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 210 mg of gentamicin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 2.5 h. Find the clearance CL in L/h.
D = 210 mgC₀ = 10 mg/Lt½ = 2.5 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 51-year-old woman weighs 64 kg and has a serum creatinine of 2.6 mg/dL (230 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual atenolol dose is 100 mg for a creatinine clearance of 120 mL/min, and a fraction fe = 0.9 of the drug is excreted unchanged by the kidneys. Using the Dettli dose fraction Q = 1 − fe·(1 − CrCl/normal CrCl), find the adjusted dose D. Round to the nearest whole number.
Practice exercise (made-up values, not clinical guidance). A vial contains cefuroxime 750 mg as a powder. The practice label says to add 7.2 mL of sterile water; the powder adds 0.3 mL to the volume. The prescribed dose is 225 mg. What volume V do you draw up? Round to one decimal place.
750 mg7.2 mL+0.3 mL225 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 1.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 1000 mg. Draw up the dose: what volume V do you give?
2000 mg1.2 mL + 0.8 mL1000 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 70 units/kg for a patient who weighs 70 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
70 units/kg70 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 10 mL/h. The patient weighs 86 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL10 mL/h86 kg
D = mcg/kg/min
7.PharmacologyMedium
Which description fits tardive dyskinesia?
AA low white cell count with sore throat and fever
BHigh fever with lead-pipe rigidity and confusion
CA sudden painful spasm of the neck muscles and upward rolling of the eyes within days of the first dose
DInvoluntary movements of the lips, tongue and face after long-term antipsychotic use
8.PharmacologyHard
A baby born to a mother on methadone becomes irritable on day 2, with a high-pitched cry, tremors, sneezing and poor feeding. What is the most likely cause?
ANormal newborn behaviour
BNeonatal hypoglycaemia from maternal diabetes
CVitamin K deficiency bleeding
DNeonatal opioid withdrawal syndrome
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 5.822 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 = 210/10 = 21 L
Rate constant
k = 0.693/2.5 = 0.2773 h⁻¹
Clearance
CL = 0.2773·21 = 5.822 L/h
Answer
CL = 5.822 L/h
2.Clinical pharmacokinetics
Answer: D = 29 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.
Creatinine clearance (Cockcroft–Gault)
CrCl = (140 − 51)·64/(72·2.6)·0.85 = 25.86 mL/min
Dose fraction (Dettli)
Q = 1 − 0.9·(1 − 25.86/120) = 0.294
Adjusted dose
D = 0.294·100 = 29.4 ≈ 29 mg
Answer
D = 29 mg
In practice the dose is rounded to a convenient amount and checked against the product information.
3.Pharmacy calculations
Answer: V = 2.3 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.
Final volume
7.2 + 0.3 = 7.5 mL
Concentration
750/7.5 = 100 mg/mL
Volume to give
V = 225/100 = 2.25 ≈ 2.3 mL
Answer
V = 2.3 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
1.2 + 0.8 = 2 mL
C = 2000/2 = 1000 mg/mL
Volume
V = 1000/1000 = 1 mL
Answer
V = 1 mL
5.Pediatric & critical-care dosing
Answer: V = 0.98 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
70·70 = 4 900 units
Volume
V = 4900/5000 = 0.98 mL
Answer
V = 0.98 mL
6.Pediatric & critical-care dosing
Answer: D = 1.9 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
250 000/250 = 1000 mcg/mL
Micrograms per minute
10·1000 = 10000 mcg/h
10000/60 = 166.7 mcg/min
Per kilogram
D = 166.7/86 = 1.938 ≈ 1.9 mcg/kg/min
Answer
D = 1.9 mcg/kg/min
7.Pharmacology
Answer: D · Involuntary movements of the lips, tongue and face after long-term antipsychotic use
Why this is the answer
Tardive dyskinesia develops after months or years of dopamine-blocking drugs and may be permanent. Patients are screened regularly so that treatment can be changed early.
Answer
D · Involuntary movements of the lips, tongue and face after long-term antipsychotic use
8.Pharmacology
Answer: D · Neonatal opioid withdrawal syndrome
Why this is the answer
After birth the baby no longer receives opioid from the mother and develops withdrawal. Assessment uses a scoring tool, with non-drug care first and opioid treatment if signs are severe.