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 adverse effect of doxorubicin requires monitoring of heart function?

  1. ASevere hypertension during the infusion itself
  2. BPericarditis caused by infection
  3. CRapid rise in cholesterol
  4. DCumulative heart muscle damage leading to heart failure
2.PharmacologyHard

A patient on lisinopril for hypertension starts taking ibuprofen every day for knee pain. What is the main concern?

  1. AA large fall in blood pressure, with fainting and falls on standing up
  2. BFaster liver metabolism of lisinopril, so it stops working
  3. CWeaker blood pressure control, kidney injury and high potassium
  4. DA higher risk of a dry cough than with lisinopril alone
3.Dosage calculationsMedium
1:1000ampouleV = ? mL

An ampoule of epinephrine (adrenaline) is labelled 1:1000 (1 mg/mL). The prescription is 0.5 mg IM for anaphylaxis. What volume V do you draw up?

1:10000.5 mg
V = mL
4.Dosage calculationsHard
250 mg/5 mLV = ? mL

A patient weighs 169.4 lb. The prescription is 10 mg/kg as a single dose, and the stock contains 250 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give?

169.4 lb10 mg/kg250 mg/5 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
110100t (h)C (mg/L)1 h10 mg/L4 h5 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of tobramycin, the level is 10 mg/L at 1 h and 5 mg/L at 4 h. Assume first-order elimination. Find the half-life t½.

C1 = 10 mg/L (1 h)C2 = 5 mg/L (4 h)
t½ = h
6.Clinical pharmacokineticsHard
VCss,avg​ = 12 mg/LD = ? mg · q12hCL = 0.03 L/kg/h97 kg · S = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A 97 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.03 L/kg/h. What dose D in mg gives an average steady-state level of 12 mg/L?

CL = 0.03 L/kg/hτ = 12 hS = 1F = 197 kgCss,avg = 12 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: D · Cumulative heart muscle damage leading to heart failure

Why this is the answer

Anthracyclines such as doxorubicin can damage heart muscle, and the risk increases with cumulative dose. Heart function is assessed before and during treatment; the drug can also turn urine red.

Answer

D · Cumulative heart muscle damage leading to heart failure
2.Pharmacology

Answer: C · Weaker blood pressure control, kidney injury and high potassium

Why this is the answer

NSAIDs block prostaglandins that dilate the afferent arteriole and promote sodium loss. With an ACE inhibitor this can reduce blood pressure control and cause kidney injury and hyperkalaemia, especially if a diuretic is also used.

Answer

C · Weaker blood pressure control, kidney injury and high potassium
3.Dosage calculations

Answer: V = 0.5 mL

Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.

Concentration

1:1000 = 1 g/1000 mL = 1 mg/mL

Volume

V = 0.5/1 = 0.5 mL

Answer

V = 0.5 mL

US labels now state mg/mL (1 mg/mL = 1:1000; 0.1 mg/mL = 1:10 000). Never give 1 mg/mL epinephrine IV push.

4.Dosage calculations

Answer: V = 15.4 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.

Weight in kg

169.4/2.2 = 77 kg

Dose

10·77 = 770 mg

Volume

V = (770/250)·5 = 15.4 mL

Answer

V = 15.4 mL
5.Clinical pharmacokinetics

Answer: t½ = 3 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.

Elimination rate constant

k = ln(10/5)/3 = 0.6931/3 = 0.231 h⁻¹

Half-life

t½ = 0.693/0.231 = 3 h

Answer

t½ = 3 h
6.Clinical pharmacokinetics

Answer: D = 419 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 = 0.03·97 = 2.91 L/h

Dose

D = Css,avg·CL·τ/(S·F) = 12·2.91·12/(1·1) = 419 mg

Answer

D = 419 mg

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