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

A partial agonist is given together with a high dose of a full agonist. What happens to the response?

  1. AIt rises above the maximum of the full agonist
  2. BIt doubles, because both drugs activate the receptor
  3. CIt stays exactly the same as with the high dose of full agonist alone
  4. DIt falls, because the partial agonist competes for the receptors
2.PharmacologyHard

Which finding most favours serotonin syndrome over neuroleptic malignant syndrome?

  1. AA very high creatine kinase
  2. BSlow onset over days with lead-pipe rigidity
  3. CRapid onset with hyperreflexia and clonus
  4. DRecent start of an antipsychotic drug
3.Dosage calculationsMedium
80 kg10 mg/kg/day3× per dayD = ? mg

A patient weighs 80 kg. The prescribed dose is 10 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?

80 kg10 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 1.32 mg. The ampoule contains 2000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

1.32 mg2000 mcg/mL
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)C₀ = 12 mg/Lt½ = 2.5 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 210 mg of tobramycin. The level back-extrapolated to time zero is 12 mg/L and the half-life is 2.5 h. Find the volume of distribution Vd.

D = 210 mgC₀ = 12 mg/Lt½ = 2.5 h
Vd = L
6.Clinical pharmacokineticsHard
79 kg59 · manSCr 3 mg/dLfe​ = 0.66D = ? mg

Practice exercise (made-up values, not clinical guidance). A 59-year-old man weighs 79 kg and has a serum creatinine of 3 mg/dL (265 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 levetiracetam dose is 1000 mg for a creatinine clearance of 100 mL/min, and a fraction fe = 0.66 of the drug is excreted unchanged by the kidneys. Using the Dettli dose fraction Q = 1 − fe·(1 − CrCl/normal CrCl), find the adjusted dose D. Round to the nearest whole number.

59 years79 kgmanSCr = 3 mg/dL1000 mgfe = 0.66CrCl normal 100 mL/min
D = mg

3Solutions

1.Pharmacology

Answer: D · It falls, because the partial agonist competes for the receptors

Why this is the answer

A partial agonist has lower efficacy. When it displaces a full agonist from receptors, the total response drops. Buprenorphine can precipitate withdrawal in people using full opioid agonists for this reason.

Answer

D · It falls, because the partial agonist competes for the receptors
2.Pharmacology

Answer: C · 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

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

Answer: D = 266.7 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

10·80 = 800 mg

Per dose

D = 800/3 = 266.7 mg

Answer

D = 266.7 mg
4.Dosage calculations

Answer: V = 0.66 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

1.32 mg = 1320 mcg

Volume

V = 1320/2000 = 0.66 mL

Answer

V = 0.66 mL
5.Clinical pharmacokinetics

Answer: Vd = 17.5 L

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 = 210/12 = 17.5 L

Answer

Vd = 17.5 L
6.Clinical pharmacokinetics

Answer: D = 536 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 − 59)·79/(72·3) = 29.63 mL/min

Dose fraction (Dettli)

Q = 1 − 0.66·(1 − 29.63/100) = 0.5355

Adjusted dose

D = 0.5355·1000 = 535.5 ≈ 536 mg

Answer

D = 536 mg

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

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