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

During an infusion of a vesicant chemotherapy drug, the patient reports burning, and the site is swollen. What should the nurse do first?

  1. AFlush the line with a large volume of saline
  2. BStop the infusion, leave the cannula in and follow the protocol
  3. CIncrease the infusion rate to finish quickly
  4. DRemove the cannula at once and massage the area firmly
2.PharmacologyHard

Why is gentamicin dosing monitored with blood levels?

  1. AIt only works at very high concentrations
  2. BIt causes severe hypoglycaemia
  3. CIt is metabolised entirely by the liver, so liver function decides the dose
  4. DIt is nephrotoxic and ototoxic with a narrow therapeutic index
3.Dosage calculationsMedium
024681010 mL

A child weighing 7 kg is prescribed 10 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?

7 kg10 mg/kg10 mg/mL
V = mL
4.Dosage calculationsHard
36 kg138 cmBSA = √(h·w/3600)250 mg/m²D = ? mg

A patient is 138 cm tall and weighs 36 kg. The prescription is 250 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.

138 cm36 kg250 mg/m²
D = mg
5.Clinical pharmacokineticsMedium
Vd = 0.7 L/kgC = 15 mg/LLD = ? mg95 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). A 95 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 15 mg/L. The volume of distribution is 0.7 L/kg and the salt factor is S = 0.92. Find the loading dose LD of phenytoin sodium in mg.

95 kgVd = 0.7 L/kgC = 15 mg/LS = 0.92
LD = mg
6.Clinical pharmacokineticsHard
t (h)C (mg/L)Css​3 hC = ?

Practice exercise (made-up values, not clinical guidance). A theophylline infusion runs at 42 mg/h with no loading dose. The patient's clearance is 3.5 L/h and the half-life is 6 h. What is the level C after 3 h?

R = 42 mg/hCL = 3.5 L/ht½ = 6 ht = 3 h
C = mg/L

3Solutions

1.Pharmacology

Answer: B · Stop the infusion, leave the cannula in and follow the protocol

Why this is the answer

Suspected extravasation of a vesicant is an emergency. The infusion is stopped, the cannula is left in so that drug can be aspirated, and the protocol, which may include an antidote and cold or warm packs, is followed.

Answer

B · Stop the infusion, leave the cannula in and follow the protocol
2.Pharmacology

Answer: D · It is nephrotoxic and ototoxic with a narrow therapeutic index

Why this is the answer

Aminoglycosides like gentamicin can damage the kidneys and the inner ear. They are cleared renally, so levels rise in kidney impairment and are monitored.

Answer

D · It is nephrotoxic and ototoxic with a narrow therapeutic index
3.Dosage calculations

Answer: V = 7 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.

Dose from body weight

D = 10·7 = 70 mg

Volume

V = 70/10 = 7 mL

On the syringe

On this 10 mL syringe every small line is 0.2 mL.

Answer

V = 7 mL
4.Dosage calculations

Answer: D = 293.7 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).

Body surface area

BSA = √(138·36/3600) = √1.38 = 1.175 m²

Dose

D = 250·1.175 = 293.7 mg

Answer

D = 293.7 mg
5.Clinical pharmacokinetics

Answer: LD = 1084 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 = 0.7·95 = 66.5 L

Amount of active drug needed

Vd·C = 66.5·15 = 997.5 mg

Loading dose

LD = 997.5/(0.92·1) = 1084 mg

Answer

LD = 1084 mg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: C = 3.515 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 = 42/3.5 = 12 mg/L

Rate constant

k = 0.693/6 = 0.1155 h⁻¹

Level after the given time

C = 12·(1 − e−0.1155·3) = 3.515 mg/L

Answer

C = 3.515 mg/L

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