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 190 mg of gentamicin. The level back-extrapolated to time zero is 8 mg/L and the half-life is 3.5 h. Find the clearance CL in L/h.
D = 190 mgC₀ = 8 mg/Lt½ = 3.5 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 60 kg patient has a phenytoin level of 4.5 mg/L; the target is 15 mg/L. The drug is given intravenously as phenytoin sodium (S = 0.92), and the volume of distribution is 0.7 L/kg. What extra loading dose LD raises the level to the target?
60 kgVd = 0.7 L/kgC = 4.5 → 15 mg/LS = 0.92
LD = mg
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.3 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.3 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 30 g of 20% zinc oxide ointment. How many grams m of plain ointment base (0%) must you add to make a 15% ointment? Round to the nearest whole gram.
30 g · 20%0%15%
m = g
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 250 units of regular insulin in 250 mL. The order is 0.05 units/kg/h for a patient who weighs 94 kg. Find the pump rate R in mL/h. Round to one decimal place.
250 units/250 mL0.05 units/kg/h94 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 77 kg has an order for norepinephrine at 5 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 mL5 mcg/min77 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
CStopping suddenly causes the drug to work better for a while
DIt can be stopped at any time, as antidepressants cause no withdrawal effects
8.PharmacologyHard
A patient has received a sodium nitroprusside infusion for several days. He becomes confused and develops a metabolic acidosis. What should be suspected?
AHyperkalaemia from the infusion
BHypoglycaemia from nitroprusside
CCyanide toxicity from nitroprusside breakdown
DAn allergic reaction to the plastic of the infusion bag
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 4.703 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 = 190/8 = 23.75 L
Rate constant
k = 0.693/3.5 = 0.198 h⁻¹
Clearance
CL = 0.198·23.75 = 4.703 L/h
Answer
CL = 4.703 L/h
2.Clinical pharmacokinetics
Answer: LD = 479.3 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.
Volume of distribution
Vd = 0.7·60 = 42 L
Rise needed
15 − 4.5 = 10.5 mg/L
Loading dose
LD = 42·10.5/(0.92·1) = 479.3 mg
Answer
LD = 479.3 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 0.3 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.
Strength in mg/mL
1000 mg/1000 mL = 1 mg/mL
Volume
V = 0.3/1 = 0.3 mL
Answer
V = 0.3 mL
4.Pharmacy calculations
Answer: m = 10 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
20%: 15 − 0 = 15 parts
0%: 20 − 15 = 5 parts
Scale to the amount you have
m = 30·5/15 = 10 g
Answer
m = 10 g
Check: 30 g + 10 g = 40 g of 15% ointment.
5.Pediatric & critical-care dosing
Answer: R = 4.7 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
0.05·94 = 4.7 units/h
Concentration
250/250 = 1 units/mL
Pump rate
R = 4.7/1 = 4.7 mL/h
Answer
R = 4.7 mL/h
6.Pediatric & critical-care dosing
Answer: R = 18.8 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.
5·60 = 300 mcg/h
Pump rate
R = 300/16 = 18.75 ≈ 18.8 mL/h
Answer
R = 18.8 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: C · Cyanide toxicity from nitroprusside breakdown
Why this is the answer
Nitroprusside releases cyanide, which is normally converted to thiocyanate. With high doses, long infusions or poor organ function, cyanide and thiocyanate can accumulate; the infusion is also protected from light.