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 patient should usually not receive a live vaccine?

  1. AA healthy 1-year-old child
  2. BA healthy adult nurse who works on a children's ward
  3. CA patient receiving chemotherapy for leukaemia
  4. DA patient with mild seasonal allergies
2.PharmacologyHard

A patient on warfarin also takes ginkgo and high-dose garlic supplements and is having minor surgery next week. What should the nurse do?

  1. AIgnore the supplements, as natural products are safe with warfarin
  2. BAdvise taking extra supplements to improve healing
  3. CTell the surgical team, as the supplements can increase bleeding
  4. DAdvise stopping warfarin without telling anyone
3.Dosage calculationsMedium
30 kg7.5 mg/kg/day2× per dayD = ? mg

A patient weighs 30 kg. The prescribed dose is 7.5 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?

30 kg7.5 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
125 mg/5 mLV = ? mL

A child weighing 28 kg is prescribed 12.5 mg/kg per dose of an oral suspension that contains 125 mg in 5 mL. What volume V do you give?

28 kg12.5 mg/kg125 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)1 h10 mg/L3 h5.7 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 5.7 mg/L at 3 h. Assume first-order elimination. Find the half-life t½.

C1 = 10 mg/L (1 h)C2 = 5.7 mg/L (3 h)
t½ = h
6.Clinical pharmacokineticsHard
VCss,avg​ = 20 mg/LD = ? mg · q12hCL = 4.5 L/hS = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 4.5 L/h. What dose D in mg gives an average steady-state level of 20 mg/L?

CL = 4.5 L/hτ = 12 hS = 1F = 1Css,avg = 20 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: C · A patient receiving chemotherapy for leukaemia

Why this is the answer

Live attenuated vaccines can cause serious infection in immunosuppressed people and are generally avoided in pregnancy. Inactivated vaccines are safe but may give a weaker response.

Answer

C · A patient receiving chemotherapy for leukaemia
2.Pharmacology

Answer: C · Tell the surgical team, as the supplements can increase bleeding

Why this is the answer

Ginkgo and garlic may impair platelet function and add to warfarin's bleeding risk. The team needs a full list of supplements so it can plan, and the patient should not change warfarin without advice.

Answer

C · Tell the surgical team, as the supplements can increase bleeding
3.Dosage calculations

Answer: D = 112.5 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

7.5·30 = 225 mg

Per dose

D = 225/2 = 112.5 mg

Answer

D = 112.5 mg
4.Dosage calculations

Answer: V = 14 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

12.5·28 = 350 mg

Volume

V = (350/125)·5 = 14 mL

Answer

V = 14 mL
5.Clinical pharmacokinetics

Answer: t½ = 2.466 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(10/5.7)/2 = 0.5621/2 = 0.2811 h⁻¹

Half-life

t½ = 0.693/0.2811 = 2.466 h

Answer

t½ = 2.466 h
6.Clinical pharmacokinetics

Answer: D = 1080 mg

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.

Dose

D = Css,avg·CL·τ/(S·F) = 20·4.5·12/(1·1) = 1080 mg

Answer

D = 1080 mg

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