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). An 80 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 15 mg/L. The volume of distribution is 0.7 L/kg and the salt factor is S = 0.92. Find the loading dose LD of phenytoin sodium in mg.
80 kgVd = 0.7 L/kgC = 15 mg/LS = 0.92
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 95 kg patient takes oral aminophylline (S = 0.8, F = 1) every 8 h. The theophylline clearance is 0.03 L/kg/h. Each dose is 300 mg of aminophylline. Find the average steady-state level Css,avg.
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 1500 mL of 13% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 23% solution do you need? Round to the nearest whole mL.
23%3%13%1500 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 50 units of regular insulin in 50 mL runs at 10 mL/h. How many units per hour D does the patient receive?
50 units/50 mL10 mL/h
D = units/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 14 mL/h. The patient weighs 108 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL14 mL/h108 kg
D = mcg/kg/min
7.PharmacologyMedium
Which sign is typical of opioid toxicity?
APinpoint pupils
BHigh body temperature
CFast, deep breathing
DWidely dilated pupils
8.PharmacologyHard
Why is sildenafil contraindicated in a patient who uses nitrates for angina?
ABoth raise cGMP in vascular smooth muscle and can cause severe hypotension
BNitrates block the metabolism of sildenafil in the liver
CThe combination causes dangerous hyperkalaemia
DSildenafil blocks the conversion of nitrates into nitric oxide in the vessels
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 913 mg
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 = 0.7·80 = 56 L
Amount of active drug needed
Vd·C = 56·15 = 840 mg
Loading dose
LD = 840/(0.92·1) = 913 mg
Answer
LD = 913 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: Css,avg = 10.53 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.
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 = 750 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 = 1500·10/20 = 750 mL
Answer
V = 750 mL
Check: 750 mL of 23% + 750 mL of 3% = 1500 mL.
5.Pediatric & critical-care dosing
Answer: D = 10 units/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.
Concentration
50/50 = 1 units/mL
Units per hour
D = 10·1 = 10 units/h
Answer
D = 10 units/h
6.Pediatric & critical-care dosing
Answer: D = 2.2 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
14·1000 = 14000 mcg/h
14000/60 = 233.3 mcg/min
Per kilogram
D = 233.3/108 = 2.16 ≈ 2.2 mcg/kg/min
Answer
D = 2.2 mcg/kg/min
7.Pharmacology
Answer: A · Pinpoint pupils
Why this is the answer
Opioid toxicity classically causes pinpoint pupils, slow or shallow breathing and reduced consciousness. Naloxone reverses these effects.
Answer
A · Pinpoint pupils
8.Pharmacology
Answer: A · Both raise cGMP in vascular smooth muscle and can cause severe hypotension
Why this is the answer
Nitrates increase cGMP production through nitric oxide and sildenafil blocks its breakdown by PDE5. Together they cause excessive vasodilation and a dangerous fall in blood pressure.
Answer
A · Both raise cGMP in vascular smooth muscle and can cause severe hypotension