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 110 mg of tobramycin. The level back-extrapolated to time zero is 9 mg/L and the half-life is 3 h. Find the clearance CL in L/h.
D = 110 mgC₀ = 9 mg/Lt½ = 3 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 61-year-old man weighs 89 kg and has a serum creatinine of 1.6 mg/dL (141 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual levetiracetam dose is 1000 mg for a creatinine clearance of 100 mL/min, and a fraction fe = 0.66 of the drug is excreted unchanged by the kidneys. Using the Dettli dose fraction Q = 1 − fe·(1 − CrCl/normal CrCl), find the adjusted dose D. Round to the nearest whole number.
A solution has a ratio strength of 1:1000. You need 0.6 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.6 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 3.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 462.5 mg. Draw up the dose: what volume V do you give?
500 mg3.5 mL + 0.5 mL462.5 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 18 units/kg/h for a patient who weighs 104 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL18 units/kg/h104 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 74 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/min74 kg
R = mL/h
7.PharmacologyMedium
Why should doxycycline not be taken at the same time as milk or antacids?
AAntacids turn it into a toxic compound
BMilk speeds up its breakdown in the liver by inducing enzymes
CThe combination causes severe constipation
DCalcium and other metal ions bind it and reduce absorption
8.PharmacologyHard
A patient who takes clonidine stopped it suddenly two days ago. He is now agitated, has a headache and his blood pressure is very high. What is the most likely explanation?
ANormal variation unrelated to the medication
BAn allergic reaction to clonidine
CClonidine toxicity due to slow excretion by the kidneys
DRebound hypertension from abrupt clonidine withdrawal
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 2.824 L/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.
Volume of distribution
Vd = 110/9 = 12.22 L
Rate constant
k = 0.693/3 = 0.231 h⁻¹
Clearance
CL = 0.231·12.22 = 2.824 L/h
Answer
CL = 2.824 L/h
2.Clinical pharmacokinetics
Answer: D = 743 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.
Creatinine clearance (Cockcroft–Gault)
CrCl = (140 − 61)·89/(72·1.6) = 61.03 mL/min
Dose fraction (Dettli)
Q = 1 − 0.66·(1 − 61.03/100) = 0.7428
Adjusted dose
D = 0.7428·1000 = 742.8 ≈ 743 mg
Answer
D = 743 mg
In practice the dose is rounded to a convenient amount and checked against the product information.
3.Pharmacy calculations
Answer: V = 0.6 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.
Strength in mg/mL
1000 mg/1000 mL = 1 mg/mL
Volume
V = 0.6/1 = 0.6 mL
Answer
V = 0.6 mL
4.Pharmacy calculations
Answer: V = 3.7 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
3.5 + 0.5 = 4 mL
C = 500/4 = 125 mg/mL
Volume
V = 462.5/125 = 3.7 mL
Answer
V = 3.7 mL
5.Pediatric & critical-care dosing
Answer: R = 46.8 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
18·104 = 1 872 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1872/40 = 46.8 mL/h
Answer
R = 46.8 mL/h
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: D · Calcium and other metal ions bind it and reduce absorption
Why this is the answer
Tetracyclines form complexes with calcium, magnesium, aluminium and iron in the gut, which reduces absorption. Doses are separated from these products.
Answer
D · Calcium and other metal ions bind it and reduce absorption
8.Pharmacology
Answer: D · Rebound hypertension from abrupt clonidine withdrawal
Why this is the answer
Clonidine is a central alpha-2 agonist. Stopping it suddenly lets sympathetic activity surge, causing rebound hypertension, so it is tapered gradually.
Answer
D · Rebound hypertension from abrupt clonidine withdrawal