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 person who has never been vaccinated against tetanus has a deep, dirty wound. What is usually given?

  1. ATetanus vaccine only, after the wound heals
  2. BOral antibiotics only
  3. CTetanus vaccine and tetanus immunoglobulin
  4. DNo treatment unless symptoms appear
2.PharmacologyHard

Why is clavulanic acid combined with amoxicillin (co-amoxiclav)?

  1. AIt slows the kidney excretion of amoxicillin
  2. BIt makes amoxicillin cross the blood–brain barrier more easily
  3. CIt inhibits beta-lactamase enzymes that would destroy amoxicillin
  4. DIt reduces the risk of penicillin allergy
3.Dosage calculationsMedium
70 kg15 mg/kg/day2× per dayD = ? mg

A patient weighs 70 kg. The prescribed dose is 15 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?

70 kg15 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 3800 units of a drug that comes as 10000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

3800 units10000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 0.7 L/kgC = 15 mg/LLD = ? mg68 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). A 68 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 15 mg/L. The volume of distribution is 0.7 L/kg and the salt factor is S = 0.92. Find the loading dose LD of phenytoin sodium in mg.

68 kgVd = 0.7 L/kgC = 15 mg/LS = 0.92
LD = mg
6.Clinical pharmacokineticsHard
Vd = 0.5 L/kg6 → 15 mg/LLD = ? mg83 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). An 83 kg patient has a theophylline level of 6 mg/L; the target is 15 mg/L. The drug is given intravenously as aminophylline (S = 0.8), and the volume of distribution is 0.5 L/kg. What extra loading dose LD raises the level to the target?

83 kgVd = 0.5 L/kgC = 6 → 15 mg/LS = 0.8
LD = mg

3Solutions

1.Pharmacology

Answer: C · Tetanus vaccine and tetanus immunoglobulin

Why this is the answer

Tetanus immunoglobulin gives immediate passive protection, while the vaccine starts active immunity. Thorough wound cleaning is also essential.

Answer

C · Tetanus vaccine and tetanus immunoglobulin
2.Pharmacology

Answer: C · It inhibits beta-lactamase enzymes that would destroy amoxicillin

Why this is the answer

Many bacteria produce beta-lactamases that inactivate penicillins. Clavulanic acid inhibits these enzymes, so amoxicillin can work against these organisms.

Answer

C · It inhibits beta-lactamase enzymes that would destroy amoxicillin
3.Dosage calculations

Answer: D = 525 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

15·70 = 1050 mg

Per dose

D = 1050/2 = 525 mg

Answer

D = 525 mg
4.Dosage calculations

Answer: V = 0.38 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 = 3800/10000 = 0.38 mL

On the syringe

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

Answer

V = 0.38 mL
5.Clinical pharmacokinetics

Answer: LD = 776.1 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 = 0.7·68 = 47.6 L

Amount of active drug needed

Vd·C = 47.6·15 = 714 mg

Loading dose

LD = 714/(0.92·1) = 776.1 mg

Answer

LD = 776.1 mg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: LD = 466.9 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.

Volume of distribution

Vd = 0.5·83 = 41.5 L

Rise needed

15 − 6 = 9 mg/L

Loading dose

LD = 41.5·9/(0.8·1) = 466.9 mg

Answer

LD = 466.9 mg

In practice the dose is rounded to a convenient amount.

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