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

A patient given haloperidol develops a sudden painful twisting of the neck and the eyes roll upward. Which drug is usually given?

  1. ADantrolene by mouth to relax the twisted neck muscles
  2. BA second dose of haloperidol
  3. CNaloxone
  4. DAn anticholinergic such as benzatropine (benztropine)
2.PharmacologyHard

A patient on warfarin is taught about diet. Which statement shows a need for further teaching?

  1. A"I will keep the amount of green leafy vegetables I eat about the same each week."
  2. B"I will stop eating all green vegetables from now on."
  3. C"I will use a soft toothbrush and an electric razor."
  4. D"I will tell my dentist that I take warfarin."
3.Dosage calculationsMedium
18 kg20 mg/kgD = ? mg

A patient weighs 18 kg and is prescribed 20 mg/kg as a single dose. Find the dose D in mg.

18 kg20 mg/kg
D = mg
4.Dosage calculationsHard
50k units1000 mL? mL/h1500 units/h

An infusion contains 50000 units of a drug in 1000 mL. The prescription is 1500 units per hour. At what rate R do you set the pump, in mL/h?

50000 units/1000 mL1500 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
VCss​ = 12 mg/LR = ? mg/h · S = 0.8CL = 0.03 L/kg/h56 kg

Practice exercise (made-up values, not clinical guidance). A 56 kg patient is to receive an aminophylline infusion (salt factor S = 0.8: 80% of aminophylline is theophylline). The theophylline clearance is 0.03 L/kg/h. What aminophylline infusion rate R in mg/h gives a steady-state theophylline level of 12 mg/L?

56 kgCL = 0.03 L/kg/hCss = 12 mg/LS = 0.8
R = mg/h
6.Clinical pharmacokineticsHard
Vd = 0.7 L/kg8 → 20 mg/LLD = ? mg64 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). A 64 kg patient has a phenytoin level of 8 mg/L; the target is 20 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?

64 kgVd = 0.7 L/kgC = 8 → 20 mg/LS = 0.92
LD = mg

3Solutions

1.Pharmacology

Answer: D · An anticholinergic such as benzatropine (benztropine)

Why this is the answer

Acute dystonia is caused by dopamine blockade, which leaves acetylcholine activity relatively high. An IM or IV anticholinergic usually relieves it within minutes.

Answer

D · An anticholinergic such as benzatropine (benztropine)
2.Pharmacology

Answer: B · "I will stop eating all green vegetables from now on."

Why this is the answer

Patients on warfarin should keep their vitamin K intake consistent rather than avoid it. Sudden changes in green vegetable intake can make the INR unstable.

Answer

B · "I will stop eating all green vegetables from now on."
3.Dosage calculations

Answer: D = 360 mg

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.

Dose

20·18 = 360 mg

Answer

D = 360 mg
4.Dosage calculations

Answer: R = 30 mL/h

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

50000/1000 = 50 units/mL

Pump rate

R = 1500/50 = 30 mL/h

Answer

R = 30 mL/h
5.Clinical pharmacokinetics

Answer: R = 25.2 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.

Clearance

CL = 0.03·56 = 1.68 L/h

Infusion rate

R = CL·Css/S = 1.68·12/0.8 = 25.2 mg/h

Answer

R = 25.2 mg/h
6.Clinical pharmacokinetics

Answer: LD = 584.3 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 = 0.7·64 = 44.8 L

Rise needed

20 − 8 = 12 mg/L

Loading dose

LD = 44.8·12/(0.92·1) = 584.3 mg

Answer

LD = 584.3 mg

In practice the dose is rounded to a convenient amount.

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