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). After an IV dose of gentamicin, the level is 7 mg/L at 1 h and 1.2 mg/L at 6 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 7 mg/L (1 h)C2 = 1.2 mg/L (6 h)
k = h⁻¹
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 94 kg patient takes oral aminophylline (S = 0.8, F = 1) every 12 h. The theophylline clearance is 0.05 L/kg/h. What dose D in mg gives an average steady-state level of 15 mg/L?
Practice exercise (made-up values, not clinical guidance). A vial contains oxacillin 2000 mg as a powder. The practice label says to add 11.5 mL of sterile water; the powder adds 1 mL to the volume. The prescribed dose is 800 mg. What volume V do you draw up? Round to one decimal place.
2000 mg11.5 mL+1 mL800 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 2.1 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 1600 mg. Draw up the dose: what volume V do you give?
2000 mg2.1 mL + 0.4 mL1600 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 16 units/kg/h for a patient who weighs 67 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL16 units/kg/h67 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 5 mcg/kg/min for a patient who weighs 83 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL5 mcg/kg/min83 kg
R = mL/h
7.PharmacologyMedium
Which teaching about zolpidem is correct?
ATake it right before bed, only if you can sleep a full night
BTake it with alcohol to make it act faster
CTake it in the morning so that it is out of the system by night
DDrive soon after waking, as the drug has no next-day effect
8.PharmacologyHard
Why may omeprazole be avoided in a patient taking clopidogrel?
AIt increases clopidogrel absorption from the gut and causes bleeding
BIt speeds up kidney excretion of clopidogrel
CIt binds clopidogrel in the stomach and makes it insoluble
DIt inhibits CYP2C19, so less clopidogrel is converted to its active form
3Solutions
1.Clinical pharmacokinetics
Answer: k = 0.3527 h⁻¹
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.
Elimination rate constant
k = ln(7/1.2)/5 = 1.764/5 = 0.3527 h⁻¹
Answer
k = 0.3527 h⁻¹
2.Clinical pharmacokinetics
Answer: D = 1058 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 = 0.05·94 = 4.7 L/h
Dose
D = Css,avg·CL·τ/(S·F) = 15·4.7·12/(0.8·1) = 1058 mg
Answer
D = 1058 mg
3.Pharmacy calculations
Answer: V = 5 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
11.5 + 1 = 12.5 mL
Concentration
2000/12.5 = 160 mg/mL
Volume to give
V = 800/160 = 5 mL
Answer
V = 5 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
2.1 + 0.4 = 2.5 mL
C = 2000/2.5 = 800 mg/mL
Volume
V = 1600/800 = 2 mL
Answer
V = 2 mL
5.Pediatric & critical-care dosing
Answer: R = 21.4 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
16·67 = 1 072 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 1072/50 = 21.44 ≈ 21.4 mL/h
Answer
R = 21.4 mL/h
6.Pediatric & critical-care dosing
Answer: R = 15.6 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
5·83 = 415 mcg/min
415·60 = 24900 mcg/h
Pump rate
R = 24900/1600 = 15.56 ≈ 15.6 mL/h
Answer
R = 15.6 mL/h
7.Pharmacology
Answer: A · Take it right before bed, only if you can sleep a full night
Why this is the answer
Zolpidem can cause next-day impairment and complex sleep behaviours such as sleep-walking or sleep-driving. Alcohol and other sedatives increase these risks.
Answer
A · Take it right before bed, only if you can sleep a full night
8.Pharmacology
Answer: D · It inhibits CYP2C19, so less clopidogrel is converted to its active form
Why this is the answer
Clopidogrel must be activated by liver enzymes, mainly CYP2C19. Omeprazole inhibits this enzyme and can reduce its antiplatelet effect, so another acid suppressant may be chosen.
Answer
D · It inhibits CYP2C19, so less clopidogrel is converted to its active form