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 taking hydralazine for several months develops joint pain, fever and a rash. Anti-histone antibodies are positive. What is the most likely diagnosis?

  1. ADrug-induced lupus
  2. BRheumatoid arthritis
  3. CAn acute viral infection
  4. DGout
3.Dosage calculationsMedium
70 kg25 mg/kg/day2× per dayD = ? mg

A patient weighs 70 kg. The prescribed dose is 25 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?

70 kg25 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
20%stockV₁ = ? mL

You must prepare 250 mL of a 2.5% (w/v) solution from a 20% (w/v) stock solution. What volume of stock V₁ do you need?

C₁ = 20%C₂ = 2.5%V₂ = 250 mL
V₁ = mL
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 0.8 mcg/LLD = ? mcg88 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). An 88 kg patient is to be loaded with digoxin tablets to reach a level of 0.8 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.

88 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
Vd = 7 L/kg0.5 → 0.8 mcg/LLD = ? mcg89 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). An 89 kg patient has a digoxin level of 0.5 mcg/L; the target is 0.8 mcg/L. The volume of distribution is 7 L/kg and the tablets have F = 0.7. What extra loading dose LD raises the level to the target?

89 kgVd = 7 L/kgC = 0.5 → 0.8 mcg/LF = 0.7
LD = mcg

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 · Drug-induced lupus

Why this is the answer

Hydralazine and procainamide are classic causes of drug-induced lupus, especially in slow acetylators. Symptoms usually resolve after the drug is stopped.

Answer

A · Drug-induced lupus
3.Dosage calculations

Answer: D = 875 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

25·70 = 1750 mg

Per dose

D = 1750/2 = 875 mg

Answer

D = 875 mg
4.Dosage calculations

Answer: V₁ = 31.25 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 = 2.5·250/20 = 31.25 mL

Answer

V₁ = 31.25 mL
5.Clinical pharmacokinetics

Answer: LD = 704 mcg

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 = 7·88 = 616 L

Amount of active drug needed

Vd·C = 616·0.8 = 492.8 mcg

Loading dose

LD = 492.8/(1·0.7) = 704 mcg

Answer

LD = 704 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: LD = 267 mcg

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 = 7·89 = 623 L

Rise needed

0.8 − 0.5 = 0.3 mcg/L

Loading dose

LD = 623·0.3/(1·0.7) = 267 mcg

Answer

LD = 267 mcg

In practice the dose is rounded to a convenient amount.

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