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 long does it take, approximately, for a drug given at regular intervals to reach a steady state?

  1. AIt depends only on the dose size
  2. B10 half-lives
  3. C4 to 5 half-lives
  4. D1 half-life
2.PharmacologyHard

A patient receiving cisplatin is given large volumes of IV fluid before and after each dose. What is the main purpose?

  1. ATo prevent hair loss
  2. BTo prevent bleeding
  3. CTo increase drug absorption from the gut
  4. DTo reduce kidney damage
3.Dosage calculationsMedium
46 kgBSA = 1.37 m²20 mg/m²D = ? mg

A patient weighing 46 kg has a body surface area of 1.37 m². The prescription is 20 mg/m². Find the dose D in mg.

46 kgBSA = 1.37 m²20 mg/m²
D = mg
4.Dosage calculationsHard
200 mg/5 mLV = ? mL

A child weighing 10 kg is prescribed 10 mg/kg per dose of an oral suspension that contains 200 mg in 5 mL. What volume V do you give?

10 kg10 mg/kg200 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 10 mg/LR = ? mg/h · S = 0.8CL = 0.035 L/kg/h100 kg

Practice exercise (made-up values, not clinical guidance). A 100 kg patient is to receive an aminophylline infusion (salt factor S = 0.8: 80% of aminophylline is theophylline). The theophylline clearance is 0.035 L/kg/h. What aminophylline infusion rate R in mg/h gives a steady-state theophylline level of 10 mg/L?

100 kgCL = 0.035 L/kg/hCss = 10 mg/LS = 0.8
R = mg/h
6.Clinical pharmacokineticsHard
Vd = 7 L/kg0.5 → 0.8 mcg/LLD = ? mcg91 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 91 kg patient has a digoxin level of 0.5 mcg/L; the target is 0.8 mcg/L. The volume of distribution is 7 L/kg and the tablets have F = 0.7. What extra loading dose LD raises the level to the target?

91 kgVd = 7 L/kgC = 0.5 → 0.8 mcg/LF = 0.7
LD = mcg

3Solutions

1.Pharmacology

Answer: C · 4 to 5 half-lives

Why this is the answer

With repeated dosing, the level approaches steady state after about 4–5 half-lives, whatever the dose. A loading dose can be used to reach it faster.

Answer

C · 4 to 5 half-lives
2.Pharmacology

Answer: D · To reduce kidney damage

Why this is the answer

Cisplatin is nephrotoxic, and hydration helps protect the kidneys. It also causes ototoxicity, peripheral neuropathy, severe nausea and low magnesium.

Answer

D · To reduce kidney damage
3.Dosage calculations

Answer: D = 27.4 mg

Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).

Dose

D = 20·1.37 = 27.4 mg

Answer

D = 27.4 mg
4.Dosage calculations

Answer: V = 2.5 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.

Dose from weight

10·10 = 100 mg

Volume

V = (100/200)·5 = 2.5 mL

Answer

V = 2.5 mL
5.Clinical pharmacokinetics

Answer: R = 43.75 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 = 0.035·100 = 3.5 L/h

Infusion rate

R = CL·Css/S = 3.5·10/0.8 = 43.75 mg/h

Answer

R = 43.75 mg/h
6.Clinical pharmacokinetics

Answer: LD = 273 mcg

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 = 7·91 = 637 L

Rise needed

0.8 − 0.5 = 0.3 mcg/L

Loading dose

LD = 637·0.3/(1·0.7) = 273 mcg

Answer

LD = 273 mcg

In practice the dose is rounded to a convenient amount.

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