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 patient receives an IV bolus of 150 mg of gentamicin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 3.5 h. Find the volume of distribution Vd.
D = 150 mgC₀ = 10 mg/Lt½ = 3.5 h
Vd = L
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 76 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.045 L/kg/h. Each dose is 200 mg of theophylline. Find the average steady-state level Css,avg.
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 18.2 mL of diluent. The prescribed dose is 400 000 units. What volume V do you draw up? Round to one decimal place.
18.2 mL → 250 000 units/mL400 000 units
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 400 mL of 15% dextrose by mixing 50% and 10% dextrose. How many mL V of the 50% solution do you need? Round to the nearest whole mL.
50%10%15%400 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 20 units/kg/h for a patient who weighs 52 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL20 units/kg/h52 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 8 mL/h. The patient weighs 109 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL8 mL/h109 kg
D = mcg/kg/min
7.PharmacologyMedium
A patient with a peanut allergy is taught to use an adrenaline auto-injector. Which statement is correct?
ACall emergency services after using it, even if symptoms improve
BUse it only if the antihistamine has not worked after an hour
CKeep it at home so it is not lost
DThere is no need to see a doctor if the swelling goes down
8.PharmacologyHard
Why are patients on long-acting nitrates advised to have a nitrate-free period of several hours each day?
ATo reduce the risk of bleeding
BTo prevent tolerance to the nitrate
CTo let the liver recover from toxicity
DTo avoid nitrate accumulation in fat tissue
3Solutions
1.Clinical pharmacokinetics
Answer: Vd = 15 L
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 = 150/10 = 15 L
Answer
Vd = 15 L
2.Clinical pharmacokinetics
Answer: Css,avg = 4.873 mg/L
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.
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Concentration from the label
18.2 mL → 250 000 units/mL
Volume to give
V = 400 000/250 000 = 1.6 mL
Answer
V = 1.6 mL
4.Pharmacy calculations
Answer: V = 50 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
50%: 15 − 10 = 5 parts
10%: 50 − 15 = 35 parts
total: 40 parts
Share the volume
V = 400·5/40 = 50 mL
Answer
V = 50 mL
Check: 50 mL of 50% + 350 mL of 10% = 400 mL.
5.Pediatric & critical-care dosing
Answer: R = 26 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
20·52 = 1 040 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1040/40 = 26 mL/h
Answer
R = 26 mL/h
6.Pediatric & critical-care dosing
Answer: D = 1.2 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
8·1000 = 8000 mcg/h
8000/60 = 133.3 mcg/min
Per kilogram
D = 133.3/109 = 1.223 ≈ 1.2 mcg/kg/min
Answer
D = 1.2 mcg/kg/min
7.Pharmacology
Answer: A · Call emergency services after using it, even if symptoms improve
Why this is the answer
Anaphylaxis can recur after the adrenaline wears off (a biphasic reaction). The person always calls for help after using it, carries two auto-injectors and uses adrenaline early.
Answer
A · Call emergency services after using it, even if symptoms improve
8.Pharmacology
Answer: B · To prevent tolerance to the nitrate
Why this is the answer
Tolerance to nitrates develops quickly with constant levels. An asymmetric dosing schedule or removing patches overnight keeps them effective.