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 80 mg of tobramycin. The level back-extrapolated to time zero is 6 mg/L and the half-life is 3 h. Find the clearance CL in L/h.
D = 80 mgC₀ = 6 mg/Lt½ = 3 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 64 kg patient has a theophylline level of 6 mg/L; the target is 12 mg/L. The drug is given intravenously as aminophylline (S = 0.8), and the volume of distribution is 0.5 L/kg. What extra loading dose LD raises the level to the target?
64 kgVd = 0.5 L/kgC = 6 → 12 mg/LS = 0.8
LD = mg
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.11 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.11 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 3.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 1200 mg. Draw up the dose: what volume V do you give?
2000 mg3.4 mL + 0.6 mL1200 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 500 mL. The order is 15 units/kg/h for a patient who weighs 78 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL15 units/kg/h78 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 22 mL/h. The patient weighs 106 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL22 mL/h106 kg
D = mcg/kg/min
7.PharmacologyMedium
How does sucralfate help a peptic ulcer heal?
AIt forms a protective coating over the ulcer base
BIt blocks histamine H2 receptors in the stomach
CIt kills Helicobacter pylori directly
DIt neutralises acid by releasing bicarbonate
8.PharmacologyHard
A patient with heart failure on furosemide is also given metolazone, a thiazide-like diuretic. Which risk increases most?
ASevere hypokalaemia, hyponatraemia and dehydration
BHypoglycaemia and weight gain
CHyperkalaemia and fluid overload
DSevere hypertension, tachycardia and fluid retention
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 3.081 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 = 80/6 = 13.33 L
Rate constant
k = 0.693/3 = 0.231 h⁻¹
Clearance
CL = 0.231·13.33 = 3.081 L/h
Answer
CL = 3.081 L/h
2.Clinical pharmacokinetics
Answer: LD = 240 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 = 0.5·64 = 32 L
Rise needed
12 − 6 = 6 mg/L
Loading dose
LD = 32·6/(0.8·1) = 240 mg
Answer
LD = 240 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 0.11 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 = 0.11/1 = 0.11 mL
Answer
V = 0.11 mL
4.Pharmacy calculations
Answer: V = 2.4 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.
Final volume and concentration
3.4 + 0.6 = 4 mL
C = 2000/4 = 500 mg/mL
Volume
V = 1200/500 = 2.4 mL
Answer
V = 2.4 mL
5.Pediatric & critical-care dosing
Answer: R = 23.4 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
15·78 = 1 170 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1170/50 = 23.4 mL/h
Answer
R = 23.4 mL/h
6.Pediatric & critical-care dosing
Answer: D = 5.5 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
400 000/250 = 1600 mcg/mL
Micrograms per minute
22·1600 = 35200 mcg/h
35200/60 = 586.7 mcg/min
Per kilogram
D = 586.7/106 = 5.535 ≈ 5.5 mcg/kg/min
Answer
D = 5.5 mcg/kg/min
7.Pharmacology
Answer: A · It forms a protective coating over the ulcer base
Why this is the answer
Sucralfate forms a gel-like barrier that sticks to the ulcer and protects it from acid and pepsin. It is taken on an empty stomach and can reduce the absorption of other drugs taken at the same time.
Answer
A · It forms a protective coating over the ulcer base
8.Pharmacology
Answer: A · 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
A · Severe hypokalaemia, hyponatraemia and dehydration