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). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 55 mL/min. What infusion rate R in mg/h gives a steady-state level of 20 mg/L?
CL = 55 mL/minCss = 20 mg/L
R = mg/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 75 mg/h with no loading dose. The patient's clearance is 3 L/h and the half-life is 6 h. What is the level C after 2 h?
R = 75 mg/hCL = 3 L/ht½ = 6 ht = 2 h
C = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.66 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.66 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 4.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 370 mg. Draw up the dose: what volume V do you give?
500 mg4.5 mL + 0.5 mL370 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 50 units of regular insulin in 50 mL. The order is 0.1 units/kg/h for a patient who weighs 62 kg. Find the pump rate R in mL/h. Round to one decimal place.
50 units/50 mL0.1 units/kg/h62 kg
R = mL/h
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 3 mcg/kg/min for a patient who weighs 56 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL3 mcg/kg/min56 kg
R = mL/h
7.PharmacologyMedium
Which patient should usually not use the combined oral contraceptive pill?
AA 38-year-old woman who smokes 20 cigarettes a day
BA 25-year-old woman with heavy periods
CA 22-year-old non-smoker with acne
DA 30-year-old non-smoker with no medical problems
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?
AHigher blood glucose, so more frequent glucose checks are needed
BLower potassium only, with no effect on glucose
CLower blood glucose, so the diabetes medicines should be stopped
DNo change in glucose, as steroids act only in the lungs
3Solutions
1.Clinical pharmacokinetics
Answer: R = 66 mg/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.
Clearance in L/h
55·60/1000 = 3.3 L/h
Infusion rate
R = 3.3·20 = 66 mg/h
Answer
R = 66 mg/h
2.Clinical pharmacokinetics
Answer: C = 5.157 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.
Steady-state level
Css = 75/3 = 25 mg/L
Rate constant
k = 0.693/6 = 0.1155 h⁻¹
Level after the given time
C = 25·(1 − e−0.1155·2) = 5.157 mg/L
Answer
C = 5.157 mg/L
3.Pharmacy calculations
Answer: V = 6.6 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 = 0.66/0.1 = 6.6 mL
Answer
V = 6.6 mL
4.Pharmacy calculations
Answer: V = 3.7 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
4.5 + 0.5 = 5 mL
C = 500/5 = 100 mg/mL
Volume
V = 370/100 = 3.7 mL
Answer
V = 3.7 mL
5.Pediatric & critical-care dosing
Answer: R = 6.2 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
0.1·62 = 6.2 units/h
Concentration
50/50 = 1 units/mL
Pump rate
R = 6.2/1 = 6.2 mL/h
Answer
R = 6.2 mL/h
6.Pediatric & critical-care dosing
Answer: R = 6.3 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
3·56 = 168 mcg/min
168·60 = 10080 mcg/h
Pump rate
R = 10080/1600 = 6.3 mL/h
Answer
R = 6.3 mL/h
7.Pharmacology
Answer: A · A 38-year-old woman who smokes 20 cigarettes a day
Why this is the answer
Smoking over the age of 35 greatly increases the risk of myocardial infarction and stroke with combined hormonal contraception. Progestogen-only or non-hormonal methods are preferred.
Answer
A · A 38-year-old woman who smokes 20 cigarettes a day
8.Pharmacology
Answer: A · 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
A · Higher blood glucose, so more frequent glucose checks are needed