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 87 kg patient is to receive an aminophylline infusion (salt factor S = 0.8: 80% of aminophylline is theophylline). The theophylline clearance is 0.035 L/kg/h. What aminophylline infusion rate R in mg/h gives a steady-state theophylline level of 15 mg/L?
87 kgCL = 0.035 L/kg/hCss = 15 mg/LS = 0.8
R = mg/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 66 kg patient takes oral theophylline (F = 1) every 8 h. The 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 0.75 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.75 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 4.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 140 mg. Draw up the dose: what volume V do you give?
250 mg4.8 mL + 0.2 mL140 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 250 units of regular insulin in 250 mL. The order is 0.1 units/kg/h for a patient who weighs 98 kg. Find the pump rate R in mL/h. Round to one decimal place.
250 units/250 mL0.1 units/kg/h98 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 4 mL/h. The patient weighs 64 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL4 mL/h64 kg
D = mcg/kg/min
7.PharmacologyMedium
Which drug is the antidote for an opioid overdose?
AAtropine
BNaloxone
CAcetylcysteine
DFlumazenil
8.PharmacologyHard
A patient with asthma starts timolol eye drops for glaucoma and soon becomes wheezy. What is the most likely explanation?
AThe wheeze is unrelated to the eye drops
BTimolol activates histamine receptors in the lungs
CTimolol is absorbed and blocks beta-2 receptors in the airways
DThe eye drops contain an allergen that causes hay fever and asthma
3Solutions
1.Clinical pharmacokinetics
Answer: R = 57.09 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
CL = 0.035·87 = 3.045 L/h
Infusion rate
R = CL·Css/S = 3.045·15/0.8 = 57.09 mg/h
Answer
R = 57.09 mg/h
2.Clinical pharmacokinetics
Answer: D = 190.1 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 = 0.03·66 = 1.98 L/h
Dose
D = Css,avg·CL·τ/(S·F) = 12·1.98·8/(1·1) = 190.1 mg
Answer
D = 190.1 mg
3.Pharmacy calculations
Answer: V = 0.75 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 = 0.75/1 = 0.75 mL
Answer
V = 0.75 mL
4.Pharmacy calculations
Answer: V = 2.8 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.
Final volume and concentration
4.8 + 0.2 = 5 mL
C = 250/5 = 50 mg/mL
Volume
V = 140/50 = 2.8 mL
Answer
V = 2.8 mL
5.Pediatric & critical-care dosing
Answer: R = 9.8 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
0.1·98 = 9.8 units/h
Concentration
250/250 = 1 units/mL
Pump rate
R = 9.8/1 = 9.8 mL/h
Answer
R = 9.8 mL/h
6.Pediatric & critical-care dosing
Answer: D = 1.7 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
800 000/500 = 1600 mcg/mL
Micrograms per minute
4·1600 = 6400 mcg/h
6400/60 = 106.7 mcg/min
Per kilogram
D = 106.7/64 = 1.667 ≈ 1.7 mcg/kg/min
Answer
D = 1.7 mcg/kg/min
7.Pharmacology
Answer: B · Naloxone
Why this is the answer
Naloxone reverses opioid-induced respiratory depression. Flumazenil reverses benzodiazepines, acetylcysteine treats paracetamol overdose and atropine treats bradycardia or organophosphate poisoning.
Answer
B · Naloxone
8.Pharmacology
Answer: C · Timolol is absorbed and blocks beta-2 receptors in the airways
Why this is the answer
Ophthalmic timolol is a non-selective beta blocker and can reach the circulation in amounts that cause bronchospasm or bradycardia. It is generally avoided in asthma.
Answer
C · Timolol is absorbed and blocks beta-2 receptors in the airways