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 vancomycin, the level is 25 mg/L at 1 h and 6.3 mg/L at 13 h. Assume first-order elimination. Find the half-life t½.
C1 = 25 mg/L (1 h)C2 = 6.3 mg/L (13 h)
t½ = h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 60 mg/h with no loading dose. The patient's clearance is 3 L/h and the half-life is 10 h. What is the level C after 12 h?
R = 60 mg/hCL = 3 L/ht½ = 10 ht = 12 h
C = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.29 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.29 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 4.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 150 mg. Draw up the dose: what volume V do you give?
500 mg4.6 mL + 0.4 mL150 mg
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 87 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg87 kg1 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 71 kg has an order for nitroglycerin at 10 mcg/min. The bag contains 50 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
50 mg/250 mL10 mcg/min71 kg
R = mL/h
7.PharmacologyMedium
A person who has never been vaccinated against tetanus has a deep, dirty wound. What is usually given?
ANo treatment unless symptoms appear
BOral antibiotics only
CTetanus vaccine only, after the wound heals
DTetanus vaccine and tetanus immunoglobulin
8.PharmacologyHard
Which antiepileptic drug carries the highest well-known risk of neural tube defects and developmental problems when taken in pregnancy?
ALevetiracetam
BSodium valproate
CLamotrigine
DGabapentin
3Solutions
1.Clinical pharmacokinetics
Answer: t½ = 6.035 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.
Elimination rate constant
k = ln(25/6.3)/12 = 1.378/12 = 0.1149 h⁻¹
Half-life
t½ = 0.693/0.1149 = 6.035 h
Answer
t½ = 6.035 h
2.Clinical pharmacokinetics
Answer: C = 11.29 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.
Steady-state level
Css = 60/3 = 20 mg/L
Rate constant
k = 0.693/10 = 0.06931 h⁻¹
Level after the given time
C = 20·(1 − e−0.06931·12) = 11.29 mg/L
Answer
C = 11.29 mg/L
3.Pharmacy calculations
Answer: V = 0.29 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/1000 mL = 1 mg/mL
Volume
V = 0.29/1 = 0.29 mL
Answer
V = 0.29 mL
4.Pharmacy calculations
Answer: V = 1.5 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
4.6 + 0.4 = 5 mL
C = 500/5 = 100 mg/mL
Volume
V = 150/100 = 1.5 mL
Answer
V = 1.5 mL
5.Pediatric & critical-care dosing
Answer: V = 6.1 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
70·87 = 6 090 units
Volume
V = 6090/1000 = 6.09 ≈ 6.1 mL
Answer
V = 6.1 mL
6.Pediatric & critical-care dosing
Answer: R = 3 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
50 000/250 = 200 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
10·60 = 600 mcg/h
Pump rate
R = 600/200 = 3 mL/h
Answer
R = 3 mL/h
7.Pharmacology
Answer: D · Tetanus vaccine and tetanus immunoglobulin
Why this is the answer
Tetanus immunoglobulin gives immediate passive protection, while the vaccine starts active immunity. Thorough wound cleaning is also essential.
Answer
D · Tetanus vaccine and tetanus immunoglobulin
8.Pharmacology
Answer: B · Sodium valproate
Why this is the answer
Valproate is strongly teratogenic, causing neural tube defects and other malformations, and it affects neurodevelopment. It should be avoided in pregnancy unless no alternative works.