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

While giving medicines, a patient says, "That pill looks different from the one I usually take." What should the nurse do?

  1. AExplain that only the staff decide which medicines are given
  2. BStop and recheck the order and the medicine before giving it
  3. CReassure the patient and give the pill anyway
  4. DGive the pill and check the chart afterwards
2.PharmacologyHard

A patient on heparin for 7 days has a platelet count that has fallen by more than half, and a new leg vein thrombosis. What is the most likely cause and the key action?

  1. ANormal dilution of platelets; continue and recheck in a week
  2. BVitamin K deficiency; give vitamin K and continue heparin
  3. CHeparin-induced thrombocytopenia; stop all heparin
  4. DWarfarin skin necrosis; switch from heparin to warfarin at once
3.Dosage calculationsMedium
80 kg10 mg/kgD = ? mg

A patient weighs 80 kg and is prescribed 10 mg/kg as a single dose. Find the dose D in mg.

80 kg10 mg/kg
D = mg
4.Dosage calculationsHard
40 mg/1 mLV = ? mL

A child weighing 10 kg is prescribed 5 mg/kg per dose of an oral suspension that contains 40 mg in 1 mL. What volume V do you give? Round to one decimal place.

10 kg5 mg/kg40 mg/1 mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 0.5 L/kgC = 15 mg/LLD = ? mg85 kg · S = 0.8 · F = 1

Practice exercise (made-up values, not clinical guidance). An 85 kg patient is to be loaded intravenously with aminophylline to reach a theophylline level of 15 mg/L. The volume of distribution is 0.5 L/kg and the salt factor is S = 0.8. Find the loading dose LD of aminophylline in mg.

85 kgVd = 0.5 L/kgC = 15 mg/LS = 0.8
LD = mg
6.Clinical pharmacokineticsHard
60 kg46 · manSCr 1.7 mg/dLCrCl → D = ? mg

Practice exercise (made-up values, not clinical guidance). A 46-year-old man weighs 60 kg and has a serum creatinine of 1.7 mg/dL (150 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual gentamicin dose is 120 mg every 8 h for a creatinine clearance of 120 mL/min. Keeping the interval, the dose is reduced in proportion to the creatinine clearance. Find the adjusted dose D. Round to the nearest whole number.

46 years60 kgmanSCr = 1.7 mg/dL120 mg q8hCrCl normal 120 mL/min
D = mg

3Solutions

1.Pharmacology

Answer: B · Stop and recheck the order and the medicine before giving it

Why this is the answer

A patient's concern can reveal a wrong drug or wrong patient error. The nurse rechecks the order and product, and may call the pharmacy; a different brand or strength may explain the change.

Answer

B · Stop and recheck the order and the medicine before giving it
2.Pharmacology

Answer: C · Heparin-induced thrombocytopenia; stop all heparin

Why this is the answer

Heparin-induced thrombocytopenia (HIT) is caused by antibodies against heparin–platelet factor 4 complexes. It usually starts 5–10 days after heparin begins and causes thrombosis, so all heparin is stopped and a non-heparin anticoagulant is used.

Answer

C · Heparin-induced thrombocytopenia; stop all heparin
3.Dosage calculations

Answer: D = 800 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

10·80 = 800 mg

Answer

D = 800 mg
4.Dosage calculations

Answer: V = 1.3 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.

Dose from weight

5·10 = 50 mg

Volume

V = (50/40)·1 = 1.25 ≈ 1.3 mL

Answer

V = 1.3 mL
5.Clinical pharmacokinetics

Answer: LD = 796.9 mg

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.

Volume of distribution

Vd = 0.5·85 = 42.5 L

Amount of active drug needed

Vd·C = 42.5·15 = 637.5 mg

Loading dose

LD = 637.5/(0.8·1) = 796.9 mg

Answer

LD = 796.9 mg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: D = 46 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.

Creatinine clearance (Cockcroft–Gault)

CrCl = (140 − 46)·60/(72·1.7) = 46.08 mL/min

Adjusted dose

D = 120·46.08/120 = 46.08 ≈ 46 mg

Answer

D = 46 mg

In practice the dose is rounded to a convenient amount and checked against the product information.

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