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). An 86 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 15 mg/L. The volume of distribution is 0.7 L/kg and the salt factor is S = 0.92. Find the loading dose LD of phenytoin sodium in mg.
86 kgVd = 0.7 L/kgC = 15 mg/LS = 0.92
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 51 kg patient on regular gentamicin doses is at steady state. The target is a peak of 8 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.3 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 18.2 mL of diluent. The prescribed dose is 1 200 000 units. What volume V do you draw up? Round to one decimal place.
18.2 mL → 250 000 units/mL1 200 000 units
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 9.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 210 mg. Draw up the dose: what volume V do you give?
500 mg9.8 mL + 0.2 mL210 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 16 units/kg/h for a patient who weighs 76 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL16 units/kg/h76 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 30 mL/h. The patient weighs 102 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL30 mL/h102 kg
D = mcg/kg/min
7.PharmacologyMedium
Which adverse effect of ciprofloxacin should a patient report at once?
APain or swelling in a tendon, such as the Achilles tendon
BMild tiredness in the first few days
CA slightly bitter or metallic taste for a while after each dose
DDarker stools than usual
8.PharmacologyHard
A patient has received a sodium nitroprusside infusion for several days. He becomes confused and develops a metabolic acidosis. What should be suspected?
AHyperkalaemia from the infusion
BAn allergic reaction to the plastic of the infusion bag
CCyanide toxicity from nitroprusside breakdown
DHypoglycaemia from nitroprusside
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 981.5 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 = 0.7·86 = 60.2 L
Amount of active drug needed
Vd·C = 60.2·15 = 903 mg
Loading dose
LD = 903/(0.92·1) = 981.5 mg
Answer
LD = 981.5 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: D = 114.7 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 = 0.3·51 = 15.3 L
Dose
D = 15.3·(8 − 0.5) = 114.7 mg
Answer
D = 114.7 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 4.8 mL
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Concentration from the label
18.2 mL → 250 000 units/mL
Volume to give
V = 1 200 000/250 000 = 4.8 mL
Answer
V = 4.8 mL
4.Pharmacy calculations
Answer: V = 4.2 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.
Final volume and concentration
9.8 + 0.2 = 10 mL
C = 500/10 = 50 mg/mL
Volume
V = 210/50 = 4.2 mL
Answer
V = 4.2 mL
5.Pediatric & critical-care dosing
Answer: R = 12.2 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
16·76 = 1 216 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 1216/100 = 12.16 ≈ 12.2 mL/h
Answer
R = 12.2 mL/h
6.Pediatric & critical-care dosing
Answer: D = 7.8 mcg/kg/min
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
400 000/250 = 1600 mcg/mL
Micrograms per minute
30·1600 = 48000 mcg/h
48000/60 = 800 mcg/min
Per kilogram
D = 800/102 = 7.843 ≈ 7.8 mcg/kg/min
Answer
D = 7.8 mcg/kg/min
7.Pharmacology
Answer: A · Pain or swelling in a tendon, such as the Achilles tendon
Why this is the answer
Fluoroquinolones can cause tendinitis and tendon rupture. Patients should stop exercise and report tendon pain promptly.
Answer
A · Pain or swelling in a tendon, such as the Achilles tendon
8.Pharmacology
Answer: C · Cyanide toxicity from nitroprusside breakdown
Why this is the answer
Nitroprusside releases cyanide, which is normally converted to thiocyanate. With high doses, long infusions or poor organ function, cyanide and thiocyanate can accumulate; the infusion is also protected from light.