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 10 mg/L and the half-life is 3 h. Find the clearance CL in L/h.
D = 160 mgC₀ = 10 mg/Lt½ = 3 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 44-year-old woman weighs 74 kg and has a serum creatinine of 2.3 mg/dL (203 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 tobramycin regimen is 120 mg every 8 h for a creatinine clearance of 120 mL/min. Keeping the dose, the interval is lengthened in proportion to the fall in clearance. Find the new dosing interval τ. Round to one decimal place.
A solution has a ratio strength of 1:1000. You need 0.54 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.54 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 750 mL of 5% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 3% solution do you need? Round to the nearest whole mL.
23%3%5%750 mL
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 110 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg110 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 83 kg has an order for norepinephrine at 6 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 mL6 mcg/min83 kg
R = mL/h
7.PharmacologyMedium
How should a patient take oral alendronate?
AWith breakfast and coffee to protect the stomach
BWith milk at bedtime, then lying down straight away to aid absorption
CWith plain water on an empty stomach, staying upright for 30 minutes
DCrushed into yoghurt with calcium supplements
8.PharmacologyHard
A patient on warfarin is taught about diet. Which statement shows a need for further teaching?
A"I will use a soft toothbrush and an electric razor."
B"I will tell my dentist that I take warfarin."
C"I will keep the amount of green leafy vegetables I eat about the same each week."
D"I will stop eating all green vegetables from now on."
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 3.697 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 = 160/10 = 16 L
Rate constant
k = 0.693/3 = 0.231 h⁻¹
Clearance
CL = 0.231·16 = 3.697 L/h
Answer
CL = 3.697 L/h
2.Clinical pharmacokinetics
Answer: τ = 26.3 h
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 − 44)·74/(72·2.3)·0.85 = 36.46 mL/min
New interval
τ = 8·120/36.46 = 26.33 ≈ 26.3 h
Answer
τ = 26.3 h
In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.
3.Pharmacy calculations
Answer: V = 0.54 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 = 0.54/1 = 0.54 mL
Answer
V = 0.54 mL
4.Pharmacy calculations
Answer: V = 675 mL
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
23%: 5 − 3 = 2 parts
3%: 23 − 5 = 18 parts
total: 20 parts
Share the volume
V = 750·18/20 = 675 mL
Answer
V = 675 mL
Check: 75 mL of 23% + 675 mL of 3% = 750 mL.
5.Pediatric & critical-care dosing
Answer: V = 1.3 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
60·110 = 6 600 units
Volume
V = 6600/5000 = 1.32 ≈ 1.3 mL
Answer
V = 1.3 mL
6.Pediatric & critical-care dosing
Answer: R = 11.3 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.
6·60 = 360 mcg/h
Pump rate
R = 360/32 = 11.25 ≈ 11.3 mL/h
Answer
R = 11.3 mL/h
7.Pharmacology
Answer: C · With plain water on an empty stomach, staying upright for 30 minutes
Why this is the answer
Alendronate is taken first thing in the morning with water only, before food or other drugs. Staying upright reduces the risk of oesophageal ulceration, and food or calcium blocks its absorption.
Answer
C · With plain water on an empty stomach, staying upright for 30 minutes
8.Pharmacology
Answer: D · "I will stop eating all green vegetables from now on."
Why this is the answer
Patients on warfarin should keep their vitamin K intake consistent rather than avoid it. Sudden changes in green vegetable intake can make the INR unstable.
Answer
D · "I will stop eating all green vegetables from now on."