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

A patient has oral mucositis after chemotherapy. Which advice is appropriate?

  1. ABrush hard with a firm toothbrush to remove debris
  2. BEat spicy and acidic foods to stimulate healing
  3. CUse an alcohol-based mouthwash several times a day to kill germs
  4. DUse a soft toothbrush and rinse with saline or a bland mouthwash
2.PharmacologyHard

Why can beta blockers mask the warning signs of hypoglycaemia in people with diabetes?

  1. AThey cause hyperthermia that hides sweating
  2. BThey raise blood glucose so that hypoglycaemia cannot occur at all
  3. CThey blunt adrenergic symptoms such as tremor and palpitations
  4. DThey block insulin release completely
3.Dosage calculationsMedium
15 kg25 mg/kgD = ? mg

A patient weighs 15 kg and is prescribed 25 mg/kg as a single dose. Find the dose D in mg.

15 kg25 mg/kg
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 0.19 mg. The ampoule contains 1000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

0.19 mg1000 mcg/mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 12 mg/LR = ? mg/h · S = 0.8CL = 0.04 L/kg/h58 kg

Practice exercise (made-up values, not clinical guidance). A 58 kg patient is to receive an aminophylline infusion (salt factor S = 0.8: 80% of aminophylline is theophylline). The theophylline clearance is 0.04 L/kg/h. What aminophylline infusion rate R in mg/h gives a steady-state theophylline level of 12 mg/L?

58 kgCL = 0.04 L/kg/hCss = 12 mg/LS = 0.8
R = mg/h
6.Clinical pharmacokineticsHard
78 kg55 · manSCr 2.7 mg/dLCrCl → D = ? mg

Practice exercise (made-up values, not clinical guidance). A 55-year-old man weighs 78 kg and has a serum creatinine of 2.7 mg/dL (239 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 levetiracetam dose is 1000 mg every 12 h for a creatinine clearance of 100 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.

55 years78 kgmanSCr = 2.7 mg/dL1000 mg q12hCrCl normal 100 mL/min
D = mg

3Solutions

1.Pharmacology

Answer: D · Use a soft toothbrush and rinse with saline or a bland mouthwash

Why this is the answer

Chemotherapy damages rapidly dividing mucosal cells. Gentle oral care, saline rinses and avoiding alcohol, spicy and acidic foods reduce pain and infection risk.

Answer

D · Use a soft toothbrush and rinse with saline or a bland mouthwash
2.Pharmacology

Answer: C · They blunt adrenergic symptoms such as tremor and palpitations

Why this is the answer

Tremor, palpitations and anxiety in hypoglycaemia are adrenaline-driven; beta blockade dampens them, so patients may notice low glucose later. Sweating is cholinergic and often persists.

Answer

C · They blunt adrenergic symptoms such as tremor and palpitations
3.Dosage calculations

Answer: D = 375 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

25·15 = 375 mg

Answer

D = 375 mg
4.Dosage calculations

Answer: V = 0.19 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.

Same units

0.19 mg = 190 mcg

Volume

V = 190/1000 = 0.19 mL

Answer

V = 0.19 mL
5.Clinical pharmacokinetics

Answer: R = 34.8 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 = 0.04·58 = 2.32 L/h

Infusion rate

R = CL·Css/S = 2.32·12/0.8 = 34.8 mg/h

Answer

R = 34.8 mg/h
6.Clinical pharmacokinetics

Answer: D = 341 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 − 55)·78/(72·2.7) = 34.1 mL/min

Adjusted dose

D = 1000·34.1/100 = 341 mg

Answer

D = 341 mg

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

ExamProblems · examproblems.com/courses/pharmacology