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 vancomycin, the level is 40 mg/L at 1 h and 15.9 mg/L at 17 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 40 mg/L (1 h)C2 = 15.9 mg/L (17 h)
k = h⁻¹
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 91 kg patient has a digoxin level of 0.6 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?
91 kgVd = 7 L/kgC = 0.6 → 1 mcg/LF = 0.7
LD = mcg
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefuroxime 750 mg as a powder. The practice label says to add 7.2 mL of sterile water; the powder adds 0.3 mL to the volume. What is the concentration C in mg/mL after reconstitution?
750 mg7.2 mL+0.3 mL
C = mg/mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 40 g of 10% salicylic acid ointment. How many grams m of 2% salicylic acid ointment must you add to make a 6% ointment? Round to the nearest whole gram.
40 g · 10%2%6%
m = g
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 100 mL. The order is 0.1 units/kg/h for a patient who weighs 96 kg. Find the pump rate R in mL/h. Round to one decimal place.
100 units/100 mL0.1 units/kg/h96 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 39 mL/h. The patient weighs 59 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL39 mL/h59 kg
D = mcg/kg/min
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 with an epidural infusion of local anaesthetic becomes hypotensive. What is the most likely mechanism?
AThe epidural catheter has caused heavy bleeding
BThe drug increases urine output and causes dehydration
CBlockade of sympathetic nerves causes vasodilation
DThe local anaesthetic causes a severe allergic reaction
3Solutions
1.Clinical pharmacokinetics
Answer: k = 0.05766 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(40/15.9)/16 = 0.9226/16 = 0.05766 h⁻¹
Answer
k = 0.05766 h⁻¹
2.Clinical pharmacokinetics
Answer: LD = 364 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 = 7·91 = 637 L
Rise needed
1 − 0.6 = 0.4 mcg/L
Loading dose
LD = 637·0.4/(1·0.7) = 364 mcg
Answer
LD = 364 mcg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: C = 100 mg/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
7.2 + 0.3 = 7.5 mL
Concentration
C = 750/7.5 = 100 mg/mL
Answer
C = 100 mg/mL
4.Pharmacy calculations
Answer: m = 40 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
10%: 6 − 2 = 4 parts
2%: 10 − 6 = 4 parts
Scale to the amount you have
m = 40·4/4 = 40 g
Answer
m = 40 g
Check: 40 g + 40 g = 80 g of 6% ointment.
5.Pediatric & critical-care dosing
Answer: R = 9.6 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
0.1·96 = 9.6 units/h
Concentration
100/100 = 1 units/mL
Pump rate
R = 9.6/1 = 9.6 mL/h
Answer
R = 9.6 mL/h
6.Pediatric & critical-care dosing
Answer: D = 17.6 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
39·1600 = 62400 mcg/h
62400/60 = 1040 mcg/min
Per kilogram
D = 1040/59 = 17.63 ≈ 17.6 mcg/kg/min
Answer
D = 17.6 mcg/kg/min
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: C · Blockade of sympathetic nerves causes vasodilation
Why this is the answer
Epidural local anaesthetics block sympathetic fibres as well as sensory nerves. This dilates blood vessels and lowers blood pressure, so fluids, position changes or vasopressors may be needed.
Answer
C · Blockade of sympathetic nerves causes vasodilation