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 180 mg of gentamicin. The level back-extrapolated to time zero is 12 mg/L and the half-life is 2.5 h. Find the clearance CL in L/h.
D = 180 mgC₀ = 12 mg/Lt½ = 2.5 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 4.5 L/h. Each dose is 1000 mg of vancomycin. Find the average steady-state level Css,avg.
CL = 4.5 L/hτ = 12 hS = 1F = 1D = 1000 mg
Css,avg = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.15 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.15 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 200 g of 2.5% hydrocortisone ointment. How many grams m of 0.5% hydrocortisone ointment must you add to make a 1% ointment? Round to the nearest whole gram.
200 g · 2.5%0.5%1%
m = g
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 12 500 units of heparin in 250 mL. The order is 16 units/kg/h for a patient who weighs 56 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL16 units/kg/h56 kg
R = mL/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 2 mcg/kg/min for a patient who weighs 63 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL2 mcg/kg/min63 kg
R = mL/h
7.PharmacologyMedium
A patient with suspected sepsis has blood cultures ordered and a first antibiotic dose due. What should the nurse do?
AGive the antibiotic first, then take blood cultures the next day
BGive the antibiotic only if the temperature is above 40 °C (104 °F)
CWait for the culture results before giving any antibiotic
DTake the blood cultures first, then give the antibiotic at once
8.PharmacologyHard
An older patient on amlodipine develops ankle swelling and is prescribed furosemide. She then becomes dizzy and falls. What does this sequence illustrate?
AA prescribing cascade
BEnzyme induction
CA type B allergic reaction
DDrug tolerance
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 4.159 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 = 180/12 = 15 L
Rate constant
k = 0.693/2.5 = 0.2773 h⁻¹
Clearance
CL = 0.2773·15 = 4.159 L/h
Answer
CL = 4.159 L/h
2.Clinical pharmacokinetics
Answer: Css,avg = 18.52 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.
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 = 0.15/1 = 0.15 mL
Answer
V = 0.15 mL
4.Pharmacy calculations
Answer: m = 600 g
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Alligation parts
2.5%: 1 − 0.5 = 0.5 parts
0.5%: 2.5 − 1 = 1.5 parts
Scale to the amount you have
m = 200·1.5/0.5 = 600 g
Answer
m = 600 g
Check: 200 g + 600 g = 800 g of 1% ointment.
5.Pediatric & critical-care dosing
Answer: R = 17.9 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
16·56 = 896 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 896/50 = 17.92 ≈ 17.9 mL/h
Answer
R = 17.9 mL/h
6.Pediatric & critical-care dosing
Answer: R = 4.7 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
2·63 = 126 mcg/min
126·60 = 7560 mcg/h
Pump rate
R = 7560/1600 = 4.725 ≈ 4.7 mL/h
Answer
R = 4.7 mL/h
7.Pharmacology
Answer: D · Take the blood cultures first, then give the antibiotic at once
Why this is the answer
Cultures are taken before antibiotics so the organism can be identified, but antibiotics must not be delayed in sepsis. Taking cultures quickly and then giving the antibiotic meets both aims.
Answer
D · Take the blood cultures first, then give the antibiotic at once
8.Pharmacology
Answer: A · A prescribing cascade
Why this is the answer
In a prescribing cascade, an adverse effect of one drug is mistaken for a new condition and treated with another drug, which brings new risks. Amlodipine oedema does not respond well to diuretics; reviewing the original drug is better.