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 79 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 20 mg/L. The volume of distribution is 0.7 L/kg and the salt factor is S = 0.92. Find the loading dose LD of phenytoin sodium in mg.
79 kgVd = 0.7 L/kgC = 20 mg/LS = 0.92
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 95 kg patient takes oral theophylline (F = 1) every 8 h. The clearance is 0.03 L/kg/h. Each dose is 450 mg of theophylline. Find the average steady-state level Css,avg.
CL = 0.03 L/kg/hτ = 8 hS = 1F = 195 kgD = 450 mg
Css,avg = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.68 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.68 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 1500 mL of 20% dextrose by mixing 50% and 5% dextrose. How many mL V of the 50% solution do you need? Round to the nearest whole mL.
50%5%20%1500 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 109 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg109 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 9 mL/h. The patient weighs 90 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL9 mL/h90 kg
D = mcg/kg/min
7.PharmacologyMedium
During an infusion of a vesicant chemotherapy drug, the patient reports burning, and the site is swollen. What should the nurse do first?
AIncrease the infusion rate to finish quickly
BRemove the cannula at once and massage the area firmly
CStop the infusion, leave the cannula in and follow the protocol
DFlush the line with a large volume of saline
8.PharmacologyHard
A patient who used heroin a few hours ago is given a first dose of buprenorphine and quickly develops severe withdrawal. Why?
ABuprenorphine has no effect at opioid receptors
BBuprenorphine causes an allergic reaction in heroin users
CBuprenorphine is a pure antagonist like naloxone with no agonist effect
DBuprenorphine is a high-affinity partial agonist that displaces heroin
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 1202 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 = 0.7·79 = 55.3 L
Amount of active drug needed
Vd·C = 55.3·20 = 1106 mg
Loading dose
LD = 1106/(0.92·1) = 1202 mg
Answer
LD = 1202 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: Css,avg = 19.74 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/10 000 mL = 0.1 mg/mL
Volume
V = 0.68/0.1 = 6.8 mL
Answer
V = 6.8 mL
4.Pharmacy calculations
Answer: V = 500 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
50%: 20 − 5 = 15 parts
5%: 50 − 20 = 30 parts
total: 45 parts
Share the volume
V = 1500·15/45 = 500 mL
Answer
V = 500 mL
Check: 500 mL of 50% + 1000 mL of 5% = 1500 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
60·109 = 6 540 units
Volume
V = 6540/5000 = 1.308 ≈ 1.3 mL
Answer
V = 1.3 mL
6.Pediatric & critical-care dosing
Answer: D = 2.7 mcg/kg/min
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
400 000/250 = 1600 mcg/mL
Micrograms per minute
9·1600 = 14400 mcg/h
14400/60 = 240 mcg/min
Per kilogram
D = 240/90 = 2.667 ≈ 2.7 mcg/kg/min
Answer
D = 2.7 mcg/kg/min
7.Pharmacology
Answer: C · Stop the infusion, leave the cannula in and follow the protocol
Why this is the answer
Suspected extravasation of a vesicant is an emergency. The infusion is stopped, the cannula is left in so that drug can be aspirated, and the protocol, which may include an antidote and cold or warm packs, is followed.
Answer
C · Stop the infusion, leave the cannula in and follow the protocol
8.Pharmacology
Answer: D · Buprenorphine is a high-affinity partial agonist that displaces heroin
Why this is the answer
Buprenorphine binds mu receptors more strongly than heroin but activates them less, so it can precipitate withdrawal. Induction is started when the patient already has mild to moderate withdrawal signs.
Answer
D · Buprenorphine is a high-affinity partial agonist that displaces heroin