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 makes an overdose of tricyclic antidepressants such as amitriptyline especially dangerous?

  1. ASevere liver failure within hours
  2. BCardiac arrhythmias and seizures
  3. CSudden high blood glucose
  4. DKidney stones
2.PharmacologyHard

A patient with myasthenia gravis took extra pyridostigmine doses. She now has increasing weakness, heavy salivation, sweating, small pupils and diarrhoea. What is the most likely cause?

  1. AA stroke unrelated to the medication
  2. BMyasthenic crisis from too little anticholinesterase drug
  3. CAn allergic reaction to pyridostigmine
  4. DCholinergic crisis from too much anticholinesterase drug
3.Dosage calculationsMedium
500 mg+ 9.6 mLV = ? mL

A vial contains 500 mg of powder. The label says: add 9.6 mL of water for injection to give a total volume of 10 mL. The prescription is 30 mg. What volume V of the reconstituted solution do you give?

500 mg+ 9.6 mL → 10 mL30 mg
V = mL
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 740 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

740 units1000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)1 h10 mg/L4 h3.5 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 10 mg/L at 1 h and 3.5 mg/L at 4 h. Assume first-order elimination. Find the half-life t½.

C1 = 10 mg/L (1 h)C2 = 3.5 mg/L (4 h)
t½ = h
6.Clinical pharmacokineticsHard
VCss,avg​ = 10 mg/LD = ? mg · q8hCL = 0.045 L/kg/h54 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). A 54 kg patient takes oral aminophylline (S = 0.8, F = 1) every 8 h. The theophylline clearance is 0.045 L/kg/h. What dose D in mg gives an average steady-state level of 10 mg/L?

CL = 0.045 L/kg/hτ = 8 hS = 0.8F = 154 kgCss,avg = 10 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: B · Cardiac arrhythmias and seizures

Why this is the answer

Tricyclics block cardiac sodium channels (widening the QRS complex) and have anticholinergic effects. In overdose they cause arrhythmias, hypotension, seizures and coma.

Answer

B · Cardiac arrhythmias and seizures
2.Pharmacology

Answer: D · Cholinergic crisis from too much anticholinesterase drug

Why this is the answer

Excess acetylcholine causes muscarinic signs (salivation, sweating, miosis, diarrhoea) and depolarising weakness. In myasthenic crisis, weakness occurs without these cholinergic signs; both can cause respiratory failure.

Answer

D · Cholinergic crisis from too much anticholinesterase drug
3.Dosage calculations

Answer: V = 0.6 mL

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 after mixing

500 mg/10 mL = 50 mg/mL

Volume

V = 30/50 = 0.6 mL

Answer

V = 0.6 mL
4.Dosage calculations

Answer: V = 0.74 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.

Volume

V = 740/1000 = 0.74 mL

On the syringe

On this 1 mL syringe every small line is 0.01 mL.

Answer

V = 0.74 mL
5.Clinical pharmacokinetics

Answer: t½ = 1.981 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(10/3.5)/3 = 1.05/3 = 0.3499 h⁻¹

Half-life

t½ = 0.693/0.3499 = 1.981 h

Answer

t½ = 1.981 h
6.Clinical pharmacokinetics

Answer: D = 243 mg

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.

Clearance

CL = 0.045·54 = 2.43 L/h

Dose

D = Css,avg·CL·τ/(S·F) = 10·2.43·8/(0.8·1) = 243 mg

Answer

D = 243 mg

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