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 group of signs suggests opioid withdrawal?

  1. AYawning, runny nose, sweating, dilated pupils and diarrhoea
  2. BConstipation, itching and a slow heart rate
  3. CDry mouth, urinary retention, blurred vision and confusion
  4. DPinpoint pupils, slow breathing and drowsiness
2.PharmacologyHard

The volume of distribution of a drug is very large (for example 500 L in an adult). What does this suggest?

  1. AThe drug cannot be given intravenously
  2. BThe drug is quickly excreted by the kidneys
  3. CThe drug stays almost entirely in the plasma compartment
  4. DThe drug is extensively taken up into tissues
3.Dosage calculationsMedium
024681010 mL

A child weighing 20 kg is prescribed 2 mg/kg of a drug. The stock solution contains 20 mg/mL. Draw up the dose: what volume V do you give?

20 kg2 mg/kg20 mg/mL
V = mL
4.Dosage calculationsHard
25k units500 mL? mL/h1250 units/h

An infusion contains 25000 units of a drug in 500 mL. The prescription is 1250 units per hour. At what rate R do you set the pump, in mL/h?

25000 units/500 mL1250 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 0.8 mcg/LLD = ? mcg70 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 70 kg patient is to be loaded with digoxin tablets to reach a level of 0.8 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.

70 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
Vd = 0.3 L/kg0.5 → 10 mg/LD = ? mg50 kg

Practice exercise (made-up values, not clinical guidance). A 50 kg patient on regular gentamicin doses is at steady state. The target is a peak of 10 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.3 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?

50 kgVd = 0.3 L/kgCpeak = 10 mg/LCtrough = 0.5 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: A · Yawning, runny nose, sweating, dilated pupils and diarrhoea

Why this is the answer

Opioid withdrawal causes rhinorrhoea, lacrimation, yawning, sweating, mydriasis, cramps, diarrhoea and anxiety. It is very unpleasant but rarely life-threatening in healthy adults.

Answer

A · Yawning, runny nose, sweating, dilated pupils and diarrhoea
2.Pharmacology

Answer: D · The drug is extensively taken up into tissues

Why this is the answer

A Vd far above total body water means the plasma concentration is low because most of the drug sits in tissues (for example fat or muscle), as with digoxin or amiodarone.

Answer

D · The drug is extensively taken up into tissues
3.Dosage calculations

Answer: V = 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 = 2·20 = 40 mg

Volume

V = 40/20 = 2 mL

On the syringe

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

Answer

V = 2 mL
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

25000/500 = 50 units/mL

Pump rate

R = 1250/50 = 25 mL/h

Answer

R = 25 mL/h
5.Clinical pharmacokinetics

Answer: LD = 560 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 = 7·70 = 490 L

Amount of active drug needed

Vd·C = 490·0.8 = 392 mcg

Loading dose

LD = 392/(1·0.7) = 560 mcg

Answer

LD = 560 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: D = 142.5 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.

Volume of distribution

Vd = 0.3·50 = 15 L

Dose

D = 15·(10 − 0.5) = 142.5 mg

Answer

D = 142.5 mg

In practice the dose is rounded to a convenient amount.

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