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 uses a salbutamol (albuterol) inhaler and a corticosteroid inhaler at the same time of day. Which order is usually taught?

  1. AThe order does not matter and no waiting is needed
  2. BUse the steroid first, then the salbutamol right after without any gap
  3. CUse the salbutamol first, wait a few minutes, then use the steroid
  4. DUse both in the same breath to save time
2.PharmacologyHard

Five days after starting clindamycin, a patient has frequent watery diarrhoea, abdominal cramps and a fever. What should the nurse suspect and do?

  1. AC. difficile infection; send stool, use contact precautions, avoid antidiarrhoeals
  2. BA normal side effect; give loperamide and continue as usual
  3. CFood poisoning; encourage a high-fibre diet and plenty of milk products
  4. DAn allergy to clindamycin; give an antihistamine and continue the antibiotic
3.Dosage calculationsMedium
024681010 mL

A child weighing 37 kg is prescribed 2 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?

37 kg2 mg/kg10 mg/mL
V = mL
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 2600 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?

2600 units5000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
VCss​ = 25 mg/LR = ? mg/hCL = 55 mL/min

Practice exercise (made-up values, not clinical guidance). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 55 mL/min. What infusion rate R in mg/h gives a steady-state level of 25 mg/L?

CL = 55 mL/minCss = 25 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
0.1110t (h)C (mg/L)Cpeak​ = 7τ = ?Ctrough​ = 1

Practice exercise (made-up values, not clinical guidance). A patient's tobramycin half-life is 3 h. The target is a peak of 7 mg/L and a trough of 1 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.

t½ = 3 hCpeak = 7 mg/LCtrough = 1 mg/L
τ = h

3Solutions

1.Pharmacology

Answer: C · Use the salbutamol first, wait a few minutes, then use the steroid

Why this is the answer

The bronchodilator opens the airways so that the inhaled steroid can reach further into the lungs. A short wait between the inhalers is usually advised.

Answer

C · Use the salbutamol first, wait a few minutes, then use the steroid
2.Pharmacology

Answer: A · C. difficile infection; send stool, use contact precautions, avoid antidiarrhoeals

Why this is the answer

Broad-spectrum antibiotics, especially clindamycin, allow C. difficile to overgrow and release toxins. Stool is tested, contact precautions with soap-and-water handwashing are used, and antidiarrhoeals are avoided because they keep toxin in the gut.

Answer

A · C. difficile infection; send stool, use contact precautions, avoid antidiarrhoeals
3.Dosage calculations

Answer: V = 7.4 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 = 2·37 = 74 mg

Volume

V = 74/10 = 7.4 mL

On the syringe

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

Answer

V = 7.4 mL
4.Dosage calculations

Answer: V = 0.52 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 = 2600/5000 = 0.52 mL

On the syringe

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

Answer

V = 0.52 mL
5.Clinical pharmacokinetics

Answer: R = 82.5 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

55·60/1000 = 3.3 L/h

Infusion rate

R = 3.3·25 = 82.5 mg/h

Answer

R = 82.5 mg/h
6.Clinical pharmacokinetics

Answer: τ = 8.4 h

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.

Rate constant

k = 0.693/3 = 0.231 h⁻¹

Dosing interval

τ = ln(7/1)/0.231 = 1.946/0.231 = 8.422 ≈ 8.4 h

Answer

τ = 8.4 h

In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.

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