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

Which sign is typical of opioid toxicity?

AHigh body temperature
BWidely dilated pupils
CPinpoint pupils
DFast, deep breathing

2.PharmacologyHard

Why is glibenclamide (glyburide) generally avoided in older adults?

AIt causes high blood glucose in older adults
BIt is not absorbed in people over 65
CIt causes severe weight loss and muscle wasting in older people
DIt is long-acting and can cause prolonged, severe hypoglycaemia

3.Dosage calculationsMedium

A child weighing 12 kg is prescribed 5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?

12 kg5 mg/kg25 mg/mL

V = mL

4.Dosage calculationsHard

The prescription is 480 micrograms. The ampoule contains 4 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

480 mcg4 mg/mL

V = mL

5.Clinical pharmacokineticsMedium

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 170 mg of gentamicin. The level back-extrapolated to time zero is 7 mg/L and the half-life is 3.5 h. Find the clearance CL in L/h.

D = 170 mgC₀ = 7 mg/Lt½ = 3.5 h

CL = L/h

6.Clinical pharmacokineticsHard

Practice exercise (made-up values, not clinical guidance). A theophylline infusion is started without a loading dose. The half-life in this patient is 6 h. How long t does it take to reach 75% of the steady-state level?

t½ = 6 h75% C_ss

t = h

3Solutions

1.Pharmacology

Answer: C · Pinpoint pupils

Why this is the answer

Opioid toxicity classically causes pinpoint pupils, slow or shallow breathing and reduced consciousness. Naloxone reverses these effects.

Answer

C · Pinpoint pupils

2.Pharmacology

Answer: D · It is long-acting and can cause prolonged, severe hypoglycaemia

Why this is the answer

Glibenclamide has a long action and active metabolites that accumulate when kidney function declines. Older adults are at high risk of prolonged hypoglycaemia, so shorter-acting agents or other drug classes are preferred.

Answer

D · It is long-acting and can cause prolonged, severe hypoglycaemia

3.Dosage calculations

Answer: V = 2.4 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 = 5·12 = 60 mg

Volume

V = 60/25 = 2.4 mL

On the syringe

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

Answer

V = 2.4 mL

4.Dosage calculations

Answer: V = 0.12 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.

Same units

4 mg/mL = 4000 mcg/mL

Volume

V = 480/4000 = 0.12 mL

Answer

V = 0.12 mL

5.Clinical pharmacokinetics

Answer: CL = 4.81 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 = 170/7 = 24.29 L

Rate constant

k = 0.693/3.5 = 0.198 h⁻¹

Clearance

CL = 0.198·24.29 = 4.81 L/h

Answer

CL = 4.81 L/h

6.Clinical pharmacokinetics

Answer: t = 12 h

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.

Rate constant

k = 0.693/6 = 0.1155 h⁻¹

Time to the given fraction of steady state

t = −ln(1 − 0.75)/0.1155 = 1.386/0.1155 = 12 h

Answer

t = 12 h

That is 2 half-lives.

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