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

A patient uses two different eye drops at the same time of day. What should the nurse advise?

  1. AUse only one of them each day
  2. BMix the drops in one bottle first
  3. CWait at least 5 minutes between the two drops
  4. DPut both drops in at exactly the same moment
2.PharmacologyHard

Which drug class can cause life-threatening hyperkalaemia when combined with an ACE inhibitor?

  1. APotassium-sparing diuretics such as spironolactone
  2. BLoop diuretics such as high-dose intravenous furosemide
  3. CThiazide diuretics
  4. DProton pump inhibitors
3.Dosage calculationsMedium
25 kg10 mg/kg/day3× per dayD = ? mg

A patient weighs 25 kg. The prescribed dose is 10 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?

25 kg10 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
20k units1000 mL? mL/h800 units/h

An infusion contains 20000 units of a drug in 1000 mL. The prescription is 800 units per hour. At what rate R do you set the pump, in mL/h?

20000 units/1000 mL800 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
Vd = 0.5 L/kgC = 15 mg/LLD = ? mg66 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). A 66 kg patient is to be loaded intravenously with aminophylline to reach a theophylline level of 15 mg/L. The volume of distribution is 0.5 L/kg and the salt factor is S = 0.8. Find the loading dose LD of aminophylline in mg.

66 kgVd = 0.5 L/kgC = 15 mg/LS = 0.8
LD = mg
6.Clinical pharmacokineticsHard
86 kg60 · womanSCr 1.5 mg/dLCrCl → τ = ? h

Practice exercise (made-up values, not clinical guidance). A 60-year-old woman weighs 86 kg and has a serum creatinine of 1.5 mg/dL (133 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual gentamicin regimen is 80 mg every 8 h for a creatinine clearance of 100 mL/min. Keeping the dose, the interval is lengthened in proportion to the fall in clearance. Find the new dosing interval τ. Round to one decimal place.

60 years86 kgwomanSCr = 1.5 mg/dL80 mg q8hCrCl normal 100 mL/min
τ = h

3Solutions

1.Pharmacology

Answer: C · Wait at least 5 minutes between the two drops

Why this is the answer

Waiting several minutes allows the first drop to be absorbed before the next is applied. Eye ointments are usually applied last.

Answer

C · Wait at least 5 minutes between the two drops
2.Pharmacology

Answer: A · Potassium-sparing diuretics such as spironolactone

Why this is the answer

ACE inhibitors lower aldosterone and spironolactone blocks its receptor; together they reduce potassium excretion and can raise potassium dangerously.

Answer

A · Potassium-sparing diuretics such as spironolactone
3.Dosage calculations

Answer: D = 83.33 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

10·25 = 250 mg

Per dose

D = 250/3 = 83.33 mg

Answer

D = 83.33 mg
4.Dosage calculations

Answer: R = 40 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

20000/1000 = 20 units/mL

Pump rate

R = 800/20 = 40 mL/h

Answer

R = 40 mL/h
5.Clinical pharmacokinetics

Answer: LD = 618.8 mg

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 = 0.5·66 = 33 L

Amount of active drug needed

Vd·C = 33·15 = 495 mg

Loading dose

LD = 495/(0.8·1) = 618.8 mg

Answer

LD = 618.8 mg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: τ = 14.8 h

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.

Creatinine clearance (Cockcroft–Gault)

CrCl = (140 − 60)·86/(72·1.5)·0.85 = 54.15 mL/min

New interval

τ = 8·100/54.15 = 14.77 ≈ 14.8 h

Answer

τ = 14.8 h

In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.

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