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 4 L/h. What infusion rate R in mg/h gives a steady-state level of 25 mg/L?
CL = 4 L/hCss = 25 mg/L
R = mg/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient's tobramycin half-life is 2.5 h. The target is a peak of 6 mg/L and a trough of 0.5 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.
t½ = 2.5 hCpeak = 6 mg/LCtrough = 0.5 mg/L
τ = h
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.61 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.61 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 4.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 280 mg. Draw up the dose: what volume V do you give?
500 mg4.6 mL + 0.4 mL280 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 70 units/kg for a patient who weighs 102 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg102 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 15 mcg/kg/min for a patient who weighs 89 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL15 mcg/kg/min89 kg
R = mL/h
7.PharmacologyMedium
A patient wants to stop paroxetine suddenly. What should the nurse explain?
AIt can cause dizziness, "electric shock" feelings and irritability
BIt can be stopped at any time, as antidepressants cause no withdrawal effects
DStopping suddenly causes the drug to work better for a while
8.PharmacologyHard
A patient on warfarin also takes ginkgo and high-dose garlic supplements and is having minor surgery next week. What should the nurse do?
AAdvise taking extra supplements to improve healing
BIgnore the supplements, as natural products are safe with warfarin
CAdvise stopping warfarin without telling anyone
DTell the surgical team, as the supplements can increase bleeding
3Solutions
1.Clinical pharmacokinetics
Answer: R = 100 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.
Infusion rate
R = 4·25 = 100 mg/h
Answer
R = 100 mg/h
2.Clinical pharmacokinetics
Answer: τ = 9 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.
Rate constant
k = 0.693/2.5 = 0.2773 h⁻¹
Dosing interval
τ = ln(6/0.5)/0.2773 = 2.485/0.2773 = 8.962 ≈ 9 h
Answer
τ = 9 h
In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.
3.Pharmacy calculations
Answer: V = 0.61 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 = 0.61/1 = 0.61 mL
Answer
V = 0.61 mL
4.Pharmacy calculations
Answer: V = 2.8 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
4.6 + 0.4 = 5 mL
C = 500/5 = 100 mg/mL
Volume
V = 280/100 = 2.8 mL
Answer
V = 2.8 mL
5.Pediatric & critical-care dosing
Answer: V = 1.4 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
70·102 = 7 140 units
Volume
V = 7140/5000 = 1.428 ≈ 1.4 mL
Answer
V = 1.4 mL
6.Pediatric & critical-care dosing
Answer: R = 50.1 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
15·89 = 1335 mcg/min
1335·60 = 80100 mcg/h
Pump rate
R = 80100/1600 = 50.06 ≈ 50.1 mL/h
Answer
R = 50.1 mL/h
7.Pharmacology
Answer: A · It can cause dizziness, "electric shock" feelings and irritability
Why this is the answer
Antidepressant discontinuation syndrome is common with short half-life drugs such as paroxetine and venlafaxine. The dose is tapered gradually under supervision.
Answer
A · It can cause dizziness, "electric shock" feelings and irritability
8.Pharmacology
Answer: D · Tell the surgical team, as the supplements can increase bleeding
Why this is the answer
Ginkgo and garlic may impair platelet function and add to warfarin's bleeding risk. The team needs a full list of supplements so it can plan, and the patient should not change warfarin without advice.
Answer
D · Tell the surgical team, as the supplements can increase bleeding