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

How should oral potassium chloride tablets be taken?

  1. AWith food and plenty of water, swallowed whole if slow-release
  2. BCrushed and dissolved under the tongue
  3. COn an empty stomach with only a small sip of water, then lie down
  4. DLying down straight after the dose
2.PharmacologyHard

Why is glibenclamide (glyburide) generally avoided in older adults?

  1. AIt is long-acting and can cause prolonged, severe hypoglycaemia
  2. BIt causes severe weight loss and muscle wasting in older people
  3. CIt is not absorbed in people over 65
  4. DIt causes high blood glucose in older adults
3.Dosage calculationsMedium
25 kgBSA = 1.05 m²175 mg/m²D = ? mg

A patient weighing 25 kg has a body surface area of 1.05 m². The prescription is 175 mg/m². Find the dose D in mg.

25 kgBSA = 1.05 m²175 mg/m²
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 2.08 mg. The ampoule contains 4000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

2.08 mg4000 mcg/mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 0.5 L/kgC = 12 mg/LLD = ? mg86 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). An 86 kg patient is to be loaded intravenously with aminophylline to reach a theophylline level of 12 mg/L. The volume of distribution is 0.5 L/kg and the salt factor is S = 0.8. Find the loading dose LD of aminophylline in mg.

86 kgVd = 0.5 L/kgC = 12 mg/LS = 0.8
LD = mg
6.Clinical pharmacokineticsHard
82 kg88 · manSCr 2.6 mg/dLfe​ = 0.9D = ? mg

Practice exercise (made-up values, not clinical guidance). An 88-year-old man weighs 82 kg and has a serum creatinine of 2.6 mg/dL (230 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.

88 years82 kgmanSCr = 2.6 mg/dL100 mgfe = 0.9CrCl normal 100 mL/min
D = mg

3Solutions

1.Pharmacology

Answer: A · With food and plenty of water, swallowed whole if slow-release

Why this is the answer

Oral potassium can cause nausea and, if a tablet lodges, ulceration of the oesophagus or gut. Taking it with food and plenty of water and staying upright reduces this; levels are monitored.

Answer

A · With food and plenty of water, swallowed whole if slow-release
2.Pharmacology

Answer: A · It is long-acting and can cause prolonged, severe hypoglycaemia

Why this is the answer

Glibenclamide has a long action and active metabolites that accumulate when kidney function declines. Older adults are at high risk of prolonged hypoglycaemia, so shorter-acting agents or other drug classes are preferred.

Answer

A · It is long-acting and can cause prolonged, severe hypoglycaemia
3.Dosage calculations

Answer: D = 183.8 mg

Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).

Dose

D = 175·1.05 = 183.8 mg

Answer

D = 183.8 mg
4.Dosage calculations

Answer: V = 0.52 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

2.08 mg = 2080 mcg

Volume

V = 2080/4000 = 0.52 mL

Answer

V = 0.52 mL
5.Clinical pharmacokinetics

Answer: LD = 645 mg

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 = 0.5·86 = 43 L

Amount of active drug needed

Vd·C = 43·12 = 516 mg

Loading dose

LD = 516/(0.8·1) = 645 mg

Answer

LD = 645 mg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: D = 31 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 − 88)·82/(72·2.6) = 22.78 mL/min

Dose fraction (Dettli)

Q = 1 − 0.9·(1 − 22.78/100) = 0.305

Adjusted dose

D = 0.305·100 = 30.5 ≈ 31 mg

Answer

D = 31 mg

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

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