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 62 kg patient is to be loaded intravenously with aminophylline to reach a theophylline level of 15 mg/L. The volume of distribution is 0.5 L/kg and the salt factor is S = 0.8. Find the loading dose LD of aminophylline in mg.
62 kgVd = 0.5 L/kgC = 15 mg/LS = 0.8
LD = mg
2.Clinical pharmacokineticsHard
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 0.5 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 = 0.5 mg/L
τ = h
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 1000 mg as a powder. The practice label says to add 9.6 mL of sterile water; the powder adds 0.4 mL to the volume. What is the concentration C in mg/mL after reconstitution?
1000 mg9.6 mL+0.4 mL
C = mg/mL
4.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 4.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 120 mg. Draw up the dose: what volume V do you give?
1000 mg4.4 mL + 0.6 mL120 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 250 mL. The order is 10 units/h. Find the pump rate R in mL/h. Round to one decimal place.
100 units/250 mL10 units/h
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 76 kg has an order for norepinephrine at 8 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
8 mg/250 mL8 mcg/min76 kg
R = mL/h
7.PharmacologyMedium
Which is a well-known adverse effect of long-term oral corticosteroids?
ALow blood pressure
BWeight loss
CHypoglycaemia
DOsteoporosis
8.PharmacologyHard
Why must several weeks pass before starting an MAO inhibitor after stopping fluoxetine?
AFluoxetine permanently and irreversibly blocks MAO enzymes
BFluoxetine and its active metabolite have very long half-lives
CFluoxetine must first be converted into an MAO inhibitor
DMAO inhibitors are absorbed only after fluoxetine is gone
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 581.3 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 = 0.5·62 = 31 L
Amount of active drug needed
Vd·C = 31·15 = 465 mg
Loading dose
LD = 465/(0.8·1) = 581.3 mg
Answer
LD = 581.3 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: τ = 11.4 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(7/0.5)/0.231 = 2.639/0.231 = 11.42 ≈ 11.4 h
Answer
τ = 11.4 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.
3.Pharmacy calculations
Answer: C = 100 mg/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.
Final volume
9.6 + 0.4 = 10 mL
Concentration
C = 1000/10 = 100 mg/mL
Answer
C = 100 mg/mL
4.Pharmacy calculations
Answer: V = 0.6 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 = 1000/5 = 200 mg/mL
Volume
V = 120/200 = 0.6 mL
Answer
V = 0.6 mL
5.Pediatric & critical-care dosing
Answer: R = 25 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.
Concentration
100/250 = 0.4 units/mL
Pump rate
R = 10/0.4 = 25 mL/h
Answer
R = 25 mL/h
6.Pediatric & critical-care dosing
Answer: R = 15 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
8 000/250 = 32 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
8·60 = 480 mcg/h
Pump rate
R = 480/32 = 15 mL/h
Answer
R = 15 mL/h
7.Pharmacology
Answer: D · Osteoporosis
Why this is the answer
Long-term corticosteroids reduce bone formation and raise fracture risk. They also cause weight gain, high blood glucose, hypertension and a higher infection risk.
Answer
D · Osteoporosis
8.Pharmacology
Answer: B · Fluoxetine and its active metabolite have very long half-lives
Why this is the answer
Norfluoxetine, the active metabolite of fluoxetine, stays in the body for weeks. A long washout is needed before an MAOI to avoid serotonin syndrome.
Answer
B · Fluoxetine and its active metabolite have very long half-lives