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 do NSAIDs such as ibuprofen increase the risk of stomach ulcers?

  1. AThey raise the pH of gastric acid
  2. BThey directly dissolve the mucus layer
  3. CThey increase the number of Helicobacter pylori bacteria in the stomach
  4. DThey reduce protective prostaglandins in the stomach lining
2.PharmacologyHard

Morphine 4 mg IV is ordered. The ampoule contains 10 mg/mL. What volume should be drawn up?

  1. A0.4 mL
  2. B2.5 mL
  3. C0.04 mL
  4. D4 mL
3.Dosage calculationsMedium
2%2 mLm = ? mg

How many milligrams of drug m are in 2 mL of a 2% (w/v) solution?

2% w/v2 mL
m = mg
4.Dosage calculationsHard
10%stockV₁ = ? mL

You must prepare 500 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 = 500 mL
V₁ = mL
5.Clinical pharmacokineticsMedium
VCss​ = 15 mg/LR = ? mg/hCL = 0.05 L/kg/h85 kg

Practice exercise (made-up values, not clinical guidance). An 85 kg patient receives a theophylline infusion. The clearance is 0.05 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 15 mg/L?

85 kgCL = 0.05 L/kg/hCss = 15 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
t (h)C (mg/L)Css​23 hC = ?

Practice exercise (made-up values, not clinical guidance). A theophylline infusion runs at 20 mg/h with no loading dose. The patient's clearance is 2 L/h and the half-life is 8 h. What is the level C after 23 h?

R = 20 mg/hCL = 2 L/ht½ = 8 ht = 23 h
C = mg/L

3Solutions

1.Pharmacology

Answer: D · They reduce protective prostaglandins in the stomach lining

Why this is the answer

NSAIDs inhibit COX-1, lowering prostaglandins that maintain mucus, bicarbonate secretion and blood flow in the stomach lining.

Answer

D · They reduce protective prostaglandins in the stomach lining
2.Pharmacology

Answer: A · 0.4 mL

Why this is the answer

4 mg ÷ 10 mg/mL = 0.4 mL. The unused remainder of a controlled drug is discarded with a witness.

Answer

A · 0.4 mL
3.Dosage calculations

Answer: m = 40 mg

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.

Concentration

2% = 2 g/100 mL = 20 mg/mL

Mass of drug

m = 20·2 = 40 mg

Answer

m = 40 mg
4.Dosage calculations

Answer: V₁ = 125 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 = 2.5·500/10 = 125 mL

Answer

V₁ = 125 mL
5.Clinical pharmacokinetics

Answer: R = 63.75 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

CL = 0.05·85 = 4.25 L/h

Infusion rate

R = 4.25·15 = 63.75 mg/h

Answer

R = 63.75 mg/h
6.Clinical pharmacokinetics

Answer: C = 8.637 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.

Steady-state level

Css = 20/2 = 10 mg/L

Rate constant

k = 0.693/8 = 0.08664 h⁻¹

Level after the given time

C = 10·(1 − e−0.08664·23) = 8.637 mg/L

Answer

C = 8.637 mg/L

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