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 550 mL/min. What infusion rate R in mg/min keeps the steady-state level at 3 mg/L?
CL = 550 mL/minCss = 3 mg/L
R = mg/min
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient's tobramycin half-life is 2.5 h. The target is a peak of 6 mg/L and a trough of 0.5 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.
t½ = 2.5 hCpeak = 6 mg/LCtrough = 0.5 mg/L
τ = h
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 3.2 mL of diluent. The prescribed dose is 2 400 000 units. What volume V do you draw up? Round to one decimal place.
3.2 mL → 1 000 000 units/mL2 400 000 units
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 450 mL of 30% dextrose by mixing 70% and 10% dextrose. How many mL V of the 70% solution do you need? Round to the nearest whole mL.
70%10%30%450 mL
V = mL
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 20 units/kg/h for a patient who weighs 56 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL20 units/kg/h56 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 7.5 mcg/kg/min for a patient who weighs 76 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL7.5 mcg/kg/min76 kg
R = mL/h
7.PharmacologyMedium
A patient with a peanut allergy is taught to use an adrenaline auto-injector. Which statement is correct?
AThere is no need to see a doctor if the swelling goes down
BUse it only if the antihistamine has not worked after an hour
CKeep it at home so it is not lost
DCall emergency services after using it, even if symptoms improve
8.PharmacologyHard
A patient who uses insulin is taught sick-day rules. Which statement shows a need for further teaching?
A"I will seek help if I keep vomiting or have ketones."
B"I will check my blood glucose and ketones more often while I am ill."
C"If I am ill and not eating, I will stop my insulin completely."
D"I will keep drinking fluids, even if I cannot eat much."
3Solutions
1.Clinical pharmacokinetics
Answer: R = 1.65 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
550 mL/min = 0.55 L/min
Infusion rate
R = 0.55·3 = 1.65 mg/min
Answer
R = 1.65 mg/min
2.Clinical pharmacokinetics
Answer: τ = 9 h
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.
Rate constant
k = 0.693/2.5 = 0.2773 h⁻¹
Dosing interval
τ = ln(6/0.5)/0.2773 = 2.485/0.2773 = 8.962 ≈ 9 h
Answer
τ = 9 h
In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.
3.Pharmacy calculations
Answer: V = 2.4 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.
Concentration from the label
3.2 mL → 1 000 000 units/mL
Volume to give
V = 2 400 000/1 000 000 = 2.4 mL
Answer
V = 2.4 mL
4.Pharmacy calculations
Answer: V = 150 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
70%: 30 − 10 = 20 parts
10%: 70 − 30 = 40 parts
total: 60 parts
Share the volume
V = 450·20/60 = 150 mL
Answer
V = 150 mL
Check: 150 mL of 70% + 300 mL of 10% = 450 mL.
5.Pediatric & critical-care dosing
Answer: R = 22.4 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
20·56 = 1 120 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1120/50 = 22.4 mL/h
Answer
R = 22.4 mL/h
6.Pediatric & critical-care dosing
Answer: R = 17.1 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
7.5·76 = 570 mcg/min
570·60 = 34200 mcg/h
Pump rate
R = 34200/2000 = 17.1 mL/h
Answer
R = 17.1 mL/h
7.Pharmacology
Answer: D · Call emergency services after using it, even if symptoms improve
Why this is the answer
Anaphylaxis can recur after the adrenaline wears off (a biphasic reaction). The person always calls for help after using it, carries two auto-injectors and uses adrenaline early.
Answer
D · Call emergency services after using it, even if symptoms improve
8.Pharmacology
Answer: C · "If I am ill and not eating, I will stop my insulin completely."
Why this is the answer
Stress hormones during illness often raise glucose, so basal insulin is usually continued and doses may need adjusting. Stopping insulin in type 1 diabetes can lead to ketoacidosis.
Answer
C · "If I am ill and not eating, I will stop my insulin completely."