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 76 kg patient is to be loaded with digoxin tablets to reach a level of 1 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.
76 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 66 kg patient has a digoxin level of 0.4 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?
66 kgVd = 7 L/kgC = 0.4 → 0.8 mcg/LF = 0.7
LD = mcg
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 500 mg as a powder. The practice label says to add 1.8 mL of sterile water; the powder adds 0.2 mL to the volume. The prescribed dose is 200 mg. What volume V do you draw up? Round to one decimal place.
500 mg1.8 mL+0.2 mL200 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 2.3 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 110 mg. Draw up the dose: what volume V do you give?
250 mg2.3 mL + 0.2 mL110 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 80 units/kg for a patient who weighs 56 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg56 kg1 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 76 kg has an order for nitroglycerin at 5 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 mL5 mcg/min76 kg
R = mL/h
7.PharmacologyMedium
A patient is starting doxazosin, an alpha-1 blocker. What should the nurse advise about the first dose?
ATake it in the morning with a cup of strong coffee to stay alert
BTake it at bedtime, because it can cause dizziness and fainting
CExpect a short rise in blood pressure after the dose
DTake it only if the urine is darker than usual
8.PharmacologyHard
An older patient on amlodipine develops ankle swelling and is prescribed furosemide. She then becomes dizzy and falls. What does this sequence illustrate?
AEnzyme induction
BA type B allergic reaction
CA prescribing cascade
DDrug tolerance
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 760 mcg
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 = 7·76 = 532 L
Amount of active drug needed
Vd·C = 532·1 = 532 mcg
Loading dose
LD = 532/(1·0.7) = 760 mcg
Answer
LD = 760 mcg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: LD = 264 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 = 7·66 = 462 L
Rise needed
0.8 − 0.4 = 0.4 mcg/L
Loading dose
LD = 462·0.4/(1·0.7) = 264 mcg
Answer
LD = 264 mcg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 0.8 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
1.8 + 0.2 = 2 mL
Concentration
500/2 = 250 mg/mL
Volume to give
V = 200/250 = 0.8 mL
Answer
V = 0.8 mL
4.Pharmacy calculations
Answer: V = 1.1 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
2.3 + 0.2 = 2.5 mL
C = 250/2.5 = 100 mg/mL
Volume
V = 110/100 = 1.1 mL
Answer
V = 1.1 mL
5.Pediatric & critical-care dosing
Answer: V = 4.5 mL
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 needed
80·56 = 4 480 units
Volume
V = 4480/1000 = 4.48 ≈ 4.5 mL
Answer
V = 4.5 mL
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
25 000/250 = 100 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
5·60 = 300 mcg/h
Pump rate
R = 300/100 = 3 mL/h
Answer
R = 3 mL/h
7.Pharmacology
Answer: B · Take it at bedtime, because it can cause dizziness and fainting
Why this is the answer
Alpha-1 blockers dilate blood vessels and can cause marked orthostatic hypotension after the first dose. Taking it at bedtime and rising slowly reduces the risk of falls.
Answer
B · Take it at bedtime, because it can cause dizziness and fainting
8.Pharmacology
Answer: C · A prescribing cascade
Why this is the answer
In a prescribing cascade, an adverse effect of one drug is mistaken for a new condition and treated with another drug, which brings new risks. Amlodipine oedema does not respond well to diuretics; reviewing the original drug is better.