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 74 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.
74 kgVd = 0.7 L/kgC = 20 mg/LS = 0.92
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 67 kg patient takes oral theophylline (F = 1) every 8 h. The clearance is 0.05 L/kg/h. Each dose is 400 mg of theophylline. Find the average steady-state level Css,avg.
CL = 0.05 L/kg/hτ = 8 hS = 1F = 167 kgD = 400 mg
Css,avg = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.58 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.58 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 9.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 35 mg. Draw up the dose: what volume V do you give?
250 mg9.6 mL + 0.4 mL35 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 100 units of regular insulin in 100 mL runs at 5 mL/h. How many units per hour D does the patient receive?
100 units/100 mL5 mL/h
D = units/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 800 mg in 500 mL. The order is 6 mcg/kg/min for a patient who weighs 98 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL6 mcg/kg/min98 kg
R = mL/h
7.PharmacologyMedium
Which teaching about antiepileptic drugs is most important?
AStop the drug when you have had no seizures for one whole week
BTake a double dose if you feel a seizure coming
CAlcohol has no effect on seizure control
DDo not stop the drug suddenly, as this can trigger severe seizures
8.PharmacologyHard
A patient with severe liver cirrhosis needs a benzodiazepine for alcohol withdrawal. Why is lorazepam often chosen instead of diazepam?
ALorazepam is cleared by simple conjugation and has no active metabolites
BLorazepam does not cause sedation in liver disease
CLorazepam is a stronger anticonvulsant than all other benzodiazepines
DLorazepam is excreted unchanged in the urine without any metabolism
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 1126 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 = 0.7·74 = 51.8 L
Amount of active drug needed
Vd·C = 51.8·20 = 1036 mg
Loading dose
LD = 1036/(0.92·1) = 1126 mg
Answer
LD = 1126 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: Css,avg = 14.93 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.
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 = 0.58/0.1 = 5.8 mL
Answer
V = 5.8 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
9.6 + 0.4 = 10 mL
C = 250/10 = 25 mg/mL
Volume
V = 35/25 = 1.4 mL
Answer
V = 1.4 mL
5.Pediatric & critical-care dosing
Answer: D = 5 units/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.
Concentration
100/100 = 1 units/mL
Units per hour
D = 5·1 = 5 units/h
Answer
D = 5 units/h
6.Pediatric & critical-care dosing
Answer: R = 22.1 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
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
6·98 = 588 mcg/min
588·60 = 35280 mcg/h
Pump rate
R = 35280/1600 = 22.05 ≈ 22.1 mL/h
Answer
R = 22.1 mL/h
7.Pharmacology
Answer: D · Do not stop the drug suddenly, as this can trigger severe seizures
Why this is the answer
Abrupt withdrawal of antiepileptic drugs can cause rebound seizures and even status epilepticus. Any change is made gradually under medical supervision.
Answer
D · Do not stop the drug suddenly, as this can trigger severe seizures
8.Pharmacology
Answer: A · Lorazepam is cleared by simple conjugation and has no active metabolites
Why this is the answer
Diazepam is metabolised by CYP enzymes into long-acting active metabolites, which accumulate in liver failure. Lorazepam, oxazepam and temazepam are glucuronidated, a process better preserved in liver disease.
Answer
A · Lorazepam is cleared by simple conjugation and has no active metabolites