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 160 mg of tobramycin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 2 h. Find the clearance CL in L/h.
D = 160 mgC₀ = 10 mg/Lt½ = 2 h
CL = L/h
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 80 mg/h with no loading dose. The patient's clearance is 4 L/h and the half-life is 8 h. What is the level C after 2 h?
R = 80 mg/hCL = 4 L/ht½ = 8 ht = 2 h
C = mg/L
3.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.68 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.68 mg
V = mL
4.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 300 mL of 20% dextrose by mixing 70% and 10% dextrose. How many mL V of the 10% solution do you need? Round to the nearest whole mL.
70%10%20%300 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 102 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg102 kg1 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 27 mL/h. The patient weighs 84 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL27 mL/h84 kg
D = mcg/kg/min
7.PharmacologyMedium
How do ACE inhibitors lower blood pressure?
AThey increase sodium reabsorption in the kidney
BThey block the conversion of angiotensin I to angiotensin II
CThey block L-type calcium channels in vascular smooth muscle cells
DThey block beta-1 receptors in the heart
8.PharmacologyHard
A woman using the combined oral contraceptive pill starts carbamazepine for epilepsy. What is the main concern?
ASevere hypoglycaemia from the combination
BNo concern, because the drugs do not interact
CContraceptive failure because the hormones are metabolised faster
DCarbamazepine toxicity because the pill strongly blocks its metabolism
3Solutions
1.Clinical pharmacokinetics
Answer: CL = 5.545 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 = 160/10 = 16 L
Rate constant
k = 0.693/2 = 0.3466 h⁻¹
Clearance
CL = 0.3466·16 = 5.545 L/h
Answer
CL = 5.545 L/h
2.Clinical pharmacokinetics
Answer: C = 3.182 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.
Steady-state level
Css = 80/4 = 20 mg/L
Rate constant
k = 0.693/8 = 0.08664 h⁻¹
Level after the given time
C = 20·(1 − e−0.08664·2) = 3.182 mg/L
Answer
C = 3.182 mg/L
3.Pharmacy calculations
Answer: V = 0.68 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 = 0.68/1 = 0.68 mL
Answer
V = 0.68 mL
4.Pharmacy calculations
Answer: V = 250 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
70%: 20 − 10 = 10 parts
10%: 70 − 20 = 50 parts
total: 60 parts
Share the volume
V = 300·50/60 = 250 mL
Answer
V = 250 mL
Check: 50 mL of 70% + 250 mL of 10% = 300 mL.
5.Pediatric & critical-care dosing
Answer: V = 6.1 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
60·102 = 6 120 units
Volume
V = 6120/1000 = 6.12 ≈ 6.1 mL
Answer
V = 6.1 mL
6.Pediatric & critical-care dosing
Answer: D = 10.7 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
27·2000 = 54000 mcg/h
54000/60 = 900 mcg/min
Per kilogram
D = 900/84 = 10.71 ≈ 10.7 mcg/kg/min
Answer
D = 10.7 mcg/kg/min
7.Pharmacology
Answer: B · They block the conversion of angiotensin I to angiotensin II
Why this is the answer
ACE inhibitors (such as ramipril) reduce angiotensin II, causing vasodilation and less aldosterone. They also reduce bradykinin breakdown, which explains the dry cough.
Answer
B · They block the conversion of angiotensin I to angiotensin II
8.Pharmacology
Answer: C · Contraceptive failure because the hormones are metabolised faster
Why this is the answer
Carbamazepine induces CYP3A4, speeding up the breakdown of oestrogen and progestogen. Contraceptive levels fall and pregnancy can occur, so another method is advised.
Answer
C · Contraceptive failure because the hormones are metabolised faster