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 88 kg patient is to be loaded intravenously with aminophylline to reach a theophylline level of 12 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.
88 kgVd = 0.5 L/kgC = 12 mg/LS = 0.8
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A vancomycin infusion is started without a loading dose. The half-life in this patient is 6 h. How long t does it take to reach 90% of the steady-state level?
t½ = 6 h90% Css
t = h
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.86 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.86 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 4.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 680 mg. Draw up the dose: what volume V do you give?
1000 mg4.4 mL + 0.6 mL680 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 92 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg92 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 97 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/min97 kg
R = mL/h
7.PharmacologyMedium
A patient refuses a prescribed oral medicine. What should the nurse do?
AExplore the reason, respect the decision, document and inform the prescriber
BHide the tablet in the patient's food
CLeave the tablet on the bedside table for later
DRecord the medicine as given, so that the chart stays complete for the next shift
8.PharmacologyHard
A patient receiving cisplatin is given large volumes of IV fluid before and after each dose. What is the main purpose?
ATo prevent bleeding
BTo increase drug absorption from the gut
CTo prevent hair loss
DTo reduce kidney damage
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 660 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 = 0.5·88 = 44 L
Amount of active drug needed
Vd·C = 44·12 = 528 mg
Loading dose
LD = 528/(0.8·1) = 660 mg
Answer
LD = 660 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: t = 19.93 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.
Rate constant
k = 0.693/6 = 0.1155 h⁻¹
Time to the given fraction of steady state
t = −ln(1 − 0.9)/0.1155 = 2.303/0.1155 = 19.93 h
Answer
t = 19.93 h
That is 3.322 half-lives.
3.Pharmacy calculations
Answer: V = 0.86 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 = 0.86/1 = 0.86 mL
Answer
V = 0.86 mL
4.Pharmacy calculations
Answer: V = 3.4 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
4.4 + 0.6 = 5 mL
C = 1000/5 = 200 mg/mL
Volume
V = 680/200 = 3.4 mL
Answer
V = 3.4 mL
5.Pediatric & critical-care dosing
Answer: V = 1.5 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
80·92 = 7 360 units
Volume
V = 7360/5000 = 1.472 ≈ 1.5 mL
Answer
V = 1.5 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: A · 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
A · Explore the reason, respect the decision, document and inform the prescriber
8.Pharmacology
Answer: D · To reduce kidney damage
Why this is the answer
Cisplatin is nephrotoxic, and hydration helps protect the kidneys. It also causes ototoxicity, peripheral neuropathy, severe nausea and low magnesium.