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 with digoxin tablets to reach a level of 0.8 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.
93 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). An 82-year-old woman weighs 81 kg and has a serum creatinine of 1.5 mg/dL (133 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 100 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 0.88 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.88 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 450 mL of 5% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 3% solution do you need? Round to the nearest whole mL.
23%3%5%450 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 70 units/kg for a patient who weighs 99 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg99 kg5 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 22 mL/h. The patient weighs 82 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL22 mL/h82 kg
D = mcg/kg/min
7.PharmacologyMedium
When should a patient take a once-daily proton pump inhibitor such as omeprazole?
AStraight after a large evening meal
BWith a glass of milk at bedtime, when acid output is highest
COnly when heartburn is severe
DAbout 30–60 minutes before the first meal of the day
8.PharmacologyHard
In aspirin overdose the urine may be made alkaline with sodium bicarbonate. Why does this increase salicylate excretion?
ABicarbonate speeds up the liver metabolism of salicylate to inactive forms
BBicarbonate binds salicylate and makes it inactive
CMore salicylate is ionised in the tubule, so less is reabsorbed
DAlkaline urine increases glomerular filtration
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 744 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 = 7·93 = 651 L
Amount of active drug needed
Vd·C = 651·0.8 = 520.8 mcg
Loading dose
LD = 520.8/(1·0.7) = 744 mcg
Answer
LD = 744 mcg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: τ = 21.6 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 − 82)·81/(72·1.5)·0.85 = 36.98 mL/min
New interval
τ = 8·100/36.98 = 21.64 ≈ 21.6 h
Answer
τ = 21.6 h
In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.
3.Pharmacy calculations
Answer: V = 8.8 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 = 0.88/0.1 = 8.8 mL
Answer
V = 8.8 mL
4.Pharmacy calculations
Answer: V = 405 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
23%: 5 − 3 = 2 parts
3%: 23 − 5 = 18 parts
total: 20 parts
Share the volume
V = 450·18/20 = 405 mL
Answer
V = 405 mL
Check: 45 mL of 23% + 405 mL of 3% = 450 mL.
5.Pediatric & critical-care dosing
Answer: V = 1.4 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
70·99 = 6 930 units
Volume
V = 6930/5000 = 1.386 ≈ 1.4 mL
Answer
V = 1.4 mL
6.Pediatric & critical-care dosing
Answer: D = 4.5 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
22·1000 = 22000 mcg/h
22000/60 = 366.7 mcg/min
Per kilogram
D = 366.7/82 = 4.472 ≈ 4.5 mcg/kg/min
Answer
D = 4.5 mcg/kg/min
7.Pharmacology
Answer: D · About 30–60 minutes before the first meal of the day
Why this is the answer
Proton pump inhibitors block pumps that are active, so they work best when taken before breakfast. Food then activates the pumps when the drug level is high.
Answer
D · About 30–60 minutes before the first meal of the day
8.Pharmacology
Answer: C · More salicylate is ionised in the tubule, so less is reabsorbed
Why this is the answer
Salicylate is a weak acid. In alkaline urine more of it is in the ionised form, which is "trapped" in the tubule and excreted. This is called ion trapping.
Answer
C · More salicylate is ionised in the tubule, so less is reabsorbed