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

Benzathine benzylpenicillin (penicillin G benzathine) is ordered. Which route is correct?

  1. AIntravenous infusion over 30 minutes
  2. BDeep intramuscular only
  3. CIntravenous push
  4. DSubcutaneous in the abdomen
2.PharmacologyHard

A patient has SIADH with mild hyponatraemia and no neurological symptoms. What is usually the first-line treatment?

  1. AFluid restriction
  2. BA rapid bolus of hypertonic saline
  3. CLarge volumes of IV glucose 5%
  4. DDesmopressin
3.Dosage calculationsMedium
80 kg7.5 mg/kgD = ? mg

A patient weighs 80 kg and is prescribed 7.5 mg/kg as a single dose. Find the dose D in mg.

80 kg7.5 mg/kg
D = mg
4.Dosage calculationsHard
50k units500 mL? mL/h1000 units/h

An infusion contains 50000 units of a drug in 500 mL. The prescription is 1000 units per hour. At what rate R do you set the pump, in mL/h?

50000 units/500 mL1000 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
VCss​ = 25 mg/LR = ? mg/hCL = 65 mL/min

Practice exercise (made-up values, not clinical guidance). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 65 mL/min. What infusion rate R in mg/h gives a steady-state level of 25 mg/L?

CL = 65 mL/minCss = 25 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
VCss,avg​ = ?1000 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. Each dose is 1000 mg of vancomycin. Find the average steady-state level Css,avg.

CL = 4 L/hτ = 12 hS = 1F = 1D = 1000 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: B · Deep intramuscular only

Why this is the answer

Benzathine penicillin is a depot suspension given deep IM. Accidental intravenous injection can cause cardiorespiratory arrest and death.

Answer

B · Deep intramuscular only
2.Pharmacology

Answer: A · Fluid restriction

Why this is the answer

In SIADH, excess ADH makes the kidneys retain water. Restricting fluid intake raises sodium gradually; hypertonic saline is kept for severe symptomatic cases, and hypotonic fluids and desmopressin would worsen it.

Answer

A · Fluid restriction
3.Dosage calculations

Answer: D = 600 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.

Dose

7.5·80 = 600 mg

Answer

D = 600 mg
4.Dosage calculations

Answer: R = 10 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

50000/500 = 100 units/mL

Pump rate

R = 1000/100 = 10 mL/h

Answer

R = 10 mL/h
5.Clinical pharmacokinetics

Answer: R = 97.5 mg/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.

Clearance in L/h

65·60/1000 = 3.9 L/h

Infusion rate

R = 3.9·25 = 97.5 mg/h

Answer

R = 97.5 mg/h
6.Clinical pharmacokinetics

Answer: Css,avg = 20.83 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.

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 1·1·1000/(4·12) = 20.83 mg/L

Answer

Css,avg = 20.83 mg/L

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