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 69 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.
69 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 kg patient has a digoxin level of 0.6 mcg/L; the target is 1 mcg/L. The volume of distribution is 7 L/kg and the tablets have F = 0.7. What extra loading dose LD raises the level to the target?
82 kgVd = 7 L/kgC = 0.6 → 1 mcg/LF = 0.7
LD = mcg
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefazolin 1000 mg as a powder. The practice label says to add 4.5 mL of sterile water; the powder adds 0.5 mL to the volume. The prescribed dose is 250 mg. What volume V do you draw up? Round to one decimal place.
1000 mg4.5 mL+0.5 mL250 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 750 mL of 5% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 23% solution do you need? Round to the nearest whole mL.
23%3%5%750 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 50 units of regular insulin in 50 mL runs at 5 mL/h. How many units per hour D does the patient receive?
50 units/50 mL5 mL/h
D = units/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 66 kg has an order for norepinephrine at 10 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
8 mg/250 mL10 mcg/min66 kg
R = mL/h
7.PharmacologyMedium
Which lab tests are monitored in a patient taking carbamazepine?
ASerum amylase and lipase
BFull blood count and serum sodium
CINR and aPTT
DThyroid antibodies and cortisol
8.PharmacologyHard
A patient with heart failure on furosemide is also given metolazone, a thiazide-like diuretic. Which risk increases most?
ASevere hypertension, tachycardia and fluid retention
BSevere hypokalaemia, hyponatraemia and dehydration
CHypoglycaemia and weight gain
DHyperkalaemia and fluid overload
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 552 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 = 7·69 = 483 L
Amount of active drug needed
Vd·C = 483·0.8 = 386.4 mcg
Loading dose
LD = 386.4/(1·0.7) = 552 mcg
Answer
LD = 552 mcg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: LD = 328 mcg
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 = 7·82 = 574 L
Rise needed
1 − 0.6 = 0.4 mcg/L
Loading dose
LD = 574·0.4/(1·0.7) = 328 mcg
Answer
LD = 328 mcg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 1.3 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
4.5 + 0.5 = 5 mL
Concentration
1000/5 = 200 mg/mL
Volume to give
V = 250/200 = 1.25 ≈ 1.3 mL
Answer
V = 1.3 mL
4.Pharmacy calculations
Answer: V = 75 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 = 750·2/20 = 75 mL
Answer
V = 75 mL
Check: 75 mL of 23% + 675 mL of 3% = 750 mL.
5.Pediatric & critical-care dosing
Answer: D = 5 units/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.
Concentration
50/50 = 1 units/mL
Units per hour
D = 5·1 = 5 units/h
Answer
D = 5 units/h
6.Pediatric & critical-care dosing
Answer: R = 18.8 mL/h
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
8 000/250 = 32 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
10·60 = 600 mcg/h
Pump rate
R = 600/32 = 18.75 ≈ 18.8 mL/h
Answer
R = 18.8 mL/h
7.Pharmacology
Answer: B · Full blood count and serum sodium
Why this is the answer
Carbamazepine can rarely cause bone marrow suppression and commonly lowers serum sodium. Blood counts, sodium and liver tests are checked, especially early in treatment.
Answer
B · Full blood count and serum sodium
8.Pharmacology
Answer: B · Severe hypokalaemia, hyponatraemia and dehydration
Why this is the answer
Combining a loop and a thiazide diuretic gives a strong synergistic diuresis. This can cause marked electrolyte loss and volume depletion, so weight, electrolytes and kidney function are monitored closely.
Answer
B · Severe hypokalaemia, hyponatraemia and dehydration