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 8 mg/L at 1 h and 2 mg/L at 5 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 8 mg/L (1 h)C2 = 2 mg/L (5 h)
k = h⁻¹
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 63 kg patient takes oral aminophylline (S = 0.8, F = 1) every 8 h. The theophylline clearance is 0.04 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 0.85 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.85 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 20 g of 5% coal tar ointment. How many grams m of 1% coal tar ointment must you add to make a 2% ointment? Round to the nearest whole gram.
20 g · 5%1%2%
m = g
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 61 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
60 units/kg61 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 95 kg has an order for norepinephrine at 8 mcg/min. The bag contains 4 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
4 mg/250 mL8 mcg/min95 kg
R = mL/h
7.PharmacologyMedium
Why are benzodiazepines used with great caution in older people?
AThey cause severe high blood pressure in older people
BThey raise the risk of confusion, falls and fractures
CThey are not absorbed from the gut after age 65
DThey cause permanent hearing loss in older people
8.PharmacologyHard
Why may omeprazole be avoided in a patient taking clopidogrel?
AIt speeds up kidney excretion of clopidogrel
BIt inhibits CYP2C19, so less clopidogrel is converted to its active form
CIt binds clopidogrel in the stomach and makes it insoluble
DIt increases clopidogrel absorption from the gut and causes bleeding
3Solutions
1.Clinical pharmacokinetics
Answer: k = 0.3466 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(8/2)/4 = 1.386/4 = 0.3466 h⁻¹
Answer
k = 0.3466 h⁻¹
2.Clinical pharmacokinetics
Answer: Css,avg = 19.84 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 = 0.85/1 = 0.85 mL
Answer
V = 0.85 mL
4.Pharmacy calculations
Answer: m = 60 g
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Alligation parts
5%: 2 − 1 = 1 parts
1%: 5 − 2 = 3 parts
Scale to the amount you have
m = 20·3/1 = 60 g
Answer
m = 60 g
Check: 20 g + 60 g = 80 g of 2% ointment.
5.Pediatric & critical-care dosing
Answer: V = 0.73 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
60·61 = 3 660 units
Volume
V = 3660/5000 = 0.732 ≈ 0.73 mL
Answer
V = 0.73 mL
6.Pediatric & critical-care dosing
Answer: R = 30 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
4 000/250 = 16 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 = 480/16 = 30 mL/h
Answer
R = 30 mL/h
7.Pharmacology
Answer: B · They raise the risk of confusion, falls and fractures
Why this is the answer
Older people are more sensitive to benzodiazepines and often eliminate them more slowly. Sedation, unsteadiness and confusion raise the risk of falls and fractures.
Answer
B · They raise the risk of confusion, falls and fractures
8.Pharmacology
Answer: B · 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
B · It inhibits CYP2C19, so less clopidogrel is converted to its active form