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 200 mg of gentamicin. The level back-extrapolated to time zero is 9 mg/L and the half-life is 2 h. Find the clearance CL in L/h.
D = 200 mgC₀ = 9 mg/Lt½ = 2 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 100 kg patient on regular tobramycin doses is at steady state. The target is a peak of 7 mg/L and a trough of 0.5 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?
A solution has a ratio strength of 1:1000. You need 0.21 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.21 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 150 g of 5% coal tar ointment. How many grams m of 1% coal tar ointment must you add to make a 3% ointment? Round to the nearest whole gram.
150 g · 5%1%3%
m = g
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 50 units of regular insulin in 50 mL. The order is 1 unit/h. Find the pump rate R in mL/h. Round to one decimal place.
50 units/50 mL1 units/h
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 10 mcg/kg/min for a patient who weighs 91 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL10 mcg/kg/min91 kg
R = mL/h
7.PharmacologyMedium
Which approach is usually recommended to prevent constipation in a patient on regular opioids?
ABulk-forming fibre alone, with fluid intake restricted
BAn antidiarrhoeal drug at night to slow the gut
CA stimulant laxative such as senna, often with a stool softener
DNo laxative until the patient has not opened the bowels for a week
8.PharmacologyHard
A patient taking long-term hydroxychloroquine for lupus is advised to have regular eye examinations. Why?
AThe drug stains the cornea blue
BThe drug can cause retinal toxicity that may be permanent
CThe drug raises pressure inside the eye
DThe drug causes cataracts within a few weeks of starting
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 7.702 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 = 200/9 = 22.22 L
Rate constant
k = 0.693/2 = 0.3466 h⁻¹
Clearance
CL = 0.3466·22.22 = 7.702 L/h
Answer
CL = 7.702 L/h
2.Clinical pharmacokinetics
Answer: D = 162.5 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 = 0.25·100 = 25 L
Dose
D = 25·(7 − 0.5) = 162.5 mg
Answer
D = 162.5 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 0.21 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 = 0.21/1 = 0.21 mL
Answer
V = 0.21 mL
4.Pharmacy calculations
Answer: m = 150 g
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
5%: 3 − 1 = 2 parts
1%: 5 − 3 = 2 parts
Scale to the amount you have
m = 150·2/2 = 150 g
Answer
m = 150 g
Check: 150 g + 150 g = 300 g of 3% ointment.
5.Pediatric & critical-care dosing
Answer: R = 1 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.
Concentration
50/50 = 1 units/mL
Pump rate
R = 1/1 = 1 mL/h
Answer
R = 1 mL/h
6.Pediatric & critical-care dosing
Answer: R = 34.1 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
10·91 = 910 mcg/min
910·60 = 54600 mcg/h
Pump rate
R = 54600/1600 = 34.13 ≈ 34.1 mL/h
Answer
R = 34.1 mL/h
7.Pharmacology
Answer: C · A stimulant laxative such as senna, often with a stool softener
Why this is the answer
Opioid-induced constipation does not usually resolve with time, so a laxative is started with the opioid. Stimulant laxatives counter reduced motility; bulk-forming laxatives alone can worsen symptoms if fluid intake is low.
Answer
C · A stimulant laxative such as senna, often with a stool softener
8.Pharmacology
Answer: B · The drug can cause retinal toxicity that may be permanent
Why this is the answer
Hydroxychloroquine can damage the retina, and the risk rises with dose and duration. Regular screening allows the drug to be stopped before vision is seriously affected.
Answer
B · The drug can cause retinal toxicity that may be permanent