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 0.8 mg/L at 7 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 6 mg/L (1 h)C2 = 0.8 mg/L (7 h)
k = h⁻¹
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 62 kg patient on regular tobramycin 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 0.3 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 cefuroxime 750 mg as a powder. The practice label says to add 7.2 mL of sterile water; the powder adds 0.3 mL to the volume. What is the concentration C in mg/mL after reconstitution?
750 mg7.2 mL+0.3 mL
C = mg/mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 200 mL of 45% ethanol from a 90% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
90%0%45%200 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 60 units/kg for a patient who weighs 58 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
60 units/kg58 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 2.5 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.
500 mg/250 mL2.5 mcg/kg/min80 kg
R = mL/h
7.PharmacologyMedium
Which adverse effects are typical of donepezil?
AHair loss and skin pigmentation
BNausea, diarrhoea and a slow heart rate
CWeight gain and high blood glucose
DDry mouth, constipation and a fast heart rate
8.PharmacologyHard
A patient who has had several courses of bleomycin develops a dry cough and worsening breathlessness. What should the nurse suspect?
APulmonary fibrosis from bleomycin
BHeart failure from bleomycin
CAsthma caused by anxiety
DA normal effect that will pass in a day
3Solutions
1.Clinical pharmacokinetics
Answer: k = 0.3358 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(6/0.8)/6 = 2.015/6 = 0.3358 h⁻¹
Answer
k = 0.3358 h⁻¹
2.Clinical pharmacokinetics
Answer: D = 102.3 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 = 0.3·62 = 18.6 L
Dose
D = 18.6·(6 − 0.5) = 102.3 mg
Answer
D = 102.3 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: C = 100 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
7.2 + 0.3 = 7.5 mL
Concentration
C = 750/7.5 = 100 mg/mL
Answer
C = 100 mg/mL
4.Pharmacy calculations
Answer: V = 100 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
90%: 45 − 0 = 45 parts
0%: 90 − 45 = 45 parts
total: 90 parts
Water
V = 200·45/90 = 100 mL
Answer
V = 100 mL
Check: 100 mL of 90% contains 90 mL of drug, which is 45% of 200 mL. This assumes the volumes simply add up; in practice ethanol is made up to volume.
5.Pediatric & critical-care dosing
Answer: V = 0.7 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
60·58 = 3 480 units
Volume
V = 3480/5000 = 0.696 ≈ 0.7 mL
Answer
V = 0.7 mL
6.Pediatric & critical-care dosing
Answer: R = 6 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
2.5·80 = 200 mcg/min
200·60 = 12000 mcg/h
Pump rate
R = 12000/2000 = 6 mL/h
Answer
R = 6 mL/h
7.Pharmacology
Answer: B · Nausea, diarrhoea and a slow heart rate
Why this is the answer
Cholinesterase inhibitors cause cholinergic effects such as nausea, vomiting, diarrhoea and bradycardia. Patients are watched for dizziness and fainting from a slow pulse.
Answer
B · Nausea, diarrhoea and a slow heart rate
8.Pharmacology
Answer: A · Pulmonary fibrosis from bleomycin
Why this is the answer
Bleomycin can cause pneumonitis and pulmonary fibrosis, especially at higher cumulative doses. New respiratory symptoms are reported, and lung function may be monitored.