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 does neostigmine improve muscle strength in myasthenia gravis?

  1. AIt inhibits acetylcholinesterase so more acetylcholine reaches the receptors
  2. BIt increases the number of acetylcholine receptors at the neuromuscular junction
  3. CIt blocks the autoantibodies against the receptor
  4. DIt directly stimulates muscarinic receptors in muscle
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 is extensively taken up into tissues
  2. BThe drug cannot be given intravenously
  3. CThe drug is quickly excreted by the kidneys
  4. DThe drug stays almost entirely in the plasma compartment
3.Dosage calculationsMedium
024681010 mL

A child weighing 26 kg is prescribed 7.5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?

26 kg7.5 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
41 kg153 cmBSA = √(h·w/3600)50 mg/m²D = ? mg

A patient is 153 cm tall and weighs 41 kg. The prescription is 50 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.

153 cm41 kg50 mg/m²
D = mg
5.Clinical pharmacokineticsMedium
VCss​ = 2 mg/LR = ? mg/minCL = 550 mL/min

Practice exercise (made-up values, not clinical guidance). A patient has a lidocaine clearance of 550 mL/min. What infusion rate R in mg/min keeps the steady-state level at 2 mg/L?

CL = 550 mL/minCss = 2 mg/L
R = mg/min
6.Clinical pharmacokineticsHard
92 kg73 · womanSCr 2.5 mg/dLfe​ = 0.7D = ? mcg

Practice exercise (made-up values, not clinical guidance). A 73-year-old woman weighs 92 kg and has a serum creatinine of 2.5 mg/dL (221 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual digoxin dose is 250 mcg for a creatinine clearance of 100 mL/min, and a fraction fe = 0.7 of the drug is excreted unchanged by the kidneys. Using the Dettli dose fraction Q = 1 − fe·(1 − CrCl/normal CrCl), find the adjusted dose D. Round to the nearest whole number.

73 years92 kgwomanSCr = 2.5 mg/dL250 mcgfe = 0.7CrCl normal 100 mL/min
D = mcg

3Solutions

1.Pharmacology

Answer: A · It inhibits acetylcholinesterase so more acetylcholine reaches the receptors

Why this is the answer

Neostigmine inhibits acetylcholinesterase at the neuromuscular junction, so acetylcholine lasts longer and can activate the remaining nicotinic receptors more effectively.

Answer

A · It inhibits acetylcholinesterase so more acetylcholine reaches the receptors
2.Pharmacology

Answer: A · 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

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

Answer: V = 7.8 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.

Dose from body weight

D = 7.5·26 = 195 mg

Volume

V = 195/25 = 7.8 mL

On the syringe

On this 10 mL syringe every small line is 0.2 mL.

Answer

V = 7.8 mL
4.Dosage calculations

Answer: D = 66 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).

Body surface area

BSA = √(153·41/3600) = √1.742 = 1.32 m²

Dose

D = 50·1.32 = 66 mg

Answer

D = 66 mg
5.Clinical pharmacokinetics

Answer: R = 1.1 mg/min

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 in L/min

550 mL/min = 0.55 L/min

Infusion rate

R = 0.55·2 = 1.1 mg/min

Answer

R = 1.1 mg/min
6.Clinical pharmacokinetics

Answer: D = 126 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.

Creatinine clearance (Cockcroft–Gault)

CrCl = (140 − 73)·92/(72·2.5)·0.85 = 29.11 mL/min

Dose fraction (Dettli)

Q = 1 − 0.7·(1 − 29.11/100) = 0.5038

Adjusted dose

D = 0.5038·250 = 125.9 ≈ 126 mcg

Answer

D = 126 mcg

In practice the dose is rounded to a convenient amount and checked against the product information.

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