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 is aspirin avoided in children and teenagers with viral illnesses such as flu or chickenpox?

  1. AIt is linked to Reye's syndrome, which harms the liver and brain
  2. BIt causes grey baby syndrome
  3. CIt stops the vaccine from working
  4. DIt causes severe, permanent hearing loss in young children
2.PharmacologyHard

During general anaesthesia with a volatile agent and suxamethonium (succinylcholine), a patient develops muscle rigidity, rising end-tidal CO2 and a fast-rising temperature. Which drug is the specific treatment?

  1. ANeostigmine
  2. BParacetamol
  3. CDantrolene
  4. DNaloxone
3.Dosage calculationsMedium
024681010 mL

A child weighing 20 kg is prescribed 2 mg/kg of a drug. The stock solution contains 20 mg/mL. Draw up the dose: what volume V do you give?

20 kg2 mg/kg20 mg/mL
V = mL
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 330 micrograms. The ampoule contains 1 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

330 mcg1 mg/mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 25 mg/LR = ? mg/hCL = 4 L/h

Practice exercise (made-up values, not clinical guidance). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 4 L/h. What infusion rate R in mg/h gives a steady-state level of 25 mg/L?

CL = 4 L/hCss = 25 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
Vd = 0.7 L/kg6 → 20 mg/LLD = ? mg86 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). An 86 kg patient has a phenytoin level of 6 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?

86 kgVd = 0.7 L/kgC = 6 → 20 mg/LS = 0.92
LD = mg

3Solutions

1.Pharmacology

Answer: A · It is linked to Reye's syndrome, which harms the liver and brain

Why this is the answer

Aspirin given during viral infections in young people is associated with Reye's syndrome, causing acute encephalopathy and liver failure. Paracetamol or ibuprofen is used for fever instead.

Answer

A · It is linked to Reye's syndrome, which harms the liver and brain
2.Pharmacology

Answer: C · Dantrolene

Why this is the answer

Malignant hyperthermia is caused by uncontrolled calcium release from the sarcoplasmic reticulum. Dantrolene blocks this release, and the triggering agents are stopped at once.

Answer

C · Dantrolene
3.Dosage calculations

Answer: V = 2 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 = 2·20 = 40 mg

Volume

V = 40/20 = 2 mL

On the syringe

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

Answer

V = 2 mL
4.Dosage calculations

Answer: V = 0.33 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

1 mg/mL = 1000 mcg/mL

Volume

V = 330/1000 = 0.33 mL

Answer

V = 0.33 mL
5.Clinical pharmacokinetics

Answer: R = 100 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.

Infusion rate

R = 4·25 = 100 mg/h

Answer

R = 100 mg/h
6.Clinical pharmacokinetics

Answer: LD = 916.1 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 = 0.7·86 = 60.2 L

Rise needed

20 − 6 = 14 mg/L

Loading dose

LD = 60.2·14/(0.92·1) = 916.1 mg

Answer

LD = 916.1 mg

In practice the dose is rounded to a convenient amount.

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