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 teaching about zolpidem is correct?

  1. ATake it in the morning so that it is out of the system by night
  2. BDrive soon after waking, as the drug has no next-day effect
  3. CTake it with alcohol to make it act faster
  4. DTake it right before bed, only if you can sleep a full night
2.PharmacologyHard

A patient who takes clonidine stopped it suddenly two days ago. He is now agitated, has a headache and his blood pressure is very high. What is the most likely explanation?

  1. AClonidine toxicity due to slow excretion by the kidneys
  2. BNormal variation unrelated to the medication
  3. CRebound hypertension from abrupt clonidine withdrawal
  4. DAn allergic reaction to clonidine
3.Dosage calculationsMedium
80 kg7.5 mg/kgD = ? mg

A patient weighs 80 kg and is prescribed 7.5 mg/kg as a single dose. Find the dose D in mg.

80 kg7.5 mg/kg
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 4100 units of a drug that comes as 5000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

4100 units5000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 20 mg/LR = ? mg/hCL = 50 mL/min

Practice exercise (made-up values, not clinical guidance). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 50 mL/min. What infusion rate R in mg/h gives a steady-state level of 20 mg/L?

CL = 50 mL/minCss = 20 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
73 kg46 · womanSCr 2.2 mg/dLfe​ = 0.6D = ? mg

Practice exercise (made-up values, not clinical guidance). A 46-year-old woman weighs 73 kg and has a serum creatinine of 2.2 mg/dL (194 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 ciprofloxacin dose is 500 mg for a creatinine clearance of 100 mL/min, and a fraction fe = 0.6 of the drug is excreted unchanged by the kidneys. Using the Dettli dose fraction Q = 1 − fe·(1 − CrCl/normal CrCl), find the adjusted dose D. Round to the nearest whole number.

46 years73 kgwomanSCr = 2.2 mg/dL500 mgfe = 0.6CrCl normal 100 mL/min
D = mg

3Solutions

1.Pharmacology

Answer: D · Take it right before bed, only if you can sleep a full night

Why this is the answer

Zolpidem can cause next-day impairment and complex sleep behaviours such as sleep-walking or sleep-driving. Alcohol and other sedatives increase these risks.

Answer

D · Take it right before bed, only if you can sleep a full night
2.Pharmacology

Answer: C · Rebound hypertension from abrupt clonidine withdrawal

Why this is the answer

Clonidine is a central alpha-2 agonist. Stopping it suddenly lets sympathetic activity surge, causing rebound hypertension, so it is tapered gradually.

Answer

C · Rebound hypertension from abrupt clonidine withdrawal
3.Dosage calculations

Answer: D = 600 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

7.5·80 = 600 mg

Answer

D = 600 mg
4.Dosage calculations

Answer: V = 0.82 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 = 4100/5000 = 0.82 mL

On the syringe

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

Answer

V = 0.82 mL
5.Clinical pharmacokinetics

Answer: R = 60 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 in L/h

50·60/1000 = 3 L/h

Infusion rate

R = 3·20 = 60 mg/h

Answer

R = 60 mg/h
6.Clinical pharmacokinetics

Answer: D = 310 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)·73/(72·2.2)·0.85 = 36.82 mL/min

Dose fraction (Dettli)

Q = 1 − 0.6·(1 − 36.82/100) = 0.6209

Adjusted dose

D = 0.6209·500 = 310.5 ≈ 310 mg

Answer

D = 310 mg

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

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