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 patient has oral mucositis after chemotherapy. Which advice is appropriate?

  1. AUse an alcohol-based mouthwash several times a day to kill germs
  2. BUse a soft toothbrush and rinse with saline or a bland mouthwash
  3. CBrush hard with a firm toothbrush to remove debris
  4. DEat spicy and acidic foods to stimulate healing
2.PharmacologyHard

An older patient with coronary artery disease is starting levothyroxine for hypothyroidism. Why is a low starting dose used?

  1. AOlder patients absorb levothyroxine much better, so small doses are all they need
  2. BHigh starting doses cause permanent hypothyroidism
  3. CFast replacement raises cardiac oxygen demand and can cause angina
  4. DLevothyroxine causes severe hypoglycaemia in older patients
3.Dosage calculationsMedium
15 kg10 mg/kg/day2× per dayD = ? mg

A patient weighs 15 kg. The prescribed dose is 10 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?

15 kg10 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 700 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?

700 units1000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)C₀ = 10 mg/Lt½ = 3 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 280 mg of gentamicin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 3 h. Find the clearance CL in L/h.

D = 280 mgC₀ = 10 mg/Lt½ = 3 h
CL = L/h
6.Clinical pharmacokineticsHard
t (h)C (mg/L)Css​t = ?75%

Practice exercise (made-up values, not clinical guidance). A theophylline infusion is started without a loading dose. The half-life in this patient is 8 h. How long t does it take to reach 75% of the steady-state level?

t½ = 8 h75% Css
t = h

3Solutions

1.Pharmacology

Answer: B · Use a soft toothbrush and rinse with saline or a bland mouthwash

Why this is the answer

Chemotherapy damages rapidly dividing mucosal cells. Gentle oral care, saline rinses and avoiding alcohol, spicy and acidic foods reduce pain and infection risk.

Answer

B · Use a soft toothbrush and rinse with saline or a bland mouthwash
2.Pharmacology

Answer: C · Fast replacement raises cardiac oxygen demand and can cause angina

Why this is the answer

Thyroid hormone increases metabolic rate, heart rate and contractility. In older people and those with heart disease, the dose is started low and increased slowly to avoid ischaemia and arrhythmias.

Answer

C · Fast replacement raises cardiac oxygen demand and can cause angina
3.Dosage calculations

Answer: D = 75 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

10·15 = 150 mg

Per dose

D = 150/2 = 75 mg

Answer

D = 75 mg
4.Dosage calculations

Answer: V = 0.7 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 = 700/1000 = 0.7 mL

On the syringe

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

Answer

V = 0.7 mL
5.Clinical pharmacokinetics

Answer: CL = 6.469 L/h

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 = 280/10 = 28 L

Rate constant

k = 0.693/3 = 0.231 h⁻¹

Clearance

CL = 0.231·28 = 6.469 L/h

Answer

CL = 6.469 L/h
6.Clinical pharmacokinetics

Answer: t = 16 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.

Rate constant

k = 0.693/8 = 0.08664 h⁻¹

Time to the given fraction of steady state

t = −ln(1 − 0.75)/0.08664 = 1.386/0.08664 = 16 h

Answer

t = 16 h

That is 2 half-lives.

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