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 74 kg patient is to be loaded with digoxin tablets to reach a level of 1 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.
74 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 63 kg patient on regular tobramycin doses is at steady state. The target is a peak of 7 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.3 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
A solution has a ratio strength of 1:1000. You need 0.39 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.39 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 2 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 260 mg. Draw up the dose: what volume V do you give?
500 mg2 mL + 0.5 mL260 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 500 mL. The order is 20 units/kg/h for a patient who weighs 85 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL20 units/kg/h85 kg
R = mL/h
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 10 mcg/kg/min for a patient who weighs 74 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL10 mcg/kg/min74 kg
R = mL/h
7.PharmacologyMedium
A nurse realises that a patient has been given the wrong dose of a medicine. What is the first action?
AComplete the incident report before anything else
BWait to see whether the patient notices
CCorrect the chart so it shows the right dose
DAssess the patient for effects of the error
8.PharmacologyHard
Why is sildenafil contraindicated in a patient who uses nitrates for angina?
ASildenafil blocks the conversion of nitrates into nitric oxide in the vessels
BBoth raise cGMP in vascular smooth muscle and can cause severe hypotension
CNitrates block the metabolism of sildenafil in the liver
DThe combination causes dangerous hyperkalaemia
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 740 mcg
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 = 7·74 = 518 L
Amount of active drug needed
Vd·C = 518·1 = 518 mcg
Loading dose
LD = 518/(1·0.7) = 740 mcg
Answer
LD = 740 mcg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: D = 122.8 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.
Volume of distribution
Vd = 0.3·63 = 18.9 L
Dose
D = 18.9·(7 − 0.5) = 122.8 mg
Answer
D = 122.8 mg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 0.39 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 = 0.39/1 = 0.39 mL
Answer
V = 0.39 mL
4.Pharmacy calculations
Answer: V = 1.3 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
2 + 0.5 = 2.5 mL
C = 500/2.5 = 200 mg/mL
Volume
V = 260/200 = 1.3 mL
Answer
V = 1.3 mL
5.Pediatric & critical-care dosing
Answer: R = 34 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
20·85 = 1 700 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1700/50 = 34 mL/h
Answer
R = 34 mL/h
6.Pediatric & critical-care dosing
Answer: R = 44.4 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
10·74 = 740 mcg/min
740·60 = 44400 mcg/h
Pump rate
R = 44400/1000 = 44.4 mL/h
Answer
R = 44.4 mL/h
7.Pharmacology
Answer: D · Assess the patient for effects of the error
Why this is the answer
The first priority is to assess and monitor the patient, then inform the prescriber so treatment can be given if needed. The error is documented factually and reported through the incident system.
Answer
D · Assess the patient for effects of the error
8.Pharmacology
Answer: B · Both raise cGMP in vascular smooth muscle and can cause severe hypotension
Why this is the answer
Nitrates increase cGMP production through nitric oxide and sildenafil blocks its breakdown by PDE5. Together they cause excessive vasodilation and a dangerous fall in blood pressure.
Answer
B · Both raise cGMP in vascular smooth muscle and can cause severe hypotension