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

Why are patients taking simvastatin often advised to avoid large amounts of grapefruit juice?

  1. AGrapefruit blocks cholesterol absorption and causes low cholesterol
  2. BGrapefruit makes the tablet dissolve in the mouth
  3. CGrapefruit inhibits CYP3A4 in the gut, raising simvastatin levels and myopathy risk
  4. DGrapefruit speeds up simvastatin breakdown in the liver, so the drug stops working
2.PharmacologyHard

A patient receives high-dose IV aciclovir for herpes encephalitis. Which nursing action reduces the main risk to the kidneys?

  1. AGive a loop diuretic before each dose
  2. BRestrict oral and IV fluids to prevent brain swelling
  3. CGive the infusion as a rapid push
  4. DKeep the patient well hydrated and give the infusion slowly
3.Dosage calculationsMedium
80 kg7.5 mg/kg/day2× per dayD = ? mg

A patient weighs 80 kg. The prescribed dose is 7.5 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?

80 kg7.5 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 560 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

560 units1000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 10 mg/LR = ? mg/h · S = 0.8CL = 0.03 L/kg/h67 kg

Practice exercise (made-up values, not clinical guidance). A 67 kg patient is to receive an aminophylline infusion (salt factor S = 0.8: 80% of aminophylline is theophylline). The theophylline clearance is 0.03 L/kg/h. What aminophylline infusion rate R in mg/h gives a steady-state theophylline level of 10 mg/L?

67 kgCL = 0.03 L/kg/hCss = 10 mg/LS = 0.8
R = mg/h
6.Clinical pharmacokineticsHard
Vd = 0.7 L/kg8 → 20 mg/LLD = ? mg81 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). An 81 kg patient has a phenytoin level of 8 mg/L; the target is 20 mg/L. The drug is given intravenously as phenytoin sodium (S = 0.92), and the volume of distribution is 0.7 L/kg. What extra loading dose LD raises the level to the target?

81 kgVd = 0.7 L/kgC = 8 → 20 mg/LS = 0.92
LD = mg

3Solutions

1.Pharmacology

Answer: C · Grapefruit inhibits CYP3A4 in the gut, raising simvastatin levels and myopathy risk

Why this is the answer

Grapefruit compounds inhibit intestinal CYP3A4, so more simvastatin is absorbed. Higher levels increase the risk of muscle damage; drugs such as some calcium channel blockers and ciclosporin are also affected.

Answer

C · Grapefruit inhibits CYP3A4 in the gut, raising simvastatin levels and myopathy risk
2.Pharmacology

Answer: D · Keep the patient well hydrated and give the infusion slowly

Why this is the answer

Aciclovir can crystallise in the tubules and cause acute kidney injury. Good hydration, slow infusion and monitoring of kidney function reduce this risk.

Answer

D · Keep the patient well hydrated and give the infusion slowly
3.Dosage calculations

Answer: D = 300 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

7.5·80 = 600 mg

Per dose

D = 600/2 = 300 mg

Answer

D = 300 mg
4.Dosage calculations

Answer: V = 0.56 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.

Volume

V = 560/1000 = 0.56 mL

On the syringe

On this 1 mL syringe every small line is 0.01 mL.

Answer

V = 0.56 mL
5.Clinical pharmacokinetics

Answer: R = 25.12 mg/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.

Clearance

CL = 0.03·67 = 2.01 L/h

Infusion rate

R = CL·Css/S = 2.01·10/0.8 = 25.12 mg/h

Answer

R = 25.12 mg/h
6.Clinical pharmacokinetics

Answer: LD = 739.6 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 = 0.7·81 = 56.7 L

Rise needed

20 − 8 = 12 mg/L

Loading dose

LD = 56.7·12/(0.92·1) = 739.6 mg

Answer

LD = 739.6 mg

In practice the dose is rounded to a convenient amount.

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