Pharmacology: cram pack

Formula sheets, the key method steps for every topic and 6 practice problems, with full solutions at the back.

New problemsBack to the course

In the print window, choose “Save as PDF” to keep a copy on your device.

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 should a patient store sublingual glyceryl trinitrate (nitroglycerin) tablets?

  1. AIn the fridge in a damp, open container to keep them fresh and cool
  2. BIn a plastic weekly pill box with other tablets
  3. CLoose in a shirt pocket close to the body for quick access
  4. DIn the original dark glass bottle, away from heat, light and moisture
2.PharmacologyHard

A 19-year-old woman is starting isotretinoin for severe acne. Which requirement is most important?

  1. AA high-vitamin A diet to boost the effect
  2. BReliable contraception and pregnancy tests, as it is highly teratogenic
  3. CTaking the drug only at weekends
  4. DWeekly hearing tests and monthly eye examinations during treatment
3.Dosage calculationsMedium
1 g+ 4.2 mLV = ? mL

A vial contains 1 g of powder. The label says: add 4.2 mL of water for injection to give a total volume of 5 mL. The prescription is 600 mg. What volume V of the reconstituted solution do you give?

1 g+ 4.2 mL → 5 mL600 mg
V = mL
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 910 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

910 units1000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)1 h7 mg/L5 h2.8 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 7 mg/L at 1 h and 2.8 mg/L at 5 h. Assume first-order elimination. Find the half-life t½.

C1 = 7 mg/L (1 h)C2 = 2.8 mg/L (5 h)
t½ = h
6.Clinical pharmacokineticsHard
VCss,avg​ = 10 mg/LD = ? mg · q8hCL = 0.05 L/kg/h91 kg · S = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A 91 kg patient takes oral theophylline (F = 1) every 8 h. The clearance is 0.05 L/kg/h. What dose D in mg gives an average steady-state level of 10 mg/L?

CL = 0.05 L/kg/hτ = 8 hS = 1F = 191 kgCss,avg = 10 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: D · In the original dark glass bottle, away from heat, light and moisture

Why this is the answer

Nitroglycerin tablets lose potency when exposed to light, heat, air and moisture. They are kept in their original tightly closed dark container, and expired tablets are replaced.

Answer

D · In the original dark glass bottle, away from heat, light and moisture
2.Pharmacology

Answer: B · Reliable contraception and pregnancy tests, as it is highly teratogenic

Why this is the answer

Isotretinoin causes severe birth defects. Pregnancy prevention programmes require effective contraception and regular pregnancy tests before, during and after treatment.

Answer

B · Reliable contraception and pregnancy tests, as it is highly teratogenic
3.Dosage calculations

Answer: V = 3 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/5 mL = 200 mg/mL

Volume

V = 600/200 = 3 mL

Answer

V = 3 mL
4.Dosage calculations

Answer: V = 0.91 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.

Volume

V = 910/1000 = 0.91 mL

On the syringe

On this 1 mL syringe every small line is 0.01 mL.

Answer

V = 0.91 mL
5.Clinical pharmacokinetics

Answer: t½ = 3.026 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(7/2.8)/4 = 0.9163/4 = 0.2291 h⁻¹

Half-life

t½ = 0.693/0.2291 = 3.026 h

Answer

t½ = 3.026 h
6.Clinical pharmacokinetics

Answer: D = 364 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 = 0.05·91 = 4.55 L/h

Dose

D = Css,avg·CL·τ/(S·F) = 10·4.55·8/(1·1) = 364 mg

Answer

D = 364 mg

ExamProblems · examproblems.com/courses/pharmacology