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 260 mg of gentamicin. The level back-extrapolated to time zero is 9 mg/L and the half-life is 3 h. Find the clearance CL in L/h.
D = 260 mgC₀ = 9 mg/Lt½ = 3 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 8 h. How long t does it take to reach 80% of the steady-state level?
t½ = 8 h80% Css
t = h
3.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefuroxime 750 mg as a powder. The practice label says to add 7.2 mL of sterile water; the powder adds 0.3 mL to the volume. What is the concentration C in mg/mL after reconstitution?
750 mg7.2 mL+0.3 mL
C = mg/mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 100 mL of 30% 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%30%100 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 80 units/kg for a patient who weighs 100 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg100 kg1 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 32 mL/h. The patient weighs 62 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL32 mL/h62 kg
D = mcg/kg/min
7.PharmacologyMedium
Why should loperamide usually be avoided in bloody diarrhoea with fever?
ASlowing the gut may keep bacteria and toxins in the bowel longer
BLoperamide makes the bleeding worse by blocking platelets
CLoperamide causes severe hypertension when there is an infection
DLoperamide is an antibiotic that causes resistance
8.PharmacologyHard
A patient taking dabigatran has a life-threatening bleed. Which specific reversal agent is used?
AAndexanet alfa
BVitamin K
CIdarucizumab
DProtamine sulfate
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 6.675 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 = 260/9 = 28.89 L
Rate constant
k = 0.693/3 = 0.231 h⁻¹
Clearance
CL = 0.231·28.89 = 6.675 L/h
Answer
CL = 6.675 L/h
2.Clinical pharmacokinetics
Answer: t = 18.58 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 = 0.693/8 = 0.08664 h⁻¹
Time to the given fraction of steady state
t = −ln(1 − 0.8)/0.08664 = 1.609/0.08664 = 18.58 h
Answer
t = 18.58 h
That is 2.322 half-lives.
3.Pharmacy calculations
Answer: C = 100 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
7.2 + 0.3 = 7.5 mL
Concentration
C = 750/7.5 = 100 mg/mL
Answer
C = 100 mg/mL
4.Pharmacy calculations
Answer: V = 50 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%: 30 − 10 = 20 parts
10%: 50 − 30 = 20 parts
total: 40 parts
Share the volume
V = 100·20/40 = 50 mL
Answer
V = 50 mL
Check: 50 mL of 50% + 50 mL of 10% = 100 mL.
5.Pediatric & critical-care dosing
Answer: V = 8 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
80·100 = 8 000 units
Volume
V = 8000/1000 = 8 mL
Answer
V = 8 mL
6.Pediatric & critical-care dosing
Answer: D = 13.8 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
400 000/250 = 1600 mcg/mL
Micrograms per minute
32·1600 = 51200 mcg/h
51200/60 = 853.3 mcg/min
Per kilogram
D = 853.3/62 = 13.76 ≈ 13.8 mcg/kg/min
Answer
D = 13.8 mcg/kg/min
7.Pharmacology
Answer: A · Slowing the gut may keep bacteria and toxins in the bowel longer
Why this is the answer
In dysentery or suspected C. difficile infection, antimotility drugs may prolong illness and increase complications such as toxic megacolon. The cause is assessed and fluids are replaced first.
Answer
A · Slowing the gut may keep bacteria and toxins in the bowel longer
8.Pharmacology
Answer: C · Idarucizumab
Why this is the answer
Idarucizumab is an antibody fragment that binds dabigatran. Andexanet alfa reverses factor Xa inhibitors, protamine reverses heparin, and vitamin K reverses warfarin.