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.
2Practice problems
1.PharmacologyMedium
How do ACE inhibitors lower blood pressure?
AThey block the conversion of angiotensin I to angiotensin II
BThey block L-type calcium channels in vascular smooth muscle cells
CThey block beta-1 receptors in the heart
DThey increase sodium reabsorption in the kidney
2.PharmacologyHard
A woman with epilepsy who takes an antiepileptic drug plans to become pregnant. Which advice is standard?
AStop all antiepileptic drugs straight away as soon as she stops contraception
BTake folic acid before conception and seek specialist review of her medication
CAvoid folic acid because it lowers drug levels
DNo change is needed, as antiepileptics carry no risk in pregnancy
3.Dosage calculationsMedium
A patient weighs 60 kg. The prescribed dose is 10 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
60 kg10 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
A patient weighs 88 lb. The prescription is 5 mg/kg as a single dose, and the stock contains 40 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give?
88 lb5 mg/kg40 mg/1 mL1 kg = 2.2 lb
V = mL
5.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 10 mg/L and the half-life is 3 h. Find the clearance CL in L/h.
D = 180 mgC₀ = 10 mg/Lt½ = 3 h
CL = L/h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 96 kg patient on regular gentamicin doses is at steady state. The target is a peak of 7 mg/L and a trough of 0.5 mg/L, and the volume of distribution is 0.25 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
Answer: A · 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
A · They block the conversion of angiotensin I to angiotensin II
2.Pharmacology
Answer: B · Take folic acid before conception and seek specialist review of her medication
Why this is the answer
Folic acid before and in early pregnancy reduces the risk of neural tube defects. Medication should be reviewed before conception, but drugs should not be stopped suddenly because uncontrolled seizures are also dangerous.
Answer
B · Take folic acid before conception and seek specialist review of her medication
3.Dosage calculations
Answer: D = 200 mg
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Total per day
10·60 = 600 mg
Per dose
D = 600/3 = 200 mg
Answer
D = 200 mg
4.Dosage calculations
Answer: V = 5 mL
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Weight in kg
88/2.2 = 40 kg
Dose
5·40 = 200 mg
Volume
V = (200/40)·1 = 5 mL
Answer
V = 5 mL
5.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 = 180/10 = 18 L
Rate constant
k = 0.693/3 = 0.231 h⁻¹
Clearance
CL = 0.231·18 = 4.159 L/h
Answer
CL = 4.159 L/h
6.Clinical pharmacokinetics
Answer: D = 156 mg
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 = 0.25·96 = 24 L
Dose
D = 24·(7 − 0.5) = 156 mg
Answer
D = 156 mg
In practice the dose is rounded to a convenient amount.