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 9 mg/L at 2 h and 1.8 mg/L at 10 h. Assume first-order elimination. Find the half-life t½.
C1 = 9 mg/L (2 h)C2 = 1.8 mg/L (10 h)
t½ = h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 97 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.045 L/kg/h. Each dose is 300 mg of theophylline. Find the average steady-state level Css,avg.
A solution has a ratio strength of 1:1000. You need 0.71 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.71 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 4.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 600 mg. Draw up the dose: what volume V do you give?
2000 mg4.6 mL + 0.4 mL600 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 250 mL. The order is 12 units/kg/h for a patient who weighs 83 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL12 units/kg/h83 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 500 mg in 250 mL. The order is 5 mcg/kg/min for a patient who weighs 108 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL5 mcg/kg/min108 kg
R = mL/h
7.PharmacologyMedium
Why is aspirin avoided in children and teenagers with viral illnesses such as flu or chickenpox?
AIt stops the vaccine from working
BIt causes severe, permanent hearing loss in young children
CIt causes grey baby syndrome
DIt is linked to Reye's syndrome, which harms the liver and brain
8.PharmacologyHard
Before starting rituximab, patients are tested for hepatitis B. Why?
ARituximab is made from the hepatitis B virus
BRituximab is a vaccine against hepatitis B
CHepatitis B infection makes rituximab completely ineffective
DRituximab can reactivate hepatitis B and cause liver failure
3Solutions
1.Clinical pharmacokinetics
Answer: t½ = 3.445 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.
Elimination rate constant
k = ln(9/1.8)/8 = 1.609/8 = 0.2012 h⁻¹
Half-life
t½ = 0.693/0.2012 = 3.445 h
Answer
t½ = 3.445 h
2.Clinical pharmacokinetics
Answer: Css,avg = 5.727 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 = 0.71/1 = 0.71 mL
Answer
V = 0.71 mL
4.Pharmacy calculations
Answer: V = 1.5 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 = 2000/5 = 400 mg/mL
Volume
V = 600/400 = 1.5 mL
Answer
V = 1.5 mL
5.Pediatric & critical-care dosing
Answer: R = 10 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
12·83 = 996 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 996/100 = 9.96 ≈ 10 mL/h
Answer
R = 10 mL/h
6.Pediatric & critical-care dosing
Answer: R = 16.2 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
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
5·108 = 540 mcg/min
540·60 = 32400 mcg/h
Pump rate
R = 32400/2000 = 16.2 mL/h
Answer
R = 16.2 mL/h
7.Pharmacology
Answer: D · It is linked to Reye's syndrome, which harms the liver and brain
Why this is the answer
Aspirin given during viral infections in young people is associated with Reye's syndrome, causing acute encephalopathy and liver failure. Paracetamol or ibuprofen is used for fever instead.
Answer
D · It is linked to Reye's syndrome, which harms the liver and brain
8.Pharmacology
Answer: D · Rituximab can reactivate hepatitis B and cause liver failure
Why this is the answer
Rituximab destroys CD20-positive B cells, weakening control of latent hepatitis B. Reactivation can cause fulminant hepatitis, so carriers receive monitoring or antiviral prophylaxis.
Answer
D · Rituximab can reactivate hepatitis B and cause liver failure