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 210 mg of gentamicin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 3.5 h. Find the clearance CL in L/h.
D = 210 mgC₀ = 10 mg/Lt½ = 3.5 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 65 kg patient on regular gentamicin doses is at steady state. The target is a peak of 10 mg/L and a trough of 1 mg/L, and the volume of distribution is 0.25 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 500 mg as a powder. The practice label says to add 1.8 mL of sterile water; the powder adds 0.2 mL to the volume. What is the concentration C in mg/mL after reconstitution?
500 mg1.8 mL+0.2 mL
C = mg/mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 500 mL of 2% chlorhexidine from a 20% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
20%0%2%500 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 250 units of regular insulin in 250 mL. The order is 0.1 units/kg/h for a patient who weighs 80 kg. Find the pump rate R in mL/h. Round to one decimal place.
250 units/250 mL0.1 units/kg/h80 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 40 mL/h. The patient weighs 106 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL40 mL/h106 kg
D = mcg/kg/min
7.PharmacologyMedium
A partial agonist is given together with a high dose of a full agonist. What happens to the response?
AIt falls, because the partial agonist competes for the receptors
BIt doubles, because both drugs activate the receptor
CIt stays exactly the same as with the high dose of full agonist alone
DIt rises above the maximum of the full agonist
8.PharmacologyHard
Gentamicin is combined with high-dose intravenous furosemide. Which risk is especially increased?
ADamage to hearing
BHypoglycaemia
CLiver failure
DBleeding
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 4.159 L/h
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 = 210/10 = 21 L
Rate constant
k = 0.693/3.5 = 0.198 h⁻¹
Clearance
CL = 0.198·21 = 4.159 L/h
Answer
CL = 4.159 L/h
2.Clinical pharmacokinetics
Answer: D = 146.3 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.
Volume of distribution
Vd = 0.25·65 = 16.25 L
Dose
D = 16.25·(10 − 1) = 146.3 mg
Answer
D = 146.3 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: C = 250 mg/mL
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.
Final volume
1.8 + 0.2 = 2 mL
Concentration
C = 500/2 = 250 mg/mL
Answer
C = 250 mg/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
20%: 2 − 0 = 2 parts
0%: 20 − 2 = 18 parts
total: 20 parts
Water
V = 500·18/20 = 450 mL
Answer
V = 450 mL
Check: 50 mL of 20% contains 10 g of drug, which is 2% of 500 mL.
5.Pediatric & critical-care dosing
Answer: R = 8 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
0.1·80 = 8 units/h
Concentration
250/250 = 1 units/mL
Pump rate
R = 8/1 = 8 mL/h
Answer
R = 8 mL/h
6.Pediatric & critical-care dosing
Answer: D = 12.6 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
500 000/250 = 2000 mcg/mL
Micrograms per minute
40·2000 = 80000 mcg/h
80000/60 = 1333 mcg/min
Per kilogram
D = 1333/106 = 12.58 ≈ 12.6 mcg/kg/min
Answer
D = 12.6 mcg/kg/min
7.Pharmacology
Answer: A · It falls, because the partial agonist competes for the receptors
Why this is the answer
A partial agonist has lower efficacy. When it displaces a full agonist from receptors, the total response drops. Buprenorphine can precipitate withdrawal in people using full opioid agonists for this reason.
Answer
A · It falls, because the partial agonist competes for the receptors
8.Pharmacology
Answer: A · Damage to hearing
Why this is the answer
Both aminoglycosides and loop diuretics can damage the inner ear. The combination increases the risk of ototoxicity, so it needs caution and monitoring.