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

Why should doxycycline not be taken at the same time as milk or antacids?

  1. ACalcium and other metal ions bind it and reduce absorption
  2. BAntacids turn it into a toxic compound
  3. CThe combination causes severe constipation
  4. DMilk speeds up its breakdown in the liver by inducing enzymes
2.PharmacologyHard

A patient on warfarin is taught about diet. Which statement shows a need for further teaching?

  1. A"I will tell my dentist that I take warfarin."
  2. B"I will keep the amount of green leafy vegetables I eat about the same each week."
  3. C"I will stop eating all green vegetables from now on."
  4. D"I will use a soft toothbrush and an electric razor."
3.Dosage calculationsMedium
90 kg2 mg/kg/day2× per dayD = ? mg

A patient weighs 90 kg. The prescribed dose is 2 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?

90 kg2 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 0.49 mg. The ampoule contains 1000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

0.49 mg1000 mcg/mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 0.8 mcg/LLD = ? mcg51 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 51 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.

51 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
VCss,avg​ = 15 mg/LD = ? mg · q8hCL = 0.045 L/kg/h96 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). A 96 kg patient takes oral aminophylline (S = 0.8, F = 1) every 8 h. The theophylline clearance is 0.045 L/kg/h. What dose D in mg gives an average steady-state level of 15 mg/L?

CL = 0.045 L/kg/hτ = 8 hS = 0.8F = 196 kgCss,avg = 15 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: A · Calcium and other metal ions bind it and reduce absorption

Why this is the answer

Tetracyclines form complexes with calcium, magnesium, aluminium and iron in the gut, which reduces absorption. Doses are separated from these products.

Answer

A · Calcium and other metal ions bind it and reduce absorption
2.Pharmacology

Answer: C · "I will stop eating all green vegetables from now on."

Why this is the answer

Patients on warfarin should keep their vitamin K intake consistent rather than avoid it. Sudden changes in green vegetable intake can make the INR unstable.

Answer

C · "I will stop eating all green vegetables from now on."
3.Dosage calculations

Answer: D = 90 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

2·90 = 180 mg

Per dose

D = 180/2 = 90 mg

Answer

D = 90 mg
4.Dosage calculations

Answer: V = 0.49 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

0.49 mg = 490 mcg

Volume

V = 490/1000 = 0.49 mL

Answer

V = 0.49 mL
5.Clinical pharmacokinetics

Answer: LD = 408 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 = 7·51 = 357 L

Amount of active drug needed

Vd·C = 357·0.8 = 285.6 mcg

Loading dose

LD = 285.6/(1·0.7) = 408 mcg

Answer

LD = 408 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: D = 648 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.

Clearance

CL = 0.045·96 = 4.32 L/h

Dose

D = Css,avg·CL·τ/(S·F) = 15·4.32·8/(0.8·1) = 648 mg

Answer

D = 648 mg

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