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 140 mg of tobramycin. The level back-extrapolated to time zero is 6 mg/L and the half-life is 2 h. Find the clearance CL in L/h.
D = 140 mgC₀ = 6 mg/Lt½ = 2 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 74 kg patient takes oral theophylline (F = 1) every 8 h. The clearance is 0.035 L/kg/h. Each dose is 200 mg of theophylline. Find the average steady-state level Css,avg.
CL = 0.035 L/kg/hτ = 8 hS = 1F = 174 kgD = 200 mg
Css,avg = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.36 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.36 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 3.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 300 mg. Draw up the dose: what volume V do you give?
2000 mg3.8 mL + 0.2 mL300 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 250 mL runs at 5 mL/h. How many units per hour D does the patient receive?
100 units/250 mL5 mL/h
D = units/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 11 mL/h. The patient weighs 75 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL11 mL/h75 kg
D = mcg/kg/min
7.PharmacologyMedium
During an infusion of a vesicant chemotherapy drug, the patient reports burning, and the site is swollen. What should the nurse do first?
AIncrease the infusion rate to finish quickly
BRemove the cannula at once and massage the area firmly
CFlush the line with a large volume of saline
DStop the infusion, leave the cannula in and follow the protocol
8.PharmacologyHard
In myxoedema coma, why is hydrocortisone often given before or with thyroid hormone?
AHydrocortisone makes thyroid hormone work faster
BThyroid hormone can trigger adrenal crisis if cortisol is also low
CHydrocortisone prevents the hypoglycaemia caused by levothyroxine
DThyroid hormone is inactive unless hydrocortisone is given
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 8.087 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 = 140/6 = 23.33 L
Rate constant
k = 0.693/2 = 0.3466 h⁻¹
Clearance
CL = 0.3466·23.33 = 8.087 L/h
Answer
CL = 8.087 L/h
2.Clinical pharmacokinetics
Answer: Css,avg = 9.653 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.
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/10 000 mL = 0.1 mg/mL
Volume
V = 0.36/0.1 = 3.6 mL
Answer
V = 3.6 mL
4.Pharmacy calculations
Answer: V = 0.6 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
3.8 + 0.2 = 4 mL
C = 2000/4 = 500 mg/mL
Volume
V = 300/500 = 0.6 mL
Answer
V = 0.6 mL
5.Pediatric & critical-care dosing
Answer: D = 2 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
100/250 = 0.4 units/mL
Units per hour
D = 5·0.4 = 2 units/h
Answer
D = 2 units/h
6.Pediatric & critical-care dosing
Answer: D = 2.4 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
250 000/250 = 1000 mcg/mL
Micrograms per minute
11·1000 = 11000 mcg/h
11000/60 = 183.3 mcg/min
Per kilogram
D = 183.3/75 = 2.444 ≈ 2.4 mcg/kg/min
Answer
D = 2.4 mcg/kg/min
7.Pharmacology
Answer: D · Stop the infusion, leave the cannula in and follow the protocol
Why this is the answer
Suspected extravasation of a vesicant is an emergency. The infusion is stopped, the cannula is left in so that drug can be aspirated, and the protocol, which may include an antidote and cold or warm packs, is followed.
Answer
D · Stop the infusion, leave the cannula in and follow the protocol
8.Pharmacology
Answer: B · Thyroid hormone can trigger adrenal crisis if cortisol is also low
Why this is the answer
Restoring thyroid hormone increases metabolic rate and cortisol clearance. If adrenal reserve is also low, this can precipitate adrenal crisis, so steroid cover is given until adrenal insufficiency is excluded.
Answer
B · Thyroid hormone can trigger adrenal crisis if cortisol is also low