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

Which teaching about antiepileptic drugs is most important?

  1. AAlcohol has no effect on seizure control
  2. BStop the drug when you have had no seizures for one whole week
  3. CDo not stop the drug suddenly, as this can trigger severe seizures
  4. DTake a double dose if you feel a seizure coming
2.PharmacologyHard

Which finding most favours serotonin syndrome over neuroleptic malignant syndrome?

  1. ARecent start of an antipsychotic drug
  2. BSlow onset over days with lead-pipe rigidity
  3. CA very high creatine kinase
  4. DRapid onset with hyperreflexia and clonus
3.Dosage calculationsMedium
18 kg15 mg/kgD = ? mg

A patient weighs 18 kg and is prescribed 15 mg/kg as a single dose. Find the dose D in mg.

18 kg15 mg/kg
D = mg
4.Dosage calculationsHard
250 mg/5 mLV = ? mL

A child weighing 12 kg is prescribed 5 mg/kg per dose of an oral suspension that contains 250 mg in 5 mL. What volume V do you give?

12 kg5 mg/kg250 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 1 mcg/LLD = ? mcg67 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 67 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.

67 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
51 kg55 · manSCr 1.4 mg/dLCrCl → τ = ? h

Practice exercise (made-up values, not clinical guidance). A 55-year-old man weighs 51 kg and has a serum creatinine of 1.4 mg/dL (124 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 tobramycin regimen is 120 mg every 8 h for a creatinine clearance of 120 mL/min. Keeping the dose, the interval is lengthened in proportion to the fall in clearance. Find the new dosing interval τ. Round to one decimal place.

55 years51 kgmanSCr = 1.4 mg/dL120 mg q8hCrCl normal 120 mL/min
τ = h

3Solutions

1.Pharmacology

Answer: C · Do not stop the drug suddenly, as this can trigger severe seizures

Why this is the answer

Abrupt withdrawal of antiepileptic drugs can cause rebound seizures and even status epilepticus. Any change is made gradually under medical supervision.

Answer

C · Do not stop the drug suddenly, as this can trigger severe seizures
2.Pharmacology

Answer: D · Rapid onset with hyperreflexia and clonus

Why this is the answer

Serotonin syndrome develops within hours of a serotonergic drug and causes clonus, hyperreflexia, agitation, dilated pupils and diarrhoea. NMS develops over days after a dopamine antagonist, with lead-pipe rigidity and slow reflexes.

Answer

D · Rapid onset with hyperreflexia and clonus
3.Dosage calculations

Answer: D = 270 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.

Dose

15·18 = 270 mg

Answer

D = 270 mg
4.Dosage calculations

Answer: V = 1.2 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

5·12 = 60 mg

Volume

V = (60/250)·5 = 1.2 mL

Answer

V = 1.2 mL
5.Clinical pharmacokinetics

Answer: LD = 670 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 = 7·67 = 469 L

Amount of active drug needed

Vd·C = 469·1 = 469 mcg

Loading dose

LD = 469/(1·0.7) = 670 mcg

Answer

LD = 670 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: τ = 22.3 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.

Creatinine clearance (Cockcroft–Gault)

CrCl = (140 − 55)·51/(72·1.4) = 43.01 mL/min

New interval

τ = 8·120/43.01 = 22.32 ≈ 22.3 h

Answer

τ = 22.3 h

In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.

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