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

What should the nurse teach a patient about taking levothyroxine?

  1. ATake it with milk at dinner, as calcium protects the stomach lining
  2. BTake it on an empty stomach, 30–60 minutes before breakfast
  3. CTake it only on days when feeling tired
  4. DTake it together with the iron tablet to save time
2.PharmacologyHard

A patient has received a sodium nitroprusside infusion for several days. He becomes confused and develops a metabolic acidosis. What should be suspected?

  1. AAn allergic reaction to the plastic of the infusion bag
  2. BCyanide toxicity from nitroprusside breakdown
  3. CHyperkalaemia from the infusion
  4. DHypoglycaemia from nitroprusside
3.Dosage calculationsMedium
31 kgBSA = 1.11 m²50 mg/m²D = ? mg

A patient weighing 31 kg has a body surface area of 1.11 m². The prescription is 50 mg/m². Find the dose D in mg.

31 kgBSA = 1.11 m²50 mg/m²
D = mg
4.Dosage calculationsHard
100 mg/1 mLV = ? mL

A patient weighs 136.4 lb. The prescription is 15 mg/kg as a single dose, and the stock contains 100 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give?

136.4 lb15 mg/kg100 mg/1 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 1 mcg/LLD = ? mcg92 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 92 kg patient is to be loaded with digoxin tablets to reach a level of 1 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.

92 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
68 kg41 · manSCr 2.6 mg/dLCrCl → D = ? mg

Practice exercise (made-up values, not clinical guidance). A 41-year-old man weighs 68 kg and has a serum creatinine of 2.6 mg/dL (230 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 dose is 120 mg every 8 h for a creatinine clearance of 100 mL/min. Keeping the interval, the dose is reduced in proportion to the creatinine clearance. Find the adjusted dose D. Round to the nearest whole number.

41 years68 kgmanSCr = 2.6 mg/dL120 mg q8hCrCl normal 100 mL/min
D = mg

3Solutions

1.Pharmacology

Answer: B · Take it on an empty stomach, 30–60 minutes before breakfast

Why this is the answer

Levothyroxine is best absorbed on an empty stomach, and calcium, iron and antacids should be taken some hours apart. It is taken every day, usually for life.

Answer

B · Take it on an empty stomach, 30–60 minutes before breakfast
2.Pharmacology

Answer: B · Cyanide toxicity from nitroprusside breakdown

Why this is the answer

Nitroprusside releases cyanide, which is normally converted to thiocyanate. With high doses, long infusions or poor organ function, cyanide and thiocyanate can accumulate; the infusion is also protected from light.

Answer

B · Cyanide toxicity from nitroprusside breakdown
3.Dosage calculations

Answer: D = 55.5 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 = 50·1.11 = 55.5 mg

Answer

D = 55.5 mg
4.Dosage calculations

Answer: V = 9.3 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.

Weight in kg

136.4/2.2 = 62 kg

Dose

15·62 = 930 mg

Volume

V = (930/100)·1 = 9.3 mL

Answer

V = 9.3 mL
5.Clinical pharmacokinetics

Answer: LD = 920 mcg

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 = 7·92 = 644 L

Amount of active drug needed

Vd·C = 644·1 = 644 mcg

Loading dose

LD = 644/(1·0.7) = 920 mcg

Answer

LD = 920 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: D = 43 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.

Creatinine clearance (Cockcroft–Gault)

CrCl = (140 − 41)·68/(72·2.6) = 35.96 mL/min

Adjusted dose

D = 120·35.96/100 = 43.15 ≈ 43 mg

Answer

D = 43 mg

In practice the dose is rounded to a convenient amount and checked against the product information.

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