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). After an IV dose of gentamicin, the level is 8 mg/L at 2 h and 1.4 mg/L at 7 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 8 mg/L (2 h)C2 = 1.4 mg/L (7 h)
k = h⁻¹
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 3.5 L/h. What dose D in mg gives an average steady-state level of 20 mg/L?
CL = 3.5 L/hτ = 12 hS = 1F = 1Css,avg = 20 mg/L
D = mg
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 2000 mg of powder. You add 9.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 600 mg. Draw up the dose: what volume V do you give?
2000 mg9.2 mL + 0.8 mL600 mg
V = mL
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 18 units/kg/h for a patient who weighs 98 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL18 units/kg/h98 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 27 mL/h. The patient weighs 87 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL27 mL/h87 kg
D = mcg/kg/min
7.PharmacologyMedium
What should the nurse teach a patient starting nitrofurantoin?
AStop it as soon as the burning settles
BTake it with food, and the urine may turn dark yellow or brown
CExpect blue urine, which shows that the drug is working well
DTake it on an empty stomach with an antacid
8.PharmacologyHard
A patient on adalimumab for rheumatoid arthritis has a fever and cough on the day of her next injection. What should the nurse advise?
AGive the injection, as it will help the fever
BDouble the next dose to make up for the infection
CWithhold the injection and get the infection assessed first
DStop the drug permanently without telling the prescriber
3Solutions
1.Clinical pharmacokinetics
Answer: k = 0.3486 h⁻¹
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.
Elimination rate constant
k = ln(8/1.4)/5 = 1.743/5 = 0.3486 h⁻¹
Answer
k = 0.3486 h⁻¹
2.Clinical pharmacokinetics
Answer: D = 840 mg
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.
Dose
D = Css,avg·CL·τ/(S·F) = 20·3.5·12/(1·1) = 840 mg
Answer
D = 840 mg
3.Pharmacy calculations
Answer: V = 3.8 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
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 = 3 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
9.2 + 0.8 = 10 mL
C = 2000/10 = 200 mg/mL
Volume
V = 600/200 = 3 mL
Answer
V = 3 mL
5.Pediatric & critical-care dosing
Answer: R = 35.3 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
18·98 = 1 764 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 1764/50 = 35.28 ≈ 35.3 mL/h
Answer
R = 35.3 mL/h
6.Pediatric & critical-care dosing
Answer: D = 8.3 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
800 000/500 = 1600 mcg/mL
Micrograms per minute
27·1600 = 43200 mcg/h
43200/60 = 720 mcg/min
Per kilogram
D = 720/87 = 8.276 ≈ 8.3 mcg/kg/min
Answer
D = 8.3 mcg/kg/min
7.Pharmacology
Answer: B · Take it with food, and the urine may turn dark yellow or brown
Why this is the answer
Nitrofurantoin is taken with food to reduce nausea and can harmlessly darken the urine. The full course is completed, and cough, breathlessness or numbness should be reported.
Answer
B · Take it with food, and the urine may turn dark yellow or brown
8.Pharmacology
Answer: C · Withhold the injection and get the infection assessed first
Why this is the answer
TNF inhibitors increase the risk of serious infections and can mask their signs. Doses are usually withheld during an active infection until it has been assessed and treated.
Answer
C · Withhold the injection and get the infection assessed first