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 gentamicin, the level is 7 mg/L at 1 h and 2.8 mg/L at 5 h. Assume first-order elimination. Find the half-life t½.
C1 = 7 mg/L (1 h)C2 = 2.8 mg/L (5 h)
t½ = h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 69 kg patient takes oral aminophylline (S = 0.8, F = 1) every 12 h. The theophylline clearance is 0.03 L/kg/h. What dose D in mg gives an average steady-state level of 12 mg/L?
A solution has a ratio strength of 1:1000. You need 0.8 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.8 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 4.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 150 mg. Draw up the dose: what volume V do you give?
250 mg4.6 mL + 0.4 mL150 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 12 500 units of heparin in 250 mL. The order is 12 units/kg/h for a patient who weighs 81 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL12 units/kg/h81 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 93 kg has an order for nitroglycerin at 20 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 mL20 mcg/min93 kg
R = mL/h
7.PharmacologyMedium
Why is a progestogen added to oestrogen in hormone replacement therapy for a woman who still has her uterus?
ATo lower the risk of blood clots to zero
BTo prevent breast cancer completely
CTo reduce hot flushes much more than oestrogen alone can
DTo protect against endometrial hyperplasia and cancer
8.PharmacologyHard
Which property makes a drug more likely to cross the blood–brain barrier?
APositive charge at physiological pH
BHigh lipid solubility and small size
CHigh water solubility and strong ionisation
DLarge molecular weight and strong protein binding
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(7/2.8)/4 = 0.9163/4 = 0.2291 h⁻¹
Half-life
t½ = 0.693/0.2291 = 3.026 h
Answer
t½ = 3.026 h
2.Clinical pharmacokinetics
Answer: D = 372.6 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 = 0.03·69 = 2.07 L/h
Dose
D = Css,avg·CL·τ/(S·F) = 12·2.07·12/(0.8·1) = 372.6 mg
Answer
D = 372.6 mg
3.Pharmacy calculations
Answer: V = 0.8 mL
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/1000 mL = 1 mg/mL
Volume
V = 0.8/1 = 0.8 mL
Answer
V = 0.8 mL
4.Pharmacy calculations
Answer: V = 3 mL
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.
Final volume and concentration
4.6 + 0.4 = 5 mL
C = 250/5 = 50 mg/mL
Volume
V = 150/50 = 3 mL
Answer
V = 3 mL
5.Pediatric & critical-care dosing
Answer: R = 19.4 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
12·81 = 972 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 972/50 = 19.44 ≈ 19.4 mL/h
Answer
R = 19.4 mL/h
6.Pediatric & critical-care dosing
Answer: R = 12 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.
20·60 = 1200 mcg/h
Pump rate
R = 1200/100 = 12 mL/h
Answer
R = 12 mL/h
7.Pharmacology
Answer: D · To protect against endometrial hyperplasia and cancer
Why this is the answer
Oestrogen alone causes endometrial proliferation and increases the risk of endometrial cancer. A progestogen protects the endometrium; women without a uterus can take oestrogen alone.
Answer
D · To protect against endometrial hyperplasia and cancer
8.Pharmacology
Answer: B · High lipid solubility and small size
Why this is the answer
Small, lipophilic, non-ionised molecules diffuse across endothelial cell membranes. Charged or large, protein-bound drugs mostly stay out.