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 330 mg of tobramycin. The level back-extrapolated to time zero is 12 mg/L and the half-life is 3 h. Find the clearance CL in L/h.
D = 330 mgC₀ = 12 mg/Lt½ = 3 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 70 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.045 L/kg/h. What dose D in mg gives an average steady-state level of 12 mg/L?
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 4% 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%4%500 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 60 units/kg for a patient who weighs 52 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg52 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 27 mL/h. The patient weighs 97 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL27 mL/h97 kg
D = mcg/kg/min
7.PharmacologyMedium
What should the nurse teach a patient starting nitrofurantoin?
AStop it as soon as the burning settles
BTake it on an empty stomach with an antacid
CExpect blue urine, which shows that the drug is working well
DTake it with food, and the urine may turn dark yellow or brown
8.PharmacologyHard
Why is intravenous insulin given with glucose in severe hyperkalaemia?
AInsulin moves potassium from the blood into cells
BGlucose binds potassium in the blood
CInsulin increases potassium excretion by the kidney
DInsulin protects the heart muscle directly from potassium
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 6.354 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 = 330/12 = 27.5 L
Rate constant
k = 0.693/3 = 0.231 h⁻¹
Clearance
CL = 0.231·27.5 = 6.354 L/h
Answer
CL = 6.354 L/h
2.Clinical pharmacokinetics
Answer: D = 453.6 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.
Clearance
CL = 0.045·70 = 3.15 L/h
Dose
D = Css,avg·CL·τ/(S·F) = 12·3.15·12/(1·1) = 453.6 mg
Answer
D = 453.6 mg
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 = 400 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%: 4 − 0 = 4 parts
0%: 20 − 4 = 16 parts
total: 20 parts
Water
V = 500·16/20 = 400 mL
Answer
V = 400 mL
Check: 100 mL of 20% contains 20 g of drug, which is 4% of 500 mL.
5.Pediatric & critical-care dosing
Answer: V = 3.1 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
60·52 = 3 120 units
Volume
V = 3120/1000 = 3.12 ≈ 3.1 mL
Answer
V = 3.1 mL
6.Pediatric & critical-care dosing
Answer: D = 4.6 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
250 000/250 = 1000 mcg/mL
Micrograms per minute
27·1000 = 27000 mcg/h
27000/60 = 450 mcg/min
Per kilogram
D = 450/97 = 4.639 ≈ 4.6 mcg/kg/min
Answer
D = 4.6 mcg/kg/min
7.Pharmacology
Answer: D · Take it with food, and the urine may turn dark yellow or brown
Why this is the answer
Nitrofurantoin is taken with food to reduce nausea and can harmlessly darken the urine. The full course is completed, and cough, breathlessness or numbness should be reported.
Answer
D · Take it with food, and the urine may turn dark yellow or brown
8.Pharmacology
Answer: A · Insulin moves potassium from the blood into cells
Why this is the answer
Insulin activates the Na⁺/K⁺-ATPase and drives potassium into cells, lowering plasma levels within minutes. Glucose is given to prevent hypoglycaemia. The effect is temporary; potassium must still be removed from the body.
Answer
A · Insulin moves potassium from the blood into cells