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 parent will give a liquid medicine to a child at home. Which advice is safest?

  1. AUse the oral syringe or measuring cup supplied with it
  2. BMix the dose into a full bottle of milk
  3. CUse any kitchen teaspoon
  4. DEstimate the dose by pouring the liquid into a small cup
2.PharmacologyHard

A patient with epilepsy needs pain relief. Why is tramadol used with caution?

  1. AIt speeds up the metabolism of all antiepileptic drugs
  2. BIt lowers the seizure threshold
  3. CIt causes a sharp rise in blood glucose
  4. DIt always causes respiratory arrest in epilepsy
3.Dosage calculationsMedium
024681010 mL

A child weighing 19 kg is prescribed 10 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?

19 kg10 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
200 mg/5 mLV = ? mL

A child weighing 8 kg is prescribed 5 mg/kg per dose of an oral suspension that contains 200 mg in 5 mL. What volume V do you give?

8 kg5 mg/kg200 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)1 h8 mg/L9 h1.3 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 1.3 mg/L at 9 h. Assume first-order elimination. Find the half-life t½.

C1 = 8 mg/L (1 h)C2 = 1.3 mg/L (9 h)
t½ = h
6.Clinical pharmacokineticsHard
t (h)C (mg/L)Css​22 hC = ?

Practice exercise (made-up values, not clinical guidance). A theophylline infusion runs at 42 mg/h with no loading dose. The patient's clearance is 3.5 L/h and the half-life is 9 h. What is the level C after 22 h?

R = 42 mg/hCL = 3.5 L/ht½ = 9 ht = 22 h
C = mg/L

3Solutions

1.Pharmacology

Answer: A · Use the oral syringe or measuring cup supplied with it

Why this is the answer

Kitchen spoons are inaccurate and can cause under- or overdosing. Oral syringes in millilitres are the most accurate, and mixing doses into a whole bottle risks the child not getting the full dose.

Answer

A · Use the oral syringe or measuring cup supplied with it
2.Pharmacology

Answer: B · It lowers the seizure threshold

Why this is the answer

Tramadol can cause seizures, especially at high doses or with other drugs that lower the seizure threshold. Its serotonergic action also raises the risk of serotonin syndrome.

Answer

B · It lowers the seizure threshold
3.Dosage calculations

Answer: V = 7.6 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 = 10·19 = 190 mg

Volume

V = 190/25 = 7.6 mL

On the syringe

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

Answer

V = 7.6 mL
4.Dosage calculations

Answer: V = 1 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.

Dose from weight

5·8 = 40 mg

Volume

V = (40/200)·5 = 1 mL

Answer

V = 1 mL
5.Clinical pharmacokinetics

Answer: t½ = 3.052 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(8/1.3)/8 = 1.817/8 = 0.2271 h⁻¹

Half-life

t½ = 0.693/0.2271 = 3.052 h

Answer

t½ = 3.052 h
6.Clinical pharmacokinetics

Answer: C = 9.795 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.

Steady-state level

Css = 42/3.5 = 12 mg/L

Rate constant

k = 0.693/9 = 0.07702 h⁻¹

Level after the given time

C = 12·(1 − e−0.07702·22) = 9.795 mg/L

Answer

C = 9.795 mg/L

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