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 receives an IV bolus of 320 mg of tobramycin. The level back-extrapolated to time zero is 12 mg/L and the half-life is 3 h. Find the clearance CL in L/h.
D = 320 mgC₀ = 12 mg/Lt½ = 3 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A theophylline infusion runs at 35 mg/h with no loading dose. The patient's clearance is 3.5 L/h and the half-life is 6 h. What is the level C after 3 h?
R = 35 mg/hCL = 3.5 L/ht½ = 6 ht = 3 h
C = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.64 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.64 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 9.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 50 mg. Draw up the dose: what volume V do you give?
500 mg9.8 mL + 0.2 mL50 mg
V = mL
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 59 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg59 kg1 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 15 mL/h. The patient weighs 54 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL15 mL/h54 kg
D = mcg/kg/min
7.PharmacologyMedium
A patient given haloperidol develops a sudden painful twisting of the neck and the eyes roll upward. Which drug is usually given?
AA second dose of haloperidol
BNaloxone
CAn anticholinergic such as benzatropine (benztropine)
DDantrolene by mouth to relax the twisted neck muscles
8.PharmacologyHard
A breastfeeding mother needs a mild analgesic. Which drug is generally considered compatible with breastfeeding?
AParacetamol (acetaminophen)
BAspirin
CPethidine (meperidine)
DCodeine (as co-codamol)
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 6.161 L/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.
Volume of distribution
Vd = 320/12 = 26.67 L
Rate constant
k = 0.693/3 = 0.231 h⁻¹
Clearance
CL = 0.231·26.67 = 6.161 L/h
Answer
CL = 6.161 L/h
2.Clinical pharmacokinetics
Answer: C = 2.929 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 = 35/3.5 = 10 mg/L
Rate constant
k = 0.693/6 = 0.1155 h⁻¹
Level after the given time
C = 10·(1 − e−0.1155·3) = 2.929 mg/L
Answer
C = 2.929 mg/L
3.Pharmacy calculations
Answer: V = 6.4 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/10 000 mL = 0.1 mg/mL
Volume
V = 0.64/0.1 = 6.4 mL
Answer
V = 6.4 mL
4.Pharmacy calculations
Answer: V = 1 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
9.8 + 0.2 = 10 mL
C = 500/10 = 50 mg/mL
Volume
V = 50/50 = 1 mL
Answer
V = 1 mL
5.Pediatric & critical-care dosing
Answer: V = 4.7 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
80·59 = 4 720 units
Volume
V = 4720/1000 = 4.72 ≈ 4.7 mL
Answer
V = 4.7 mL
6.Pediatric & critical-care dosing
Answer: D = 7.4 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
15·1600 = 24000 mcg/h
24000/60 = 400 mcg/min
Per kilogram
D = 400/54 = 7.407 ≈ 7.4 mcg/kg/min
Answer
D = 7.4 mcg/kg/min
7.Pharmacology
Answer: C · An anticholinergic such as benzatropine (benztropine)
Why this is the answer
Acute dystonia is caused by dopamine blockade, which leaves acetylcholine activity relatively high. An IM or IV anticholinergic usually relieves it within minutes.
Answer
C · An anticholinergic such as benzatropine (benztropine)
8.Pharmacology
Answer: A · Paracetamol (acetaminophen)
Why this is the answer
Paracetamol passes into milk in small amounts and is widely regarded as safe. Codeine can cause dangerous opioid levels in babies of ultra-rapid metaboliser mothers, aspirin carries a Reye's risk and pethidine's metabolite accumulates in infants.