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 98 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.
98 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 63-year-old woman weighs 60 kg and has a serum creatinine of 1.7 mg/dL (150 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual levetiracetam dose is 1000 mg for a creatinine clearance of 100 mL/min, and a fraction fe = 0.66 of the drug is excreted unchanged by the kidneys. Using the Dettli dose fraction Q = 1 − fe·(1 − CrCl/normal CrCl), find the adjusted dose D. Round to the nearest whole number.
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 1000 mg as a powder. The practice label says to add 3.5 mL of sterile water; the powder adds 0.5 mL to the volume. What is the concentration C in mg/mL after reconstitution?
1000 mg3.5 mL+0.5 mL
C = mg/mL
4.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 4.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 920 mg. Draw up the dose: what volume V do you give?
2000 mg4.4 mL + 0.6 mL920 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 60 units/kg for a patient who weighs 94 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg94 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 800 mg in 500 mL. The order is 10 mcg/kg/min for a patient who weighs 110 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL10 mcg/kg/min110 kg
R = mL/h
7.PharmacologyMedium
Why should long-term oral corticosteroids not be stopped suddenly?
AThe immune system would immediately attack the liver and adrenal glands
BStopping causes a sudden rise in blood glucose
CThe adrenal glands are suppressed and may not make enough cortisol
DThe drug forms toxic metabolites when stopped
8.PharmacologyHard
A man taking doxazosin for hypertension starts sildenafil for erectile dysfunction. What is the main risk?
AHyperkalaemia
BSevere hypertension and a pounding headache
CBronchospasm
DSymptomatic low blood pressure and fainting
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 980 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 = 7·98 = 686 L
Amount of active drug needed
Vd·C = 686·1 = 686 mcg
Loading dose
LD = 686/(1·0.7) = 980 mcg
Answer
LD = 980 mcg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: D = 552 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.
Creatinine clearance (Cockcroft–Gault)
CrCl = (140 − 63)·60/(72·1.7)·0.85 = 32.08 mL/min
Dose fraction (Dettli)
Q = 1 − 0.66·(1 − 32.08/100) = 0.5517
Adjusted dose
D = 0.5517·1000 = 551.8 ≈ 552 mg
Answer
D = 552 mg
In practice the dose is rounded to a convenient amount and checked against the product information.
3.Pharmacy calculations
Answer: C = 250 mg/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
3.5 + 0.5 = 4 mL
Concentration
C = 1000/4 = 250 mg/mL
Answer
C = 250 mg/mL
4.Pharmacy calculations
Answer: V = 2.3 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
4.4 + 0.6 = 5 mL
C = 2000/5 = 400 mg/mL
Volume
V = 920/400 = 2.3 mL
Answer
V = 2.3 mL
5.Pediatric & critical-care dosing
Answer: V = 1.1 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
60·94 = 5 640 units
Volume
V = 5640/5000 = 1.128 ≈ 1.1 mL
Answer
V = 1.1 mL
6.Pediatric & critical-care dosing
Answer: R = 41.3 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
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
10·110 = 1100 mcg/min
1100·60 = 66000 mcg/h
Pump rate
R = 66000/1600 = 41.25 ≈ 41.3 mL/h
Answer
R = 41.3 mL/h
7.Pharmacology
Answer: C · The adrenal glands are suppressed and may not make enough cortisol
Why this is the answer
Steroid therapy suppresses the hypothalamic–pituitary–adrenal axis. Sudden withdrawal can cause an adrenal crisis, so doses are reduced gradually.
Answer
C · The adrenal glands are suppressed and may not make enough cortisol
8.Pharmacology
Answer: D · Symptomatic low blood pressure and fainting
Why this is the answer
Alpha blockers and PDE5 inhibitors both cause vasodilation, so together they can cause marked hypotension. Patients should be stable on the alpha blocker, and the PDE5 inhibitor is started at a low dose.