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 is starting olanzapine. Which monitoring is most important over the following months?

  1. AHearing tests and vision tests every month
  2. BINR and platelet count
  3. CWeight, blood glucose and blood lipids
  4. DPeak expiratory flow
2.PharmacologyHard

A drug is ordered at 5 micrograms/kg/min for an 80 kg patient. The infusion contains 1,600 micrograms per mL. What rate in mL/h is needed?

  1. A150 mL/h
  2. B4 mL/h
  3. C15 mL/h
  4. D25 mL/h
3.Dosage calculationsMedium
024681010 mL

A child weighing 10 kg is prescribed 20 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?

10 kg20 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
250 mg/5 mLV = ? mL

A child weighing 20 kg is prescribed 10 mg/kg per dose of an oral suspension that contains 250 mg in 5 mL. What volume V do you give?

20 kg10 mg/kg250 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 4 mg/LR = ? mg/minCL = 650 mL/min

Practice exercise (made-up values, not clinical guidance). A patient has a lidocaine clearance of 650 mL/min. What infusion rate R in mg/min keeps the steady-state level at 4 mg/L?

CL = 650 mL/minCss = 4 mg/L
R = mg/min
6.Clinical pharmacokineticsHard
Vd = 0.25 L/kg0.5 → 7 mg/LD = ? mg60 kg

Practice exercise (made-up values, not clinical guidance). A 60 kg patient on regular gentamicin doses is at steady state. The target is a peak of 7 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.25 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?

60 kgVd = 0.25 L/kgCpeak = 7 mg/LCtrough = 0.5 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: C · Weight, blood glucose and blood lipids

Why this is the answer

Olanzapine and several other atypical antipsychotics cause weight gain, insulin resistance and dyslipidaemia. Weight, waist size, glucose and lipids are checked regularly.

Answer

C · Weight, blood glucose and blood lipids
2.Pharmacology

Answer: C · 15 mL/h

Why this is the answer

5 × 80 = 400 micrograms/min, × 60 = 24,000 micrograms/h, ÷ 1,600 micrograms/mL = 15 mL/h. Weight-based infusions are double-checked because errors are easy to make.

Answer

C · 15 mL/h
3.Dosage calculations

Answer: V = 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 = 20·10 = 200 mg

Volume

V = 200/25 = 8 mL

On the syringe

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

Answer

V = 8 mL
4.Dosage calculations

Answer: V = 4 mL

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.

Dose from weight

10·20 = 200 mg

Volume

V = (200/250)·5 = 4 mL

Answer

V = 4 mL
5.Clinical pharmacokinetics

Answer: R = 2.6 mg/min

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.

Clearance in L/min

650 mL/min = 0.65 L/min

Infusion rate

R = 0.65·4 = 2.6 mg/min

Answer

R = 2.6 mg/min
6.Clinical pharmacokinetics

Answer: D = 97.5 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 = 0.25·60 = 15 L

Dose

D = 15·(7 − 0.5) = 97.5 mg

Answer

D = 97.5 mg

In practice the dose is rounded to a convenient amount.

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