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 130 mg of tobramycin. The level back-extrapolated to time zero is 8 mg/L and the half-life is 2 h. Find the clearance CL in L/h.
D = 130 mgC₀ = 8 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 5 L/h and the half-life is 6 h. What is the level C after 2 h?
R = 100 mg/hCL = 5 L/ht½ = 6 ht = 2 h
C = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.8 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.8 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 2.3 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 680 mg. Draw up the dose: what volume V do you give?
1000 mg2.3 mL + 0.2 mL680 mg
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 66 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg66 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 64 kg has an order for nitroglycerin at 30 mcg/min. The bag contains 25 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
25 mg/250 mL30 mcg/min64 kg
R = mL/h
7.PharmacologyMedium
Typical antipsychotics such as haloperidol work mainly by blocking:
ADopamine D2 receptors
BSerotonin reuptake
CGABA-A receptors
DAcetylcholinesterase
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
BHypoglycaemia from reduced liver glucose output
CSevere hypertension from the combination
DLoss of antibiotic effect because methotrexate binds trimethoprim
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 5.632 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 = 130/8 = 16.25 L
Rate constant
k = 0.693/2 = 0.3466 h⁻¹
Clearance
CL = 0.3466·16.25 = 5.632 L/h
Answer
CL = 5.632 L/h
2.Clinical pharmacokinetics
Answer: C = 4.126 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 = 100/5 = 20 mg/L
Rate constant
k = 0.693/6 = 0.1155 h⁻¹
Level after the given time
C = 20·(1 − e−0.1155·2) = 4.126 mg/L
Answer
C = 4.126 mg/L
3.Pharmacy calculations
Answer: V = 8 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 = 0.8/0.1 = 8 mL
Answer
V = 8 mL
4.Pharmacy calculations
Answer: V = 1.7 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.
Final volume and concentration
2.3 + 0.2 = 2.5 mL
C = 1000/2.5 = 400 mg/mL
Volume
V = 680/400 = 1.7 mL
Answer
V = 1.7 mL
5.Pediatric & critical-care dosing
Answer: V = 1.1 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
80·66 = 5 280 units
Volume
V = 5280/5000 = 1.056 ≈ 1.1 mL
Answer
V = 1.1 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
25 000/250 = 100 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
30·60 = 1800 mcg/h
Pump rate
R = 1800/100 = 18 mL/h
Answer
R = 18 mL/h
7.Pharmacology
Answer: A · Dopamine D2 receptors
Why this is the answer
Haloperidol blocks D2 receptors in the mesolimbic pathway, reducing positive symptoms. Blocking D2 in other pathways causes extrapyramidal effects and raised prolactin.
Answer
A · Dopamine D2 receptors
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