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 has a lidocaine clearance of 600 mL/min. What infusion rate R in mg/min keeps the steady-state level at 2.5 mg/L?
CL = 600 mL/minCss = 2.5 mg/L
R = mg/min
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A theophylline infusion runs at 52.5 mg/h with no loading dose. The patient's clearance is 3.5 L/h and the half-life is 9 h. What is the level C after 22 h?
R = 52.5 mg/hCL = 3.5 L/ht½ = 9 ht = 22 h
C = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.4 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.4 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 30 g of 10% salicylic acid ointment. How many grams m of 2% salicylic acid ointment must you add to make a 6% ointment? Round to the nearest whole gram.
30 g · 10%2%6%
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 10 units/h. Find the pump rate R in mL/h. Round to one decimal place.
100 units/100 mL10 units/h
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 18 mL/h. The patient weighs 83 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL18 mL/h83 kg
D = mcg/kg/min
7.PharmacologyMedium
Which blood test is commonly used to monitor a continuous infusion of unfractionated heparin?
AINR (international normalised ratio, prothrombin time)
BActivated partial thromboplastin time (aPTT)
CSerum potassium
DHaemoglobin A1c
8.PharmacologyHard
Which drug class can cause life-threatening hyperkalaemia when combined with an ACE inhibitor?
ALoop diuretics such as high-dose intravenous furosemide
BPotassium-sparing diuretics such as spironolactone
CThiazide diuretics
DProton pump inhibitors
3Solutions
1.Clinical pharmacokinetics
Answer: R = 1.5 mg/min
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.
Clearance in L/min
600 mL/min = 0.6 L/min
Infusion rate
R = 0.6·2.5 = 1.5 mg/min
Answer
R = 1.5 mg/min
2.Clinical pharmacokinetics
Answer: C = 12.24 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 = 52.5/3.5 = 15 mg/L
Rate constant
k = 0.693/9 = 0.07702 h⁻¹
Level after the given time
C = 15·(1 − e−0.07702·22) = 12.24 mg/L
Answer
C = 12.24 mg/L
3.Pharmacy calculations
Answer: V = 0.4 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.
Strength in mg/mL
1000 mg/1000 mL = 1 mg/mL
Volume
V = 0.4/1 = 0.4 mL
Answer
V = 0.4 mL
4.Pharmacy calculations
Answer: m = 30 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%: 6 − 2 = 4 parts
2%: 10 − 6 = 4 parts
Scale to the amount you have
m = 30·4/4 = 30 g
Answer
m = 30 g
Check: 30 g + 30 g = 60 g of 6% ointment.
5.Pediatric & critical-care dosing
Answer: R = 10 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
100/100 = 1 units/mL
Pump rate
R = 10/1 = 10 mL/h
Answer
R = 10 mL/h
6.Pediatric & critical-care dosing
Answer: D = 7.2 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
18·2000 = 36000 mcg/h
36000/60 = 600 mcg/min
Per kilogram
D = 600/83 = 7.229 ≈ 7.2 mcg/kg/min
Answer
D = 7.2 mcg/kg/min
7.Pharmacology
Answer: B · Activated partial thromboplastin time (aPTT)
Why this is the answer
Unfractionated heparin is often monitored with the aPTT, and the infusion rate is adjusted according to a protocol. Low-molecular-weight heparins usually do not need routine aPTT checks.
Answer
B · Activated partial thromboplastin time (aPTT)
8.Pharmacology
Answer: B · 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
B · Potassium-sparing diuretics such as spironolactone