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 serious but rare adverse effect of statins should patients report straight away?

  1. AA metallic taste
  2. BUnexplained muscle pain or weakness
  3. CAnkle swelling
  4. DA dry cough
2.PharmacologyHard

Why is adenosine used with caution in patients with asthma?

  1. AIt can cause bronchospasm
  2. BIt reduces the effect of inhaled steroids
  3. CIt is broken down too slowly in asthma
  4. DIt causes severe hypertension in asthma
3.Dosage calculationsMedium
1 g+ 9.6 mLV = ? mL

A vial contains 1 g of powder. The label says: add 9.6 mL of water for injection to give a total volume of 10 mL. The prescription is 240 mg. What volume V of the reconstituted solution do you give?

1 g+ 9.6 mL → 10 mL240 mg
V = mL
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 1.36 mg. The ampoule contains 2000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

1.36 mg2000 mcg/mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 3 mg/LR = ? mg/minCL = 500 mL/min

Practice exercise (made-up values, not clinical guidance). A patient has a lidocaine clearance of 500 mL/min. What infusion rate R in mg/min keeps the steady-state level at 3 mg/L?

CL = 500 mL/minCss = 3 mg/L
R = mg/min
6.Clinical pharmacokineticsHard
VCss,avg​ = ?500 mg · q12hCL = 0.045 L/kg/h63 kg · S = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A 63 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.045 L/kg/h. Each dose is 500 mg of theophylline. Find the average steady-state level Css,avg.

CL = 0.045 L/kg/hτ = 12 hS = 1F = 163 kgD = 500 mg
Css,avg = mg/L

3Solutions

1.Pharmacology

Answer: B · Unexplained muscle pain or weakness

Why this is the answer

Statins can cause myopathy, which rarely progresses to rhabdomyolysis with kidney damage. Unexplained muscle pain should be checked, for example with a creatine kinase level.

Answer

B · Unexplained muscle pain or weakness
2.Pharmacology

Answer: A · It can cause bronchospasm

Why this is the answer

Adenosine can trigger bronchospasm in people with asthma or COPD. Other treatment options, such as verapamil, may be chosen.

Answer

A · It can cause bronchospasm
3.Dosage calculations

Answer: V = 2.4 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.

Concentration after mixing

1000 mg/10 mL = 100 mg/mL

Volume

V = 240/100 = 2.4 mL

Answer

V = 2.4 mL
4.Dosage calculations

Answer: V = 0.68 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

1.36 mg = 1360 mcg

Volume

V = 1360/2000 = 0.68 mL

Answer

V = 0.68 mL
5.Clinical pharmacokinetics

Answer: R = 1.5 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

500 mL/min = 0.5 L/min

Infusion rate

R = 0.5·3 = 1.5 mg/min

Answer

R = 1.5 mg/min
6.Clinical pharmacokinetics

Answer: Css,avg = 14.7 mg/L

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 = 0.045·63 = 2.835 L/h

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 1·1·500/(2.835·12) = 14.7 mg/L

Answer

Css,avg = 14.7 mg/L

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