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 should a patient rinse the mouth after using an inhaled corticosteroid?

  1. ATo make the drug work faster in the lungs
  2. BTo stop the drug being absorbed too quickly into the blood
  3. CTo prevent a fall in blood glucose
  4. DTo reduce the risk of oral thrush (candidiasis) and hoarseness
2.PharmacologyHard

Why are antipsychotics used with great caution in older people with dementia?

  1. AThey always cure the dementia and stop all behaviour problems
  2. BThey are not absorbed in people over 65
  3. CThey cause severe hypoglycaemia in older people
  4. DThey are linked to a higher risk of stroke and death
3.Dosage calculationsMedium
1:1000ampouleV = ? mL

An ampoule of epinephrine (adrenaline) is labelled 1:1000 (1 mg/mL). The prescription is 0.5 mg IM for anaphylaxis. What volume V do you draw up?

1:10000.5 mg
V = mL
4.Dosage calculationsHard
45 kg127 cmBSA = √(h·w/3600)250 mg/m²D = ? mg

A patient is 127 cm tall and weighs 45 kg. The prescription is 250 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.

127 cm45 kg250 mg/m²
D = mg
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)1 h8 mg/L9 h1.6 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 8 mg/L at 1 h and 1.6 mg/L at 9 h. Assume first-order elimination. Find the half-life t½.

C1 = 8 mg/L (1 h)C2 = 1.6 mg/L (9 h)
t½ = h
6.Clinical pharmacokineticsHard
VCss,avg​ = ?1000 mg · q12hCL = 3.5 L/hS = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 3.5 L/h. Each dose is 1000 mg of vancomycin. Find the average steady-state level Css,avg.

CL = 3.5 L/hτ = 12 hS = 1F = 1D = 1000 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: D · To reduce the risk of oral thrush (candidiasis) and hoarseness

Why this is the answer

Steroid left in the mouth and throat suppresses local immunity and can cause candidiasis and a hoarse voice. Rinsing and spitting, and using a spacer, reduce this risk.

Answer

D · To reduce the risk of oral thrush (candidiasis) and hoarseness
2.Pharmacology

Answer: D · They are linked to a higher risk of stroke and death

Why this is the answer

In older people with dementia, antipsychotics increase the risk of stroke and death. Non-drug approaches are tried first, and antipsychotics are used at low doses for short periods if needed.

Answer

D · They are linked to a higher risk of stroke and death
3.Dosage calculations

Answer: V = 0.5 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.

Concentration

1:1000 = 1 g/1000 mL = 1 mg/mL

Volume

V = 0.5/1 = 0.5 mL

Answer

V = 0.5 mL

US labels now state mg/mL (1 mg/mL = 1:1000; 0.1 mg/mL = 1:10 000). Never give 1 mg/mL epinephrine IV push.

4.Dosage calculations

Answer: D = 315 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 = √(127·45/3600) = √1.587 = 1.26 m²

Dose

D = 250·1.26 = 315 mg

Answer

D = 315 mg
5.Clinical pharmacokinetics

Answer: t½ = 3.445 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.

Elimination rate constant

k = ln(8/1.6)/8 = 1.609/8 = 0.2012 h⁻¹

Half-life

t½ = 0.693/0.2012 = 3.445 h

Answer

t½ = 3.445 h
6.Clinical pharmacokinetics

Answer: Css,avg = 23.81 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.

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 1·1·1000/(3.5·12) = 23.81 mg/L

Answer

Css,avg = 23.81 mg/L

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