Pharmacology: cram pack

Formula sheets, the key method steps for every topic and 6 practice problems, with full solutions at the back.

New problemsBack to the course

In the print window, choose “Save as PDF” to keep a copy on your device.

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

Before starting a TNF-alpha inhibitor such as adalimumab, which test is required?

  1. AAn echocardiogram in every patient
  2. BScreening for latent tuberculosis
  3. CA glucose tolerance test
  4. DA bone density scan
2.PharmacologyHard

Why are antipsychotics used with great caution in older people with dementia?

  1. AThey are linked to a higher risk of stroke and death
  2. BThey cause severe hypoglycaemia in older people
  3. CThey are not absorbed in people over 65
  4. DThey always cure the dementia and stop all behaviour problems
3.Dosage calculationsMedium
024681010 mL

A child weighing 35 kg is prescribed 4 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?

35 kg4 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
20k units1000 mL? mL/h1500 units/h

An infusion contains 20000 units of a drug in 1000 mL. The prescription is 1500 units per hour. At what rate R do you set the pump, in mL/h?

20000 units/1000 mL1500 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)1 h6 mg/L3 h3 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of tobramycin, the level is 6 mg/L at 1 h and 3 mg/L at 3 h. Assume first-order elimination. Find the elimination rate constant k.

C1 = 6 mg/L (1 h)C2 = 3 mg/L (3 h)
k = h⁻¹
6.Clinical pharmacokineticsHard
Vd = 0.25 L/kg1 → 7 mg/LD = ? mg79 kg

Practice exercise (made-up values, not clinical guidance). A 79 kg patient on regular tobramycin doses is at steady state. The target is a peak of 7 mg/L and a trough of 1 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?

79 kgVd = 0.25 L/kgCpeak = 7 mg/LCtrough = 1 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: B · Screening for latent tuberculosis

Why this is the answer

TNF inhibitors can reactivate latent TB, so patients are screened with a TB blood test or skin test and chest X-ray. Hepatitis B is usually checked as well.

Answer

B · Screening for latent tuberculosis
2.Pharmacology

Answer: A · They are linked to a higher risk of stroke and death

Why this is the answer

In older people with dementia, antipsychotics increase the risk of stroke and death. Non-drug approaches are tried first, and antipsychotics are used at low doses for short periods if needed.

Answer

A · They are linked to a higher risk of stroke and death
3.Dosage calculations

Answer: V = 2.8 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 = 4·35 = 140 mg

Volume

V = 140/50 = 2.8 mL

On the syringe

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

Answer

V = 2.8 mL
4.Dosage calculations

Answer: R = 75 mL/h

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.

Concentration

20000/1000 = 20 units/mL

Pump rate

R = 1500/20 = 75 mL/h

Answer

R = 75 mL/h
5.Clinical pharmacokinetics

Answer: k = 0.3466 h⁻¹

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.

Elimination rate constant

k = ln(6/3)/2 = 0.6931/2 = 0.3466 h⁻¹

Answer

k = 0.3466 h⁻¹
6.Clinical pharmacokinetics

Answer: D = 118.5 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 = 0.25·79 = 19.75 L

Dose

D = 19.75·(7 − 1) = 118.5 mg

Answer

D = 118.5 mg

In practice the dose is rounded to a convenient amount.

ExamProblems · examproblems.com/courses/pharmacology