺-ATPase in parietal cells
BCoating the ulcer to protect it
CCompetitive blocking of histamine H2 receptors on parietal cells
DNeutralising acid in the stomach

3.Dosage calculationsMedium

A patient weighs 70 kg. The prescribed dose is 25 mg/kg per day, given in 4 equal doses. How many milligrams D are given per dose?

70 kg25 mg/kg/day4× per day

D = mg

4.Dosage calculationsHard

A child weighing 12 kg is prescribed 15 mg/kg per dose of an oral suspension that contains 250 mg in 5 mL. What volume V do you give?

12 kg15 mg/kg250 mg/5 mL

V = mL

5.Clinical pharmacokineticsMedium

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 130 mg of gentamicin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 2.5 h. Find the clearance CL in L/h.

D = 130 mgC₀ = 10 mg/Lt½ = 2.5 h

CL = L/h

6.Clinical pharmacokineticsHard

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 10 h. What is the level C after 4 h?

R = 60 mg/hCL = 3 L/ht½ = 10 ht = 4 h

C = mg/L

3Solutions

1.Pharmacology

Answer: A · 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

A · Alcohol

2.Pharmacology

Answer: A · Irreversible inhibition of the H⁺/K⁺-ATPase in parietal cells

Why this is the answer

PPIs irreversibly block the proton pump, the last step of acid secretion. H2 blockers (such as famotidine) act earlier and are less powerful; antacids only neutralise.

Answer

A · Irreversible inhibition of the H⁺/K⁺-ATPase in parietal cells

3.Dosage calculations

Answer: D = 437.5 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.

Total per day

25·70 = 1750 mg

Per dose

D = 1750/4 = 437.5 mg

Answer

D = 437.5 mg

4.Dosage calculations

Answer: V = 3.6 mL

Dose from weight

15·12 = 180 mg

Volume

V = (180/250)·5 = 3.6 mL

Answer

V = 3.6 mL

5.Clinical pharmacokinetics

Answer: CL = 3.604 L/h

Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × C_ss. 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 = 130/10 = 13 L

Rate constant

k = 0.693/2.5 = 0.2773 h⁻¹

Clearance

CL = 0.2773·13 = 3.604 L/h

Answer

CL = 3.604 L/h

6.Clinical pharmacokinetics

Answer: C = 4.843 mg/L

Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(C_peak/C_trough)/k and the dose that restores the peak is Vd × (C_peak − C_trough). The average steady-state level is C_ss,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

C_ss = 60/3 = 20 mg/L

Rate constant

k = 0.693/10 = 0.06931 h⁻¹

Level after the given time

C = 20·(1 − e^{−0.06931·4}) = 4.843 mg/L

Answer

C = 4.843 mg/L

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