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 81 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 15 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.
81 kgVd = 0.7 L/kgC = 15 mg/LS = 0.92
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 66-year-old woman weighs 71 kg and has a serum creatinine of 2.9 mg/dL (256 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 0.72 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.72 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 120 g of 5% coal tar ointment. How many grams m of 1% coal tar ointment must you add to make a 2% ointment? Round to the nearest whole gram.
120 g · 5%1%2%
m = g
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 82 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg82 kg1 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 25 mL/h. The patient weighs 71 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL25 mL/h71 kg
D = mcg/kg/min
7.PharmacologyMedium
A man takes finasteride. What should be explained about handling the tablets?
AThe tablets must be crushed before swallowing
BThe tablets must be stored in the fridge
CPregnant women should not handle crushed or broken tablets
DAnyone can handle the tablets, as they contain no active drug
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?
AStop the drug permanently without telling the prescriber
BWithhold the injection and get the infection assessed first
CGive the injection, as it will help the fever
DDouble the next dose to make up for the infection
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 924.5 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 = 0.7·81 = 56.7 L
Amount of active drug needed
Vd·C = 56.7·15 = 850.5 mg
Loading dose
LD = 850.5/(0.92·1) = 924.5 mg
Answer
LD = 924.5 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: τ = 44.9 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 − 66)·71/(72·2.9)·0.85 = 21.39 mL/min
New interval
τ = 8·120/21.39 = 44.88 ≈ 44.9 h
Answer
τ = 44.9 h
In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.
3.Pharmacy calculations
Answer: V = 7.2 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 = 0.72/0.1 = 7.2 mL
Answer
V = 7.2 mL
4.Pharmacy calculations
Answer: m = 360 g
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
5%: 2 − 1 = 1 parts
1%: 5 − 2 = 3 parts
Scale to the amount you have
m = 120·3/1 = 360 g
Answer
m = 360 g
Check: 120 g + 360 g = 480 g of 2% ointment.
5.Pediatric & critical-care dosing
Answer: V = 6.6 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
80·82 = 6 560 units
Volume
V = 6560/1000 = 6.56 ≈ 6.6 mL
Answer
V = 6.6 mL
6.Pediatric & critical-care dosing
Answer: D = 5.9 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
25·1000 = 25000 mcg/h
25000/60 = 416.7 mcg/min
Per kilogram
D = 416.7/71 = 5.869 ≈ 5.9 mcg/kg/min
Answer
D = 5.9 mcg/kg/min
7.Pharmacology
Answer: C · Pregnant women should not handle crushed or broken tablets
Why this is the answer
Finasteride can be absorbed through the skin and may affect genital development of a male fetus. Women who are or may become pregnant should avoid contact with crushed or broken tablets.
Answer
C · Pregnant women should not handle crushed or broken tablets
8.Pharmacology
Answer: B · 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
B · Withhold the injection and get the infection assessed first