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 about taking levothyroxine?

  1. ATake it on an empty stomach, 30–60 minutes before breakfast
  2. BTake it together with the iron tablet to save time
  3. CTake it only on days when feeling tired
  4. DTake it with milk at dinner, as calcium protects the stomach lining
2.PharmacologyHard

A patient on lisinopril for hypertension starts taking ibuprofen every day for knee pain. What is the main concern?

  1. AFaster liver metabolism of lisinopril, so it stops working
  2. BA large fall in blood pressure, with fainting and falls on standing up
  3. CA higher risk of a dry cough than with lisinopril alone
  4. DWeaker blood pressure control, kidney injury and high potassium
3.Dosage calculationsMedium
20%100 mLm = ? mg

How many milligrams of drug m are in 100 mL of a 20% (w/v) solution?

20% w/v100 mL
m = mg
4.Dosage calculationsHard
20k units1000 mL? mL/h500 units/h

An infusion contains 20000 units of a drug in 1000 mL. The prescription is 500 units per hour. At what rate R do you set the pump, in mL/h?

20000 units/1000 mL500 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
Vd = 0.5 L/kgC = 12 mg/LLD = ? mg91 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). A 91 kg patient is to be loaded intravenously with aminophylline to reach a theophylline level of 12 mg/L. The volume of distribution is 0.5 L/kg and the salt factor is S = 0.8. Find the loading dose LD of aminophylline in mg.

91 kgVd = 0.5 L/kgC = 12 mg/LS = 0.8
LD = mg
6.Clinical pharmacokineticsHard
0.1110t (h)C (mg/L)Cpeak​ = 6τ = ?Ctrough​ = 1

Practice exercise (made-up values, not clinical guidance). A patient's tobramycin half-life is 3.5 h. The target is a peak of 6 mg/L and a trough of 1 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.

t½ = 3.5 hCpeak = 6 mg/LCtrough = 1 mg/L
τ = h

3Solutions

1.Pharmacology

Answer: A · Take it on an empty stomach, 30–60 minutes before breakfast

Why this is the answer

Levothyroxine is best absorbed on an empty stomach, and calcium, iron and antacids should be taken some hours apart. It is taken every day, usually for life.

Answer

A · Take it on an empty stomach, 30–60 minutes before breakfast
2.Pharmacology

Answer: D · Weaker blood pressure control, kidney injury and high potassium

Why this is the answer

NSAIDs block prostaglandins that dilate the afferent arteriole and promote sodium loss. With an ACE inhibitor this can reduce blood pressure control and cause kidney injury and hyperkalaemia, especially if a diuretic is also used.

Answer

D · Weaker blood pressure control, kidney injury and high potassium
3.Dosage calculations

Answer: m = 20000 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

20% = 20 g/100 mL = 200 mg/mL

Mass of drug

m = 200·100 = 20000 mg

Answer

m = 20000 mg
4.Dosage calculations

Answer: R = 25 mL/h

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.

Concentration

20000/1000 = 20 units/mL

Pump rate

R = 500/20 = 25 mL/h

Answer

R = 25 mL/h
5.Clinical pharmacokinetics

Answer: LD = 682.5 mg

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 = 0.5·91 = 45.5 L

Amount of active drug needed

Vd·C = 45.5·12 = 546 mg

Loading dose

LD = 546/(0.8·1) = 682.5 mg

Answer

LD = 682.5 mg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: τ = 9 h

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.

Rate constant

k = 0.693/3.5 = 0.198 h⁻¹

Dosing interval

τ = ln(6/1)/0.198 = 1.792/0.198 = 9.047 ≈ 9 h

Answer

τ = 9 h

In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.

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