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 90 mg of gentamicin. The level back-extrapolated to time zero is 6 mg/L and the half-life is 2 h. Find the clearance CL in L/h.
D = 90 mgC₀ = 6 mg/Lt½ = 2 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 67 kg patient takes oral theophylline (F = 1) every 8 h. The clearance is 0.035 L/kg/h. What dose D in mg gives an average steady-state level of 12 mg/L?
Practice exercise (made-up values, not clinical guidance). A vial contains cefazolin 1000 mg as a powder. The practice label says to add 4.5 mL of sterile water; the powder adds 0.5 mL to the volume. The prescribed dose is 500 mg. What volume V do you draw up? Round to one decimal place.
1000 mg4.5 mL+0.5 mL500 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 600 mL of 13% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 3% solution do you need? Round to the nearest whole mL.
23%3%13%600 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 16 units/kg/h for a patient who weighs 57 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL16 units/kg/h57 kg
R = mL/h
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 10 mcg/kg/min for a patient who weighs 105 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL10 mcg/kg/min105 kg
R = mL/h
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
A patient on weekly methotrexate is prescribed trimethoprim for a urinary infection. What is the main risk?
ASevere hypertension from the combination
BLoss of antibiotic effect because methotrexate binds trimethoprim
CBone marrow suppression, because both drugs inhibit folate metabolism
DHypoglycaemia from reduced liver glucose output
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 5.199 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 = 90/6 = 15 L
Rate constant
k = 0.693/2 = 0.3466 h⁻¹
Clearance
CL = 0.3466·15 = 5.199 L/h
Answer
CL = 5.199 L/h
2.Clinical pharmacokinetics
Answer: D = 225.1 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.
Clearance
CL = 0.035·67 = 2.345 L/h
Dose
D = Css,avg·CL·τ/(S·F) = 12·2.345·8/(1·1) = 225.1 mg
Answer
D = 225.1 mg
3.Pharmacy calculations
Answer: V = 2.5 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
4.5 + 0.5 = 5 mL
Concentration
1000/5 = 200 mg/mL
Volume to give
V = 500/200 = 2.5 mL
Answer
V = 2.5 mL
4.Pharmacy calculations
Answer: V = 300 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
23%: 13 − 3 = 10 parts
3%: 23 − 13 = 10 parts
total: 20 parts
Share the volume
V = 600·10/20 = 300 mL
Answer
V = 300 mL
Check: 300 mL of 23% + 300 mL of 3% = 600 mL.
5.Pediatric & critical-care dosing
Answer: R = 22.8 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
16·57 = 912 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 912/40 = 22.8 mL/h
Answer
R = 22.8 mL/h
6.Pediatric & critical-care dosing
Answer: R = 31.5 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
10·105 = 1050 mcg/min
1050·60 = 63000 mcg/h
Pump rate
R = 63000/2000 = 31.5 mL/h
Answer
R = 31.5 mL/h
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: C · 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
C · Bone marrow suppression, because both drugs inhibit folate metabolism