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 250 mg of tobramycin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 2.5 h. Find the clearance CL in L/h.
D = 250 mgC₀ = 10 mg/Lt½ = 2.5 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 41-year-old man weighs 52 kg and has a serum creatinine of 2 mg/dL (177 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual gentamicin regimen is 80 mg every 8 h for a creatinine clearance of 100 mL/min. Keeping the dose, the interval is lengthened in proportion to the fall in clearance. Find the new dosing interval τ. Round to one decimal place.
A solution has a ratio strength of 1:1000. You need 0.62 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.62 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 900 mg. Draw up the dose: what volume V do you give?
1000 mg3.2 mL + 0.8 mL900 mg
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 66 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/h66 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 92 kg has an order for norepinephrine at 6 mcg/min. The bag contains 4 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
4 mg/250 mL6 mcg/min92 kg
R = mL/h
7.PharmacologyMedium
A child weighing 20 kg is prescribed a drug at 15 mg/kg per dose. What is the dose?
A35 mg
B150 mg
C3000 mg
D300 mg
8.PharmacologyHard
A patient on digoxin is started on amiodarone. What change should the nurse expect?
AAmiodarone levels fall to zero
BDigoxin levels rise, so the digoxin dose is often reduced
CNo interaction is expected
DDigoxin levels fall sharply, so the digoxin dose is doubled
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 6.931 L/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.
Volume of distribution
Vd = 250/10 = 25 L
Rate constant
k = 0.693/2.5 = 0.2773 h⁻¹
Clearance
CL = 0.2773·25 = 6.931 L/h
Answer
CL = 6.931 L/h
2.Clinical pharmacokinetics
Answer: τ = 22.4 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.
Creatinine clearance (Cockcroft–Gault)
CrCl = (140 − 41)·52/(72·2) = 35.75 mL/min
New interval
τ = 8·100/35.75 = 22.38 ≈ 22.4 h
Answer
τ = 22.4 h
In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.
3.Pharmacy calculations
Answer: V = 0.62 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.
Strength in mg/mL
1000 mg/1000 mL = 1 mg/mL
Volume
V = 0.62/1 = 0.62 mL
Answer
V = 0.62 mL
4.Pharmacy calculations
Answer: V = 3.6 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
3.2 + 0.8 = 4 mL
C = 1000/4 = 250 mg/mL
Volume
V = 900/250 = 3.6 mL
Answer
V = 3.6 mL
5.Pediatric & critical-care dosing
Answer: R = 26.4 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
16·66 = 1 056 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1056/40 = 26.4 mL/h
Answer
R = 26.4 mL/h
6.Pediatric & critical-care dosing
Answer: R = 22.5 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
4 000/250 = 16 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
6·60 = 360 mcg/h
Pump rate
R = 360/16 = 22.5 mL/h
Answer
R = 22.5 mL/h
7.Pharmacology
Answer: D · 300 mg
Why this is the answer
20 kg × 15 mg/kg = 300 mg. The result is also checked against the safe dose range and the adult maximum.
Answer
D · 300 mg
8.Pharmacology
Answer: B · 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
B · Digoxin levels rise, so the digoxin dose is often reduced