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 71 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.
71 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 60 kg patient on regular tobramycin doses is at steady state. The target is a peak of 10 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.25 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
Practice exercise (made-up values, not clinical guidance). A vial contains cefazolin 1000 mg as a powder. The practice label says to add 4.5 mL of sterile water; the powder adds 0.5 mL to the volume. The prescribed dose is 800 mg. What volume V do you draw up? Round to one decimal place.
1000 mg4.5 mL+0.5 mL800 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 1.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 300 mg. Draw up the dose: what volume V do you give?
500 mg1.6 mL + 0.4 mL300 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 52 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
80 units/kg52 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 500 mg in 250 mL. The order is 7.5 mcg/kg/min for a patient who weighs 70 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL7.5 mcg/kg/min70 kg
R = mL/h
7.PharmacologyMedium
What makes an overdose of tricyclic antidepressants such as amitriptyline especially dangerous?
AKidney stones
BCardiac arrhythmias and seizures
CSudden high blood glucose
DSevere liver failure within hours
8.PharmacologyHard
A patient has a serum potassium of 7.0 mmol/L (mEq/L) and peaked T waves on the ECG. Which drug is given first to protect the heart?
AOral sodium polystyrene sulfonate
BOral potassium chloride
CIntravenous furosemide
DIntravenous calcium gluconate
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 710 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 = 7·71 = 497 L
Amount of active drug needed
Vd·C = 497·1 = 497 mcg
Loading dose
LD = 497/(1·0.7) = 710 mcg
Answer
LD = 710 mcg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: D = 142.5 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 = 0.25·60 = 15 L
Dose
D = 15·(10 − 0.5) = 142.5 mg
Answer
D = 142.5 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 4 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
4.5 + 0.5 = 5 mL
Concentration
1000/5 = 200 mg/mL
Volume to give
V = 800/200 = 4 mL
Answer
V = 4 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
1.6 + 0.4 = 2 mL
C = 500/2 = 250 mg/mL
Volume
V = 300/250 = 1.2 mL
Answer
V = 1.2 mL
5.Pediatric & critical-care dosing
Answer: V = 0.83 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
80·52 = 4 160 units
Volume
V = 4160/5000 = 0.832 ≈ 0.83 mL
Answer
V = 0.83 mL
6.Pediatric & critical-care dosing
Answer: R = 15.8 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
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
7.5·70 = 525 mcg/min
525·60 = 31500 mcg/h
Pump rate
R = 31500/2000 = 15.75 ≈ 15.8 mL/h
Answer
R = 15.8 mL/h
7.Pharmacology
Answer: B · Cardiac arrhythmias and seizures
Why this is the answer
Tricyclics block cardiac sodium channels (widening the QRS complex) and have anticholinergic effects. In overdose they cause arrhythmias, hypotension, seizures and coma.
Answer
B · Cardiac arrhythmias and seizures
8.Pharmacology
Answer: D · Intravenous calcium gluconate
Why this is the answer
IV calcium stabilises the myocardial cell membrane within minutes and reduces the risk of arrhythmia. Other treatments then shift potassium into cells (insulin with glucose) or remove it from the body.