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 patient receives an IV bolus of 220 mg of tobramycin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 3 h. Find the volume of distribution Vd.
D = 220 mgC₀ = 10 mg/Lt½ = 3 h
Vd = L
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient's tobramycin half-life is 3.5 h. The target is a peak of 6 mg/L and a trough of 1 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.
t½ = 3.5 hCpeak = 6 mg/LCtrough = 1 mg/L
τ = h
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 500 mg as a powder. The practice label says to add 1.8 mL of sterile water; the powder adds 0.2 mL to the volume. What is the concentration C in mg/mL after reconstitution?
500 mg1.8 mL+0.2 mL
C = mg/mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 900 mL of 10% hydrogen peroxide from a 30% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
30%0%10%900 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 250 mL. The order is 12 units/kg/h for a patient who weighs 82 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL12 units/kg/h82 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 24 mL/h. The patient weighs 105 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL24 mL/h105 kg
D = mcg/kg/min
7.PharmacologyMedium
After several years of levodopa treatment, which problem is common?
APermanent hearing loss
BDyskinesias and "on–off" fluctuations in response
CComplete and permanent loss of all Parkinson's symptoms
DSevere hypoglycaemia after each dose
8.PharmacologyHard
Ten days after chemotherapy, a patient has a temperature of 38.5 °C (101.3 °F) but says she feels fine. What should happen?
AStart oral antibiotics only if a rash develops
BWait 48 hours to see whether the fever settles
CParacetamol at home and review at the next routine clinic visit
DUrgent cultures and IV broad-spectrum antibiotics without delay
3Solutions
1.Clinical pharmacokinetics
Answer: Vd = 22 L
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 = 220/10 = 22 L
Answer
Vd = 22 L
2.Clinical pharmacokinetics
Answer: τ = 9 h
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.
Rate constant
k = 0.693/3.5 = 0.198 h⁻¹
Dosing interval
τ = ln(6/1)/0.198 = 1.792/0.198 = 9.047 ≈ 9 h
Answer
τ = 9 h
In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.
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
1.8 + 0.2 = 2 mL
Concentration
C = 500/2 = 250 mg/mL
Answer
C = 250 mg/mL
4.Pharmacy calculations
Answer: V = 600 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
30%: 10 − 0 = 10 parts
0%: 30 − 10 = 20 parts
total: 30 parts
Water
V = 900·20/30 = 600 mL
Answer
V = 600 mL
Check: 300 mL of 30% contains 90 g of drug, which is 10% of 900 mL.
5.Pediatric & critical-care dosing
Answer: R = 9.8 mL/h
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 per hour
12·82 = 984 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 984/100 = 9.84 ≈ 9.8 mL/h
Answer
R = 9.8 mL/h
6.Pediatric & critical-care dosing
Answer: D = 3.8 mcg/kg/min
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
250 000/250 = 1000 mcg/mL
Micrograms per minute
24·1000 = 24000 mcg/h
24000/60 = 400 mcg/min
Per kilogram
D = 400/105 = 3.81 ≈ 3.8 mcg/kg/min
Answer
D = 3.8 mcg/kg/min
7.Pharmacology
Answer: B · Dyskinesias and "on–off" fluctuations in response
Why this is the answer
Long-term levodopa use often leads to motor fluctuations, with periods of good control and periods of stiffness, and to dyskinesias at peak dose. Dose timing and add-on drugs are adjusted to manage this.
Answer
B · Dyskinesias and "on–off" fluctuations in response
8.Pharmacology
Answer: D · Urgent cultures and IV broad-spectrum antibiotics without delay
Why this is the answer
Fever during neutropenia is treated as a medical emergency because infection can progress rapidly. Cultures are taken and empirical IV antibiotics are started promptly, ideally within one hour.
Answer
D · Urgent cultures and IV broad-spectrum antibiotics without delay