Pick the relation: C = C₀·e−kt, LD = Vd·C/(S·F), maintenance rate = CL·Css/(S·F), τ = ln(Cpeak/Ctrough)/k.
For kidney function, estimate CrCl with Cockcroft–Gault first, then scale the dose or the interval.
Check the result: levels fall by half every half-life, and steady state takes about five half-lives.
Pharmacy calculations
Percentage strength
% w/v = g per 100 mL
Amount in a solution
g = % × mL / 100
Ratio strength
1:X = 1 g in X mL; % = 100 / X
Reconstitution
final volume = diluent + powder volume
Concentration
mg/mL = drug in vial / final volume
Alligation
parts of H = T − L, parts of L = H − T
Water or base
0%
Pediatric & critical-care dosing
Daily dose
mg/day = mg/kg/day × weight (kg)
Doses per day
number = 24 h / dosing interval (h)
Pounds to kilograms
kg = lb / 2.2
Infusion concentration
units/mL = units in bag / bag volume
Pump rate
mL/h = dose per hour / concentration
Titrated drip
mL/h = mcg/kg/min × kg × 60 / (mcg/mL)
Dose from pump rate
mcg/kg/min = mL/h × (mcg/mL) / (60 × kg)
Units
1 mg = 1000 mcg
2Practice problems
1.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A 77 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 15 mg/L?
77 kgCL = 0.04 L/kg/hCss = 15 mg/LS = 0.8
R = mg/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 59 kg patient on regular gentamicin doses is at steady state. The target is a peak of 10 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.25 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
A solution has a ratio strength of 1:10 000. You need 0.22 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.22 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 4.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 55 mg. Draw up the dose: what volume V do you give?
250 mg4.4 mL + 0.6 mL55 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 250 mL. The order is 12 units/kg/h for a patient who weighs 66 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL12 units/kg/h66 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 82 kg has an order for nitroglycerin at 40 mcg/min. The bag contains 50 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
50 mg/250 mL40 mcg/min82 kg
R = mL/h
7.PharmacologyMedium
Which common side effect is typical of ACE inhibitors?
AHypoglycaemia
BDry cough
CAnkle swelling caused by vasodilation
DBradycardia
8.PharmacologyHard
Which drug class can cause life-threatening hyperkalaemia when combined with an ACE inhibitor?
APotassium-sparing diuretics such as spironolactone
BThiazide diuretics
CLoop diuretics such as high-dose intravenous furosemide
DProton pump inhibitors
3Solutions
1.Clinical pharmacokinetics
Answer: R = 57.75 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 = 0.04·77 = 3.08 L/h
Infusion rate
R = CL·Css/S = 3.08·15/0.8 = 57.75 mg/h
Answer
R = 57.75 mg/h
2.Clinical pharmacokinetics
Answer: D = 140.1 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 = 0.25·59 = 14.75 L
Dose
D = 14.75·(10 − 0.5) = 140.1 mg
Answer
D = 140.1 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 2.2 mL
Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.
Strength in mg/mL
1000 mg/10 000 mL = 0.1 mg/mL
Volume
V = 0.22/0.1 = 2.2 mL
Answer
V = 2.2 mL
4.Pharmacy calculations
Answer: V = 1.1 mL
Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.
Final volume and concentration
4.4 + 0.6 = 5 mL
C = 250/5 = 50 mg/mL
Volume
V = 55/50 = 1.1 mL
Answer
V = 1.1 mL
5.Pediatric & critical-care dosing
Answer: R = 7.9 mL/h
Heparin and insulin infusions: concentration = units in the bag/bag volume (units/mL). Pump rate (mL/h) = units per hour/concentration, and units per hour = mL/h × concentration. For a weight-based order, units/h = units/kg/h × weight first. A bolus volume = units needed/vial strength. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Units per hour
12·66 = 792 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 792/100 = 7.92 ≈ 7.9 mL/h
Answer
R = 7.9 mL/h
6.Pediatric & critical-care dosing
Answer: R = 12 mL/h
Titrated drips: first find the concentration in mcg/mL (mg × 1000/mL). For a weight-based order, mcg/min = mcg/kg/min × weight. Then mL/h = mcg/min × 60/concentration. Working backwards, mcg/kg/min = mL/h × concentration/(60 × weight). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Concentration
50 000/250 = 200 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
40·60 = 2400 mcg/h
Pump rate
R = 2400/200 = 12 mL/h
Answer
R = 12 mL/h
7.Pharmacology
Answer: B · Dry cough
Why this is the answer
ACE also breaks down bradykinin. When it is inhibited, bradykinin accumulates in the airways and causes a persistent dry cough in some patients.
Answer
B · Dry cough
8.Pharmacology
Answer: A · Potassium-sparing diuretics such as spironolactone
Why this is the answer
ACE inhibitors lower aldosterone and spironolactone blocks its receptor; together they reduce potassium excretion and can raise potassium dangerously.
Answer
A · Potassium-sparing diuretics such as spironolactone