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 190 mg of tobramycin. The level back-extrapolated to time zero is 12 mg/L and the half-life is 3 h. Find the volume of distribution Vd.
D = 190 mgC₀ = 12 mg/Lt½ = 3 h
Vd = L
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 42-year-old man weighs 63 kg and has a serum creatinine of 2.3 mg/dL (203 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual levetiracetam dose is 1000 mg for a creatinine clearance of 100 mL/min, and a fraction fe = 0.66 of the drug is excreted unchanged by the kidneys. Using the Dettli dose fraction Q = 1 − fe·(1 − CrCl/normal CrCl), find the adjusted dose D. Round to the nearest whole number.
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. What is the concentration C in mg/mL after reconstitution?
1000 mg4.5 mL+0.5 mL
C = mg/mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 150 g of 20% zinc oxide ointment. How many grams m of plain ointment base (0%) must you add to make a 15% ointment? Round to the nearest whole gram.
150 g · 20%0%15%
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 52 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg52 kg1 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 12 mL/h. The patient weighs 68 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL12 mL/h68 kg
D = mcg/kg/min
7.PharmacologyMedium
Why is directly observed therapy (DOT) often used for tuberculosis?
APatients with TB cannot swallow tablets
BTreatment lasts months, and missed doses cause resistance
CThe drugs work only if a nurse is present
DTB drugs must always be given intravenously in hospital
8.PharmacologyHard
Why is gentamicin dosing monitored with blood levels?
AIt is nephrotoxic and ototoxic with a narrow therapeutic index
BIt is metabolised entirely by the liver, so liver function decides the dose
CIt causes severe hypoglycaemia
DIt only works at very high concentrations
3Solutions
1.Clinical pharmacokinetics
Answer: Vd = 15.83 L
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 = 190/12 = 15.83 L
Answer
Vd = 15.83 L
2.Clinical pharmacokinetics
Answer: D = 586 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.
Creatinine clearance (Cockcroft–Gault)
CrCl = (140 − 42)·63/(72·2.3) = 37.28 mL/min
Dose fraction (Dettli)
Q = 1 − 0.66·(1 − 37.28/100) = 0.5861
Adjusted dose
D = 0.5861·1000 = 586.1 ≈ 586 mg
Answer
D = 586 mg
In practice the dose is rounded to a convenient amount and checked against the product information.
3.Pharmacy calculations
Answer: C = 200 mg/mL
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
C = 1000/5 = 200 mg/mL
Answer
C = 200 mg/mL
4.Pharmacy calculations
Answer: m = 50 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
20%: 15 − 0 = 15 parts
0%: 20 − 15 = 5 parts
Scale to the amount you have
m = 150·5/15 = 50 g
Answer
m = 50 g
Check: 150 g + 50 g = 200 g of 15% ointment.
5.Pediatric & critical-care dosing
Answer: V = 3.1 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
60·52 = 3 120 units
Volume
V = 3120/1000 = 3.12 ≈ 3.1 mL
Answer
V = 3.1 mL
6.Pediatric & critical-care dosing
Answer: D = 4.7 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
800 000/500 = 1600 mcg/mL
Micrograms per minute
12·1600 = 19200 mcg/h
19200/60 = 320 mcg/min
Per kilogram
D = 320/68 = 4.706 ≈ 4.7 mcg/kg/min
Answer
D = 4.7 mcg/kg/min
7.Pharmacology
Answer: B · Treatment lasts months, and missed doses cause resistance
Why this is the answer
Standard TB treatment usually lasts six months or more with several drugs. Poor adherence leads to relapse and multidrug-resistant TB, so supervised dosing improves completion.
Answer
B · Treatment lasts months, and missed doses cause resistance
8.Pharmacology
Answer: A · It is nephrotoxic and ototoxic with a narrow therapeutic index
Why this is the answer
Aminoglycosides like gentamicin can damage the kidneys and the inner ear. They are cleared renally, so levels rise in kidney impairment and are monitored.
Answer
A · It is nephrotoxic and ototoxic with a narrow therapeutic index