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

Why do NSAIDs such as ibuprofen increase the risk of stomach ulcers?

  1. AThey increase the number of Helicobacter pylori bacteria in the stomach
  2. BThey raise the pH of gastric acid
  3. CThey reduce protective prostaglandins in the stomach lining
  4. DThey directly dissolve the mucus layer
2.PharmacologyHard

Why is strict aseptic technique and a limited hang time needed for propofol infusions?

  1. ALight exposure changes propofol into an opioid
  2. BIts lipid emulsion lets bacteria grow if it is contaminated
  3. CPropofol breaks down into a toxic gas after a few hours
  4. DPropofol becomes more potent the longer it hangs
3.Dosage calculationsMedium
024681010 mL

A child weighing 20 kg is prescribed 5 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?

20 kg5 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
100 mg/1 mLV = ? mL

A patient weighs 169.4 lb. The prescription is 15 mg/kg as a single dose, and the stock contains 100 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to one decimal place.

169.4 lb15 mg/kg100 mg/1 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 25 mg/LR = ? mg/hCL = 4 L/h

Practice exercise (made-up values, not clinical guidance). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 4 L/h. What infusion rate R in mg/h gives a steady-state level of 25 mg/L?

CL = 4 L/hCss = 25 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
Vd = 0.7 L/kg6 → 15 mg/LLD = ? mg82 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). An 82 kg patient has a phenytoin level of 6 mg/L; the target is 15 mg/L. The drug is given intravenously as phenytoin sodium (S = 0.92), and the volume of distribution is 0.7 L/kg. What extra loading dose LD raises the level to the target?

82 kgVd = 0.7 L/kgC = 6 → 15 mg/LS = 0.92
LD = mg

3Solutions

1.Pharmacology

Answer: C · They reduce protective prostaglandins in the stomach lining

Why this is the answer

NSAIDs inhibit COX-1, lowering prostaglandins that maintain mucus, bicarbonate secretion and blood flow in the stomach lining.

Answer

C · They reduce protective prostaglandins in the stomach lining
2.Pharmacology

Answer: B · Its lipid emulsion lets bacteria grow if it is contaminated

Why this is the answer

Propofol is formulated in a soybean oil emulsion, which is a good growth medium for bacteria. Contaminated propofol has caused sepsis, so it is handled aseptically and tubing and containers are changed at set intervals.

Answer

B · Its lipid emulsion lets bacteria grow if it is contaminated
3.Dosage calculations

Answer: V = 2 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 = 5·20 = 100 mg

Volume

V = 100/50 = 2 mL

On the syringe

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

Answer

V = 2 mL
4.Dosage calculations

Answer: V = 11.6 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

15·77 = 1155 mg

Volume

V = (1155/100)·1 = 11.55 ≈ 11.6 mL

Answer

V = 11.6 mL
5.Clinical pharmacokinetics

Answer: R = 100 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.

Infusion rate

R = 4·25 = 100 mg/h

Answer

R = 100 mg/h
6.Clinical pharmacokinetics

Answer: LD = 561.5 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.

Volume of distribution

Vd = 0.7·82 = 57.4 L

Rise needed

15 − 6 = 9 mg/L

Loading dose

LD = 57.4·9/(0.92·1) = 561.5 mg

Answer

LD = 561.5 mg

In practice the dose is rounded to a convenient amount.

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