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
BSunlight
CDairy products
DGrapefruit juice

2.PharmacologyHard

A baby born to a mother on methadone becomes irritable on day 2, with a high-pitched cry, tremors, sneezing and poor feeding. What is the most likely cause?

ANeonatal hypoglycaemia from maternal diabetes
BNormal newborn behaviour
CVitamin K deficiency bleeding
DNeonatal opioid withdrawal syndrome

3.Dosage calculationsMedium

A vial contains 500 mg of powder. The label says: add 9.6 mL of water for injection to give a total volume of 10 mL. The prescription is 150 mg. What volume V of the reconstituted solution do you give?

500 mg+ 9.6 mL → 10 mL150 mg

V = mL

4.Dosage calculationsHard

A child weighing 8 kg is prescribed 15 mg/kg per dose of an oral suspension that contains 120 mg in 5 mL. What volume V do you give?

8 kg15 mg/kg120 mg/5 mL

V = mL

5.Clinical pharmacokineticsMedium

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 140 mg of gentamicin. The level back-extrapolated to time zero is 6 mg/L and the half-life is 3 h. Find the volume of distribution Vd.

D = 140 mgC₀ = 6 mg/Lt½ = 3 h

Vd = L

6.Clinical pharmacokineticsHard

Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 75 mg/h with no loading dose. The patient's clearance is 3 L/h and the half-life is 8 h. What is the level C after 10 h?

R = 75 mg/hCL = 3 L/ht½ = 8 ht = 10 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: D · Neonatal opioid withdrawal syndrome

Why this is the answer

After birth the baby no longer receives opioid from the mother and develops withdrawal. Assessment uses a scoring tool, with non-drug care first and opioid treatment if signs are severe.

Answer

D · Neonatal opioid withdrawal syndrome

3.Dosage calculations

Answer: V = 3 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.

Concentration after mixing

500 mg/10 mL = 50 mg/mL

Volume

V = 150/50 = 3 mL

Answer

V = 3 mL

4.Dosage calculations

Answer: V = 5 mL

Dose from weight

15·8 = 120 mg

Volume

V = (120/120)·5 = 5 mL

Answer

V = 5 mL

5.Clinical pharmacokinetics

Answer: Vd = 23.33 L

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 = 140/6 = 23.33 L

Answer

Vd = 23.33 L

6.Clinical pharmacokinetics

Answer: C = 14.49 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 = 75/3 = 25 mg/L

Rate constant

k = 0.693/8 = 0.08664 h⁻¹

Level after the given time

C = 25·(1 − e^{−0.08664·10}) = 14.49 mg/L

Answer

C = 14.49 mg/L

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