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). An 87 kg patient is to receive an aminophylline infusion (salt factor S = 0.8: 80% of aminophylline is theophylline). The theophylline clearance is 0.03 L/kg/h. What aminophylline infusion rate R in mg/h gives a steady-state theophylline level of 10 mg/L?
87 kgCL = 0.03 L/kg/hCss = 10 mg/LS = 0.8
R = mg/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 68-year-old woman weighs 72 kg and has a serum creatinine of 2.3 mg/dL (203 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual tobramycin regimen is 120 mg every 8 h for a creatinine clearance of 120 mL/min. Keeping the dose, the interval is lengthened in proportion to the fall in clearance. Find the new dosing interval τ. Round to one decimal place.
A solution has a ratio strength of 1:10 000. You need 0.48 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.48 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 1.7 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 180 mg. Draw up the dose: what volume V do you give?
250 mg1.7 mL + 0.8 mL180 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 0.05 units/kg/h for a patient who weighs 86 kg. Find the pump rate R in mL/h. Round to one decimal place.
50 units/50 mL0.05 units/kg/h86 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 58 kg has an order for norepinephrine at 10 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 mL10 mcg/min58 kg
R = mL/h
7.PharmacologyMedium
How should a patient store sublingual glyceryl trinitrate (nitroglycerin) tablets?
AIn a plastic weekly pill box with other tablets
BLoose in a shirt pocket close to the body for quick access
CIn the fridge in a damp, open container to keep them fresh and cool
DIn the original dark glass bottle, away from heat, light and moisture
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 = 32.62 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
CL = 0.03·87 = 2.61 L/h
Infusion rate
R = CL·Css/S = 2.61·10/0.8 = 32.62 mg/h
Answer
R = 32.62 mg/h
2.Clinical pharmacokinetics
Answer: τ = 36.1 h
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.
Creatinine clearance (Cockcroft–Gault)
CrCl = (140 − 68)·72/(72·2.3)·0.85 = 26.61 mL/min
New interval
τ = 8·120/26.61 = 36.08 ≈ 36.1 h
Answer
τ = 36.1 h
In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.
3.Pharmacy calculations
Answer: V = 4.8 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.
Strength in mg/mL
1000 mg/10 000 mL = 0.1 mg/mL
Volume
V = 0.48/0.1 = 4.8 mL
Answer
V = 4.8 mL
4.Pharmacy calculations
Answer: V = 1.8 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
1.7 + 0.8 = 2.5 mL
C = 250/2.5 = 100 mg/mL
Volume
V = 180/100 = 1.8 mL
Answer
V = 1.8 mL
5.Pediatric & critical-care dosing
Answer: R = 4.3 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
0.05·86 = 4.3 units/h
Concentration
50/50 = 1 units/mL
Pump rate
R = 4.3/1 = 4.3 mL/h
Answer
R = 4.3 mL/h
6.Pediatric & critical-care dosing
Answer: R = 37.5 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.
10·60 = 600 mcg/h
Pump rate
R = 600/16 = 37.5 mL/h
Answer
R = 37.5 mL/h
7.Pharmacology
Answer: D · In the original dark glass bottle, away from heat, light and moisture
Why this is the answer
Nitroglycerin tablets lose potency when exposed to light, heat, air and moisture. They are kept in their original tightly closed dark container, and expired tablets are replaced.
Answer
D · In the original dark glass bottle, away from heat, light and moisture
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