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 85 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 20 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.
85 kgVd = 0.7 L/kgC = 20 mg/LS = 0.92
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 69 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.03 L/kg/h. Each dose is 400 mg of theophylline. Find the average steady-state level Css,avg.
CL = 0.03 L/kg/hτ = 12 hS = 1F = 169 kgD = 400 mg
Css,avg = mg/L
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefuroxime 750 mg as a powder. The practice label says to add 7.2 mL of sterile water; the powder adds 0.3 mL to the volume. The prescribed dose is 225 mg. What volume V do you draw up? Round to one decimal place.
750 mg7.2 mL+0.3 mL225 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 1000 mL of 3% hydrogen peroxide from a 30% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
30%0%3%1000 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 16 units/kg/h for a patient who weighs 108 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL16 units/kg/h108 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 5 mL/h. The patient weighs 102 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL5 mL/h102 kg
D = mcg/kg/min
7.PharmacologyMedium
Digoxin 0.25 mg is ordered. The tablets available are 0.125 mg. How many tablets should be given?
A1 tablet
B0.5 tablet
C4 tablets
D2 tablets
8.PharmacologyHard
On admission, a patient's home medicine list includes warfarin for atrial fibrillation, but warfarin is not on the admission orders. What should the nurse do?
AGive the patient's own warfarin brought from home without an order
BTell the patient to stop warfarin permanently
CAssume the omission is intended and do nothing
DClarify the omission with the prescriber (medication reconciliation)
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 1293 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 = 0.7·85 = 59.5 L
Amount of active drug needed
Vd·C = 59.5·20 = 1190 mg
Loading dose
LD = 1190/(0.92·1) = 1293 mg
Answer
LD = 1293 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: Css,avg = 16.1 mg/L
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.
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
7.2 + 0.3 = 7.5 mL
Concentration
750/7.5 = 100 mg/mL
Volume to give
V = 225/100 = 2.25 ≈ 2.3 mL
Answer
V = 2.3 mL
4.Pharmacy calculations
Answer: V = 900 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
30%: 3 − 0 = 3 parts
0%: 30 − 3 = 27 parts
total: 30 parts
Water
V = 1000·27/30 = 900 mL
Answer
V = 900 mL
Check: 100 mL of 30% contains 30 g of drug, which is 3% of 1000 mL.
5.Pediatric & critical-care dosing
Answer: R = 43.2 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
16·108 = 1 728 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1728/40 = 43.2 mL/h
Answer
R = 43.2 mL/h
6.Pediatric & critical-care dosing
Answer: D = 1.6 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
5·2000 = 10000 mcg/h
10000/60 = 166.7 mcg/min
Per kilogram
D = 166.7/102 = 1.634 ≈ 1.6 mcg/kg/min
Answer
D = 1.6 mcg/kg/min
7.Pharmacology
Answer: D · 2 tablets
Why this is the answer
0.25 mg ÷ 0.125 mg = 2 tablets. Doses that need more than a few tablets or unusual fractions should be double-checked.
Answer
D · 2 tablets
8.Pharmacology
Answer: D · Clarify the omission with the prescriber (medication reconciliation)
Why this is the answer
Medication reconciliation compares the patient's home medicines with current orders to find omissions, duplications and errors. The nurse raises the difference with the prescriber, who decides whether to continue, hold or change the drug.
Answer
D · Clarify the omission with the prescriber (medication reconciliation)