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 90 kg patient is to receive an aminophylline infusion (salt factor S = 0.8: 80% of aminophylline is theophylline). The theophylline clearance is 0.035 L/kg/h. What aminophylline infusion rate R in mg/h gives a steady-state theophylline level of 12 mg/L?
90 kgCL = 0.035 L/kg/hCss = 12 mg/LS = 0.8
R = mg/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 76 kg patient on regular tobramycin doses is at steady state. The target is a peak of 10 mg/L and a trough of 1 mg/L, and the volume of distribution is 0.25 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
A solution has a ratio strength of 1:1000. You need 0.6 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.6 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 9.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 130 mg. Draw up the dose: what volume V do you give?
1000 mg9.6 mL + 0.4 mL130 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 80 units/kg for a patient who weighs 58 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg58 kg1 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 32 mL/h. The patient weighs 54 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL32 mL/h54 kg
D = mcg/kg/min
7.PharmacologyMedium
A patient refuses a prescribed oral medicine. What should the nurse do?
ALeave the tablet on the bedside table for later
BExplore the reason, respect the decision, document and inform the prescriber
CRecord the medicine as given, so that the chart stays complete for the next shift
DHide the tablet in the patient's food
8.PharmacologyHard
A patient taking dabigatran has a life-threatening bleed. Which specific reversal agent is used?
AIdarucizumab
BAndexanet alfa
CProtamine sulfate
DVitamin K
3Solutions
1.Clinical pharmacokinetics
Answer: R = 47.25 mg/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.
Clearance
CL = 0.035·90 = 3.15 L/h
Infusion rate
R = CL·Css/S = 3.15·12/0.8 = 47.25 mg/h
Answer
R = 47.25 mg/h
2.Clinical pharmacokinetics
Answer: D = 171 mg
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.
Volume of distribution
Vd = 0.25·76 = 19 L
Dose
D = 19·(10 − 1) = 171 mg
Answer
D = 171 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 0.6 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 = 0.6/1 = 0.6 mL
Answer
V = 0.6 mL
4.Pharmacy calculations
Answer: V = 1.3 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
9.6 + 0.4 = 10 mL
C = 1000/10 = 100 mg/mL
Volume
V = 130/100 = 1.3 mL
Answer
V = 1.3 mL
5.Pediatric & critical-care dosing
Answer: V = 4.6 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
80·58 = 4 640 units
Volume
V = 4640/1000 = 4.64 ≈ 4.6 mL
Answer
V = 4.6 mL
6.Pediatric & critical-care dosing
Answer: D = 15.8 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
32·1600 = 51200 mcg/h
51200/60 = 853.3 mcg/min
Per kilogram
D = 853.3/54 = 15.8 mcg/kg/min
Answer
D = 15.8 mcg/kg/min
7.Pharmacology
Answer: B · Explore the reason, respect the decision, document and inform the prescriber
Why this is the answer
Competent patients may refuse treatment. The nurse explores concerns, explains the purpose and risks, documents the refusal and informs the prescriber; covert administration needs formal legal and clinical procedures.
Answer
B · Explore the reason, respect the decision, document and inform the prescriber
8.Pharmacology
Answer: A · Idarucizumab
Why this is the answer
Idarucizumab is an antibody fragment that binds dabigatran. Andexanet alfa reverses factor Xa inhibitors, protamine reverses heparin, and vitamin K reverses warfarin.