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 200 mg of gentamicin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 2 h. Find the clearance CL in L/h.
D = 200 mgC₀ = 10 mg/Lt½ = 2 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient's gentamicin half-life is 2.5 h. The target is a peak of 10 mg/L and a trough of 1 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.
t½ = 2.5 hCpeak = 10 mg/LCtrough = 1 mg/L
τ = h
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.42 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.42 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 4.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 380 mg. Draw up the dose: what volume V do you give?
500 mg4.8 mL + 0.2 mL380 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 100 units of regular insulin in 100 mL runs at 10 mL/h. How many units per hour D does the patient receive?
100 units/100 mL10 mL/h
D = units/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 800 mg in 500 mL. The order is 5 mcg/kg/min for a patient who weighs 52 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL5 mcg/kg/min52 kg
R = mL/h
7.PharmacologyMedium
An IV site is cool, swollen and pale, and the infusion is running slowly. What should the nurse do?
AIncrease the infusion rate to push through and clear the blockage
BApply a tight bandage over the site
CStop the infusion, remove the cannula and elevate the limb
DFlush the cannula forcefully with saline
8.PharmacologyHard
A 19-year-old woman is starting isotretinoin for severe acne. Which requirement is most important?
ATaking the drug only at weekends
BReliable contraception and pregnancy tests, as it is highly teratogenic
CA high-vitamin A diet to boost the effect
DWeekly hearing tests and monthly eye examinations during treatment
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 6.931 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 = 200/10 = 20 L
Rate constant
k = 0.693/2 = 0.3466 h⁻¹
Clearance
CL = 0.3466·20 = 6.931 L/h
Answer
CL = 6.931 L/h
2.Clinical pharmacokinetics
Answer: τ = 8.3 h
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.
Rate constant
k = 0.693/2.5 = 0.2773 h⁻¹
Dosing interval
τ = ln(10/1)/0.2773 = 2.303/0.2773 = 8.305 ≈ 8.3 h
Answer
τ = 8.3 h
In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.
3.Pharmacy calculations
Answer: V = 0.42 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 = 0.42/1 = 0.42 mL
Answer
V = 0.42 mL
4.Pharmacy calculations
Answer: V = 3.8 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 = 500/5 = 100 mg/mL
Volume
V = 380/100 = 3.8 mL
Answer
V = 3.8 mL
5.Pediatric & critical-care dosing
Answer: D = 10 units/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.
Concentration
100/100 = 1 units/mL
Units per hour
D = 10·1 = 10 units/h
Answer
D = 10 units/h
6.Pediatric & critical-care dosing
Answer: R = 9.8 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
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
5·52 = 260 mcg/min
260·60 = 15600 mcg/h
Pump rate
R = 15600/1600 = 9.75 ≈ 9.8 mL/h
Answer
R = 9.8 mL/h
7.Pharmacology
Answer: C · Stop the infusion, remove the cannula and elevate the limb
Why this is the answer
These signs suggest infiltration. The infusion is stopped and the cannula removed, the limb is elevated, and a new cannula is placed elsewhere; vesicant drugs need the extravasation protocol.
Answer
C · Stop the infusion, remove the cannula and elevate the limb
8.Pharmacology
Answer: B · Reliable contraception and pregnancy tests, as it is highly teratogenic
Why this is the answer
Isotretinoin causes severe birth defects. Pregnancy prevention programmes require effective contraception and regular pregnancy tests before, during and after treatment.
Answer
B · Reliable contraception and pregnancy tests, as it is highly teratogenic