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

Which fraction of a drug in plasma can reach the receptor and produce an effect?

  1. AThe fraction bound to albumin
  2. BThe fraction stored in red blood cells
  3. CThe fraction bound to globulins
  4. DThe unbound (free) fraction
2.PharmacologyHard

The volume of distribution of a drug is very large (for example 500 L in an adult). What does this suggest?

  1. AThe drug cannot be given intravenously
  2. BThe drug is quickly excreted by the kidneys
  3. CThe drug is extensively taken up into tissues
  4. DThe drug stays almost entirely in the plasma compartment
3.Dosage calculationsMedium
80 kg30 mg/kg/day3× per dayD = ? mg

A patient weighs 80 kg. The prescribed dose is 30 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?

80 kg30 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 65 micrograms. The ampoule contains 0.5 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

65 mcg0.5 mg/mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 10 mg/LR = ? mg/h · S = 0.8CL = 0.03 L/kg/h89 kg

Practice exercise (made-up values, not clinical guidance). An 89 kg patient is to receive an aminophylline infusion (salt factor S = 0.8: 80% of aminophylline is theophylline). The theophylline clearance is 0.03 L/kg/h. What aminophylline infusion rate R in mg/h gives a steady-state theophylline level of 10 mg/L?

89 kgCL = 0.03 L/kg/hCss = 10 mg/LS = 0.8
R = mg/h
6.Clinical pharmacokineticsHard
Vd = 0.5 L/kg4.5 → 15 mg/LLD = ? mg63 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). A 63 kg patient has a theophylline level of 4.5 mg/L; the target is 15 mg/L. The drug is given intravenously as aminophylline (S = 0.8), and the volume of distribution is 0.5 L/kg. What extra loading dose LD raises the level to the target?

63 kgVd = 0.5 L/kgC = 4.5 → 15 mg/LS = 0.8
LD = mg

3Solutions

1.Pharmacology

Answer: D · The unbound (free) fraction

Why this is the answer

Only the free drug can diffuse into tissues, act on receptors and be metabolised or excreted. Protein-bound drug acts as a reservoir.

Answer

D · The unbound (free) fraction
2.Pharmacology

Answer: C · The drug is extensively taken up into tissues

Why this is the answer

A Vd far above total body water means the plasma concentration is low because most of the drug sits in tissues (for example fat or muscle), as with digoxin or amiodarone.

Answer

C · The drug is extensively taken up into tissues
3.Dosage calculations

Answer: D = 800 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

30·80 = 2400 mg

Per dose

D = 2400/3 = 800 mg

Answer

D = 800 mg
4.Dosage calculations

Answer: V = 0.13 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

0.5 mg/mL = 500 mcg/mL

Volume

V = 65/500 = 0.13 mL

Answer

V = 0.13 mL
5.Clinical pharmacokinetics

Answer: R = 33.38 mg/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.

Clearance

CL = 0.03·89 = 2.67 L/h

Infusion rate

R = CL·Css/S = 2.67·10/0.8 = 33.38 mg/h

Answer

R = 33.38 mg/h
6.Clinical pharmacokinetics

Answer: LD = 413.4 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 = 0.5·63 = 31.5 L

Rise needed

15 − 4.5 = 10.5 mg/L

Loading dose

LD = 31.5·10.5/(0.8·1) = 413.4 mg

Answer

LD = 413.4 mg

In practice the dose is rounded to a convenient amount.

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