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 factor increases the risk of lithium toxicity?

  1. ATaking the dose with food
  2. BA high-salt diet
  3. CDehydration
  4. DDrinking extra water
2.PharmacologyHard

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

  1. AIt means the dose must be given five times
  2. BThe pharmacy cannot supply doses that contain a decimal point
  3. CThe decimal point may be missed, and the dose read as 50 mg
  4. DIt is too precise for most drugs
3.Dosage calculationsMedium
80 kg10 mg/kg/day4× per dayD = ? mg

A patient weighs 80 kg. The prescribed dose is 10 mg/kg per day, given in 4 equal doses. How many milligrams D are given per dose?

80 kg10 mg/kg/day4× per day
D = mg
4.Dosage calculationsHard
20k units500 mL? mL/h500 units/h

An infusion contains 20000 units of a drug in 500 mL. The prescription is 500 units per hour. At what rate R do you set the pump, in mL/h?

20000 units/500 mL500 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)C₀ = 9 mg/Lt½ = 2 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 200 mg of tobramycin. The level back-extrapolated to time zero is 9 mg/L and the half-life is 2 h. Find the clearance CL in L/h.

D = 200 mgC₀ = 9 mg/Lt½ = 2 h
CL = L/h
6.Clinical pharmacokineticsHard
VCss,avg​ = ?450 mg · q8hCL = 0.05 L/kg/h88 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). An 88 kg patient takes oral aminophylline (S = 0.8, F = 1) every 8 h. The theophylline clearance is 0.05 L/kg/h. Each dose is 450 mg of aminophylline. Find the average steady-state level Css,avg.

CL = 0.05 L/kg/hτ = 8 hS = 0.8F = 188 kgD = 450 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: C · Dehydration

Why this is the answer

When the body is short of water or sodium, the kidney reabsorbs more lithium, so its level rises. Thiazides, ACE inhibitors and NSAIDs can have the same effect.

Answer

C · Dehydration
2.Pharmacology

Answer: C · 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

C · The decimal point may be missed, and the dose read as 50 mg
3.Dosage calculations

Answer: D = 200 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

10·80 = 800 mg

Per dose

D = 800/4 = 200 mg

Answer

D = 200 mg
4.Dosage calculations

Answer: R = 12.5 mL/h

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

20000/500 = 40 units/mL

Pump rate

R = 500/40 = 12.5 mL/h

Answer

R = 12.5 mL/h
5.Clinical pharmacokinetics

Answer: CL = 7.702 L/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.

Volume of distribution

Vd = 200/9 = 22.22 L

Rate constant

k = 0.693/2 = 0.3466 h⁻¹

Clearance

CL = 0.3466·22.22 = 7.702 L/h

Answer

CL = 7.702 L/h
6.Clinical pharmacokinetics

Answer: Css,avg = 10.23 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 = 0.05·88 = 4.4 L/h

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 0.8·1·450/(4.4·8) = 10.23 mg/L

Answer

Css,avg = 10.23 mg/L

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