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 210 mg of gentamicin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 2.5 h. Find the clearance CL in L/h.
D = 210 mgC₀ = 10 mg/Lt½ = 2.5 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient's tobramycin half-life is 2 h. The target is a peak of 7 mg/L and a trough of 0.5 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.
t½ = 2 hCpeak = 7 mg/LCtrough = 0.5 mg/L
τ = h
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.1 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.1 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 50 g of 10% salicylic acid ointment. How many grams m of 2% salicylic acid ointment must you add to make a 3% ointment? Round to the nearest whole gram.
50 g · 10%2%3%
m = g
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 100 mL. The order is 0.05 units/kg/h for a patient who weighs 84 kg. Find the pump rate R in mL/h. Round to one decimal place.
100 units/100 mL0.05 units/kg/h84 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 13 mL/h. The patient weighs 54 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL13 mL/h54 kg
D = mcg/kg/min
7.PharmacologyMedium
A man taking tamsulosin is planning cataract surgery. What should the nurse advise?
ATell the eye surgeon, as it can cause floppy iris syndrome
BThe drug has no link with eye surgery
CStop the drug for one day and no further action is needed
DTake a double dose on the day of surgery
8.PharmacologyHard
Which drug class can cause life-threatening hyperkalaemia when combined with an ACE inhibitor?
AThiazide diuretics
BProton pump inhibitors
CPotassium-sparing diuretics such as spironolactone
DLoop diuretics such as high-dose intravenous furosemide
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 5.822 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 = 210/10 = 21 L
Rate constant
k = 0.693/2.5 = 0.2773 h⁻¹
Clearance
CL = 0.2773·21 = 5.822 L/h
Answer
CL = 5.822 L/h
2.Clinical pharmacokinetics
Answer: τ = 7.6 h
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.
Rate constant
k = 0.693/2 = 0.3466 h⁻¹
Dosing interval
τ = ln(7/0.5)/0.3466 = 2.639/0.3466 = 7.615 ≈ 7.6 h
Answer
τ = 7.6 h
In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.
3.Pharmacy calculations
Answer: V = 0.1 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 = 0.1/1 = 0.1 mL
Answer
V = 0.1 mL
4.Pharmacy calculations
Answer: m = 350 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
10%: 3 − 2 = 1 parts
2%: 10 − 3 = 7 parts
Scale to the amount you have
m = 50·7/1 = 350 g
Answer
m = 350 g
Check: 50 g + 350 g = 400 g of 3% ointment.
5.Pediatric & critical-care dosing
Answer: R = 4.2 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
0.05·84 = 4.2 units/h
Concentration
100/100 = 1 units/mL
Pump rate
R = 4.2/1 = 4.2 mL/h
Answer
R = 4.2 mL/h
6.Pediatric & critical-care dosing
Answer: D = 6.4 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
13·1600 = 20800 mcg/h
20800/60 = 346.7 mcg/min
Per kilogram
D = 346.7/54 = 6.42 ≈ 6.4 mcg/kg/min
Answer
D = 6.4 mcg/kg/min
7.Pharmacology
Answer: A · Tell the eye surgeon, as it can cause floppy iris syndrome
Why this is the answer
Tamsulosin can cause intraoperative floppy iris syndrome, which complicates cataract surgery. The surgeon needs to know so that the technique can be adapted.
Answer
A · Tell the eye surgeon, as it can cause floppy iris syndrome
8.Pharmacology
Answer: C · Potassium-sparing diuretics such as spironolactone
Why this is the answer
ACE inhibitors lower aldosterone and spironolactone blocks its receptor; together they reduce potassium excretion and can raise potassium dangerously.
Answer
C · Potassium-sparing diuretics such as spironolactone