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

How do ACE inhibitors lower blood pressure?

  1. AThey block the conversion of angiotensin I to angiotensin II
  2. BThey block L-type calcium channels in vascular smooth muscle cells
  3. CThey block beta-1 receptors in the heart
  4. DThey increase sodium reabsorption in the kidney
2.PharmacologyHard

A woman with epilepsy who takes an antiepileptic drug plans to become pregnant. Which advice is standard?

  1. AStop all antiepileptic drugs straight away as soon as she stops contraception
  2. BTake folic acid before conception and seek specialist review of her medication
  3. CAvoid folic acid because it lowers drug levels
  4. DNo change is needed, as antiepileptics carry no risk in pregnancy
3.Dosage calculationsMedium
60 kg10 mg/kg/day3× per dayD = ? mg

A patient weighs 60 kg. The prescribed dose is 10 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?

60 kg10 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
40 mg/1 mLV = ? mL

A patient weighs 88 lb. The prescription is 5 mg/kg as a single dose, and the stock contains 40 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give?

88 lb5 mg/kg40 mg/1 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)C₀ = 10 mg/Lt½ = 3 hC₀/2

Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 180 mg of gentamicin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 3 h. Find the clearance CL in L/h.

D = 180 mgC₀ = 10 mg/Lt½ = 3 h
CL = L/h
6.Clinical pharmacokineticsHard
Vd = 0.25 L/kg0.5 → 7 mg/LD = ? mg96 kg

Practice exercise (made-up values, not clinical guidance). A 96 kg patient on regular gentamicin doses is at steady state. The target is a peak of 7 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.25 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?

96 kgVd = 0.25 L/kgCpeak = 7 mg/LCtrough = 0.5 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: A · They block the conversion of angiotensin I to angiotensin II

Why this is the answer

ACE inhibitors (such as ramipril) reduce angiotensin II, causing vasodilation and less aldosterone. They also reduce bradykinin breakdown, which explains the dry cough.

Answer

A · They block the conversion of angiotensin I to angiotensin II
2.Pharmacology

Answer: B · Take folic acid before conception and seek specialist review of her medication

Why this is the answer

Folic acid before and in early pregnancy reduces the risk of neural tube defects. Medication should be reviewed before conception, but drugs should not be stopped suddenly because uncontrolled seizures are also dangerous.

Answer

B · Take folic acid before conception and seek specialist review of her medication
3.Dosage calculations

Answer: D = 200 mg

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.

Total per day

10·60 = 600 mg

Per dose

D = 600/3 = 200 mg

Answer

D = 200 mg
4.Dosage calculations

Answer: V = 5 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

88/2.2 = 40 kg

Dose

5·40 = 200 mg

Volume

V = (200/40)·1 = 5 mL

Answer

V = 5 mL
5.Clinical pharmacokinetics

Answer: CL = 4.159 L/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.

Volume of distribution

Vd = 180/10 = 18 L

Rate constant

k = 0.693/3 = 0.231 h⁻¹

Clearance

CL = 0.231·18 = 4.159 L/h

Answer

CL = 4.159 L/h
6.Clinical pharmacokinetics

Answer: D = 156 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 = 0.25·96 = 24 L

Dose

D = 24·(7 − 0.5) = 156 mg

Answer

D = 156 mg

In practice the dose is rounded to a convenient amount.

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