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

Which teaching about zolpidem is correct?

  1. ATake it in the morning so that it is out of the system by night
  2. BTake it right before bed, only if you can sleep a full night
  3. CDrive soon after waking, as the drug has no next-day effect
  4. DTake it with alcohol to make it act faster
2.PharmacologyHard

Why should a dose never be written as "5.0 mg" on a medication order?

  1. AThe pharmacy cannot supply doses that contain a decimal point
  2. BIt is too precise for most drugs
  3. CIt means the dose must be given five times
  4. DThe decimal point may be missed, and the dose read as 50 mg
3.Dosage calculationsMedium
1 g+ 3.4 mLV = ? mL

A vial contains 1 g of powder. The label says: add 3.4 mL of water for injection to give a total volume of 4 mL. The prescription is 750 mg. What volume V of the reconstituted solution do you give?

1 g+ 3.4 mL → 4 mL750 mg
V = mL
4.Dosage calculationsHard
120 mg/5 mLV = ? mL

A child weighing 24 kg is prescribed 5 mg/kg per dose of an oral suspension that contains 120 mg in 5 mL. What volume V do you give?

24 kg5 mg/kg120 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)1 h10 mg/L6 h2.5 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of tobramycin, the level is 10 mg/L at 1 h and 2.5 mg/L at 6 h. Assume first-order elimination. Find the half-life t½.

C1 = 10 mg/L (1 h)C2 = 2.5 mg/L (6 h)
t½ = h
6.Clinical pharmacokineticsHard
VCss,avg​ = ?400 mg · q12hCL = 0.05 L/kg/h55 kg · S = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A 55 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.05 L/kg/h. Each dose is 400 mg of theophylline. Find the average steady-state level Css,avg.

CL = 0.05 L/kg/hτ = 12 hS = 1F = 155 kgD = 400 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: B · Take it right before bed, only if you can sleep a full night

Why this is the answer

Zolpidem can cause next-day impairment and complex sleep behaviours such as sleep-walking or sleep-driving. Alcohol and other sedatives increase these risks.

Answer

B · Take it right before bed, only if you can sleep a full night
2.Pharmacology

Answer: D · The decimal point may be missed, and the dose read as 50 mg

Why this is the answer

Trailing zeros (5.0) and missing leading zeros (.5) are well-known causes of tenfold errors. Safe practice is to write 5 mg and 0.5 mg.

Answer

D · The decimal point may be missed, and the dose read as 50 mg
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

1000 mg/4 mL = 250 mg/mL

Volume

V = 750/250 = 3 mL

Answer

V = 3 mL
4.Dosage calculations

Answer: V = 5 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.

Dose from weight

5·24 = 120 mg

Volume

V = (120/120)·5 = 5 mL

Answer

V = 5 mL
5.Clinical pharmacokinetics

Answer: t½ = 2.5 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.

Elimination rate constant

k = ln(10/2.5)/5 = 1.386/5 = 0.2773 h⁻¹

Half-life

t½ = 0.693/0.2773 = 2.5 h

Answer

t½ = 2.5 h
6.Clinical pharmacokinetics

Answer: Css,avg = 12.12 mg/L

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.

Clearance

CL = 0.05·55 = 2.75 L/h

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 1·1·400/(2.75·12) = 12.12 mg/L

Answer

Css,avg = 12.12 mg/L

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