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

Which early signs suggest systemic toxicity from a local anaesthetic?

  1. AItchy rash and swelling only at the injection site
  2. BHeavy sweating, salivation and diarrhoea
  3. CNumbness around the mouth, metallic taste and tinnitus
  4. DPinpoint pupils and slow, shallow breathing
2.PharmacologyHard

A patient on weekly methotrexate is prescribed trimethoprim for a urinary infection. What is the main risk?

  1. ASevere hypertension from the combination
  2. BLoss of antibiotic effect because methotrexate binds trimethoprim
  3. CHypoglycaemia from reduced liver glucose output
  4. DBone marrow suppression, because both drugs inhibit folate metabolism
3.Dosage calculationsMedium
024681010 mL

A child weighing 40 kg is prescribed 4 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?

40 kg4 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
25k units1000 mL? mL/h500 units/h

An infusion contains 25000 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?

25000 units/1000 mL500 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 1 mcg/LLD = ? mcg98 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 98 kg patient is to be loaded with digoxin tablets to reach a level of 1 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.

98 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
VCss,avg​ = 20 mg/LD = ? mg · q12hCL = 3 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 L/h. What dose D in mg gives an average steady-state level of 20 mg/L?

CL = 3 L/hτ = 12 hS = 1F = 1Css,avg = 20 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: C · Numbness around the mouth, metallic taste and tinnitus

Why this is the answer

Local anaesthetic toxicity starts with central nervous system signs such as perioral numbness, metallic taste, tinnitus and agitation. It can progress to seizures, arrhythmias and cardiac arrest.

Answer

C · Numbness around the mouth, metallic taste and tinnitus
2.Pharmacology

Answer: D · Bone marrow suppression, because both drugs inhibit folate metabolism

Why this is the answer

Trimethoprim and methotrexate both inhibit dihydrofolate reductase, and trimethoprim also reduces methotrexate excretion. The combination can cause severe pancytopenia, so another antibiotic is chosen.

Answer

D · Bone marrow suppression, because both drugs inhibit folate metabolism
3.Dosage calculations

Answer: V = 3.2 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 = 4·40 = 160 mg

Volume

V = 160/50 = 3.2 mL

On the syringe

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

Answer

V = 3.2 mL
4.Dosage calculations

Answer: R = 20 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

25000/1000 = 25 units/mL

Pump rate

R = 500/25 = 20 mL/h

Answer

R = 20 mL/h
5.Clinical pharmacokinetics

Answer: LD = 980 mcg

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 = 7·98 = 686 L

Amount of active drug needed

Vd·C = 686·1 = 686 mcg

Loading dose

LD = 686/(1·0.7) = 980 mcg

Answer

LD = 980 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: D = 720 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.

Dose

D = Css,avg·CL·τ/(S·F) = 20·3·12/(1·1) = 720 mg

Answer

D = 720 mg

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