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 64 kg patient is to be loaded intravenously with aminophylline to reach a theophylline level of 10 mg/L. The volume of distribution is 0.5 L/kg and the salt factor is S = 0.8. Find the loading dose LD of aminophylline in mg.
64 kgVd = 0.5 L/kgC = 10 mg/LS = 0.8
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 62 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.04 L/kg/h. Each dose is 250 mg of theophylline. Find the average steady-state level Css,avg.
CL = 0.04 L/kg/hτ = 12 hS = 1F = 162 kgD = 250 mg
Css,avg = mg/L
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefazolin 1000 mg as a powder. The practice label says to add 4.5 mL of sterile water; the powder adds 0.5 mL to the volume. What is the concentration C in mg/mL after reconstitution?
1000 mg4.5 mL+0.5 mL
C = mg/mL
4.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 9.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 400 mg. Draw up the dose: what volume V do you give?
2000 mg9.2 mL + 0.8 mL400 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 12 500 units of heparin in 250 mL. The order is 18 units/kg/h for a patient who weighs 93 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL18 units/kg/h93 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 7.5 mcg/kg/min for a patient who weighs 90 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL7.5 mcg/kg/min90 kg
R = mL/h
7.PharmacologyMedium
Why should NSAIDs be used with caution in some people with asthma?
AThey block the anti-inflammatory effect of inhaled corticosteroids
BThey cause mucus plugs by drying the airways
CThey increase the clearance of salbutamol
DThey can trigger bronchospasm in aspirin-sensitive asthma
8.PharmacologyHard
A patient on simvastatin is prescribed gemfibrozil. What is the main concern?
ALoss of all lipid-lowering effect
BA much higher risk of myopathy and rhabdomyolysis
CA sharp rise in LDL cholesterol and triglycerides
DSevere hypoglycaemia
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 400 mg
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 = 0.5·64 = 32 L
Amount of active drug needed
Vd·C = 32·10 = 320 mg
Loading dose
LD = 320/(0.8·1) = 400 mg
Answer
LD = 400 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: Css,avg = 8.401 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.
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
4.5 + 0.5 = 5 mL
Concentration
C = 1000/5 = 200 mg/mL
Answer
C = 200 mg/mL
4.Pharmacy calculations
Answer: V = 2 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
9.2 + 0.8 = 10 mL
C = 2000/10 = 200 mg/mL
Volume
V = 400/200 = 2 mL
Answer
V = 2 mL
5.Pediatric & critical-care dosing
Answer: R = 33.5 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
18·93 = 1 674 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 1674/50 = 33.48 ≈ 33.5 mL/h
Answer
R = 33.5 mL/h
6.Pediatric & critical-care dosing
Answer: R = 40.5 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
7.5·90 = 675 mcg/min
675·60 = 40500 mcg/h
Pump rate
R = 40500/1000 = 40.5 mL/h
Answer
R = 40.5 mL/h
7.Pharmacology
Answer: D · They can trigger bronchospasm in aspirin-sensitive asthma
Why this is the answer
In aspirin-exacerbated respiratory disease, COX inhibition increases leukotriene production, causing bronchospasm. These patients should avoid aspirin and other non-selective NSAIDs.
Answer
D · They can trigger bronchospasm in aspirin-sensitive asthma
8.Pharmacology
Answer: B · A much higher risk of myopathy and rhabdomyolysis
Why this is the answer
Gemfibrozil reduces statin clearance and adds its own muscle toxicity. The combination greatly increases the risk of rhabdomyolysis and is generally avoided.
Answer
B · A much higher risk of myopathy and rhabdomyolysis