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 64 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.
64 kgVd = 0.7 L/kgC = 20 mg/LS = 0.92
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 99 kg patient has a phenytoin level of 9 mg/L; the target is 15 mg/L. The drug is given intravenously as phenytoin sodium (S = 0.92), and the volume of distribution is 0.7 L/kg. What extra loading dose LD raises the level to the target?
99 kgVd = 0.7 L/kgC = 9 → 15 mg/LS = 0.92
LD = mg
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.68 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.68 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 3.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 325 mg. Draw up the dose: what volume V do you give?
1000 mg3.2 mL + 0.8 mL325 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 500 mL. The order is 12 units/kg/h for a patient who weighs 62 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL12 units/kg/h62 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 83 kg has an order for norepinephrine at 12 mcg/min. The bag contains 4 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
4 mg/250 mL12 mcg/min83 kg
R = mL/h
7.PharmacologyMedium
Which fraction of a drug in plasma can reach the receptor and produce an effect?
AThe fraction bound to globulins
BThe fraction stored in red blood cells
CThe fraction bound to albumin
DThe unbound (free) fraction
8.PharmacologyHard
A 19-year-old woman is starting isotretinoin for severe acne. Which requirement is most important?
AWeekly hearing tests and monthly eye examinations during treatment
BTaking the drug only at weekends
CA high-vitamin A diet to boost the effect
DReliable contraception and pregnancy tests, as it is highly teratogenic
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 973.9 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 = 0.7·64 = 44.8 L
Amount of active drug needed
Vd·C = 44.8·20 = 896 mg
Loading dose
LD = 896/(0.92·1) = 973.9 mg
Answer
LD = 973.9 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: LD = 452 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 = 0.7·99 = 69.3 L
Rise needed
15 − 9 = 6 mg/L
Loading dose
LD = 69.3·6/(0.92·1) = 452 mg
Answer
LD = 452 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 6.8 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.
Strength in mg/mL
1000 mg/10 000 mL = 0.1 mg/mL
Volume
V = 0.68/0.1 = 6.8 mL
Answer
V = 6.8 mL
4.Pharmacy calculations
Answer: V = 1.3 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
3.2 + 0.8 = 4 mL
C = 1000/4 = 250 mg/mL
Volume
V = 325/250 = 1.3 mL
Answer
V = 1.3 mL
5.Pediatric & critical-care dosing
Answer: R = 14.9 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
12·62 = 744 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 744/50 = 14.88 ≈ 14.9 mL/h
Answer
R = 14.9 mL/h
6.Pediatric & critical-care dosing
Answer: R = 45 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
4 000/250 = 16 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
12·60 = 720 mcg/h
Pump rate
R = 720/16 = 45 mL/h
Answer
R = 45 mL/h
7.Pharmacology
Answer: D · The unbound (free) fraction
Why this is the answer
Only the free drug can diffuse into tissues, act on receptors and be metabolised or excreted. Protein-bound drug acts as a reservoir.
Answer
D · The unbound (free) fraction
8.Pharmacology
Answer: D · Reliable contraception and pregnancy tests, as it is highly teratogenic
Why this is the answer
Isotretinoin causes severe birth defects. Pregnancy prevention programmes require effective contraception and regular pregnancy tests before, during and after treatment.
Answer
D · Reliable contraception and pregnancy tests, as it is highly teratogenic