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 160 mg of gentamicin. The level back-extrapolated to time zero is 6 mg/L and the half-life is 3.5 h. Find the volume of distribution Vd.
D = 160 mgC₀ = 6 mg/Lt½ = 3.5 h
Vd = L
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). An 80 kg patient takes oral aminophylline (S = 0.8, F = 1) every 8 h. The theophylline clearance is 0.04 L/kg/h. What dose D in mg gives an average steady-state level of 12 mg/L?
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 1000 mg as a powder. The practice label says to add 9.6 mL of sterile water; the powder adds 0.4 mL to the volume. What is the concentration C in mg/mL after reconstitution?
1000 mg9.6 mL+0.4 mL
C = mg/mL
4.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 1.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 212.5 mg. Draw up the dose: what volume V do you give?
250 mg1.6 mL + 0.4 mL212.5 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 60 units/kg for a patient who weighs 53 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg53 kg1 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 69 kg has an order for norepinephrine at 8 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
8 mg/250 mL8 mcg/min69 kg
R = mL/h
7.PharmacologyMedium
Which rule applies when giving phenytoin intravenously?
AGive it as a rapid push to stop seizures faster
BGive it in the same line as other drugs without flushing
CMix or flush it only with normal saline and give it slowly
DMix it with glucose 5% to prevent low blood sugar
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
BIts killing depends on high peak levels, with a post-antibiotic effect
CIt is absorbed slowly from the muscle over 24 hours
DIts killing depends only on the time the level stays above the MIC
3Solutions
1.Clinical pharmacokinetics
Answer: Vd = 26.67 L
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 = 160/6 = 26.67 L
Answer
Vd = 26.67 L
2.Clinical pharmacokinetics
Answer: D = 384 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.
Clearance
CL = 0.04·80 = 3.2 L/h
Dose
D = Css,avg·CL·τ/(S·F) = 12·3.2·8/(0.8·1) = 384 mg
Answer
D = 384 mg
3.Pharmacy calculations
Answer: C = 100 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
9.6 + 0.4 = 10 mL
Concentration
C = 1000/10 = 100 mg/mL
Answer
C = 100 mg/mL
4.Pharmacy calculations
Answer: V = 1.7 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
1.6 + 0.4 = 2 mL
C = 250/2 = 125 mg/mL
Volume
V = 212.5/125 = 1.7 mL
Answer
V = 1.7 mL
5.Pediatric & critical-care dosing
Answer: V = 3.2 mL
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 needed
60·53 = 3 180 units
Volume
V = 3180/1000 = 3.18 ≈ 3.2 mL
Answer
V = 3.2 mL
6.Pediatric & critical-care dosing
Answer: R = 15 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
8 000/250 = 32 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
8·60 = 480 mcg/h
Pump rate
R = 480/32 = 15 mL/h
Answer
R = 15 mL/h
7.Pharmacology
Answer: C · Mix or flush it only with normal saline and give it slowly
Why this is the answer
Phenytoin precipitates in glucose solutions, so only normal saline is used. Rapid infusion can cause hypotension and arrhythmias, so the rate is limited and the patient is monitored.
Answer
C · Mix or flush it only with normal saline and give it slowly
8.Pharmacology
Answer: B · 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
B · Its killing depends on high peak levels, with a post-antibiotic effect