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). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 105 mL/min. What infusion rate R in mg/h gives a steady-state level of 20 mg/L?
CL = 105 mL/minCss = 20 mg/L
R = mg/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 8 h. What is the level C after 19 h?
R = 100 mg/hCL = 5 L/ht½ = 8 ht = 19 h
C = mg/L
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 8.2 mL of diluent. The prescribed dose is 300 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL300 000 units
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 300 mL of 20% dextrose by mixing 50% and 10% dextrose. How many mL V of the 50% solution do you need? Round to the nearest whole mL.
50%10%20%300 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 60 units/kg for a patient who weighs 85 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg85 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 4 mL/h. The patient weighs 82 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL4 mL/h82 kg
D = mcg/kg/min
7.PharmacologyMedium
How does sucralfate help a peptic ulcer heal?
AIt forms a protective coating over the ulcer base
BIt kills Helicobacter pylori directly
CIt blocks histamine H2 receptors in the stomach
DIt neutralises acid by releasing bicarbonate
8.PharmacologyHard
Why are antipsychotics used with great caution in older people with dementia?
AThey always cure the dementia and stop all behaviour problems
BThey cause severe hypoglycaemia in older people
CThey are not absorbed in people over 65
DThey are linked to a higher risk of stroke and death
3Solutions
1.Clinical pharmacokinetics
Answer: R = 126 mg/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.
Clearance in L/h
105·60/1000 = 6.3 L/h
Infusion rate
R = 6.3·20 = 126 mg/h
Answer
R = 126 mg/h
2.Clinical pharmacokinetics
Answer: C = 16.14 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 = 0.693/8 = 0.08664 h⁻¹
Level after the given time
C = 20·(1 − e−0.08664·19) = 16.14 mg/L
Answer
C = 16.14 mg/L
3.Pharmacy calculations
Answer: V = 0.6 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
8.2 mL → 500 000 units/mL
Volume to give
V = 300 000/500 000 = 0.6 mL
Answer
V = 0.6 mL
4.Pharmacy calculations
Answer: V = 75 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
50%: 20 − 10 = 10 parts
10%: 50 − 20 = 30 parts
total: 40 parts
Share the volume
V = 300·10/40 = 75 mL
Answer
V = 75 mL
Check: 75 mL of 50% + 225 mL of 10% = 300 mL.
5.Pediatric & critical-care dosing
Answer: V = 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
60·85 = 5 100 units
Volume
V = 5100/5000 = 1.02 ≈ 1 mL
Answer
V = 1 mL
6.Pediatric & critical-care dosing
Answer: D = 1.3 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
400 000/250 = 1600 mcg/mL
Micrograms per minute
4·1600 = 6400 mcg/h
6400/60 = 106.7 mcg/min
Per kilogram
D = 106.7/82 = 1.301 ≈ 1.3 mcg/kg/min
Answer
D = 1.3 mcg/kg/min
7.Pharmacology
Answer: A · It forms a protective coating over the ulcer base
Why this is the answer
Sucralfate forms a gel-like barrier that sticks to the ulcer and protects it from acid and pepsin. It is taken on an empty stomach and can reduce the absorption of other drugs taken at the same time.
Answer
A · It forms a protective coating over the ulcer base
8.Pharmacology
Answer: D · They are linked to a higher risk of stroke and death
Why this is the answer
In older people with dementia, antipsychotics increase the risk of stroke and death. Non-drug approaches are tried first, and antipsychotics are used at low doses for short periods if needed.
Answer
D · They are linked to a higher risk of stroke and death