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 is starting lisinopril. Which rare but serious adverse effect should the nurse teach the patient to report immediately?

  1. ASwelling of the lips, tongue or face
  2. BA harmless rash on the palms of the hands
  3. CAn increase in appetite in the evening
  4. DDarker skin after exposure to sunlight
2.PharmacologyHard

A patient on digoxin and furosemide develops nausea, visual disturbances and an irregular pulse. Which electrolyte disturbance most likely made digoxin toxicity more likely?

  1. AHyperkalaemia
  2. BHypocalcaemia
  3. CHypernatraemia
  4. DHypokalaemia
3.Dosage calculationsMedium
63 kgBSA = 1.48 m²250 mg/m²D = ? mg

A patient weighing 63 kg has a body surface area of 1.48 m². The prescription is 250 mg/m². Find the dose D in mg.

63 kgBSA = 1.48 m²250 mg/m²
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 215 micrograms. The ampoule contains 0.5 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

215 mcg0.5 mg/mL
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)C₀ = 10 mg/Lt½ = 3.5 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 240 mg of gentamicin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 3.5 h. Find the clearance CL in L/h.

D = 240 mgC₀ = 10 mg/Lt½ = 3.5 h
CL = L/h
6.Clinical pharmacokineticsHard
0.1110t (h)C (mg/L)Cpeak​ = 7τ = ?Ctrough​ = 1

Practice exercise (made-up values, not clinical guidance). A patient's tobramycin half-life is 4 h. The target is a peak of 7 mg/L and a trough of 1 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.

t½ = 4 hCpeak = 7 mg/LCtrough = 1 mg/L
τ = h

3Solutions

1.Pharmacology

Answer: A · Swelling of the lips, tongue or face

Why this is the answer

ACE inhibitors can cause angioedema, which can obstruct the airway and needs emergency care. It is linked to raised bradykinin levels and can occur even after long use.

Answer

A · Swelling of the lips, tongue or face
2.Pharmacology

Answer: D · Hypokalaemia

Why this is the answer

Digoxin binds the Na⁺/K⁺-ATPase at the same site as potassium. Low potassium, often caused by loop or thiazide diuretics, increases digoxin binding and toxicity.

Answer

D · Hypokalaemia
3.Dosage calculations

Answer: D = 370 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).

Dose

D = 250·1.48 = 370 mg

Answer

D = 370 mg
4.Dosage calculations

Answer: V = 0.43 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

0.5 mg/mL = 500 mcg/mL

Volume

V = 215/500 = 0.43 mL

Answer

V = 0.43 mL
5.Clinical pharmacokinetics

Answer: CL = 4.753 L/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.

Volume of distribution

Vd = 240/10 = 24 L

Rate constant

k = 0.693/3.5 = 0.198 h⁻¹

Clearance

CL = 0.198·24 = 4.753 L/h

Answer

CL = 4.753 L/h
6.Clinical pharmacokinetics

Answer: τ = 11.2 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.

Rate constant

k = 0.693/4 = 0.1733 h⁻¹

Dosing interval

τ = ln(7/1)/0.1733 = 1.946/0.1733 = 11.23 ≈ 11.2 h

Answer

τ = 11.2 h

In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.

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