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). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 4.5 L/h. What infusion rate R in mg/h gives a steady-state level of 20 mg/L?
CL = 4.5 L/hCss = 20 mg/L
R = mg/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 93 kg patient takes oral aminophylline (S = 0.8, F = 1) every 12 h. The theophylline clearance is 0.045 L/kg/h. Each dose is 500 mg of aminophylline. Find the average steady-state level Css,avg.
A solution has a ratio strength of 1:1000. You need 0.61 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.61 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 3.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 1100 mg. Draw up the dose: what volume V do you give?
2000 mg3.5 mL + 0.5 mL1100 mg
V = mL
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 0.05 units/kg/h for a patient who weighs 88 kg. Find the pump rate R in mL/h. Round to one decimal place.
50 units/50 mL0.05 units/kg/h88 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 500 mg in 250 mL. The order is 7.5 mcg/kg/min for a patient who weighs 103 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL7.5 mcg/kg/min103 kg
R = mL/h
7.PharmacologyMedium
A patient uses a salbutamol (albuterol) inhaler and a corticosteroid inhaler at the same time of day. Which order is usually taught?
AThe order does not matter and no waiting is needed
BUse the salbutamol first, wait a few minutes, then use the steroid
CUse both in the same breath to save time
DUse the steroid first, then the salbutamol right after without any gap
8.PharmacologyHard
Why is vincristine labelled "for intravenous use only – fatal if given by other routes"?
DIntramuscular injection causes severe and prolonged hypoglycaemia
3Solutions
1.Clinical pharmacokinetics
Answer: R = 90 mg/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.
Infusion rate
R = 4.5·20 = 90 mg/h
Answer
R = 90 mg/h
2.Clinical pharmacokinetics
Answer: Css,avg = 7.965 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.
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 = 0.61/1 = 0.61 mL
Answer
V = 0.61 mL
4.Pharmacy calculations
Answer: V = 2.2 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
3.5 + 0.5 = 4 mL
C = 2000/4 = 500 mg/mL
Volume
V = 1100/500 = 2.2 mL
Answer
V = 2.2 mL
5.Pediatric & critical-care dosing
Answer: R = 4.4 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
0.05·88 = 4.4 units/h
Concentration
50/50 = 1 units/mL
Pump rate
R = 4.4/1 = 4.4 mL/h
Answer
R = 4.4 mL/h
6.Pediatric & critical-care dosing
Answer: R = 23.2 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
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
7.5·103 = 772.5 mcg/min
772.5·60 = 46350 mcg/h
Pump rate
R = 46350/2000 = 23.18 ≈ 23.2 mL/h
Answer
R = 23.2 mL/h
7.Pharmacology
Answer: B · Use the salbutamol first, wait a few minutes, then use the steroid
Why this is the answer
The bronchodilator opens the airways so that the inhaled steroid can reach further into the lungs. A short wait between the inhalers is usually advised.
Answer
B · Use the salbutamol first, wait a few minutes, then use the steroid
8.Pharmacology
Answer: B · Accidental intrathecal injection causes fatal ascending neurotoxicity
Why this is the answer
Vincristine given intrathecally causes ascending paralysis and death. To prevent this, it is usually given in a small IV bag rather than a syringe and kept separate from intrathecal drugs.
Answer
B · Accidental intrathecal injection causes fatal ascending neurotoxicity