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 receives lactulose for hepatic encephalopathy. Which finding shows that it is working?

  1. ATen watery stools a day and a low serum potassium
  2. BBetter alertness and orientation, with two to three soft stools a day
  3. CHigher blood ammonia with improved appetite
  4. DNo bowel movement for three days, with less confusion than before
2.PharmacologyHard

A woman with chronic hypertension who takes lisinopril is now pregnant. What is the key concern?

  1. ALisinopril works better in pregnancy, so the dose should be increased
  2. BLisinopril has no known fetal effects and should be continued
  3. CAll antihypertensives must be stopped in pregnancy
  4. DACE inhibitors harm fetal kidneys, so a safer drug is used
3.Dosage calculationsMedium
0.5%50 mLm = ? mg

How many milligrams of drug m are in 50 mL of a 0.5% (w/v) solution?

0.5% w/v50 mL
m = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 630 micrograms. The ampoule contains 1 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

630 mcg1 mg/mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 0.7 L/kgC = 15 mg/LLD = ? mg65 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). A 65 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 15 mg/L. The volume of distribution is 0.7 L/kg and the salt factor is S = 0.92. Find the loading dose LD of phenytoin sodium in mg.

65 kgVd = 0.7 L/kgC = 15 mg/LS = 0.92
LD = mg
6.Clinical pharmacokineticsHard
Vd = 0.3 L/kg0.5 → 6 mg/LD = ? mg81 kg

Practice exercise (made-up values, not clinical guidance). An 81 kg patient on regular gentamicin doses is at steady state. The target is a peak of 6 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?

81 kgVd = 0.3 L/kgCpeak = 6 mg/LCtrough = 0.5 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: B · Better alertness and orientation, with two to three soft stools a day

Why this is the answer

Lactulose is adjusted to give about two to three soft stools a day and to lower ammonia, improving mental status. Excessive diarrhoea can cause dehydration and electrolyte loss.

Answer

B · Better alertness and orientation, with two to three soft stools a day
2.Pharmacology

Answer: D · ACE inhibitors harm fetal kidneys, so a safer drug is used

Why this is the answer

ACE inhibitors and ARBs cause fetal kidney damage, oligohydramnios and other problems, especially later in pregnancy. Drugs such as labetalol, nifedipine or methyldopa are used instead.

Answer

D · ACE inhibitors harm fetal kidneys, so a safer drug is used
3.Dosage calculations

Answer: m = 250 mg

Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.

Concentration

0.5% = 0.5 g/100 mL = 5 mg/mL

Mass of drug

m = 5·50 = 250 mg

Answer

m = 250 mg
4.Dosage calculations

Answer: V = 0.63 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.

Same units

1 mg/mL = 1000 mcg/mL

Volume

V = 630/1000 = 0.63 mL

Answer

V = 0.63 mL
5.Clinical pharmacokinetics

Answer: LD = 741.8 mg

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 = 0.7·65 = 45.5 L

Amount of active drug needed

Vd·C = 45.5·15 = 682.5 mg

Loading dose

LD = 682.5/(0.92·1) = 741.8 mg

Answer

LD = 741.8 mg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: D = 133.7 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 = 0.3·81 = 24.3 L

Dose

D = 24.3·(6 − 0.5) = 133.7 mg

Answer

D = 133.7 mg

In practice the dose is rounded to a convenient amount.

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