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 gentamicin, the level is 6 mg/L at 1 h and 2 mg/L at 5 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 6 mg/L (1 h)C2 = 2 mg/L (5 h)
k = h⁻¹
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 71 kg patient has a digoxin level of 0.5 mcg/L; the target is 1 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?
71 kgVd = 7 L/kgC = 0.5 → 1 mcg/LF = 0.7
LD = mcg
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 18.2 mL of diluent. The prescribed dose is 400 000 units. What volume V do you draw up? Round to one decimal place.
18.2 mL → 250 000 units/mL400 000 units
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 300 mL of 20% dextrose by mixing 70% and 10% dextrose. How many mL V of the 70% solution do you need? Round to the nearest whole mL.
70%10%20%300 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 70 units/kg for a patient who weighs 51 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg51 kg1 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 6 mcg/kg/min for a patient who weighs 80 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL6 mcg/kg/min80 kg
R = mL/h
7.PharmacologyMedium
Which adverse effect is a well-known risk of zidovudine?
ARed–green colour blindness
BOrange-red colouring of the urine and tears
CGum overgrowth
DBone marrow suppression, especially anaemia
8.PharmacologyHard
Why is the TPMT enzyme often tested before azathioprine is started?
AHigh TPMT activity causes an allergic reaction to azathioprine
BLow TPMT activity causes toxic levels and marrow suppression
CTPMT testing shows whether the patient has tuberculosis
DTPMT is needed to absorb azathioprine from the gut
3Solutions
1.Clinical pharmacokinetics
Answer: k = 0.2747 h⁻¹
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(6/2)/4 = 1.099/4 = 0.2747 h⁻¹
Answer
k = 0.2747 h⁻¹
2.Clinical pharmacokinetics
Answer: LD = 355 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 = 7·71 = 497 L
Rise needed
1 − 0.5 = 0.5 mcg/L
Loading dose
LD = 497·0.5/(1·0.7) = 355 mcg
Answer
LD = 355 mcg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 1.6 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.
Concentration from the label
18.2 mL → 250 000 units/mL
Volume to give
V = 400 000/250 000 = 1.6 mL
Answer
V = 1.6 mL
4.Pharmacy calculations
Answer: V = 50 mL
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
70%: 20 − 10 = 10 parts
10%: 70 − 20 = 50 parts
total: 60 parts
Share the volume
V = 300·10/60 = 50 mL
Answer
V = 50 mL
Check: 50 mL of 70% + 250 mL of 10% = 300 mL.
5.Pediatric & critical-care dosing
Answer: V = 3.6 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
70·51 = 3 570 units
Volume
V = 3570/1000 = 3.57 ≈ 3.6 mL
Answer
V = 3.6 mL
6.Pediatric & critical-care dosing
Answer: R = 18 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
6·80 = 480 mcg/min
480·60 = 28800 mcg/h
Pump rate
R = 28800/1600 = 18 mL/h
Answer
R = 18 mL/h
7.Pharmacology
Answer: D · Bone marrow suppression, especially anaemia
Why this is the answer
Zidovudine, a nucleoside reverse transcriptase inhibitor, can cause anaemia and neutropenia. Blood counts are checked regularly during treatment.
Answer
D · Bone marrow suppression, especially anaemia
8.Pharmacology
Answer: B · Low TPMT activity causes toxic levels and marrow suppression
Why this is the answer
Thiopurine methyltransferase helps inactivate azathioprine and mercaptopurine. People with low or absent TPMT activity need much lower doses or another drug to avoid life-threatening myelosuppression.
Answer
B · Low TPMT activity causes toxic levels and marrow suppression