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 180 mg of gentamicin. The level back-extrapolated to time zero is 8 mg/L and the half-life is 2.5 h. Find the clearance CL in L/h.
D = 180 mgC₀ = 8 mg/Lt½ = 2.5 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 4 L/h. Each dose is 1000 mg of vancomycin. Find the average steady-state level Css,avg.
CL = 4 L/hτ = 12 hS = 1F = 1D = 1000 mg
Css,avg = mg/L
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains oxacillin 2000 mg as a powder. The practice label says to add 11.5 mL of sterile water; the powder adds 1 mL to the volume. The prescribed dose is 600 mg. What volume V do you draw up? Round to one decimal place.
2000 mg11.5 mL+1 mL600 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 4.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 260 mg. Draw up the dose: what volume V do you give?
500 mg4.5 mL + 0.5 mL260 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 100 units of regular insulin in 100 mL runs at 4 mL/h. How many units per hour D does the patient receive?
100 units/100 mL4 mL/h
D = units/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 100 kg has an order for nitroglycerin at 20 mcg/min. The bag contains 25 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
25 mg/250 mL20 mcg/min100 kg
R = mL/h
7.PharmacologyMedium
An adult patient is due to receive digoxin. The apical pulse, counted for a full minute, is 52 beats per minute. What should the nurse do?
AWithhold the dose and notify the prescriber
BGive the dose with food to slow absorption
CGive half the dose and document the pulse
DGive the dose and recheck the pulse in one hour
8.PharmacologyHard
A patient took a large paracetamol (acetaminophen) overdose 6 hours ago and feels well. Why is treatment still urgent?
AThe drug will cause kidney stones within a few hours
BThe patient is at risk of immediate respiratory arrest
CParacetamol overdose only causes harm if symptoms start in the first hour
DLiver damage appears 1–3 days later, and early treatment works best
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 6.238 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 = 180/8 = 22.5 L
Rate constant
k = 0.693/2.5 = 0.2773 h⁻¹
Clearance
CL = 0.2773·22.5 = 6.238 L/h
Answer
CL = 6.238 L/h
2.Clinical pharmacokinetics
Answer: Css,avg = 20.83 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
11.5 + 1 = 12.5 mL
Concentration
2000/12.5 = 160 mg/mL
Volume to give
V = 600/160 = 3.75 ≈ 3.8 mL
Answer
V = 3.8 mL
4.Pharmacy calculations
Answer: V = 2.6 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
4.5 + 0.5 = 5 mL
C = 500/5 = 100 mg/mL
Volume
V = 260/100 = 2.6 mL
Answer
V = 2.6 mL
5.Pediatric & critical-care dosing
Answer: D = 4 units/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.
Concentration
100/100 = 1 units/mL
Units per hour
D = 4·1 = 4 units/h
Answer
D = 4 units/h
6.Pediatric & critical-care dosing
Answer: R = 12 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
25 000/250 = 100 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
20·60 = 1200 mcg/h
Pump rate
R = 1200/100 = 12 mL/h
Answer
R = 12 mL/h
7.Pharmacology
Answer: A · Withhold the dose and notify the prescriber
Why this is the answer
Digoxin is usually withheld in adults if the apical pulse is below 60 per minute, and the prescriber is informed. Bradycardia may be an early sign of toxicity.
Answer
A · Withhold the dose and notify the prescriber
8.Pharmacology
Answer: D · Liver damage appears 1–3 days later, and early treatment works best
Why this is the answer
Paracetamol overdose often causes few symptoms at first, while the toxic metabolite damages the liver. Liver injury peaks after about 3 days, so the decision to treat is based on the timed blood level, not on symptoms.
Answer
D · Liver damage appears 1–3 days later, and early treatment works best