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

What is a loading dose used for?

ATo reach the target plasma concentration quickly
BTo test for allergic reactions
CTo reduce side effects at the start of treatment
DTo slow down the absorption of the drug

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 patient weighs 90 kg and is prescribed 5 mg/kg as a single dose. Find the dose D in mg.

90 kg5 mg/kg

D = mg

4.Dosage calculationsHard

A child weighing 10 kg is prescribed 12.5 mg/kg per dose of an oral suspension that contains 200 mg in 5 mL. What volume V do you give? Round to one decimal place.

10 kg12.5 mg/kg200 mg/5 mL

V = mL

5.Clinical pharmacokineticsMedium

Practice exercise (made-up values, not clinical guidance). After an IV dose of tobramycin, the level is 10 mg/L at 2 h and 2.5 mg/L at 8 h. Assume first-order elimination. Find the elimination rate constant k.

C₁ = 10 mg/L (2 h)C₂ = 2.5 mg/L (8 h)

k = h⁻¹

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 9 h. How long t does it take to reach 75% of the steady-state level?

t½ = 9 h75% C_ss

t = h

3Solutions

1.Pharmacology

Answer: A · To reach the target plasma concentration quickly

Why this is the answer

A loading dose fills the volume of distribution so the effective level is reached immediately, instead of waiting 4–5 half-lives for steady state.

Answer

A · To reach the target plasma concentration quickly

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: D = 450 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.

Dose

5·90 = 450 mg

Answer

D = 450 mg

4.Dosage calculations

Answer: V = 3.1 mL

Dose from weight

12.5·10 = 125 mg

Volume

V = (125/200)·5 = 3.125 ≈ 3.1 mL

Answer

V = 3.1 mL

5.Clinical pharmacokinetics

Answer: k = 0.231 h⁻¹

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.

Elimination rate constant

k = ln(10/2.5)/6 = 1.386/6 = 0.231 h⁻¹

Answer

k = 0.231 h⁻¹

6.Clinical pharmacokinetics

Answer: t = 18 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 = 0.693/9 = 0.07702 h⁻¹

Time to the given fraction of steady state

t = −ln(1 − 0.75)/0.07702 = 1.386/0.07702 = 18 h

Answer

t = 18 h

That is 2 half-lives.

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