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). After an IV dose of tobramycin, the level is 8 mg/L at 1 h and 1.4 mg/L at 6 h. Assume first-order elimination. Find the half-life t½.
C1 = 8 mg/L (1 h)C2 = 1.4 mg/L (6 h)
t½ = h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 67 kg patient on regular gentamicin doses is at steady state. The target is a peak of 6 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?
A solution has a ratio strength of 1:1000. You need 0.21 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.21 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 4.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 25 mg. Draw up the dose: what volume V do you give?
250 mg4.2 mL + 0.8 mL25 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 102 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg102 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 65 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL10 mcg/kg/min65 kg
R = mL/h
7.PharmacologyMedium
A woman taking the combined pill should seek care urgently for which symptom?
ASlight nausea in the first few weeks
BA painful, swollen calf or sudden chest pain
CLight spotting between periods early on
DMild breast tenderness in the first month
8.PharmacologyHard
A patient taking azathioprine is prescribed allopurinol for gout. What is the main danger?
AGout becomes worse because allopurinol is inactivated by azathioprine
BLiver enzyme induction, making azathioprine ineffective
CSevere bone marrow suppression, because azathioprine breakdown is reduced
DSevere hypertension from the combination
3Solutions
1.Clinical pharmacokinetics
Answer: t½ = 1.988 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.
Elimination rate constant
k = ln(8/1.4)/5 = 1.743/5 = 0.3486 h⁻¹
Half-life
t½ = 0.693/0.3486 = 1.988 h
Answer
t½ = 1.988 h
2.Clinical pharmacokinetics
Answer: D = 92.13 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 = 0.25·67 = 16.75 L
Dose
D = 16.75·(6 − 0.5) = 92.13 mg
Answer
D = 92.13 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 0.21 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 = 0.21/1 = 0.21 mL
Answer
V = 0.21 mL
4.Pharmacy calculations
Answer: V = 0.5 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
4.2 + 0.8 = 5 mL
C = 250/5 = 50 mg/mL
Volume
V = 25/50 = 0.5 mL
Answer
V = 0.5 mL
5.Pediatric & critical-care dosing
Answer: V = 1.6 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
80·102 = 8 160 units
Volume
V = 8160/5000 = 1.632 ≈ 1.6 mL
Answer
V = 1.6 mL
6.Pediatric & critical-care dosing
Answer: R = 24.4 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
10·65 = 650 mcg/min
650·60 = 39000 mcg/h
Pump rate
R = 39000/1600 = 24.38 ≈ 24.4 mL/h
Answer
R = 24.4 mL/h
7.Pharmacology
Answer: B · A painful, swollen calf or sudden chest pain
Why this is the answer
Combined hormonal contraception increases the risk of venous thromboembolism and, rarely, stroke. Leg pain or swelling, chest pain, breathlessness, severe headache or vision changes need urgent assessment.
Answer
B · A painful, swollen calf or sudden chest pain
8.Pharmacology
Answer: C · Severe bone marrow suppression, because azathioprine breakdown is reduced
Why this is the answer
Azathioprine is converted to mercaptopurine, which is partly inactivated by xanthine oxidase. Allopurinol blocks this enzyme, so levels rise and dangerous myelosuppression can occur unless the dose is greatly reduced or the combination avoided.
Answer
C · Severe bone marrow suppression, because azathioprine breakdown is reduced