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

Which lab tests are monitored in a patient taking carbamazepine?

  1. ASerum amylase and lipase
  2. BThyroid antibodies and cortisol
  3. CFull blood count and serum sodium
  4. DINR and aPTT
2.PharmacologyHard

Combining several drugs that prolong the QT interval raises the risk of which life-threatening arrhythmia?

  1. AFirst-degree heart block
  2. BSinus tachycardia
  3. CTorsades de pointes
  4. DAtrial fibrillation
3.Dosage calculationsMedium
024681010 mL

A child weighing 18 kg is prescribed 4 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?

18 kg4 mg/kg10 mg/mL
V = mL
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 1.78 mg. The ampoule contains 2000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

1.78 mg2000 mcg/mL
V = mL
5.Clinical pharmacokineticsMedium
10100t (h)C (mg/L)1 h25 mg/L7 h12.5 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 25 mg/L at 1 h and 12.5 mg/L at 7 h. Assume first-order elimination. Find the elimination rate constant k.

C1 = 25 mg/L (1 h)C2 = 12.5 mg/L (7 h)
k = h⁻¹
6.Clinical pharmacokineticsHard
VCss,avg​ = 20 mg/LD = ? mg · q12hCL = 4 L/hS = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 4 L/h. What dose D in mg gives an average steady-state level of 20 mg/L?

CL = 4 L/hτ = 12 hS = 1F = 1Css,avg = 20 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: C · Full blood count and serum sodium

Why this is the answer

Carbamazepine can rarely cause bone marrow suppression and commonly lowers serum sodium. Blood counts, sodium and liver tests are checked, especially early in treatment.

Answer

C · Full blood count and serum sodium
2.Pharmacology

Answer: C · Torsades de pointes

Why this is the answer

A long QT interval delays repolarisation and can trigger torsades de pointes, which may turn into ventricular fibrillation. Drugs such as some macrolides, antipsychotics and antiarrhythmics add to this risk.

Answer

C · Torsades de pointes
3.Dosage calculations

Answer: V = 7.2 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 = 4·18 = 72 mg

Volume

V = 72/10 = 7.2 mL

On the syringe

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

Answer

V = 7.2 mL
4.Dosage calculations

Answer: V = 0.89 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.

Same units

1.78 mg = 1780 mcg

Volume

V = 1780/2000 = 0.89 mL

Answer

V = 0.89 mL
5.Clinical pharmacokinetics

Answer: k = 0.1155 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(25/12.5)/6 = 0.6931/6 = 0.1155 h⁻¹

Answer

k = 0.1155 h⁻¹
6.Clinical pharmacokinetics

Answer: D = 960 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.

Dose

D = Css,avg·CL·τ/(S·F) = 20·4·12/(1·1) = 960 mg

Answer

D = 960 mg

ExamProblems · examproblems.com/courses/pharmacology