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

Why is IV promethazine given with great caution?

  1. AIt is a strong opioid that causes addiction
  2. BIt causes a severe rise in blood pressure when it is given intravenously
  3. CIt causes immediate kidney failure
  4. DIt can cause severe tissue injury if it leaks or enters an artery
2.PharmacologyHard

A patient on rifampicin, isoniazid, pyrazinamide and ethambutol develops a painful swollen big toe. Which drug is most likely responsible?

  1. ARifampicin
  2. BPyrazinamide
  3. CEthambutol
  4. DIsoniazid
3.Dosage calculationsMedium
39 kgBSA = 1.18 m²375 mg/m²D = ? mg

A patient weighing 39 kg has a body surface area of 1.18 m². The prescription is 375 mg/m². Find the dose D in mg.

39 kgBSA = 1.18 m²375 mg/m²
D = mg
4.Dosage calculationsHard
100 mg/1 mLV = ? mL

A patient weighs 140.8 lb. The prescription is 10 mg/kg as a single dose, and the stock contains 100 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give?

140.8 lb10 mg/kg100 mg/1 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)C₀ = 12 mg/Lt½ = 2.5 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 200 mg of gentamicin. The level back-extrapolated to time zero is 12 mg/L and the half-life is 2.5 h. Find the clearance CL in L/h.

D = 200 mgC₀ = 12 mg/Lt½ = 2.5 h
CL = L/h
6.Clinical pharmacokineticsHard
t (h)C (mg/L)Css​15 hC = ?

Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 100 mg/h with no loading dose. The patient's clearance is 5 L/h and the half-life is 6 h. What is the level C after 15 h?

R = 100 mg/hCL = 5 L/ht½ = 6 ht = 15 h
C = mg/L

3Solutions

1.Pharmacology

Answer: D · It can cause severe tissue injury if it leaks or enters an artery

Why this is the answer

Promethazine is a vesicant. Deep intramuscular injection is the preferred parenteral route, and if given IV it is diluted, given slowly into a well-running large vein, and stopped at once if the patient reports burning or pain.

Answer

D · It can cause severe tissue injury if it leaks or enters an artery
2.Pharmacology

Answer: B · Pyrazinamide

Why this is the answer

Pyrazinamide reduces uric acid excretion and can cause hyperuricaemia and gout. It is also hepatotoxic, like isoniazid and rifampicin.

Answer

B · Pyrazinamide
3.Dosage calculations

Answer: D = 442.5 mg

Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).

Dose

D = 375·1.18 = 442.5 mg

Answer

D = 442.5 mg
4.Dosage calculations

Answer: V = 6.4 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.

Weight in kg

140.8/2.2 = 64 kg

Dose

10·64 = 640 mg

Volume

V = (640/100)·1 = 6.4 mL

Answer

V = 6.4 mL
5.Clinical pharmacokinetics

Answer: CL = 4.621 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 = 200/12 = 16.67 L

Rate constant

k = 0.693/2.5 = 0.2773 h⁻¹

Clearance

CL = 0.2773·16.67 = 4.621 L/h

Answer

CL = 4.621 L/h
6.Clinical pharmacokinetics

Answer: C = 16.46 mg/L

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.

Steady-state level

Css = 100/5 = 20 mg/L

Rate constant

k = 0.693/6 = 0.1155 h⁻¹

Level after the given time

C = 20·(1 − e−0.1155·15) = 16.46 mg/L

Answer

C = 16.46 mg/L

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