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 assessments are most important during a magnesium sulfate infusion?

  1. ADeep tendon reflexes, respiratory rate and urine output
  2. BBlood glucose, pupil size and pupil reaction to light
  3. CTemperature and skin colour only
  4. DBowel sounds and appetite
2.PharmacologyHard

A patient with latent tuberculosis feels well and is not infectious. Why is treatment such as isoniazid still offered?

  1. ATo prevent progression to active TB later
  2. BTo produce a negative skin test quickly
  3. CTo cure an active lung infection
  4. DTo stop the patient spreading TB at the moment
3.Dosage calculationsMedium
12 kg2 mg/kgD = ? mg

A patient weighs 12 kg and is prescribed 2 mg/kg as a single dose. Find the dose D in mg.

12 kg2 mg/kg
D = mg
4.Dosage calculationsHard
83 kg184 cmBSA = √(h·w/3600)175 mg/m²D = ? mg

A patient is 184 cm tall and weighs 83 kg. The prescription is 175 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.

184 cm83 kg175 mg/m²
D = mg
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)C₀ = 6 mg/Lt½ = 3 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 120 mg of tobramycin. The level back-extrapolated to time zero is 6 mg/L and the half-life is 3 h. Find the volume of distribution Vd.

D = 120 mgC₀ = 6 mg/Lt½ = 3 h
Vd = L
6.Clinical pharmacokineticsHard
VCss,avg​ = 20 mg/LD = ? mg · q12hCL = 3.5 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 3.5 L/h. What dose D in mg gives an average steady-state level of 20 mg/L?

CL = 3.5 L/hτ = 12 hS = 1F = 1Css,avg = 20 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: A · Deep tendon reflexes, respiratory rate and urine output

Why this is the answer

Loss of reflexes is an early sign of magnesium toxicity, followed by respiratory depression and cardiac arrest. Low urine output allows magnesium to accumulate.

Answer

A · Deep tendon reflexes, respiratory rate and urine output
2.Pharmacology

Answer: A · To prevent progression to active TB later

Why this is the answer

People with latent TB carry dormant bacteria that can reactivate, especially if immunity weakens. Treatment reduces the risk of active disease, which would be infectious.

Answer

A · To prevent progression to active TB later
3.Dosage calculations

Answer: D = 24 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.

Dose

2·12 = 24 mg

Answer

D = 24 mg
4.Dosage calculations

Answer: D = 360.4 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 = √(184·83/3600) = √4.242 = 2.06 m²

Dose

D = 175·2.06 = 360.4 mg

Answer

D = 360.4 mg
5.Clinical pharmacokinetics

Answer: Vd = 20 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 = 120/6 = 20 L

Answer

Vd = 20 L
6.Clinical pharmacokinetics

Answer: D = 840 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) = 20·3.5·12/(1·1) = 840 mg

Answer

D = 840 mg

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