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 110 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 = 110 mgC₀ = 7 mg/Lt½ = 2 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient's gentamicin half-life is 3.5 h. The target is a peak of 10 mg/L and a trough of 0.5 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.
t½ = 3.5 hCpeak = 10 mg/LCtrough = 0.5 mg/L
τ = h
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 500 mg as a powder. The practice label says to add 1.8 mL of sterile water; the powder adds 0.2 mL to the volume. What is the concentration C in mg/mL after reconstitution?
500 mg1.8 mL+0.2 mL
C = mg/mL
4.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 1.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 700 mg. Draw up the dose: what volume V do you give?
1000 mg1.5 mL + 0.5 mL700 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 250 mL. The order is 16 units/kg/h for a patient who weighs 72 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL16 units/kg/h72 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 2.5 mcg/kg/min for a patient who weighs 96 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL2.5 mcg/kg/min96 kg
R = mL/h
7.PharmacologyMedium
Which advice helps reduce the most common side effect of varenicline?
ATake it on an empty stomach at bedtime with a little milk
BTake it after food with a full glass of water
CTake it with alcohol to reduce nausea
DTake double doses in the first week
8.PharmacologyHard
A patient develops a dry cough on an ACE inhibitor and is switched to losartan. Why is losartan less likely to cause cough?
AIt blocks histamine receptors in the airways
BIt is excreted faster by the kidney
CIt does not block the breakdown of bradykinin
DIt also acts as a bronchodilator
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 5.446 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 = 110/7 = 15.71 L
Rate constant
k = 0.693/2 = 0.3466 h⁻¹
Clearance
CL = 0.3466·15.71 = 5.446 L/h
Answer
CL = 5.446 L/h
2.Clinical pharmacokinetics
Answer: τ = 15.1 h
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.
Rate constant
k = 0.693/3.5 = 0.198 h⁻¹
Dosing interval
τ = ln(10/0.5)/0.198 = 2.996/0.198 = 15.13 ≈ 15.1 h
Answer
τ = 15.1 h
In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.
3.Pharmacy calculations
Answer: C = 250 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
1.8 + 0.2 = 2 mL
Concentration
C = 500/2 = 250 mg/mL
Answer
C = 250 mg/mL
4.Pharmacy calculations
Answer: V = 1.4 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
1.5 + 0.5 = 2 mL
C = 1000/2 = 500 mg/mL
Volume
V = 700/500 = 1.4 mL
Answer
V = 1.4 mL
5.Pediatric & critical-care dosing
Answer: R = 11.5 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
16·72 = 1 152 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 1152/100 = 11.52 ≈ 11.5 mL/h
Answer
R = 11.5 mL/h
6.Pediatric & critical-care dosing
Answer: R = 14.4 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
2.5·96 = 240 mcg/min
240·60 = 14400 mcg/h
Pump rate
R = 14400/1000 = 14.4 mL/h
Answer
R = 14.4 mL/h
7.Pharmacology
Answer: B · Take it after food with a full glass of water
Why this is the answer
Nausea is the most common adverse effect of varenicline and is reduced by taking it after food with water. Patients should also report changes in mood or behaviour.
Answer
B · Take it after food with a full glass of water
8.Pharmacology
Answer: C · It does not block the breakdown of bradykinin
Why this is the answer
ACE (kininase II) breaks down bradykinin, so ACE inhibitors raise bradykinin, which can cause cough and angioedema. ARBs block the angiotensin II receptor without affecting bradykinin breakdown.