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 tobramycin, the level is 10 mg/L at 1 h and 2.5 mg/L at 6 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 10 mg/L (1 h)C2 = 2.5 mg/L (6 h)
k = h⁻¹
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). An 85 kg patient on regular tobramycin doses is at steady state. The target is a peak of 6 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.25 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 1000 mg as a powder. The practice label says to add 3.5 mL of sterile water; the powder adds 0.5 mL to the volume. What is the concentration C in mg/mL after reconstitution?
1000 mg3.5 mL+0.5 mL
C = mg/mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 1.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 250 mg. Draw up the dose: what volume V do you give?
500 mg1.5 mL + 0.5 mL250 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 12 500 units of heparin in 250 mL. The order is 15 units/kg/h for a patient who weighs 109 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL15 units/kg/h109 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 500 mg in 250 mL. The order is 12.5 mcg/kg/min for a patient who weighs 69 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL12.5 mcg/kg/min69 kg
R = mL/h
7.PharmacologyMedium
Which description fits tardive dyskinesia?
AInvoluntary movements of the lips, tongue and face after long-term antipsychotic use
BA sudden painful spasm of the neck muscles and upward rolling of the eyes within days of the first dose
CHigh fever with lead-pipe rigidity and confusion
DA low white cell count with sore throat and fever
8.PharmacologyHard
What is the main mechanism of action of proton pump inhibitors such as omeprazole?
ANeutralising acid in the stomach
BCoating the ulcer to protect it
CIrreversible inhibition of the H⁺/K⁺-ATPase in parietal cells
DCompetitive blocking of histamine H2 receptors on parietal cells
3Solutions
1.Clinical pharmacokinetics
Answer: k = 0.2773 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(10/2.5)/5 = 1.386/5 = 0.2773 h⁻¹
Answer
k = 0.2773 h⁻¹
2.Clinical pharmacokinetics
Answer: D = 116.9 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 = 0.25·85 = 21.25 L
Dose
D = 21.25·(6 − 0.5) = 116.9 mg
Answer
D = 116.9 mg
In practice the dose is rounded to a convenient amount.
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
3.5 + 0.5 = 4 mL
Concentration
C = 1000/4 = 250 mg/mL
Answer
C = 250 mg/mL
4.Pharmacy calculations
Answer: V = 1 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 = 500/2 = 250 mg/mL
Volume
V = 250/250 = 1 mL
Answer
V = 1 mL
5.Pediatric & critical-care dosing
Answer: R = 32.7 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
15·109 = 1 635 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 1635/50 = 32.7 mL/h
Answer
R = 32.7 mL/h
6.Pediatric & critical-care dosing
Answer: R = 25.9 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
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
12.5·69 = 862.5 mcg/min
862.5·60 = 51750 mcg/h
Pump rate
R = 51750/2000 = 25.88 ≈ 25.9 mL/h
Answer
R = 25.9 mL/h
7.Pharmacology
Answer: A · Involuntary movements of the lips, tongue and face after long-term antipsychotic use
Why this is the answer
Tardive dyskinesia develops after months or years of dopamine-blocking drugs and may be permanent. Patients are screened regularly so that treatment can be changed early.
Answer
A · Involuntary movements of the lips, tongue and face after long-term antipsychotic use
8.Pharmacology
Answer: C · Irreversible inhibition of the H⁺/K⁺-ATPase in parietal cells
Why this is the answer
PPIs irreversibly block the proton pump, the last step of acid secretion. H2 blockers (such as famotidine) act earlier and are less powerful; antacids only neutralise.
Answer
C · Irreversible inhibition of the H⁺/K⁺-ATPase in parietal cells