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

Which is a well-known adverse effect of long-term oral corticosteroids?

  1. AHypoglycaemia
  2. BWeight loss
  3. CLow blood pressure
  4. DOsteoporosis
2.PharmacologyHard

A nurse gave a patient ten times the prescribed dose of hydromorphone. The patient is currently alert. What is the most appropriate sequence of actions?

  1. ASay nothing because the patient is alert
  2. BChange the chart so that it shows the correct dose, and continue to monitor
  3. CMonitor closely, have naloxone ready, inform the prescriber and report
  4. DGive another dose later to balance it out
3.Dosage calculationsMedium
25 kg2 mg/kg/day3× per dayD = ? mg

A patient weighs 25 kg. The prescribed dose is 2 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?

25 kg2 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
10%stockV₁ = ? mL

You must prepare 250 mL of a 2.5% (w/v) solution from a 10% (w/v) stock solution. What volume of stock V₁ do you need?

C₁ = 10%C₂ = 2.5%V₂ = 250 mL
V₁ = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)2 h25 mg/L14 h10.9 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 25 mg/L at 2 h and 10.9 mg/L at 14 h. Assume first-order elimination. Find the elimination rate constant k.

C1 = 25 mg/L (2 h)C2 = 10.9 mg/L (14 h)
k = h⁻¹
6.Clinical pharmacokineticsHard
Vd = 0.5 L/kg4 → 10 mg/LLD = ? mg58 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). A 58 kg patient has a theophylline level of 4 mg/L; the target is 10 mg/L. The drug is given intravenously as aminophylline (S = 0.8), and the volume of distribution is 0.5 L/kg. What extra loading dose LD raises the level to the target?

58 kgVd = 0.5 L/kgC = 4 → 10 mg/LS = 0.8
LD = mg

3Solutions

1.Pharmacology

Answer: D · Osteoporosis

Why this is the answer

Long-term corticosteroids reduce bone formation and raise fracture risk. They also cause weight gain, high blood glucose, hypertension and a higher infection risk.

Answer

D · Osteoporosis
2.Pharmacology

Answer: C · Monitor closely, have naloxone ready, inform the prescriber and report

Why this is the answer

The patient may become sedated and develop respiratory depression later, so close monitoring and a ready antidote are needed. The prescriber is informed, the patient is told honestly, and the error is reported to improve the system.

Answer

C · Monitor closely, have naloxone ready, inform the prescriber and report
3.Dosage calculations

Answer: D = 16.67 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.

Total per day

2·25 = 50 mg

Per dose

D = 50/3 = 16.67 mg

Answer

D = 16.67 mg
4.Dosage calculations

Answer: V₁ = 62.5 mL

Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.

Volume of stock

V₁ = 2.5·250/10 = 62.5 mL

Answer

V₁ = 62.5 mL
5.Clinical pharmacokinetics

Answer: k = 0.06918 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(25/10.9)/12 = 0.8301/12 = 0.06918 h⁻¹

Answer

k = 0.06918 h⁻¹
6.Clinical pharmacokinetics

Answer: LD = 217.5 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.

Volume of distribution

Vd = 0.5·58 = 29 L

Rise needed

10 − 4 = 6 mg/L

Loading dose

LD = 29·6/(0.8·1) = 217.5 mg

Answer

LD = 217.5 mg

In practice the dose is rounded to a convenient amount.

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