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 gentamicin. The level back-extrapolated to time zero is 12 mg/L and the half-life is 2 h. Find the clearance CL in L/h.
D = 320 mgC₀ = 12 mg/Lt½ = 2 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A theophylline infusion is started without a loading dose. The half-life in this patient is 6 h. How long t does it take to reach 95% of the steady-state level?
t½ = 6 h95% Css
t = h
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 1000 mg as a powder. The practice label says to add 3.5 mL of sterile water; the powder adds 0.5 mL to the volume. What is the concentration C in mg/mL after reconstitution?
1000 mg3.5 mL+0.5 mL
C = mg/mL
4.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 4.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 1120 mg. Draw up the dose: what volume V do you give?
2000 mg4.6 mL + 0.4 mL1120 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 250 mL. The order is 6 units/h. Find the pump rate R in mL/h. Round to one decimal place.
100 units/250 mL6 units/h
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 5 mcg/kg/min for a patient who weighs 103 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL5 mcg/kg/min103 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?
AApply a tight bandage over the site
BIncrease the infusion rate to push through and clear the blockage
CFlush the cannula forcefully with saline
DStop the infusion, remove the cannula and elevate the limb
8.PharmacologyHard
A woman with chronic hypertension who takes lisinopril is now pregnant. What is the key concern?
AACE inhibitors harm fetal kidneys, so a safer drug is used
BLisinopril has no known fetal effects and should be continued
CAll antihypertensives must be stopped in pregnancy
DLisinopril works better in pregnancy, so the dose should be increased
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 9.242 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 = 0.693/2 = 0.3466 h⁻¹
Clearance
CL = 0.3466·26.67 = 9.242 L/h
Answer
CL = 9.242 L/h
2.Clinical pharmacokinetics
Answer: t = 25.93 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 = 0.693/6 = 0.1155 h⁻¹
Time to the given fraction of steady state
t = −ln(1 − 0.95)/0.1155 = 2.996/0.1155 = 25.93 h
Answer
t = 25.93 h
That is 4.322 half-lives.
3.Pharmacy calculations
Answer: C = 250 mg/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
3.5 + 0.5 = 4 mL
Concentration
C = 1000/4 = 250 mg/mL
Answer
C = 250 mg/mL
4.Pharmacy calculations
Answer: V = 2.8 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
4.6 + 0.4 = 5 mL
C = 2000/5 = 400 mg/mL
Volume
V = 1120/400 = 2.8 mL
Answer
V = 2.8 mL
5.Pediatric & critical-care dosing
Answer: R = 15 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.
Concentration
100/250 = 0.4 units/mL
Pump rate
R = 6/0.4 = 15 mL/h
Answer
R = 15 mL/h
6.Pediatric & critical-care dosing
Answer: R = 30.9 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
5·103 = 515 mcg/min
515·60 = 30900 mcg/h
Pump rate
R = 30900/1000 = 30.9 mL/h
Answer
R = 30.9 mL/h
7.Pharmacology
Answer: D · 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
D · Stop the infusion, remove the cannula and elevate the limb
8.Pharmacology
Answer: A · ACE inhibitors harm fetal kidneys, so a safer drug is used
Why this is the answer
ACE inhibitors and ARBs cause fetal kidney damage, oligohydramnios and other problems, especially later in pregnancy. Drugs such as labetalol, nifedipine or methyldopa are used instead.
Answer
A · ACE inhibitors harm fetal kidneys, so a safer drug is used