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). After an IV dose of tobramycin, the level is 10 mg/L at 2 h and 1.6 mg/L at 10 h. Assume first-order elimination. Find the half-life t½.
C1 = 10 mg/L (2 h)C2 = 1.6 mg/L (10 h)
t½ = h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 3 L/h. Each dose is 750 mg of vancomycin. Find the average steady-state level Css,avg.
CL = 3 L/hτ = 12 hS = 1F = 1D = 750 mg
Css,avg = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.68 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.68 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 50 g of 2.5% hydrocortisone ointment. How many grams m of 0.5% hydrocortisone ointment must you add to make a 1% ointment? Round to the nearest whole gram.
50 g · 2.5%0.5%1%
m = g
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 94 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg94 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 98 kg has an order for nitroglycerin at 5 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 mL5 mcg/min98 kg
R = mL/h
7.PharmacologyMedium
Which assessment is most important before giving a dose of IV morphine?
APupil size and hearing
BRespiratory rate and level of sedation
CBlood glucose and temperature, checked before each dose
DBowel sounds and urine colour
8.PharmacologyHard
Why can beta blockers mask the warning signs of hypoglycaemia in people with diabetes?
AThey cause hyperthermia that hides sweating
BThey raise blood glucose so that hypoglycaemia cannot occur at all
CThey block insulin release completely
DThey blunt adrenergic symptoms such as tremor and palpitations
3Solutions
1.Clinical pharmacokinetics
Answer: t½ = 3.026 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.
Elimination rate constant
k = ln(10/1.6)/8 = 1.833/8 = 0.2291 h⁻¹
Half-life
t½ = 0.693/0.2291 = 3.026 h
Answer
t½ = 3.026 h
2.Clinical pharmacokinetics
Answer: Css,avg = 20.83 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.
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 = 0.68/0.1 = 6.8 mL
Answer
V = 6.8 mL
4.Pharmacy calculations
Answer: m = 150 g
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
2.5%: 1 − 0.5 = 0.5 parts
0.5%: 2.5 − 1 = 1.5 parts
Scale to the amount you have
m = 50·1.5/0.5 = 150 g
Answer
m = 150 g
Check: 50 g + 150 g = 200 g of 1% ointment.
5.Pediatric & critical-care dosing
Answer: V = 1.5 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
80·94 = 7 520 units
Volume
V = 7520/5000 = 1.504 ≈ 1.5 mL
Answer
V = 1.5 mL
6.Pediatric & critical-care dosing
Answer: R = 3 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.
5·60 = 300 mcg/h
Pump rate
R = 300/100 = 3 mL/h
Answer
R = 3 mL/h
7.Pharmacology
Answer: B · Respiratory rate and level of sedation
Why this is the answer
Opioids can cause respiratory depression, which is usually preceded by increasing sedation. Both are checked before and after each dose.
Answer
B · Respiratory rate and level of sedation
8.Pharmacology
Answer: D · They blunt adrenergic symptoms such as tremor and palpitations
Why this is the answer
Tremor, palpitations and anxiety in hypoglycaemia are adrenaline-driven; beta blockade dampens them, so patients may notice low glucose later. Sweating is cholinergic and often persists.
Answer
D · They blunt adrenergic symptoms such as tremor and palpitations