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 230 mg of gentamicin. The level back-extrapolated to time zero is 9 mg/L and the half-life is 2 h. Find the clearance CL in L/h.
D = 230 mgC₀ = 9 mg/Lt½ = 2 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 100 mg/h with no loading dose. The patient's clearance is 4 L/h and the half-life is 8 h. What is the level C after 20 h?
R = 100 mg/hCL = 4 L/ht½ = 8 ht = 20 h
C = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.72 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.72 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 120 g of 10% salicylic acid ointment. How many grams m of 2% salicylic acid ointment must you add to make a 5% ointment? Round to the nearest whole gram.
120 g · 10%2%5%
m = g
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 500 mL. The order is 16 units/kg/h for a patient who weighs 102 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL16 units/kg/h102 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 38 mL/h. The patient weighs 88 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL38 mL/h88 kg
D = mcg/kg/min
7.PharmacologyMedium
Patients taking metronidazole are usually advised to avoid:
ASunlight
BGrapefruit juice
CDairy products
DAlcohol
8.PharmacologyHard
A patient on weekly methotrexate is prescribed trimethoprim for a urinary infection. What is the main risk?
ABone marrow suppression, because both drugs inhibit folate metabolism
BSevere hypertension from the combination
CLoss of antibiotic effect because methotrexate binds trimethoprim
DHypoglycaemia from reduced liver glucose output
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 8.857 L/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.
Volume of distribution
Vd = 230/9 = 25.56 L
Rate constant
k = 0.693/2 = 0.3466 h⁻¹
Clearance
CL = 0.3466·25.56 = 8.857 L/h
Answer
CL = 8.857 L/h
2.Clinical pharmacokinetics
Answer: C = 20.58 mg/L
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.
Steady-state level
Css = 100/4 = 25 mg/L
Rate constant
k = 0.693/8 = 0.08664 h⁻¹
Level after the given time
C = 25·(1 − e−0.08664·20) = 20.58 mg/L
Answer
C = 20.58 mg/L
3.Pharmacy calculations
Answer: V = 7.2 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/10 000 mL = 0.1 mg/mL
Volume
V = 0.72/0.1 = 7.2 mL
Answer
V = 7.2 mL
4.Pharmacy calculations
Answer: m = 200 g
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
10%: 5 − 2 = 3 parts
2%: 10 − 5 = 5 parts
Scale to the amount you have
m = 120·5/3 = 200 g
Answer
m = 200 g
Check: 120 g + 200 g = 320 g of 5% ointment.
5.Pediatric & critical-care dosing
Answer: R = 32.6 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
16·102 = 1 632 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1632/50 = 32.64 ≈ 32.6 mL/h
Answer
R = 32.6 mL/h
6.Pediatric & critical-care dosing
Answer: D = 11.5 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
800 000/500 = 1600 mcg/mL
Micrograms per minute
38·1600 = 60800 mcg/h
60800/60 = 1013 mcg/min
Per kilogram
D = 1013/88 = 11.52 ≈ 11.5 mcg/kg/min
Answer
D = 11.5 mcg/kg/min
7.Pharmacology
Answer: D · Alcohol
Why this is the answer
Metronidazole can cause a disulfiram-like reaction with alcohol, with flushing, nausea and palpitations. Alcohol is avoided during treatment and for a short time after.
Answer
D · Alcohol
8.Pharmacology
Answer: A · Bone marrow suppression, because both drugs inhibit folate metabolism
Why this is the answer
Trimethoprim and methotrexate both inhibit dihydrofolate reductase, and trimethoprim also reduces methotrexate excretion. The combination can cause severe pancytopenia, so another antibiotic is chosen.
Answer
A · Bone marrow suppression, because both drugs inhibit folate metabolism