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 9 mg/L and the half-life is 2 h. Find the volume of distribution Vd.
D = 150 mgC₀ = 9 mg/Lt½ = 2 h
Vd = L
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 100 mg/h with no loading dose. The patient's clearance is 5 L/h and the half-life is 6 h. What is the level C after 9 h?
R = 100 mg/hCL = 5 L/ht½ = 6 ht = 9 h
C = mg/L
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 2000 mg as a powder. The practice label says to add 19.2 mL of sterile water; the powder adds 0.8 mL to the volume. The prescribed dose is 600 mg. What volume V do you draw up? Round to one decimal place.
2000 mg19.2 mL+0.8 mL600 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 100 mL of 20% 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%20%100 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 80 units/kg for a patient who weighs 99 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg99 kg1 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 23 mL/h. The patient weighs 80 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL23 mL/h80 kg
D = mcg/kg/min
7.PharmacologyMedium
How should a topical corticosteroid cream usually be applied?
AOn broken, infected skin to speed healing
BAs a thin layer to the affected area only, as directed
CUnder a tight plastic dressing every night without advice
DAs a thick layer over the whole body
8.PharmacologyHard
A patient has SIADH with mild hyponatraemia and no neurological symptoms. What is usually the first-line treatment?
AFluid restriction
BDesmopressin
CLarge volumes of IV glucose 5%
DA rapid bolus of hypertonic saline
3Solutions
1.Clinical pharmacokinetics
Answer: Vd = 16.67 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 = 150/9 = 16.67 L
Answer
Vd = 16.67 L
2.Clinical pharmacokinetics
Answer: C = 12.93 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.
Steady-state level
Css = 100/5 = 20 mg/L
Rate constant
k = 0.693/6 = 0.1155 h⁻¹
Level after the given time
C = 20·(1 − e−0.1155·9) = 12.93 mg/L
Answer
C = 12.93 mg/L
3.Pharmacy calculations
Answer: V = 6 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
19.2 + 0.8 = 20 mL
Concentration
2000/20 = 100 mg/mL
Volume to give
V = 600/100 = 6 mL
Answer
V = 6 mL
4.Pharmacy calculations
Answer: V = 25 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%: 20 − 10 = 10 parts
10%: 50 − 20 = 30 parts
total: 40 parts
Share the volume
V = 100·10/40 = 25 mL
Answer
V = 25 mL
Check: 25 mL of 50% + 75 mL of 10% = 100 mL.
5.Pediatric & critical-care dosing
Answer: V = 7.9 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
80·99 = 7 920 units
Volume
V = 7920/1000 = 7.92 ≈ 7.9 mL
Answer
V = 7.9 mL
6.Pediatric & critical-care dosing
Answer: D = 9.6 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
23·2000 = 46000 mcg/h
46000/60 = 766.7 mcg/min
Per kilogram
D = 766.7/80 = 9.583 ≈ 9.6 mcg/kg/min
Answer
D = 9.6 mcg/kg/min
7.Pharmacology
Answer: B · As a thin layer to the affected area only, as directed
Why this is the answer
Thin application to affected skin limits systemic absorption and skin atrophy. Occlusive dressings increase absorption and are used only when prescribed.
Answer
B · As a thin layer to the affected area only, as directed
8.Pharmacology
Answer: A · Fluid restriction
Why this is the answer
In SIADH, excess ADH makes the kidneys retain water. Restricting fluid intake raises sodium gradually; hypertonic saline is kept for severe symptomatic cases, and hypotonic fluids and desmopressin would worsen it.