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

What should the nurse teach a patient starting nitrofurantoin?

  1. AExpect blue urine, which shows that the drug is working well
  2. BStop it as soon as the burning settles
  3. CTake it on an empty stomach with an antacid
  4. DTake it with food, and the urine may turn dark yellow or brown
2.PharmacologyHard

A man on long-term testosterone therapy has a rising haematocrit. Why is this important?

  1. AA high haematocrit shows that the testosterone is not being absorbed
  2. BIt is a sign of liver failure caused by testosterone
  3. CIt means the testosterone dose is too low
  4. DTestosterone raises red cell production, increasing clot risk
3.Dosage calculationsMedium
15 kgBSA = 0.84 m²375 mg/m²D = ? mg

A patient weighing 15 kg has a body surface area of 0.84 m². The prescription is 375 mg/m². Find the dose D in mg.

15 kgBSA = 0.84 m²375 mg/m²
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 4600 units of a drug that comes as 10000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

4600 units10000 units/mL
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 170 mg of tobramycin. The level back-extrapolated to time zero is 9 mg/L and the half-life is 2.5 h. Find the volume of distribution Vd.

D = 170 mgC₀ = 9 mg/Lt½ = 2.5 h
Vd = L
6.Clinical pharmacokineticsHard
76 kg58 · womanSCr 2.1 mg/dLfe​ = 0.66D = ? mg

Practice exercise (made-up values, not clinical guidance). A 58-year-old woman weighs 76 kg and has a serum creatinine of 2.1 mg/dL (186 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 levetiracetam dose is 1000 mg for a creatinine clearance of 100 mL/min, and a fraction fe = 0.66 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.

58 years76 kgwomanSCr = 2.1 mg/dL1000 mgfe = 0.66CrCl normal 100 mL/min
D = mg

3Solutions

1.Pharmacology

Answer: D · Take it with food, and the urine may turn dark yellow or brown

Why this is the answer

Nitrofurantoin is taken with food to reduce nausea and can harmlessly darken the urine. The full course is completed, and cough, breathlessness or numbness should be reported.

Answer

D · Take it with food, and the urine may turn dark yellow or brown
2.Pharmacology

Answer: D · Testosterone raises red cell production, increasing clot risk

Why this is the answer

Testosterone increases erythropoiesis and can cause polycythaemia, which increases blood viscosity and thrombosis risk. Haematocrit is monitored, and the dose may be reduced or paused.

Answer

D · Testosterone raises red cell production, increasing clot risk
3.Dosage calculations

Answer: D = 315 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 = 375·0.84 = 315 mg

Answer

D = 315 mg
4.Dosage calculations

Answer: V = 0.46 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.

Volume

V = 4600/10000 = 0.46 mL

On the syringe

On this 1 mL syringe every small line is 0.01 mL.

Answer

V = 0.46 mL
5.Clinical pharmacokinetics

Answer: Vd = 18.89 L

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 = 170/9 = 18.89 L

Answer

Vd = 18.89 L
6.Clinical pharmacokinetics

Answer: D = 571 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 − 58)·76/(72·2.1)·0.85 = 35.03 mL/min

Dose fraction (Dettli)

Q = 1 − 0.66·(1 − 35.03/100) = 0.5712

Adjusted dose

D = 0.5712·1000 = 571.2 ≈ 571 mg

Answer

D = 571 mg

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

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