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 should a patient rinse the mouth after using an inhaled corticosteroid?

  1. ATo prevent a fall in blood glucose
  2. BTo reduce the risk of oral thrush (candidiasis) and hoarseness
  3. CTo stop the drug being absorbed too quickly into the blood
  4. DTo make the drug work faster in the lungs
2.PharmacologyHard

Why is vancomycin given by mouth, not intravenously, for Clostridioides difficile infection?

  1. AIntravenous vancomycin causes C. difficile infection
  2. BThe oral form is cheaper but has the same effect as IV
  3. COral vancomycin is not absorbed, so it reaches high levels in the colon
  4. DOral vancomycin is absorbed into the blood better than IV vancomycin
3.Dosage calculationsMedium
22 kg20 mg/kgD = ? mg

A patient weighs 22 kg and is prescribed 20 mg/kg as a single dose. Find the dose D in mg.

22 kg20 mg/kg
D = mg
4.Dosage calculationsHard
250 mg/5 mLV = ? mL

A patient weighs 198 lb. The prescription is 2 mg/kg as a single dose, and the stock contains 250 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give?

198 lb2 mg/kg250 mg/5 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)C₀ = 9 mg/Lt½ = 2.5 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 220 mg of tobramycin. The level back-extrapolated to time zero is 9 mg/L and the half-life is 2.5 h. Find the clearance CL in L/h.

D = 220 mgC₀ = 9 mg/Lt½ = 2.5 h
CL = L/h
6.Clinical pharmacokineticsHard
65 kg71 · manSCr 2.7 mg/dLfe​ = 0.6D = ? mg

Practice exercise (made-up values, not clinical guidance). A 71-year-old man weighs 65 kg and has a serum creatinine of 2.7 mg/dL (239 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual ciprofloxacin dose is 500 mg for a creatinine clearance of 100 mL/min, and a fraction fe = 0.6 of the drug is excreted unchanged by the kidneys. Using the Dettli dose fraction Q = 1 − fe·(1 − CrCl/normal CrCl), find the adjusted dose D. Round to the nearest whole number.

71 years65 kgmanSCr = 2.7 mg/dL500 mgfe = 0.6CrCl normal 100 mL/min
D = mg

3Solutions

1.Pharmacology

Answer: B · To reduce the risk of oral thrush (candidiasis) and hoarseness

Why this is the answer

Steroid left in the mouth and throat suppresses local immunity and can cause candidiasis and a hoarse voice. Rinsing and spitting, and using a spacer, reduce this risk.

Answer

B · To reduce the risk of oral thrush (candidiasis) and hoarseness
2.Pharmacology

Answer: C · Oral vancomycin is not absorbed, so it reaches high levels in the colon

Why this is the answer

Oral vancomycin stays in the gut and acts directly on C. difficile in the colon. IV vancomycin is not excreted into the gut in useful amounts, so it does not treat this infection.

Answer

C · Oral vancomycin is not absorbed, so it reaches high levels in the colon
3.Dosage calculations

Answer: D = 440 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

20·22 = 440 mg

Answer

D = 440 mg
4.Dosage calculations

Answer: V = 3.6 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

198/2.2 = 90 kg

Dose

2·90 = 180 mg

Volume

V = (180/250)·5 = 3.6 mL

Answer

V = 3.6 mL
5.Clinical pharmacokinetics

Answer: CL = 6.777 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 = 220/9 = 24.44 L

Rate constant

k = 0.693/2.5 = 0.2773 h⁻¹

Clearance

CL = 0.2773·24.44 = 6.777 L/h

Answer

CL = 6.777 L/h
6.Clinical pharmacokinetics

Answer: D = 269 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.

Creatinine clearance (Cockcroft–Gault)

CrCl = (140 − 71)·65/(72·2.7) = 23.07 mL/min

Dose fraction (Dettli)

Q = 1 − 0.6·(1 − 23.07/100) = 0.5384

Adjusted dose

D = 0.5384·500 = 269.2 ≈ 269 mg

Answer

D = 269 mg

In practice the dose is rounded to a convenient amount and checked against the product information.

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