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). An 80 kg patient is to be loaded intravenously with aminophylline to reach a theophylline level of 15 mg/L. The volume of distribution is 0.5 L/kg and the salt factor is S = 0.8. Find the loading dose LD of aminophylline in mg.
80 kgVd = 0.5 L/kgC = 15 mg/LS = 0.8
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 3 L/h. Each dose is 750 mg of vancomycin. Find the average steady-state level Css,avg.
CL = 3 L/hτ = 12 hS = 1F = 1D = 750 mg
Css,avg = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.39 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.39 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 62.5 mg. Draw up the dose: what volume V do you give?
500 mg3.5 mL + 0.5 mL62.5 mg
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 87 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg87 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 91 kg has an order for nitroglycerin at 15 mcg/min. The bag contains 50 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
50 mg/250 mL15 mcg/min91 kg
R = mL/h
7.PharmacologyMedium
A patient with suspected sepsis has blood cultures ordered and a first antibiotic dose due. What should the nurse do?
AGive the antibiotic first, then take blood cultures the next day
BWait for the culture results before giving any antibiotic
CTake the blood cultures first, then give the antibiotic at once
DGive the antibiotic only if the temperature is above 40 °C (104 °F)
8.PharmacologyHard
Gentamicin is combined with high-dose intravenous furosemide. Which risk is especially increased?
AHypoglycaemia
BLiver failure
CDamage to hearing
DBleeding
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 750 mg
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 = 0.5·80 = 40 L
Amount of active drug needed
Vd·C = 40·15 = 600 mg
Loading dose
LD = 600/(0.8·1) = 750 mg
Answer
LD = 750 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: Css,avg = 20.83 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 = 0.39/1 = 0.39 mL
Answer
V = 0.39 mL
4.Pharmacy calculations
Answer: V = 0.5 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
3.5 + 0.5 = 4 mL
C = 500/4 = 125 mg/mL
Volume
V = 62.5/125 = 0.5 mL
Answer
V = 0.5 mL
5.Pediatric & critical-care dosing
Answer: V = 1 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
60·87 = 5 220 units
Volume
V = 5220/5000 = 1.044 ≈ 1 mL
Answer
V = 1 mL
6.Pediatric & critical-care dosing
Answer: R = 4.5 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
50 000/250 = 200 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
15·60 = 900 mcg/h
Pump rate
R = 900/200 = 4.5 mL/h
Answer
R = 4.5 mL/h
7.Pharmacology
Answer: C · Take the blood cultures first, then give the antibiotic at once
Why this is the answer
Cultures are taken before antibiotics so the organism can be identified, but antibiotics must not be delayed in sepsis. Taking cultures quickly and then giving the antibiotic meets both aims.
Answer
C · Take the blood cultures first, then give the antibiotic at once
8.Pharmacology
Answer: C · Damage to hearing
Why this is the answer
Both aminoglycosides and loop diuretics can damage the inner ear. The combination increases the risk of ototoxicity, so it needs caution and monitoring.