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

An IV site is cool, swollen and pale, and the infusion is running slowly. What should the nurse do?

  1. AStop the infusion, remove the cannula and elevate the limb
  2. BIncrease the infusion rate to push through and clear the blockage
  3. CApply a tight bandage over the site
  4. DFlush the cannula forcefully with saline
2.PharmacologyHard

In aspirin overdose the urine may be made alkaline with sodium bicarbonate. Why does this increase salicylate excretion?

  1. AAlkaline urine increases glomerular filtration
  2. BBicarbonate speeds up the liver metabolism of salicylate to inactive forms
  3. CMore salicylate is ionised in the tubule, so less is reabsorbed
  4. DBicarbonate binds salicylate and makes it inactive
3.Dosage calculationsMedium
70 kg30 mg/kg/day4× per dayD = ? mg

A patient weighs 70 kg. The prescribed dose is 30 mg/kg per day, given in 4 equal doses. How many milligrams D are given per dose?

70 kg30 mg/kg/day4× per day
D = mg
4.Dosage calculationsHard
35 kg145 cmBSA = √(h·w/3600)250 mg/m²D = ? mg

A patient is 145 cm tall and weighs 35 kg. The prescription is 250 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.

145 cm35 kg250 mg/m²
D = mg
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)C₀ = 9 mg/Lt½ = 2.5 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 220 mg of tobramycin. The level back-extrapolated to time zero is 9 mg/L and the half-life is 2.5 h. Find the volume of distribution Vd.

D = 220 mgC₀ = 9 mg/Lt½ = 2.5 h
Vd = L
6.Clinical pharmacokineticsHard
54 kg44 · manSCr 2.5 mg/dLCrCl → τ = ? h

Practice exercise (made-up values, not clinical guidance). A 44-year-old man weighs 54 kg and has a serum creatinine of 2.5 mg/dL (221 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 tobramycin regimen is 120 mg every 8 h for a creatinine clearance of 120 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.

44 years54 kgmanSCr = 2.5 mg/dL120 mg q8hCrCl normal 120 mL/min
τ = h

3Solutions

1.Pharmacology

Answer: A · Stop the infusion, remove the cannula and elevate the limb

Why this is the answer

These signs suggest infiltration. The infusion is stopped and the cannula removed, the limb is elevated, and a new cannula is placed elsewhere; vesicant drugs need the extravasation protocol.

Answer

A · Stop the infusion, remove the cannula and elevate the limb
2.Pharmacology

Answer: C · More salicylate is ionised in the tubule, so less is reabsorbed

Why this is the answer

Salicylate is a weak acid. In alkaline urine more of it is in the ionised form, which is "trapped" in the tubule and excreted. This is called ion trapping.

Answer

C · More salicylate is ionised in the tubule, so less is reabsorbed
3.Dosage calculations

Answer: D = 525 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

30·70 = 2100 mg

Per dose

D = 2100/4 = 525 mg

Answer

D = 525 mg
4.Dosage calculations

Answer: D = 296.8 mg

Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).

Body surface area

BSA = √(145·35/3600) = √1.41 = 1.187 m²

Dose

D = 250·1.187 = 296.8 mg

Answer

D = 296.8 mg
5.Clinical pharmacokinetics

Answer: Vd = 24.44 L

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 = 220/9 = 24.44 L

Answer

Vd = 24.44 L
6.Clinical pharmacokinetics

Answer: τ = 33.3 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 − 44)·54/(72·2.5) = 28.8 mL/min

New interval

τ = 8·120/28.8 = 33.33 ≈ 33.3 h

Answer

τ = 33.3 h

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

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