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). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 3 L/h. What infusion rate R in mg/h gives a steady-state level of 20 mg/L?
CL = 3 L/hCss = 20 mg/L
R = mg/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 68 kg patient has a theophylline level of 6 mg/L; the target is 15 mg/L. The drug is given intravenously as aminophylline (S = 0.8), and the volume of distribution is 0.5 L/kg. What extra loading dose LD raises the level to the target?
68 kgVd = 0.5 L/kgC = 6 → 15 mg/LS = 0.8
LD = mg
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.68 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.68 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 9.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 100 mg. Draw up the dose: what volume V do you give?
500 mg9.4 mL + 0.6 mL100 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 250 units of regular insulin in 250 mL. The order is 0.1 units/kg/h for a patient who weighs 85 kg. Find the pump rate R in mL/h. Round to one decimal place.
250 units/250 mL0.1 units/kg/h85 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 18 mL/h. The patient weighs 73 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL18 mL/h73 kg
D = mcg/kg/min
7.PharmacologyMedium
A woman taking tamoxifen should report which symptom promptly?
AUnusual vaginal bleeding or a painful swollen leg
BSlightly dry skin
CMild hot flushes, especially at night, in the first months
DMild tiredness in the afternoon
8.PharmacologyHard
Why is gentamicin often given once daily instead of in several small doses?
AIt has a very long half-life of several days
BIt is absorbed slowly from the muscle over 24 hours
CIts killing depends only on the time the level stays above the MIC
DIts killing depends on high peak levels, with a post-antibiotic effect
3Solutions
1.Clinical pharmacokinetics
Answer: R = 60 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.
Infusion rate
R = 3·20 = 60 mg/h
Answer
R = 60 mg/h
2.Clinical pharmacokinetics
Answer: LD = 382.5 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 = 0.5·68 = 34 L
Rise needed
15 − 6 = 9 mg/L
Loading dose
LD = 34·9/(0.8·1) = 382.5 mg
Answer
LD = 382.5 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 6.8 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/10 000 mL = 0.1 mg/mL
Volume
V = 0.68/0.1 = 6.8 mL
Answer
V = 6.8 mL
4.Pharmacy calculations
Answer: V = 2 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
9.4 + 0.6 = 10 mL
C = 500/10 = 50 mg/mL
Volume
V = 100/50 = 2 mL
Answer
V = 2 mL
5.Pediatric & critical-care dosing
Answer: R = 8.5 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.
Units per hour
0.1·85 = 8.5 units/h
Concentration
250/250 = 1 units/mL
Pump rate
R = 8.5/1 = 8.5 mL/h
Answer
R = 8.5 mL/h
6.Pediatric & critical-care dosing
Answer: D = 6.6 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
800 000/500 = 1600 mcg/mL
Micrograms per minute
18·1600 = 28800 mcg/h
28800/60 = 480 mcg/min
Per kilogram
D = 480/73 = 6.575 ≈ 6.6 mcg/kg/min
Answer
D = 6.6 mcg/kg/min
7.Pharmacology
Answer: A · Unusual vaginal bleeding or a painful swollen leg
Why this is the answer
Tamoxifen has oestrogen-like effects on the uterus and clotting, increasing the risk of endometrial cancer and venous thromboembolism. Hot flushes are common and expected.
Answer
A · Unusual vaginal bleeding or a painful swollen leg
8.Pharmacology
Answer: D · Its killing depends on high peak levels, with a post-antibiotic effect
Why this is the answer
Aminoglycosides show concentration-dependent killing and a post-antibiotic effect. Once-daily dosing gives high peaks and a low trough, which may also reduce kidney and ear toxicity.
Answer
D · Its killing depends on high peak levels, with a post-antibiotic effect