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 gentamicin, the level is 6 mg/L at 1 h and 1.5 mg/L at 5 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 6 mg/L (1 h)C2 = 1.5 mg/L (5 h)
k = h⁻¹
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 90 kg patient on regular gentamicin doses is at steady state. The target is a peak of 10 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.3 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
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
Practice exercise (made-up values, not clinical guidance). You have 20 g of 20% zinc oxide ointment. How many grams m of plain ointment base (0%) must you add to make a 10% ointment? Round to the nearest whole gram.
20 g · 20%0%10%
m = g
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 100 mL. The order is 0.05 units/kg/h for a patient who weighs 66 kg. Find the pump rate R in mL/h. Round to one decimal place.
100 units/100 mL0.05 units/kg/h66 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 75 kg has an order for norepinephrine at 4 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 mL4 mcg/min75 kg
R = mL/h
7.PharmacologyMedium
A patient must mix regular (soluble) insulin and NPH (isophane) insulin in one syringe. What is the correct order?
ADraw up the clear regular insulin first, then the cloudy NPH insulin
BDraw up the cloudy NPH insulin first, then the clear regular insulin
CDraw them up in separate syringes, then mix them in a cup
DShake both vials hard, then draw them up in any order
8.PharmacologyHard
Zero-order elimination, as seen with alcohol at normal intake, means that:
AA constant fraction is eliminated per unit of time
BThe half-life stays constant whatever the level
CA constant amount is eliminated per unit of time
DElimination stops at high concentrations
3Solutions
1.Clinical pharmacokinetics
Answer: k = 0.3466 h⁻¹
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(6/1.5)/4 = 1.386/4 = 0.3466 h⁻¹
Answer
k = 0.3466 h⁻¹
2.Clinical pharmacokinetics
Answer: D = 256.5 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 = 0.3·90 = 27 L
Dose
D = 27·(10 − 0.5) = 256.5 mg
Answer
D = 256.5 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 5.8 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 = 0.58/0.1 = 5.8 mL
Answer
V = 5.8 mL
4.Pharmacy calculations
Answer: m = 20 g
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
20%: 10 − 0 = 10 parts
0%: 20 − 10 = 10 parts
Scale to the amount you have
m = 20·10/10 = 20 g
Answer
m = 20 g
Check: 20 g + 20 g = 40 g of 10% ointment.
5.Pediatric & critical-care dosing
Answer: R = 3.3 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
0.05·66 = 3.3 units/h
Concentration
100/100 = 1 units/mL
Pump rate
R = 3.3/1 = 3.3 mL/h
Answer
R = 3.3 mL/h
6.Pediatric & critical-care dosing
Answer: R = 15 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.
4·60 = 240 mcg/h
Pump rate
R = 240/16 = 15 mL/h
Answer
R = 15 mL/h
7.Pharmacology
Answer: A · Draw up the clear regular insulin first, then the cloudy NPH insulin
Why this is the answer
Drawing up regular insulin first prevents NPH from contaminating the regular insulin vial. NPH is gently rolled, not shaken, to mix it.
Answer
A · Draw up the clear regular insulin first, then the cloudy NPH insulin
8.Pharmacology
Answer: C · A constant amount is eliminated per unit of time
Why this is the answer
When the metabolising enzymes are saturated, a fixed amount is removed per hour regardless of concentration, so the half-life gets longer as the level rises. Phenytoin and high-dose aspirin can behave the same way.
Answer
C · A constant amount is eliminated per unit of time