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

During an infusion of a vesicant chemotherapy drug, the patient reports burning, and the site is swollen. What should the nurse do first?

  1. AIncrease the infusion rate to finish quickly
  2. BStop the infusion, leave the cannula in and follow the protocol
  3. CFlush the line with a large volume of saline
  4. DRemove the cannula at once and massage the area firmly
2.PharmacologyHard

A woman with epilepsy who takes an antiepileptic drug plans to become pregnant. Which advice is standard?

  1. AStop all antiepileptic drugs straight away as soon as she stops contraception
  2. BNo change is needed, as antiepileptics carry no risk in pregnancy
  3. CTake folic acid before conception and seek specialist review of her medication
  4. DAvoid folic acid because it lowers drug levels
3.Dosage calculationsMedium
024681010 mL

A child weighing 20 kg is prescribed 4 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?

20 kg4 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
120 mg/5 mLV = ? mL

A child weighing 20 kg is prescribed 15 mg/kg per dose of an oral suspension that contains 120 mg in 5 mL. What volume V do you give?

20 kg15 mg/kg120 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)1 h35 mg/L13 h10.7 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 35 mg/L at 1 h and 10.7 mg/L at 13 h. Assume first-order elimination. Find the elimination rate constant k.

C1 = 35 mg/L (1 h)C2 = 10.7 mg/L (13 h)
k = h⁻¹
6.Clinical pharmacokineticsHard
Vd = 0.3 L/kg1 → 7 mg/LD = ? mg93 kg

Practice exercise (made-up values, not clinical guidance). A 93 kg patient on regular gentamicin doses is at steady state. The target is a peak of 7 mg/L and a trough of 1 mg/L, and the volume of distribution is 0.3 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?

93 kgVd = 0.3 L/kgCpeak = 7 mg/LCtrough = 1 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: B · Stop the infusion, leave the cannula in and follow the protocol

Why this is the answer

Suspected extravasation of a vesicant is an emergency. The infusion is stopped, the cannula is left in so that drug can be aspirated, and the protocol, which may include an antidote and cold or warm packs, is followed.

Answer

B · Stop the infusion, leave the cannula in and follow the protocol
2.Pharmacology

Answer: C · Take folic acid before conception and seek specialist review of her medication

Why this is the answer

Folic acid before and in early pregnancy reduces the risk of neural tube defects. Medication should be reviewed before conception, but drugs should not be stopped suddenly because uncontrolled seizures are also dangerous.

Answer

C · Take folic acid before conception and seek specialist review of her medication
3.Dosage calculations

Answer: V = 1.6 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.

Dose from body weight

D = 4·20 = 80 mg

Volume

V = 80/50 = 1.6 mL

On the syringe

On this 10 mL syringe every small line is 0.2 mL.

Answer

V = 1.6 mL
4.Dosage calculations

Answer: V = 12.5 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.

Dose from weight

15·20 = 300 mg

Volume

V = (300/120)·5 = 12.5 mL

Answer

V = 12.5 mL
5.Clinical pharmacokinetics

Answer: k = 0.09876 h⁻¹

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.

Elimination rate constant

k = ln(35/10.7)/12 = 1.185/12 = 0.09876 h⁻¹

Answer

k = 0.09876 h⁻¹
6.Clinical pharmacokinetics

Answer: D = 167.4 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.

Volume of distribution

Vd = 0.3·93 = 27.9 L

Dose

D = 27.9·(7 − 1) = 167.4 mg

Answer

D = 167.4 mg

In practice the dose is rounded to a convenient amount.

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