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 patient receives an IV bolus of 150 mg of gentamicin. The level back-extrapolated to time zero is 8 mg/L and the half-life is 2 h. Find the volume of distribution Vd.
D = 150 mgC₀ = 8 mg/Lt½ = 2 h
Vd = L
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 75 kg patient takes oral aminophylline (S = 0.8, F = 1) every 8 h. The theophylline clearance is 0.05 L/kg/h. What dose D in mg gives an average steady-state level of 12 mg/L?
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 2000 mg as a powder. The practice label says to add 19.2 mL of sterile water; the powder adds 0.8 mL to the volume. What is the concentration C in mg/mL after reconstitution?
2000 mg19.2 mL+0.8 mL
C = mg/mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 400 mL of 40% dextrose by mixing 70% and 10% dextrose. How many mL V of the 70% solution do you need? Round to the nearest whole mL.
70%10%40%400 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 60 units/kg for a patient who weighs 110 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg110 kg1 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 2.5 mcg/kg/min for a patient who weighs 93 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL2.5 mcg/kg/min93 kg
R = mL/h
7.PharmacologyMedium
A patient taking levodopa finds that the drug works poorly after large meals. Which advice is most appropriate?
AAvoid taking doses at the same time as high-protein meals
BTake every dose with a large glass of milk and a protein snack
CDouble the dose after each meal
DTake the drug only at bedtime
8.PharmacologyHard
A 500 mg intravenous dose gives an initial plasma concentration of 10 mg/L. What is the volume of distribution?
A5 L
B50 L
C500 L
D5000 L
3Solutions
1.Clinical pharmacokinetics
Answer: Vd = 18.75 L
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 = 150/8 = 18.75 L
Answer
Vd = 18.75 L
2.Clinical pharmacokinetics
Answer: D = 450 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.
Clearance
CL = 0.05·75 = 3.75 L/h
Dose
D = Css,avg·CL·τ/(S·F) = 12·3.75·8/(0.8·1) = 450 mg
Answer
D = 450 mg
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
19.2 + 0.8 = 20 mL
Concentration
C = 2000/20 = 100 mg/mL
Answer
C = 100 mg/mL
4.Pharmacy calculations
Answer: V = 200 mL
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Alligation parts
70%: 40 − 10 = 30 parts
10%: 70 − 40 = 30 parts
total: 60 parts
Share the volume
V = 400·30/60 = 200 mL
Answer
V = 200 mL
Check: 200 mL of 70% + 200 mL of 10% = 400 mL.
5.Pediatric & critical-care dosing
Answer: V = 6.6 mL
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 needed
60·110 = 6 600 units
Volume
V = 6600/1000 = 6.6 mL
Answer
V = 6.6 mL
6.Pediatric & critical-care dosing
Answer: R = 14 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
2.5·93 = 232.5 mcg/min
232.5·60 = 13950 mcg/h
Pump rate
R = 13950/1000 = 13.95 ≈ 14 mL/h
Answer
R = 14 mL/h
7.Pharmacology
Answer: A · Avoid taking doses at the same time as high-protein meals
Why this is the answer
Dietary amino acids compete with levodopa for absorption in the gut and transport into the brain. Spreading protein through the day or timing doses away from high-protein meals improves the effect.
Answer
A · Avoid taking doses at the same time as high-protein meals
8.Pharmacology
Answer: B · 50 L
Why this is the answer
Vd = 500 mg ÷ 10 mg/L = 50 L. This is close to total body water, so the drug spreads beyond the plasma but is not extensively stored in tissues.