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 210 mg of tobramycin. The level back-extrapolated to time zero is 9 mg/L and the half-life is 2.5 h. Find the volume of distribution Vd.
D = 210 mgC₀ = 9 mg/Lt½ = 2.5 h
Vd = L
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 50 kg patient has a digoxin level of 0.5 mcg/L; the target is 0.8 mcg/L. The volume of distribution is 7 L/kg and the tablets have F = 0.7. What extra loading dose LD raises the level to the target?
50 kgVd = 7 L/kgC = 0.5 → 0.8 mcg/LF = 0.7
LD = mcg
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.51 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.51 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 300 mL of 20% dextrose by mixing 50% and 10% dextrose. How many mL V of the 50% solution do you need? Round to the nearest whole mL.
50%10%20%300 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 250 units of regular insulin in 250 mL runs at 12 mL/h. How many units per hour D does the patient receive?
250 units/250 mL12 mL/h
D = units/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 86 kg has an order for nitroglycerin at 20 mcg/min. The bag contains 25 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
25 mg/250 mL20 mcg/min86 kg
R = mL/h
7.PharmacologyMedium
After several years of levodopa treatment, which problem is common?
APermanent hearing loss
BComplete and permanent loss of all Parkinson's symptoms
CSevere hypoglycaemia after each dose
DDyskinesias and "on–off" fluctuations in response
8.PharmacologyHard
Which statement correctly contrasts donepezil and memantine in Alzheimer's disease?
DBoth drugs are dopamine agonists that differ only in their half-lives
3Solutions
1.Clinical pharmacokinetics
Answer: Vd = 23.33 L
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 = 210/9 = 23.33 L
Answer
Vd = 23.33 L
2.Clinical pharmacokinetics
Answer: LD = 150 mcg
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 = 7·50 = 350 L
Rise needed
0.8 − 0.5 = 0.3 mcg/L
Loading dose
LD = 350·0.3/(1·0.7) = 150 mcg
Answer
LD = 150 mcg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 0.51 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 = 0.51/1 = 0.51 mL
Answer
V = 0.51 mL
4.Pharmacy calculations
Answer: V = 75 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
50%: 20 − 10 = 10 parts
10%: 50 − 20 = 30 parts
total: 40 parts
Share the volume
V = 300·10/40 = 75 mL
Answer
V = 75 mL
Check: 75 mL of 50% + 225 mL of 10% = 300 mL.
5.Pediatric & critical-care dosing
Answer: D = 12 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
250/250 = 1 units/mL
Units per hour
D = 12·1 = 12 units/h
Answer
D = 12 units/h
6.Pediatric & critical-care dosing
Answer: R = 12 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
25 000/250 = 100 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
20·60 = 1200 mcg/h
Pump rate
R = 1200/100 = 12 mL/h
Answer
R = 12 mL/h
7.Pharmacology
Answer: D · Dyskinesias and "on–off" fluctuations in response
Why this is the answer
Long-term levodopa use often leads to motor fluctuations, with periods of good control and periods of stiffness, and to dyskinesias at peak dose. Dose timing and add-on drugs are adjusted to manage this.
Answer
D · Dyskinesias and "on–off" fluctuations in response
8.Pharmacology
Answer: C · Donepezil inhibits cholinesterase; memantine blocks NMDA receptors
Why this is the answer
Donepezil raises acetylcholine levels, while memantine reduces excitotoxic glutamate activity at NMDA receptors. Both give symptomatic benefit only.
Answer
C · Donepezil inhibits cholinesterase; memantine blocks NMDA receptors