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 67 kg patient is to be loaded with digoxin tablets to reach a level of 0.8 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.
67 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 70-year-old man weighs 91 kg and has a serum creatinine of 3.4 mg/dL (301 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 digoxin dose is 250 mcg for a creatinine clearance of 120 mL/min, and a fraction fe = 0.7 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.
Practice exercise (made-up values, not clinical guidance). A vial contains cefazolin 1000 mg as a powder. The practice label says to add 4.5 mL of sterile water; the powder adds 0.5 mL to the volume. The prescribed dose is 400 mg. What volume V do you draw up? Round to one decimal place.
1000 mg4.5 mL+0.5 mL400 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 3.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 237.5 mg. Draw up the dose: what volume V do you give?
500 mg3.4 mL + 0.6 mL237.5 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 250 mL. The order is 0.05 units/kg/h for a patient who weighs 82 kg. Find the pump rate R in mL/h. Round to one decimal place.
100 units/250 mL0.05 units/kg/h82 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 5 mcg/kg/min for a patient who weighs 67 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL5 mcg/kg/min67 kg
R = mL/h
7.PharmacologyMedium
A patient wants to stop paroxetine suddenly. What should the nurse explain?
AIt can cause dizziness, "electric shock" feelings and irritability
BIt can be stopped at any time, as antidepressants cause no withdrawal effects
DStopping suddenly causes the drug to work better for a while
8.PharmacologyHard
Why is the TPMT enzyme often tested before azathioprine is started?
ALow TPMT activity causes toxic levels and marrow suppression
BTPMT is needed to absorb azathioprine from the gut
CTPMT testing shows whether the patient has tuberculosis
DHigh TPMT activity causes an allergic reaction to azathioprine
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 536 mcg
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 = 7·67 = 469 L
Amount of active drug needed
Vd·C = 469·0.8 = 375.2 mcg
Loading dose
LD = 375.2/(1·0.7) = 536 mcg
Answer
LD = 536 mcg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: D = 113 mcg
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 − 70)·91/(72·3.4) = 26.02 mL/min
Dose fraction (Dettli)
Q = 1 − 0.7·(1 − 26.02/120) = 0.4518
Adjusted dose
D = 0.4518·250 = 112.9 ≈ 113 mcg
Answer
D = 113 mcg
In practice the dose is rounded to a convenient amount and checked against the product information.
3.Pharmacy calculations
Answer: V = 2 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
4.5 + 0.5 = 5 mL
Concentration
1000/5 = 200 mg/mL
Volume to give
V = 400/200 = 2 mL
Answer
V = 2 mL
4.Pharmacy calculations
Answer: V = 1.9 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
3.4 + 0.6 = 4 mL
C = 500/4 = 125 mg/mL
Volume
V = 237.5/125 = 1.9 mL
Answer
V = 1.9 mL
5.Pediatric & critical-care dosing
Answer: R = 10.3 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
0.05·82 = 4.1 units/h
Concentration
100/250 = 0.4 units/mL
Pump rate
R = 4.1/0.4 = 10.25 ≈ 10.3 mL/h
Answer
R = 10.3 mL/h
6.Pediatric & critical-care dosing
Answer: R = 20.1 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
5·67 = 335 mcg/min
335·60 = 20100 mcg/h
Pump rate
R = 20100/1000 = 20.1 mL/h
Answer
R = 20.1 mL/h
7.Pharmacology
Answer: A · It can cause dizziness, "electric shock" feelings and irritability
Why this is the answer
Antidepressant discontinuation syndrome is common with short half-life drugs such as paroxetine and venlafaxine. The dose is tapered gradually under supervision.
Answer
A · It can cause dizziness, "electric shock" feelings and irritability
8.Pharmacology
Answer: A · Low TPMT activity causes toxic levels and marrow suppression
Why this is the answer
Thiopurine methyltransferase helps inactivate azathioprine and mercaptopurine. People with low or absent TPMT activity need much lower doses or another drug to avoid life-threatening myelosuppression.
Answer
A · Low TPMT activity causes toxic levels and marrow suppression