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 96 kg patient receives a theophylline infusion. The clearance is 0.04 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 15 mg/L?
96 kgCL = 0.04 L/kg/hCss = 15 mg/L
R = mg/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). An 85 kg patient takes oral aminophylline (S = 0.8, F = 1) every 8 h. The theophylline clearance is 0.045 L/kg/h. Each dose is 450 mg of aminophylline. Find the average steady-state level Css,avg.
Practice exercise (made-up values, not clinical guidance). A vial contains cefazolin 1000 mg as a powder. The practice label says to add 4.5 mL of sterile water; the powder adds 0.5 mL to the volume. The prescribed dose is 250 mg. What volume V do you draw up? Round to one decimal place.
1000 mg4.5 mL+0.5 mL250 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 4.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 920 mg. Draw up the dose: what volume V do you give?
1000 mg4.8 mL + 0.2 mL920 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 250 mL. The order is 2 units/h. Find the pump rate R in mL/h. Round to one decimal place.
100 units/250 mL2 units/h
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 59 kg has an order for nitroglycerin at 30 mcg/min. The bag contains 25 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
25 mg/250 mL30 mcg/min59 kg
R = mL/h
7.PharmacologyMedium
How does neostigmine improve muscle strength in myasthenia gravis?
AIt directly stimulates muscarinic receptors in muscle
BIt increases the number of acetylcholine receptors at the neuromuscular junction
CIt inhibits acetylcholinesterase so more acetylcholine reaches the receptors
DIt blocks the autoantibodies against the receptor
8.PharmacologyHard
Five days after starting clindamycin, a patient has frequent watery diarrhoea, abdominal cramps and a fever. What should the nurse suspect and do?
AAn allergy to clindamycin; give an antihistamine and continue the antibiotic
BA normal side effect; give loperamide and continue as usual
CFood poisoning; encourage a high-fibre diet and plenty of milk products
DC. difficile infection; send stool, use contact precautions, avoid antidiarrhoeals
3Solutions
1.Clinical pharmacokinetics
Answer: R = 57.6 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 = 0.04·96 = 3.84 L/h
Infusion rate
R = 3.84·15 = 57.6 mg/h
Answer
R = 57.6 mg/h
2.Clinical pharmacokinetics
Answer: Css,avg = 11.76 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.
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Final volume
4.5 + 0.5 = 5 mL
Concentration
1000/5 = 200 mg/mL
Volume to give
V = 250/200 = 1.25 ≈ 1.3 mL
Answer
V = 1.3 mL
4.Pharmacy calculations
Answer: V = 4.6 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.
Final volume and concentration
4.8 + 0.2 = 5 mL
C = 1000/5 = 200 mg/mL
Volume
V = 920/200 = 4.6 mL
Answer
V = 4.6 mL
5.Pediatric & critical-care dosing
Answer: R = 5 mL/h
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.
Concentration
100/250 = 0.4 units/mL
Pump rate
R = 2/0.4 = 5 mL/h
Answer
R = 5 mL/h
6.Pediatric & critical-care dosing
Answer: R = 18 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
25 000/250 = 100 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
30·60 = 1800 mcg/h
Pump rate
R = 1800/100 = 18 mL/h
Answer
R = 18 mL/h
7.Pharmacology
Answer: C · It inhibits acetylcholinesterase so more acetylcholine reaches the receptors
Why this is the answer
Neostigmine inhibits acetylcholinesterase at the neuromuscular junction, so acetylcholine lasts longer and can activate the remaining nicotinic receptors more effectively.
Answer
C · It inhibits acetylcholinesterase so more acetylcholine reaches the receptors
8.Pharmacology
Answer: D · C. difficile infection; send stool, use contact precautions, avoid antidiarrhoeals
Why this is the answer
Broad-spectrum antibiotics, especially clindamycin, allow C. difficile to overgrow and release toxins. Stool is tested, contact precautions with soap-and-water handwashing are used, and antidiarrhoeals are avoided because they keep toxin in the gut.
Answer
D · C. difficile infection; send stool, use contact precautions, avoid antidiarrhoeals