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 adverse effect of doxorubicin requires monitoring of heart function?

  1. APericarditis caused by infection
  2. BSevere hypertension during the infusion itself
  3. CCumulative heart muscle damage leading to heart failure
  4. DRapid rise in cholesterol
2.PharmacologyHard

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

  1. AIt is long-acting and can cause prolonged, severe hypoglycaemia
  2. BIt causes severe weight loss and muscle wasting in older people
  3. CIt is not absorbed in people over 65
  4. DIt causes high blood glucose in older adults
3.Dosage calculationsMedium
45 kg15 mg/kg/day2× per dayD = ? mg

A patient weighs 45 kg. The prescribed dose is 15 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?

45 kg15 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 0.35 mg. The ampoule contains 500 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

0.35 mg500 mcg/mL
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)1 h25 mg/L17 h6.3 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 25 mg/L at 1 h and 6.3 mg/L at 17 h. Assume first-order elimination. Find the elimination rate constant k.

C1 = 25 mg/L (1 h)C2 = 6.3 mg/L (17 h)
k = h⁻¹
6.Clinical pharmacokineticsHard
VCss,avg​ = ?300 mg · q8hCL = 0.04 L/kg/h98 kg · S = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A 98 kg patient takes oral theophylline (F = 1) every 8 h. The clearance is 0.04 L/kg/h. Each dose is 300 mg of theophylline. Find the average steady-state level Css,avg.

CL = 0.04 L/kg/hτ = 8 hS = 1F = 198 kgD = 300 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: C · Cumulative heart muscle damage leading to heart failure

Why this is the answer

Anthracyclines such as doxorubicin can damage heart muscle, and the risk increases with cumulative dose. Heart function is assessed before and during treatment; the drug can also turn urine red.

Answer

C · Cumulative heart muscle damage leading to heart failure
2.Pharmacology

Answer: A · 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

A · It is long-acting and can cause prolonged, severe hypoglycaemia
3.Dosage calculations

Answer: D = 337.5 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

15·45 = 675 mg

Per dose

D = 675/2 = 337.5 mg

Answer

D = 337.5 mg
4.Dosage calculations

Answer: V = 0.7 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

0.35 mg = 350 mcg

Volume

V = 350/500 = 0.7 mL

Answer

V = 0.7 mL
5.Clinical pharmacokinetics

Answer: k = 0.08615 h⁻¹

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(25/6.3)/16 = 1.378/16 = 0.08615 h⁻¹

Answer

k = 0.08615 h⁻¹
6.Clinical pharmacokinetics

Answer: Css,avg = 9.566 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 = 0.04·98 = 3.92 L/h

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 1·1·300/(3.92·8) = 9.566 mg/L

Answer

Css,avg = 9.566 mg/L

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