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). After an IV dose of vancomycin, the level is 30 mg/L at 1 h and 9.1 mg/L at 13 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 30 mg/L (1 h)C2 = 9.1 mg/L (13 h)
k = h⁻¹
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). An 84 kg patient takes oral aminophylline (S = 0.8, F = 1) every 8 h. The theophylline clearance is 0.03 L/kg/h. Each dose is 450 mg of aminophylline. Find the average steady-state level Css,avg.
A solution has a ratio strength of 1:10 000. You need 0.16 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.16 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 30 g of 5% coal tar ointment. How many grams m of 1% coal tar ointment must you add to make a 2% ointment? Round to the nearest whole gram.
30 g · 5%1%2%
m = g
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 64 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
60 units/kg64 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 26 mL/h. The patient weighs 59 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL26 mL/h59 kg
D = mcg/kg/min
7.PharmacologyMedium
Which group of effects would the nurse expect after a dose of an anticholinergic drug such as atropine?
ADry mouth, faster heart rate and dilated pupils
BHeavy salivation, slow heart rate and small pupils
CBronchial secretions, wheeze and tearing of the eyes
DDiarrhoea, frequent urination and sweating
8.PharmacologyHard
Probenecid has been used to raise plasma penicillin levels. How does it do this?
AIt inhibits the liver metabolism of penicillin
BIt displaces penicillin from plasma proteins
CIt increases the absorption of penicillin from the small intestine
DIt blocks the tubular secretion of penicillin in the kidney
3Solutions
1.Clinical pharmacokinetics
Answer: k = 0.09941 h⁻¹
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.
Elimination rate constant
k = ln(30/9.1)/12 = 1.193/12 = 0.09941 h⁻¹
Answer
k = 0.09941 h⁻¹
2.Clinical pharmacokinetics
Answer: Css,avg = 17.86 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 = 0.16/0.1 = 1.6 mL
Answer
V = 1.6 mL
4.Pharmacy calculations
Answer: m = 90 g
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
5%: 2 − 1 = 1 parts
1%: 5 − 2 = 3 parts
Scale to the amount you have
m = 30·3/1 = 90 g
Answer
m = 90 g
Check: 30 g + 90 g = 120 g of 2% ointment.
5.Pediatric & critical-care dosing
Answer: V = 0.77 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
60·64 = 3 840 units
Volume
V = 3840/5000 = 0.768 ≈ 0.77 mL
Answer
V = 0.77 mL
6.Pediatric & critical-care dosing
Answer: D = 14.7 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
500 000/250 = 2000 mcg/mL
Micrograms per minute
26·2000 = 52000 mcg/h
52000/60 = 866.7 mcg/min
Per kilogram
D = 866.7/59 = 14.69 ≈ 14.7 mcg/kg/min
Answer
D = 14.7 mcg/kg/min
7.Pharmacology
Answer: A · Dry mouth, faster heart rate and dilated pupils
Why this is the answer
Anticholinergic drugs block muscarinic receptors, so parasympathetic effects are reduced. This gives dry mouth, tachycardia, dilated pupils, constipation and urinary retention.
Answer
A · Dry mouth, faster heart rate and dilated pupils
8.Pharmacology
Answer: D · It blocks the tubular secretion of penicillin in the kidney
Why this is the answer
Penicillins are excreted largely by organic anion transporters in the proximal tubule. Probenecid competes for these transporters, so penicillin is excreted more slowly and its level stays higher.
Answer
D · It blocks the tubular secretion of penicillin in the kidney