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). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 50 mL/min. What infusion rate R in mg/h gives a steady-state level of 25 mg/L?
CL = 50 mL/minCss = 25 mg/L
R = mg/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 53 kg patient takes oral aminophylline (S = 0.8, F = 1) every 12 h. The theophylline clearance is 0.05 L/kg/h. What dose D in mg gives an average steady-state level of 15 mg/L?
A solution has a ratio strength of 1:1000. You need 0.9 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.9 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 9.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 110 mg. Draw up the dose: what volume V do you give?
500 mg9.6 mL + 0.4 mL110 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 100 units of regular insulin in 100 mL runs at 4 mL/h. How many units per hour D does the patient receive?
100 units/100 mL4 mL/h
D = units/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 72 kg has an order for nitroglycerin at 15 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 mL15 mcg/min72 kg
R = mL/h
7.PharmacologyMedium
Which assessment is most important during IV mannitol therapy?
APlatelet count and signs of bleeding
BLiver enzymes and signs of jaundice
CUrine output, electrolytes and signs of fluid overload
DBlood glucose before meals and signs of hypoglycaemia
8.PharmacologyHard
A patient who takes clonidine stopped it suddenly two days ago. He is now agitated, has a headache and his blood pressure is very high. What is the most likely explanation?
ANormal variation unrelated to the medication
BAn allergic reaction to clonidine
CRebound hypertension from abrupt clonidine withdrawal
DClonidine toxicity due to slow excretion by the kidneys
3Solutions
1.Clinical pharmacokinetics
Answer: R = 75 mg/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.
Clearance in L/h
50·60/1000 = 3 L/h
Infusion rate
R = 3·25 = 75 mg/h
Answer
R = 75 mg/h
2.Clinical pharmacokinetics
Answer: D = 596.3 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.
Clearance
CL = 0.05·53 = 2.65 L/h
Dose
D = Css,avg·CL·τ/(S·F) = 15·2.65·12/(0.8·1) = 596.3 mg
Answer
D = 596.3 mg
3.Pharmacy calculations
Answer: V = 0.9 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 = 0.9/1 = 0.9 mL
Answer
V = 0.9 mL
4.Pharmacy calculations
Answer: V = 2.2 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
9.6 + 0.4 = 10 mL
C = 500/10 = 50 mg/mL
Volume
V = 110/50 = 2.2 mL
Answer
V = 2.2 mL
5.Pediatric & critical-care dosing
Answer: D = 4 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
100/100 = 1 units/mL
Units per hour
D = 4·1 = 4 units/h
Answer
D = 4 units/h
6.Pediatric & critical-care dosing
Answer: R = 4.5 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.
15·60 = 900 mcg/h
Pump rate
R = 900/200 = 4.5 mL/h
Answer
R = 4.5 mL/h
7.Pharmacology
Answer: C · Urine output, electrolytes and signs of fluid overload
Why this is the answer
Mannitol draws fluid into the circulation before it is excreted, which can cause heart failure and pulmonary oedema. The large diuresis can cause dehydration and electrolyte imbalance, so output and electrolytes are monitored.
Answer
C · Urine output, electrolytes and signs of fluid overload
8.Pharmacology
Answer: C · Rebound hypertension from abrupt clonidine withdrawal
Why this is the answer
Clonidine is a central alpha-2 agonist. Stopping it suddenly lets sympathetic activity surge, causing rebound hypertension, so it is tapered gradually.
Answer
C · Rebound hypertension from abrupt clonidine withdrawal