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 61 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 20 mg/L. The volume of distribution is 0.7 L/kg and the salt factor is S = 0.92. Find the loading dose LD of phenytoin sodium in mg.
61 kgVd = 0.7 L/kgC = 20 mg/LS = 0.92
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 3.5 L/h. Each dose is 750 mg of vancomycin. Find the average steady-state level Css,avg.
CL = 3.5 L/hτ = 12 hS = 1F = 1D = 750 mg
Css,avg = mg/L
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 3.2 mL of diluent. The prescribed dose is 2 400 000 units. What volume V do you draw up? Round to one decimal place.
3.2 mL → 1 000 000 units/mL2 400 000 units
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 200 mL of 40% dextrose by mixing 70% and 10% dextrose. How many mL V of the 70% solution do you need? Round to the nearest whole mL.
70%10%40%200 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 70 units/kg for a patient who weighs 82 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg82 kg5 000 units/mL
V = mL
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 7.5 mcg/kg/min for a patient who weighs 109 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL7.5 mcg/kg/min109 kg
R = mL/h
7.PharmacologyMedium
What does the clearance of a drug describe?
AThe fraction of the dose that is absorbed
BThe amount of drug removed by one dialysis session
CThe time needed for the drug to disappear completely from the plasma
DThe volume of plasma cleared of the drug per unit of time
8.PharmacologyHard
A patient who used cocaine has chest pain, agitation, a high temperature, sweating, tachycardia and dilated pupils. Which drug class is commonly first-line for the agitation and sympathetic overactivity?
AAnticholinergic drugs
BOpioid antagonists
CAntihistamines
DBenzodiazepines
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 928.3 mg
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 = 0.7·61 = 42.7 L
Amount of active drug needed
Vd·C = 42.7·20 = 854 mg
Loading dose
LD = 854/(0.92·1) = 928.3 mg
Answer
LD = 928.3 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: Css,avg = 17.86 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.
Concentration from the label
3.2 mL → 1 000 000 units/mL
Volume to give
V = 2 400 000/1 000 000 = 2.4 mL
Answer
V = 2.4 mL
4.Pharmacy calculations
Answer: V = 100 mL
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
70%: 40 − 10 = 30 parts
10%: 70 − 40 = 30 parts
total: 60 parts
Share the volume
V = 200·30/60 = 100 mL
Answer
V = 100 mL
Check: 100 mL of 70% + 100 mL of 10% = 200 mL.
5.Pediatric & critical-care dosing
Answer: V = 1.1 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
70·82 = 5 740 units
Volume
V = 5740/5000 = 1.148 ≈ 1.1 mL
Answer
V = 1.1 mL
6.Pediatric & critical-care dosing
Answer: R = 24.5 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
7.5·109 = 817.5 mcg/min
817.5·60 = 49050 mcg/h
Pump rate
R = 49050/2000 = 24.52 ≈ 24.5 mL/h
Answer
R = 24.5 mL/h
7.Pharmacology
Answer: D · The volume of plasma cleared of the drug per unit of time
Why this is the answer
Clearance is the volume of plasma from which the drug is removed per unit of time. Together with the dosing rate it determines the steady-state concentration.
Answer
D · The volume of plasma cleared of the drug per unit of time
8.Pharmacology
Answer: D · Benzodiazepines
Why this is the answer
Cocaine causes a sympathomimetic toxidrome. Benzodiazepines reduce agitation, tachycardia, hypertension and hyperthermia, while cooling and cardiac monitoring are also given.