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). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 60 mL/min. What infusion rate R in mg/h gives a steady-state level of 20 mg/L?
CL = 60 mL/minCss = 20 mg/L
R = mg/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 99 kg patient on regular tobramycin doses is at steady state. The target is a peak of 7 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 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. The prescribed dose is 400 mg. What volume V do you draw up? Round to one decimal place.
1000 mg9.6 mL+0.4 mL400 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 3.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 475 mg. Draw up the dose: what volume V do you give?
1000 mg3.2 mL + 0.8 mL475 mg
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 63 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
60 units/kg63 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 28 mL/h. The patient weighs 67 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL28 mL/h67 kg
D = mcg/kg/min
7.PharmacologyMedium
During an oxytocin infusion, contractions become very frequent and the fetal heart rate shows late decelerations. What is the nurse's first action?
AIncrease the infusion to finish labour quickly
BGive a second oxytocin bolus
CStop the oxytocin infusion
DPosition the woman flat on her back
8.PharmacologyHard
A patient with myasthenia gravis took extra pyridostigmine doses. She now has increasing weakness, heavy salivation, sweating, small pupils and diarrhoea. What is the most likely cause?
AA stroke unrelated to the medication
BCholinergic crisis from too much anticholinesterase drug
CAn allergic reaction to pyridostigmine
DMyasthenic crisis from too little anticholinesterase drug
3Solutions
1.Clinical pharmacokinetics
Answer: R = 72 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
60·60/1000 = 3.6 L/h
Infusion rate
R = 3.6·20 = 72 mg/h
Answer
R = 72 mg/h
2.Clinical pharmacokinetics
Answer: D = 193 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 = 0.3·99 = 29.7 L
Dose
D = 29.7·(7 − 0.5) = 193 mg
Answer
D = 193 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 4 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
1000/10 = 100 mg/mL
Volume to give
V = 400/100 = 4 mL
Answer
V = 4 mL
4.Pharmacy calculations
Answer: V = 1.9 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
3.2 + 0.8 = 4 mL
C = 1000/4 = 250 mg/mL
Volume
V = 475/250 = 1.9 mL
Answer
V = 1.9 mL
5.Pediatric & critical-care dosing
Answer: V = 0.76 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
60·63 = 3 780 units
Volume
V = 3780/5000 = 0.756 ≈ 0.76 mL
Answer
V = 0.76 mL
6.Pediatric & critical-care dosing
Answer: D = 13.9 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
500 000/250 = 2000 mcg/mL
Micrograms per minute
28·2000 = 56000 mcg/h
56000/60 = 933.3 mcg/min
Per kilogram
D = 933.3/67 = 13.93 ≈ 13.9 mcg/kg/min
Answer
D = 13.9 mcg/kg/min
7.Pharmacology
Answer: C · Stop the oxytocin infusion
Why this is the answer
Excessive contractions reduce placental blood flow and cause fetal distress. The oxytocin is stopped first, then the woman is turned on her side, IV fluids and oxygen are given as per protocol and the provider is informed.
Answer
C · Stop the oxytocin infusion
8.Pharmacology
Answer: B · Cholinergic crisis from too much anticholinesterase drug
Why this is the answer
Excess acetylcholine causes muscarinic signs (salivation, sweating, miosis, diarrhoea) and depolarising weakness. In myasthenic crisis, weakness occurs without these cholinergic signs; both can cause respiratory failure.
Answer
B · Cholinergic crisis from too much anticholinesterase drug