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 malnourished patient with alcohol dependence needs IV glucose. Which vitamin should be given before or with it?

  1. AThiamine (vitamin B1)
  2. BVitamin D
  3. CVitamin C
  4. DVitamin K (phytomenadione)
2.PharmacologyHard

A patient recently started on haloperidol develops high fever, "lead-pipe" muscle rigidity, confusion and a very high creatine kinase. What is the most likely diagnosis?

  1. AAcute dystonia
  2. BNeuroleptic malignant syndrome
  3. CMalignant hyperthermia from anaesthesia
  4. DSerotonin syndrome
3.Dosage calculationsMedium
25 kg2 mg/kg/day2× per dayD = ? mg

A patient weighs 25 kg. The prescribed dose is 2 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?

25 kg2 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 850 micrograms. The ampoule contains 1 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

850 mcg1 mg/mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 0.8 mcg/LLD = ? mcg87 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). An 87 kg patient is to be loaded with digoxin tablets to reach a level of 0.8 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.

87 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
62 kg42 · manSCr 2 mg/dLfe​ = 0.9D = ? mg

Practice exercise (made-up values, not clinical guidance). A 42-year-old man weighs 62 kg and has a serum creatinine of 2 mg/dL (177 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 atenolol dose is 100 mg for a creatinine clearance of 100 mL/min, and a fraction fe = 0.9 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.

42 years62 kgmanSCr = 2 mg/dL100 mgfe = 0.9CrCl normal 100 mL/min
D = mg

3Solutions

1.Pharmacology

Answer: A · Thiamine (vitamin B1)

Why this is the answer

Giving glucose without thiamine to a thiamine-deficient patient can trigger or worsen Wernicke's encephalopathy. Thiamine is therefore given before or alongside glucose.

Answer

A · Thiamine (vitamin B1)
2.Pharmacology

Answer: B · Neuroleptic malignant syndrome

Why this is the answer

Neuroleptic malignant syndrome follows dopamine antagonists and develops over days, with lead-pipe rigidity, fever and raised CK. Serotonin syndrome develops faster and features clonus and hyperreflexia.

Answer

B · Neuroleptic malignant syndrome
3.Dosage calculations

Answer: D = 25 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

2·25 = 50 mg

Per dose

D = 50/2 = 25 mg

Answer

D = 25 mg
4.Dosage calculations

Answer: V = 0.85 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 = 850/1000 = 0.85 mL

Answer

V = 0.85 mL
5.Clinical pharmacokinetics

Answer: LD = 696 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 = 7·87 = 609 L

Amount of active drug needed

Vd·C = 609·0.8 = 487.2 mcg

Loading dose

LD = 487.2/(1·0.7) = 696 mcg

Answer

LD = 696 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: D = 48 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 − 42)·62/(72·2) = 42.19 mL/min

Dose fraction (Dettli)

Q = 1 − 0.9·(1 − 42.19/100) = 0.4798

Adjusted dose

D = 0.4798·100 = 47.98 ≈ 48 mg

Answer

D = 48 mg

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

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