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 patient receives an IV bolus of 180 mg of tobramycin. The level back-extrapolated to time zero is 7 mg/L and the half-life is 2 h. Find the clearance CL in L/h.
D = 180 mgC₀ = 7 mg/Lt½ = 2 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). An 84 kg patient has a phenytoin level of 6 mg/L; the target is 20 mg/L. The drug is given intravenously as phenytoin sodium (S = 0.92), and the volume of distribution is 0.7 L/kg. What extra loading dose LD raises the level to the target?
84 kgVd = 0.7 L/kgC = 6 → 20 mg/LS = 0.92
LD = mg
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.81 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.81 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 9.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 480 mg. Draw up the dose: what volume V do you give?
2000 mg9.2 mL + 0.8 mL480 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 78 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg78 kg1 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 57 kg has an order for nitroglycerin at 20 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 mL20 mcg/min57 kg
R = mL/h
7.PharmacologyMedium
Why is propranolol usually avoided in patients with asthma?
AIt increases mucus production by blocking histamine
BIt causes tolerance to inhaled corticosteroids
CIt blocks beta-2 receptors in the airways and can cause bronchospasm
DIt stimulates alpha-1 receptors in the airways and raises blood pressure
8.PharmacologyHard
During an IV glyceryl trinitrate (nitroglycerin) infusion for chest pain, the patient's blood pressure drops to 82/50 mmHg and he feels faint. What is the nurse's first action?
AIncrease the infusion rate to improve blood flow to the heart
BSit the patient fully upright and give paracetamol for the headache
CStop or reduce the infusion as per protocol, lay the patient flat and notify the prescriber
DGive a sublingual nitroglycerin tablet and increase the rate to relieve the remaining chest pain
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 8.912 L/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.
Volume of distribution
Vd = 180/7 = 25.71 L
Rate constant
k = 0.693/2 = 0.3466 h⁻¹
Clearance
CL = 0.3466·25.71 = 8.912 L/h
Answer
CL = 8.912 L/h
2.Clinical pharmacokinetics
Answer: LD = 894.8 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 = 0.7·84 = 58.8 L
Rise needed
20 − 6 = 14 mg/L
Loading dose
LD = 58.8·14/(0.92·1) = 894.8 mg
Answer
LD = 894.8 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 0.81 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 = 0.81/1 = 0.81 mL
Answer
V = 0.81 mL
4.Pharmacy calculations
Answer: V = 2.4 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
9.2 + 0.8 = 10 mL
C = 2000/10 = 200 mg/mL
Volume
V = 480/200 = 2.4 mL
Answer
V = 2.4 mL
5.Pediatric & critical-care dosing
Answer: V = 4.7 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
60·78 = 4 680 units
Volume
V = 4680/1000 = 4.68 ≈ 4.7 mL
Answer
V = 4.7 mL
6.Pediatric & critical-care dosing
Answer: R = 6 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.
20·60 = 1200 mcg/h
Pump rate
R = 1200/200 = 6 mL/h
Answer
R = 6 mL/h
7.Pharmacology
Answer: C · It blocks beta-2 receptors in the airways and can cause bronchospasm
Why this is the answer
Non-selective beta blockers block both beta-1 and beta-2 receptors. Blocking beta-2 receptors in the bronchi removes their relaxing effect and can trigger severe bronchospasm.
Answer
C · It blocks beta-2 receptors in the airways and can cause bronchospasm
8.Pharmacology
Answer: C · Stop or reduce the infusion as per protocol, lay the patient flat and notify the prescriber
Why this is the answer
Hypotension is a major adverse effect of nitrates due to venous and arterial dilation. The infusion is stopped or reduced, the patient is positioned flat to improve venous return, and the prescriber is informed.
Answer
C · Stop or reduce the infusion as per protocol, lay the patient flat and notify the prescriber