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 patient receives an IV bolus of 190 mg of gentamicin. The level back-extrapolated to time zero is 12 mg/L and the half-life is 3 h. Find the clearance CL in L/h.
D = 190 mgC₀ = 12 mg/Lt½ = 3 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient's tobramycin half-life is 3 h. The target is a peak of 7 mg/L and a trough of 1 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.
t½ = 3 hCpeak = 7 mg/LCtrough = 1 mg/L
τ = h
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.75 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.75 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 600 mL of 6% hydrogen peroxide from a 30% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
30%0%6%600 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 15 units/kg/h for a patient who weighs 104 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL15 units/kg/h104 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 2.5 mcg/kg/min for a patient who weighs 84 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL2.5 mcg/kg/min84 kg
R = mL/h
7.PharmacologyMedium
Which side effects are most common when starting gabapentin?
AInsomnia and agitation
BCough and runny nose
CDrowsiness and dizziness
DHair loss and weight loss
8.PharmacologyHard
Why is clavulanic acid combined with amoxicillin (co-amoxiclav)?
AIt slows the kidney excretion of amoxicillin
BIt inhibits beta-lactamase enzymes that would destroy amoxicillin
CIt makes amoxicillin cross the blood–brain barrier more easily
DIt reduces the risk of penicillin allergy
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 3.658 L/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.
Volume of distribution
Vd = 190/12 = 15.83 L
Rate constant
k = 0.693/3 = 0.231 h⁻¹
Clearance
CL = 0.231·15.83 = 3.658 L/h
Answer
CL = 3.658 L/h
2.Clinical pharmacokinetics
Answer: τ = 8.4 h
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.
Rate constant
k = 0.693/3 = 0.231 h⁻¹
Dosing interval
τ = ln(7/1)/0.231 = 1.946/0.231 = 8.422 ≈ 8.4 h
Answer
τ = 8.4 h
In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.
3.Pharmacy calculations
Answer: V = 0.75 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 = 0.75/1 = 0.75 mL
Answer
V = 0.75 mL
4.Pharmacy calculations
Answer: V = 480 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
30%: 6 − 0 = 6 parts
0%: 30 − 6 = 24 parts
total: 30 parts
Water
V = 600·24/30 = 480 mL
Answer
V = 480 mL
Check: 120 mL of 30% contains 36 g of drug, which is 6% of 600 mL.
5.Pediatric & critical-care dosing
Answer: R = 39 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
15·104 = 1 560 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1560/40 = 39 mL/h
Answer
R = 39 mL/h
6.Pediatric & critical-care dosing
Answer: R = 6.3 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
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
2.5·84 = 210 mcg/min
210·60 = 12600 mcg/h
Pump rate
R = 12600/2000 = 6.3 mL/h
Answer
R = 6.3 mL/h
7.Pharmacology
Answer: C · Drowsiness and dizziness
Why this is the answer
Gabapentin and pregabalin commonly cause sedation, dizziness and unsteadiness, which raise the risk of falls. They also increase sedation when combined with opioids.
Answer
C · Drowsiness and dizziness
8.Pharmacology
Answer: B · It inhibits beta-lactamase enzymes that would destroy amoxicillin
Why this is the answer
Many bacteria produce beta-lactamases that inactivate penicillins. Clavulanic acid inhibits these enzymes, so amoxicillin can work against these organisms.
Answer
B · It inhibits beta-lactamase enzymes that would destroy amoxicillin