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 a spacer recommended with a metered-dose inhaler?

  1. AIt turns the inhaler into a nebuliser
  2. BIt doubles the dose of drug released by each puff of the inhaler
  3. CIt removes the need to shake the inhaler
  4. DMore drug reaches the lungs and less stays in the mouth
2.PharmacologyHard

Why is pyridoxine (vitamin B6) often given together with isoniazid for tuberculosis?

  1. ATo increase the absorption of isoniazid
  2. BTo prevent peripheral neuropathy
  3. CTo reduce bacterial resistance
  4. DTo prevent liver damage from isoniazid
3.Dosage calculationsMedium
024681010 mL

A child weighing 38 kg is prescribed 4 mg/kg of a drug. The stock solution contains 40 mg/mL. Draw up the dose: what volume V do you give?

38 kg4 mg/kg40 mg/mL
V = mL
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 490 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

490 units1000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 1 mcg/LLD = ? mcg85 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). An 85 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.

85 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
77 kg60 · manSCr 1.9 mg/dLCrCl → D = ? mg

Practice exercise (made-up values, not clinical guidance). A 60-year-old man weighs 77 kg and has a serum creatinine of 1.9 mg/dL (168 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 every 12 h for a creatinine clearance of 120 mL/min. Keeping the interval, the dose is reduced in proportion to the creatinine clearance. Find the adjusted dose D. Round to the nearest whole number.

60 years77 kgmanSCr = 1.9 mg/dL1000 mg q12hCrCl normal 120 mL/min
D = mg

3Solutions

1.Pharmacology

Answer: D · More drug reaches the lungs and less stays in the mouth

Why this is the answer

A spacer holds the aerosol so it can be inhaled slowly, without precise coordination. This improves lung delivery and reduces mouth side effects such as thrush from inhaled steroids.

Answer

D · More drug reaches the lungs and less stays in the mouth
2.Pharmacology

Answer: B · To prevent peripheral neuropathy

Why this is the answer

Isoniazid causes pyridoxine deficiency, which can lead to peripheral neuropathy. The risk is greater in slow acetylators, malnourished patients and people with diabetes or alcohol dependence.

Answer

B · To prevent peripheral neuropathy
3.Dosage calculations

Answer: V = 3.8 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 = 4·38 = 152 mg

Volume

V = 152/40 = 3.8 mL

On the syringe

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

Answer

V = 3.8 mL
4.Dosage calculations

Answer: V = 0.49 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.

Volume

V = 490/1000 = 0.49 mL

On the syringe

On this 1 mL syringe every small line is 0.01 mL.

Answer

V = 0.49 mL
5.Clinical pharmacokinetics

Answer: LD = 850 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 = 7·85 = 595 L

Amount of active drug needed

Vd·C = 595·1 = 595 mcg

Loading dose

LD = 595/(1·0.7) = 850 mcg

Answer

LD = 850 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: D = 375 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 − 60)·77/(72·1.9) = 45.03 mL/min

Adjusted dose

D = 1000·45.03/120 = 375.2 ≈ 375 mg

Answer

D = 375 mg

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

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