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

A patient with a fentanyl patch is given home-care advice. Which instruction is correct?

  1. ACut the patch in half if the pain is mild
  2. BAvoid heating pads, hot baths and saunas over or near the patch
  3. CThrow used patches loose into the household bin with the packaging
  4. DApply each new patch over the same skin area
2.PharmacologyHard

A patient with Parkinson's disease has nausea. Why should metoclopramide be avoided?

  1. AIt inhibits the absorption of all oral drugs
  2. BIt causes severe diarrhoea in Parkinson's disease
  3. CIt blocks dopamine receptors in the brain and can worsen the parkinsonism
  4. DIt increases dopamine levels in the brain too much and causes psychosis
3.Dosage calculationsMedium
024681010 mL

A child weighing 24 kg is prescribed 2.5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?

24 kg2.5 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
10 mg/1 mLV = ? mL

A patient weighs 173.8 lb. The prescription is 0.5 mg/kg as a single dose, and the stock contains 10 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to one decimal place.

173.8 lb0.5 mg/kg10 mg/1 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 0.8 mcg/LLD = ? mcg74 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 74 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.

74 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
t (h)C (mg/L)Css​t = ?95%

Practice exercise (made-up values, not clinical guidance). A vancomycin infusion is started without a loading dose. The half-life in this patient is 10 h. How long t does it take to reach 95% of the steady-state level?

t½ = 10 h95% Css
t = h

3Solutions

1.Pharmacology

Answer: B · Avoid heating pads, hot baths and saunas over or near the patch

Why this is the answer

Heat increases fentanyl absorption and can cause overdose. Sites are rotated, patches are never cut, and used patches are folded sticky sides together and disposed of safely, away from children and pets.

Answer

B · Avoid heating pads, hot baths and saunas over or near the patch
2.Pharmacology

Answer: C · It blocks dopamine receptors in the brain and can worsen the parkinsonism

Why this is the answer

Metoclopramide crosses the blood–brain barrier and antagonises D2 receptors. In Parkinson's disease this worsens rigidity and bradykinesia, so antiemetics that do not block central dopamine receptors are preferred.

Answer

C · It blocks dopamine receptors in the brain and can worsen the parkinsonism
3.Dosage calculations

Answer: V = 2.4 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 = 2.5·24 = 60 mg

Volume

V = 60/25 = 2.4 mL

On the syringe

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

Answer

V = 2.4 mL
4.Dosage calculations

Answer: V = 4 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.

Weight in kg

173.8/2.2 = 79 kg

Dose

0.5·79 = 39.5 mg

Volume

V = (39.5/10)·1 = 3.95 ≈ 4 mL

Answer

V = 4 mL
5.Clinical pharmacokinetics

Answer: LD = 592 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 = 7·74 = 518 L

Amount of active drug needed

Vd·C = 518·0.8 = 414.4 mcg

Loading dose

LD = 414.4/(1·0.7) = 592 mcg

Answer

LD = 592 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: t = 43.22 h

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.

Rate constant

k = 0.693/10 = 0.06931 h⁻¹

Time to the given fraction of steady state

t = −ln(1 − 0.95)/0.06931 = 2.996/0.06931 = 43.22 h

Answer

t = 43.22 h

That is 4.322 half-lives.

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