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 52 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.
52 kgVd = 0.7 L/kgC = 15 mg/LS = 0.92
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 67 kg patient has a digoxin level of 0.5 mcg/L; the target is 1 mcg/L. The volume of distribution is 7 L/kg and the tablets have F = 0.7. What extra loading dose LD raises the level to the target?
67 kgVd = 7 L/kgC = 0.5 → 1 mcg/LF = 0.7
LD = mcg
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 1000 mg as a powder. The practice label says to add 3.5 mL of sterile water; the powder adds 0.5 mL to the volume. The prescribed dose is 300 mg. What volume V do you draw up? Round to one decimal place.
1000 mg3.5 mL+0.5 mL300 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 30 g of 5% coal tar ointment. How many grams m of 1% coal tar ointment must you add to make a 3% ointment? Round to the nearest whole gram.
30 g · 5%1%3%
m = g
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 12 500 units of heparin in 250 mL. The order is 20 units/kg/h for a patient who weighs 73 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL20 units/kg/h73 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 21 mL/h. The patient weighs 87 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL21 mL/h87 kg
D = mcg/kg/min
7.PharmacologyMedium
Why are benzodiazepines used with great caution in older people?
AThey raise the risk of confusion, falls and fractures
BThey are not absorbed from the gut after age 65
CThey cause permanent hearing loss in older people
DThey cause severe high blood pressure in older people
8.PharmacologyHard
A patient on digoxin is started on amiodarone. What change should the nurse expect?
AAmiodarone levels fall to zero
BDigoxin levels fall sharply, so the digoxin dose is doubled
CNo interaction is expected
DDigoxin levels rise, so the digoxin dose is often reduced
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 593.5 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 = 0.7·52 = 36.4 L
Amount of active drug needed
Vd·C = 36.4·15 = 546 mg
Loading dose
LD = 546/(0.92·1) = 593.5 mg
Answer
LD = 593.5 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: LD = 335 mcg
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 = 7·67 = 469 L
Rise needed
1 − 0.5 = 0.5 mcg/L
Loading dose
LD = 469·0.5/(1·0.7) = 335 mcg
Answer
LD = 335 mcg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 1.2 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
3.5 + 0.5 = 4 mL
Concentration
1000/4 = 250 mg/mL
Volume to give
V = 300/250 = 1.2 mL
Answer
V = 1.2 mL
4.Pharmacy calculations
Answer: m = 30 g
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
5%: 3 − 1 = 2 parts
1%: 5 − 3 = 2 parts
Scale to the amount you have
m = 30·2/2 = 30 g
Answer
m = 30 g
Check: 30 g + 30 g = 60 g of 3% ointment.
5.Pediatric & critical-care dosing
Answer: R = 29.2 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
20·73 = 1 460 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 1460/50 = 29.2 mL/h
Answer
R = 29.2 mL/h
6.Pediatric & critical-care dosing
Answer: D = 4 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
250 000/250 = 1000 mcg/mL
Micrograms per minute
21·1000 = 21000 mcg/h
21000/60 = 350 mcg/min
Per kilogram
D = 350/87 = 4.023 ≈ 4 mcg/kg/min
Answer
D = 4 mcg/kg/min
7.Pharmacology
Answer: A · They raise the risk of confusion, falls and fractures
Why this is the answer
Older people are more sensitive to benzodiazepines and often eliminate them more slowly. Sedation, unsteadiness and confusion raise the risk of falls and fractures.
Answer
A · They raise the risk of confusion, falls and fractures
8.Pharmacology
Answer: D · Digoxin levels rise, so the digoxin dose is often reduced
Why this is the answer
Amiodarone inhibits P-glycoprotein and reduces digoxin clearance, so digoxin levels rise. The digoxin dose is often reduced, and the patient is monitored for bradycardia and toxicity; amiodarone also raises warfarin levels.
Answer
D · Digoxin levels rise, so the digoxin dose is often reduced