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 54 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.
54 kgVd = 0.7 L/kgC = 20 mg/LS = 0.92
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 53-year-old man weighs 53 kg and has a serum creatinine of 2.4 mg/dL (212 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 ciprofloxacin dose is 500 mg for a creatinine clearance of 120 mL/min, and a fraction fe = 0.6 of the drug is excreted unchanged by the kidneys. Using the Dettli dose fraction Q = 1 − fe·(1 − CrCl/normal CrCl), find the adjusted dose D. Round to the nearest whole number.
A solution has a ratio strength of 1:1000. You need 0.52 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.52 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 900 mL of 70% 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%70%900 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 80 units/kg for a patient who weighs 110 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg110 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 5 mL/h. The patient weighs 62 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL5 mL/h62 kg
D = mcg/kg/min
7.PharmacologyMedium
Why is a spacer recommended with a metered-dose inhaler?
AIt doubles the dose of drug released by each puff of the inhaler
BIt removes the need to shake the inhaler
CMore drug reaches the lungs and less stays in the mouth
DIt turns the inhaler into a nebuliser
8.PharmacologyHard
Which property makes a drug more likely to cross the blood–brain barrier?
ALarge molecular weight and strong protein binding
BHigh lipid solubility and small size
CPositive charge at physiological pH
DHigh water solubility and strong ionisation
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 821.7 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 = 0.7·54 = 37.8 L
Amount of active drug needed
Vd·C = 37.8·20 = 756 mg
Loading dose
LD = 756/(0.92·1) = 821.7 mg
Answer
LD = 821.7 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: D = 267 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.
Creatinine clearance (Cockcroft–Gault)
CrCl = (140 − 53)·53/(72·2.4) = 26.68 mL/min
Dose fraction (Dettli)
Q = 1 − 0.6·(1 − 26.68/120) = 0.5334
Adjusted dose
D = 0.5334·500 = 266.7 ≈ 267 mg
Answer
D = 267 mg
In practice the dose is rounded to a convenient amount and checked against the product information.
3.Pharmacy calculations
Answer: V = 0.52 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 = 0.52/1 = 0.52 mL
Answer
V = 0.52 mL
4.Pharmacy calculations
Answer: V = 200 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%: 70 − 0 = 70 parts
0%: 90 − 70 = 20 parts
total: 90 parts
Water
V = 900·20/90 = 200 mL
Answer
V = 200 mL
Check: 700 mL of 90% contains 630 mL of drug, which is 70% of 900 mL. This assumes the volumes simply add up; in practice ethanol is made up to volume.
5.Pediatric & critical-care dosing
Answer: V = 1.8 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
80·110 = 8 800 units
Volume
V = 8800/5000 = 1.76 ≈ 1.8 mL
Answer
V = 1.8 mL
6.Pediatric & critical-care dosing
Answer: D = 1.3 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
5·1000 = 5000 mcg/h
5000/60 = 83.33 mcg/min
Per kilogram
D = 83.33/62 = 1.344 ≈ 1.3 mcg/kg/min
Answer
D = 1.3 mcg/kg/min
7.Pharmacology
Answer: C · More drug reaches the lungs and less stays in the mouth
Why this is the answer
A spacer holds the aerosol so it can be inhaled slowly, without precise coordination. This improves lung delivery and reduces mouth side effects such as thrush from inhaled steroids.
Answer
C · More drug reaches the lungs and less stays in the mouth
8.Pharmacology
Answer: B · High lipid solubility and small size
Why this is the answer
Small, lipophilic, non-ionised molecules diffuse across endothelial cell membranes. Charged or large, protein-bound drugs mostly stay out.