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 has a lidocaine clearance of 650 mL/min. What infusion rate R in mg/min keeps the steady-state level at 4 mg/L?
CL = 650 mL/minCss = 4 mg/L
R = mg/min
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 70 kg patient has a phenytoin level of 6 mg/L; the target is 15 mg/L. The drug is given intravenously as phenytoin sodium (S = 0.92), and the volume of distribution is 0.7 L/kg. What extra loading dose LD raises the level to the target?
70 kgVd = 0.7 L/kgC = 6 → 15 mg/LS = 0.92
LD = mg
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains oxacillin 2000 mg as a powder. The practice label says to add 11.5 mL of sterile water; the powder adds 1 mL to the volume. What is the concentration C in mg/mL after reconstitution?
2000 mg11.5 mL+1 mL
C = mg/mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 600 mL of 20% dextrose by mixing 50% and 10% dextrose. How many mL V of the 10% solution do you need? Round to the nearest whole mL.
50%10%20%600 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 80 units/kg for a patient who weighs 56 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
80 units/kg56 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 36 mL/h. The patient weighs 62 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL36 mL/h62 kg
D = mcg/kg/min
7.PharmacologyMedium
Why do patients taking clozapine need regular blood counts?
AIt can cause agranulocytosis
BIt changes the blood group
CIt often causes iron-deficiency anaemia
DIt raises the platelet count dangerously
8.PharmacologyHard
A patient with epilepsy needs pain relief. Why is tramadol used with caution?
AIt lowers the seizure threshold
BIt always causes respiratory arrest in epilepsy
CIt causes a sharp rise in blood glucose
DIt speeds up the metabolism of all antiepileptic drugs
3Solutions
1.Clinical pharmacokinetics
Answer: R = 2.6 mg/min
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.
Clearance in L/min
650 mL/min = 0.65 L/min
Infusion rate
R = 0.65·4 = 2.6 mg/min
Answer
R = 2.6 mg/min
2.Clinical pharmacokinetics
Answer: LD = 479.3 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 = 0.7·70 = 49 L
Rise needed
15 − 6 = 9 mg/L
Loading dose
LD = 49·9/(0.92·1) = 479.3 mg
Answer
LD = 479.3 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: C = 160 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
11.5 + 1 = 12.5 mL
Concentration
C = 2000/12.5 = 160 mg/mL
Answer
C = 160 mg/mL
4.Pharmacy calculations
Answer: V = 450 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
50%: 20 − 10 = 10 parts
10%: 50 − 20 = 30 parts
total: 40 parts
Share the volume
V = 600·30/40 = 450 mL
Answer
V = 450 mL
Check: 150 mL of 50% + 450 mL of 10% = 600 mL.
5.Pediatric & critical-care dosing
Answer: V = 0.9 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
80·56 = 4 480 units
Volume
V = 4480/5000 = 0.896 ≈ 0.9 mL
Answer
V = 0.9 mL
6.Pediatric & critical-care dosing
Answer: D = 15.5 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
400 000/250 = 1600 mcg/mL
Micrograms per minute
36·1600 = 57600 mcg/h
57600/60 = 960 mcg/min
Per kilogram
D = 960/62 = 15.48 ≈ 15.5 mcg/kg/min
Answer
D = 15.5 mcg/kg/min
7.Pharmacology
Answer: A · It can cause agranulocytosis
Why this is the answer
Clozapine can cause severe neutropenia (agranulocytosis). Regular white cell and neutrophil counts allow treatment to be stopped before life-threatening infection occurs.
Answer
A · It can cause agranulocytosis
8.Pharmacology
Answer: A · It lowers the seizure threshold
Why this is the answer
Tramadol can cause seizures, especially at high doses or with other drugs that lower the seizure threshold. Its serotonergic action also raises the risk of serotonin syndrome.