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 68 kg patient is to be loaded with digoxin tablets to reach a level of 1 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.
68 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). An 82 kg patient has a phenytoin level of 6 mg/L; the target is 20 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?
82 kgVd = 0.7 L/kgC = 6 → 20 mg/LS = 0.92
LD = mg
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.56 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.56 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 4.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 760 mg. Draw up the dose: what volume V do you give?
1000 mg4.8 mL + 0.2 mL760 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 80 units/kg for a patient who weighs 55 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
80 units/kg55 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 10 mcg/kg/min for a patient who weighs 88 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL10 mcg/kg/min88 kg
R = mL/h
7.PharmacologyMedium
Sumatriptan is contraindicated in which patient?
AA patient with mild asthma
BA patient with a recent ankle sprain
CA patient with iron deficiency anaemia
DA patient with coronary artery disease
8.PharmacologyHard
A patient with type 2 diabetes starts a high dose of prednisolone for a flare of COPD. Which change should the nurse expect?
ALower potassium only, with no effect on glucose
BNo change in glucose, as steroids act only in the lungs
CHigher blood glucose, so more frequent glucose checks are needed
DLower blood glucose, so the diabetes medicines should be stopped
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 680 mcg
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 = 7·68 = 476 L
Amount of active drug needed
Vd·C = 476·1 = 476 mcg
Loading dose
LD = 476/(1·0.7) = 680 mcg
Answer
LD = 680 mcg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: LD = 873.5 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 = 0.7·82 = 57.4 L
Rise needed
20 − 6 = 14 mg/L
Loading dose
LD = 57.4·14/(0.92·1) = 873.5 mg
Answer
LD = 873.5 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 5.6 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.
Strength in mg/mL
1000 mg/10 000 mL = 0.1 mg/mL
Volume
V = 0.56/0.1 = 5.6 mL
Answer
V = 5.6 mL
4.Pharmacy calculations
Answer: V = 3.8 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
4.8 + 0.2 = 5 mL
C = 1000/5 = 200 mg/mL
Volume
V = 760/200 = 3.8 mL
Answer
V = 3.8 mL
5.Pediatric & critical-care dosing
Answer: V = 0.88 mL
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 needed
80·55 = 4 400 units
Volume
V = 4400/5000 = 0.88 mL
Answer
V = 0.88 mL
6.Pediatric & critical-care dosing
Answer: R = 33 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
10·88 = 880 mcg/min
880·60 = 52800 mcg/h
Pump rate
R = 52800/1600 = 33 mL/h
Answer
R = 33 mL/h
7.Pharmacology
Answer: D · A patient with coronary artery disease
Why this is the answer
Triptans can constrict coronary arteries and cause angina or myocardial infarction. They are avoided in coronary disease, uncontrolled hypertension and previous stroke.
Answer
D · A patient with coronary artery disease
8.Pharmacology
Answer: C · Higher blood glucose, so more frequent glucose checks are needed
Why this is the answer
Glucocorticoids raise blood glucose by increasing liver glucose production and insulin resistance. Glucose is monitored more often, and diabetes treatment may need to be increased during the course.
Answer
C · Higher blood glucose, so more frequent glucose checks are needed