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 has a lidocaine clearance of 500 mL/min. What infusion rate R in mg/min keeps the steady-state level at 2 mg/L?
CL = 500 mL/minCss = 2 mg/L
R = mg/min
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 98 kg patient on regular tobramycin doses is at steady state. The target is a peak of 8 mg/L and a trough of 1 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?
98 kgVd = 0.3 L/kgCpeak = 8 mg/LCtrough = 1 mg/L
D = mg
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefuroxime 750 mg as a powder. The practice label says to add 7.2 mL of sterile water; the powder adds 0.3 mL to the volume. The prescribed dose is 600 mg. What volume V do you draw up? Round to one decimal place.
750 mg7.2 mL+0.3 mL600 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 150 g of 2.5% hydrocortisone ointment. How many grams m of 0.5% hydrocortisone ointment must you add to make a 1% ointment? Round to the nearest whole gram.
150 g · 2.5%0.5%1%
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 7 units/h. Find the pump rate R in mL/h. Round to one decimal place.
100 units/100 mL7 units/h
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 33 mL/h. The patient weighs 71 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL33 mL/h71 kg
D = mcg/kg/min
7.PharmacologyMedium
Which antihypertensive class can raise blood glucose and uric acid levels, sometimes triggering gout?
AAngiotensin II receptor blockers
BACE inhibitors
CThiazide diuretics
DAlpha-1 blockers
8.PharmacologyHard
A patient on digoxin is started on amiodarone. What change should the nurse expect?
AAmiodarone levels fall to zero
BDigoxin levels fall sharply, so the digoxin dose is doubled
CDigoxin levels rise, so the digoxin dose is often reduced
DNo interaction is expected
3Solutions
1.Clinical pharmacokinetics
Answer: R = 1 mg/min
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/min
500 mL/min = 0.5 L/min
Infusion rate
R = 0.5·2 = 1 mg/min
Answer
R = 1 mg/min
2.Clinical pharmacokinetics
Answer: D = 205.8 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 = 0.3·98 = 29.4 L
Dose
D = 29.4·(8 − 1) = 205.8 mg
Answer
D = 205.8 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 6 mL
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Final volume
7.2 + 0.3 = 7.5 mL
Concentration
750/7.5 = 100 mg/mL
Volume to give
V = 600/100 = 6 mL
Answer
V = 6 mL
4.Pharmacy calculations
Answer: m = 450 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
2.5%: 1 − 0.5 = 0.5 parts
0.5%: 2.5 − 1 = 1.5 parts
Scale to the amount you have
m = 150·1.5/0.5 = 450 g
Answer
m = 450 g
Check: 150 g + 450 g = 600 g of 1% ointment.
5.Pediatric & critical-care dosing
Answer: R = 7 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.
Concentration
100/100 = 1 units/mL
Pump rate
R = 7/1 = 7 mL/h
Answer
R = 7 mL/h
6.Pediatric & critical-care dosing
Answer: D = 7.7 mcg/kg/min
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
250 000/250 = 1000 mcg/mL
Micrograms per minute
33·1000 = 33000 mcg/h
33000/60 = 550 mcg/min
Per kilogram
D = 550/71 = 7.746 ≈ 7.7 mcg/kg/min
Answer
D = 7.7 mcg/kg/min
7.Pharmacology
Answer: C · Thiazide diuretics
Why this is the answer
Thiazide diuretics reduce uric acid excretion and can worsen glucose tolerance. They also cause low potassium and sodium, so electrolytes are monitored.
Answer
C · Thiazide diuretics
8.Pharmacology
Answer: C · Digoxin levels rise, so the digoxin dose is often reduced
Why this is the answer
Amiodarone inhibits P-glycoprotein and reduces digoxin clearance, so digoxin levels rise. The digoxin dose is often reduced, and the patient is monitored for bradycardia and toxicity; amiodarone also raises warfarin levels.
Answer
C · Digoxin levels rise, so the digoxin dose is often reduced