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 93 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 20 mg/L. The volume of distribution is 0.7 L/kg and the salt factor is S = 0.92. Find the loading dose LD of phenytoin sodium in mg.
93 kgVd = 0.7 L/kgC = 20 mg/LS = 0.92
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 3.5 L/h. What dose D in mg gives an average steady-state level of 20 mg/L?
CL = 3.5 L/hτ = 12 hS = 1F = 1Css,avg = 20 mg/L
D = mg
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.78 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.78 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 900 mL of 45% ethanol from a 90% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
90%0%45%900 mL
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 7.5 mL/h. How many units per hour D does the patient receive?
100 units/250 mL7.5 mL/h
D = units/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 19 mL/h. The patient weighs 66 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL19 mL/h66 kg
D = mcg/kg/min
7.PharmacologyMedium
A nurse has a needlestick injury from a patient with HIV. When should post-exposure prophylaxis start?
AOnly after the nurse's HIV test turns positive
BAs soon as possible, and within 72 hours at the latest
COnly if the patient's viral load is above a set level
DAfter one week, when the risk of infection is clearer
8.PharmacologyHard
A patient on adalimumab for rheumatoid arthritis has a fever and cough on the day of her next injection. What should the nurse advise?
AWithhold the injection and get the infection assessed first
BGive the injection, as it will help the fever
CStop the drug permanently without telling the prescriber
DDouble the next dose to make up for the infection
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 1415 mg
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 = 0.7·93 = 65.1 L
Amount of active drug needed
Vd·C = 65.1·20 = 1302 mg
Loading dose
LD = 1302/(0.92·1) = 1415 mg
Answer
LD = 1415 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: D = 840 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.
Dose
D = Css,avg·CL·τ/(S·F) = 20·3.5·12/(1·1) = 840 mg
Answer
D = 840 mg
3.Pharmacy calculations
Answer: V = 0.78 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 = 0.78/1 = 0.78 mL
Answer
V = 0.78 mL
4.Pharmacy calculations
Answer: V = 450 mL
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
90%: 45 − 0 = 45 parts
0%: 90 − 45 = 45 parts
total: 90 parts
Water
V = 900·45/90 = 450 mL
Answer
V = 450 mL
Check: 450 mL of 90% contains 405 mL of drug, which is 45% of 900 mL. This assumes the volumes simply add up; in practice ethanol is made up to volume.
5.Pediatric & critical-care dosing
Answer: D = 3 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 = 7.5·0.4 = 3 units/h
Answer
D = 3 units/h
6.Pediatric & critical-care dosing
Answer: D = 7.7 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
800 000/500 = 1600 mcg/mL
Micrograms per minute
19·1600 = 30400 mcg/h
30400/60 = 506.7 mcg/min
Per kilogram
D = 506.7/66 = 7.677 ≈ 7.7 mcg/kg/min
Answer
D = 7.7 mcg/kg/min
7.Pharmacology
Answer: B · As soon as possible, and within 72 hours at the latest
Why this is the answer
Post-exposure prophylaxis aims to stop infection becoming established. It works best when started within hours, is not started after 72 hours, and is usually taken for 28 days.
Answer
B · As soon as possible, and within 72 hours at the latest
8.Pharmacology
Answer: A · Withhold the injection and get the infection assessed first
Why this is the answer
TNF inhibitors increase the risk of serious infections and can mask their signs. Doses are usually withheld during an active infection until it has been assessed and treated.
Answer
A · Withhold the injection and get the infection assessed first