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). An 89 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.
89 kgVd = 0.5 L/kgC = 10 mg/LS = 0.8
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 4.5 L/h. What dose D in mg gives an average steady-state level of 15 mg/L?
CL = 4.5 L/hτ = 12 hS = 1F = 1Css,avg = 15 mg/L
D = mg
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 1000 mg as a powder. The practice label says to add 3.5 mL of sterile water; the powder adds 0.5 mL to the volume. What is the concentration C in mg/mL after reconstitution?
1000 mg3.5 mL+0.5 mL
C = mg/mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 4.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 300 mg. Draw up the dose: what volume V do you give?
500 mg4.6 mL + 0.4 mL300 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 12 units/kg/h for a patient who weighs 60 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL12 units/kg/h60 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 39 mL/h. The patient weighs 58 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL39 mL/h58 kg
D = mcg/kg/min
7.PharmacologyMedium
Why should loperamide usually be avoided in bloody diarrhoea with fever?
ALoperamide is an antibiotic that causes resistance
BLoperamide makes the bleeding worse by blocking platelets
CLoperamide causes severe hypertension when there is an infection
DSlowing the gut may keep bacteria and toxins in the bowel longer
8.PharmacologyHard
Why is gentamicin often given once daily instead of in several small doses?
AIt has a very long half-life of several days
BIt is absorbed slowly from the muscle over 24 hours
CIts killing depends only on the time the level stays above the MIC
DIts killing depends on high peak levels, with a post-antibiotic effect
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 556.3 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 = 0.5·89 = 44.5 L
Amount of active drug needed
Vd·C = 44.5·10 = 445 mg
Loading dose
LD = 445/(0.8·1) = 556.3 mg
Answer
LD = 556.3 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: D = 810 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.
Dose
D = Css,avg·CL·τ/(S·F) = 15·4.5·12/(1·1) = 810 mg
Answer
D = 810 mg
3.Pharmacy calculations
Answer: C = 250 mg/mL
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
3.5 + 0.5 = 4 mL
Concentration
C = 1000/4 = 250 mg/mL
Answer
C = 250 mg/mL
4.Pharmacy calculations
Answer: V = 3 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
4.6 + 0.4 = 5 mL
C = 500/5 = 100 mg/mL
Volume
V = 300/100 = 3 mL
Answer
V = 3 mL
5.Pediatric & critical-care dosing
Answer: R = 14.4 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
12·60 = 720 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 720/50 = 14.4 mL/h
Answer
R = 14.4 mL/h
6.Pediatric & critical-care dosing
Answer: D = 11.2 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
250 000/250 = 1000 mcg/mL
Micrograms per minute
39·1000 = 39000 mcg/h
39000/60 = 650 mcg/min
Per kilogram
D = 650/58 = 11.21 ≈ 11.2 mcg/kg/min
Answer
D = 11.2 mcg/kg/min
7.Pharmacology
Answer: D · Slowing the gut may keep bacteria and toxins in the bowel longer
Why this is the answer
In dysentery or suspected C. difficile infection, antimotility drugs may prolong illness and increase complications such as toxic megacolon. The cause is assessed and fluids are replaced first.
Answer
D · Slowing the gut may keep bacteria and toxins in the bowel longer
8.Pharmacology
Answer: D · Its killing depends on high peak levels, with a post-antibiotic effect
Why this is the answer
Aminoglycosides show concentration-dependent killing and a post-antibiotic effect. Once-daily dosing gives high peaks and a low trough, which may also reduce kidney and ear toxicity.
Answer
D · Its killing depends on high peak levels, with a post-antibiotic effect