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). An 81 kg patient is to be loaded intravenously with aminophylline to reach a theophylline level of 15 mg/L. The volume of distribution is 0.5 L/kg and the salt factor is S = 0.8. Find the loading dose LD of aminophylline in mg.
81 kgVd = 0.5 L/kgC = 15 mg/LS = 0.8
LD = mg
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). An 86 kg patient has a digoxin level of 0.3 mcg/L; the target is 0.8 mcg/L. The volume of distribution is 7 L/kg and the tablets have F = 0.7. What extra loading dose LD raises the level to the target?
86 kgVd = 7 L/kgC = 0.3 → 0.8 mcg/LF = 0.7
LD = mcg
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 18.2 mL of diluent. The prescribed dose is 750 000 units. What volume V do you draw up? Round to one decimal place.
18.2 mL → 250 000 units/mL750 000 units
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 1000 mL of 25% dextrose by mixing 50% and 10% dextrose. How many mL V of the 50% solution do you need? Round to the nearest whole mL.
50%10%25%1000 mL
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 60 units/kg for a patient who weighs 59 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
60 units/kg59 kg5 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 29 mL/h. The patient weighs 97 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL29 mL/h97 kg
D = mcg/kg/min
7.PharmacologyMedium
While giving medicines, a patient says, "That pill looks different from the one I usually take." What should the nurse do?
AGive the pill and check the chart afterwards
BReassure the patient and give the pill anyway
CStop and recheck the order and the medicine before giving it
DExplain that only the staff decide which medicines are given
8.PharmacologyHard
Five days after starting clindamycin, a patient has frequent watery diarrhoea, abdominal cramps and a fever. What should the nurse suspect and do?
AFood poisoning; encourage a high-fibre diet and plenty of milk products
BC. difficile infection; send stool, use contact precautions, avoid antidiarrhoeals
CA normal side effect; give loperamide and continue as usual
DAn allergy to clindamycin; give an antihistamine and continue the antibiotic
3Solutions
1.Clinical pharmacokinetics
Answer: LD = 759.4 mg
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 = 0.5·81 = 40.5 L
Amount of active drug needed
Vd·C = 40.5·15 = 607.5 mg
Loading dose
LD = 607.5/(0.8·1) = 759.4 mg
Answer
LD = 759.4 mg
In practice the dose is rounded to a convenient amount.
2.Clinical pharmacokinetics
Answer: LD = 430 mcg
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 = 7·86 = 602 L
Rise needed
0.8 − 0.3 = 0.5 mcg/L
Loading dose
LD = 602·0.5/(1·0.7) = 430 mcg
Answer
LD = 430 mcg
In practice the dose is rounded to a convenient amount.
3.Pharmacy calculations
Answer: V = 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.
Concentration from the label
18.2 mL → 250 000 units/mL
Volume to give
V = 750 000/250 000 = 3 mL
Answer
V = 3 mL
4.Pharmacy calculations
Answer: V = 375 mL
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
50%: 25 − 10 = 15 parts
10%: 50 − 25 = 25 parts
total: 40 parts
Share the volume
V = 1000·15/40 = 375 mL
Answer
V = 375 mL
Check: 375 mL of 50% + 625 mL of 10% = 1000 mL.
5.Pediatric & critical-care dosing
Answer: V = 0.71 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
60·59 = 3 540 units
Volume
V = 3540/5000 = 0.708 ≈ 0.71 mL
Answer
V = 0.71 mL
6.Pediatric & critical-care dosing
Answer: D = 10 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
500 000/250 = 2000 mcg/mL
Micrograms per minute
29·2000 = 58000 mcg/h
58000/60 = 966.7 mcg/min
Per kilogram
D = 966.7/97 = 9.966 ≈ 10 mcg/kg/min
Answer
D = 10 mcg/kg/min
7.Pharmacology
Answer: C · Stop and recheck the order and the medicine before giving it
Why this is the answer
A patient's concern can reveal a wrong drug or wrong patient error. The nurse rechecks the order and product, and may call the pharmacy; a different brand or strength may explain the change.
Answer
C · Stop and recheck the order and the medicine before giving it
8.Pharmacology
Answer: B · C. difficile infection; send stool, use contact precautions, avoid antidiarrhoeals
Why this is the answer
Broad-spectrum antibiotics, especially clindamycin, allow C. difficile to overgrow and release toxins. Stool is tested, contact precautions with soap-and-water handwashing are used, and antidiarrhoeals are avoided because they keep toxin in the gut.
Answer
B · C. difficile infection; send stool, use contact precautions, avoid antidiarrhoeals