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 73 kg patient is to be loaded intravenously with aminophylline to reach a theophylline level of 10 mg/L. The volume of distribution is 0.5 L/kg and the salt factor is S = 0.8. Find the loading dose LD of aminophylline in mg.
73 kgVd = 0.5 L/kgC = 10 mg/LS = 0.8
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 92 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.04 L/kg/h. Each dose is 300 mg of theophylline. Find the average steady-state level Css,avg.
CL = 0.04 L/kg/hτ = 12 hS = 1F = 192 kgD = 300 mg
Css,avg = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.24 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.24 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 1.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 600 mg. Draw up the dose: what volume V do you give?
1000 mg1.4 mL + 0.6 mL600 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 250 mL. The order is 18 units/kg/h for a patient who weighs 101 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL18 units/kg/h101 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 96 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/min96 kg
R = mL/h
7.PharmacologyMedium
A patient receives lactulose for hepatic encephalopathy. Which finding shows that it is working?
ATen watery stools a day and a low serum potassium
BNo bowel movement for three days, with less confusion than before
CBetter alertness and orientation, with two to three soft stools a day
DHigher blood ammonia with improved appetite
8.PharmacologyHard
Beta-lactam antibiotics show time-dependent killing. What does this mean for administration?
ADoses should be given on time at evenly spaced intervals
BA single very large daily dose works best
CDoses can be given at any time as long as the daily total is right
DDoses should be given only when the patient has a fever
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 456.3 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 = 0.5·73 = 36.5 L
Amount of active drug needed
Vd·C = 36.5·10 = 365 mg
Loading dose
LD = 365/(0.8·1) = 456.3 mg
Answer
LD = 456.3 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: Css,avg = 6.793 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.
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 = 0.24/1 = 0.24 mL
Answer
V = 0.24 mL
4.Pharmacy calculations
Answer: V = 1.2 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
1.4 + 0.6 = 2 mL
C = 1000/2 = 500 mg/mL
Volume
V = 600/500 = 1.2 mL
Answer
V = 1.2 mL
5.Pediatric & critical-care dosing
Answer: R = 18.2 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
18·101 = 1 818 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 1818/100 = 18.18 ≈ 18.2 mL/h
Answer
R = 18.2 mL/h
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: C · Better alertness and orientation, with two to three soft stools a day
Why this is the answer
Lactulose is adjusted to give about two to three soft stools a day and to lower ammonia, improving mental status. Excessive diarrhoea can cause dehydration and electrolyte loss.
Answer
C · Better alertness and orientation, with two to three soft stools a day
8.Pharmacology
Answer: A · Doses should be given on time at evenly spaced intervals
Why this is the answer
For beta-lactams, efficacy depends on the time the drug level stays above the minimum inhibitory concentration. Evenly spaced, on-time doses, or extended infusions, support this.
Answer
A · Doses should be given on time at evenly spaced intervals