One-compartment models: IV bolus MCQs With Answer

Introduction
This quiz set focuses on one-compartment IV bolus models — a foundational topic in Advanced Biopharmaceutics & Pharmacokinetics for M.Pharm students. You will find concise questions that reinforce core concepts: instantaneous mixing, the monoexponential decline of plasma concentration, mathematical relationships (C = C0 e^-kt, t_1/2, Vd, CL, AUC), graphical estimation methods, and practical calculations used in drug development and dose design. The questions range from conceptual to calculation-based and emphasize interpretation of semi-log plots, parameter estimation, and implications for dosing. Use these MCQs to test and deepen your understanding of single-compartment IV bolus kinetics and common analytical approaches.

Q1. What is the basic assumption of a one-compartment IV bolus model?

• The body is a single homogeneous compartment where the drug instantaneously mixes after IV bolus administration
• The drug distributes into multiple tissues with different rate constants
• The absorption process is the rate-limiting step
• Elimination occurs only from peripheral tissues, not plasma

Correct Answer: The body is a single homogeneous compartment where the drug instantaneously mixes after IV bolus administration

Q2. Which equation correctly describes plasma concentration versus time in a one-compartment IV bolus model with first-order elimination?

• C = C0 × t^-k
• C = C0 e^-kt
• C = (Dose/Vd) × (1 – e^-kt)
• C = C0 / (1 + kt)

Correct Answer: C = C0 e^-kt

Q3. Which relationship correctly links clearance (CL), elimination rate constant (k) and volume of distribution (Vd) in a one-compartment model?

• CL = k / Vd
• Vd = CL / k
• CL = k × Vd
• k = CL + Vd

Correct Answer: CL = k × Vd

Q4. What is the formula for elimination half-life (t1/2) under first-order kinetics?

• t1/2 = 0.693 / k
• t1/2 = k / 0.693
• t1/2 = ln(k) / 2
• t1/2 = Dose / CL

Correct Answer: t1/2 = 0.693 / k

Q5. For an IV bolus dose, the apparent volume of distribution (Vd) is estimated by which expression?

• Vd = CL / k
• Vd = Dose / C0
• Vd = AUC × CL
• Vd = C0 / Dose

Correct Answer: Vd = Dose / C0

Q6. The total area under the plasma concentration-time curve from time zero to infinity (AUC0-∞) after an IV bolus is given by which formula?

• AUC0-∞ = C0 / k
• AUC0-∞ = Dose / CL
• AUC0-∞ = Vd / k
• AUC0-∞ = Dose × Vd

Correct Answer: AUC0-∞ = Dose / CL

Q7. What is the recommended practical method to determine the initial concentration C0 from sampled plasma data after an IV bolus?

• Take the concentration at the earliest sample time and use it as C0
• Perform linear regression on semi-log (lnC vs time) data and extrapolate the best-fit line to time zero
• Use the mean of measured concentrations at all times
• Calculate C0 as Dose / AUC

Correct Answer: Perform linear regression on semi-log (lnC vs time) data and extrapolate the best-fit line to time zero

Q8. What are the appropriate units for clearance (CL)?

• Mass (e.g., mg)
• Concentration (e.g., mg/L)
• Volume per time (e.g., L/h or mL/min)
• Time (e.g., h or min)

Correct Answer: Volume per time (e.g., L/h or mL/min)

Q9. In a one-compartment IV bolus model, mean residence time (MRT) equals which value?

• MRT = Vd / CL
• MRT = 1 / k
• MRT = t1/2 / 2
• MRT = Dose / AUC

Correct Answer: MRT = 1 / k

Q10. For a true one-compartment model, how does steady-state volume of distribution (Vss) compare with apparent Vd after IV bolus?

• Vss is always larger than Vd
• Vss equals Vd (apparent volume of distribution)
• Vss is unrelated to Vd and cannot be compared
• Vss is half of Vd

Correct Answer: Vss equals Vd (apparent volume of distribution)

Q11. Which experimental approach yields the elimination rate constant k from plasma data?

• Nonlinear regression of concentration versus log(time)
• Linear regression of ln(concentration) versus time (slope = -k)
• Area under the curve divided by dose
• Calculating the mean of concentrations over time

Correct Answer: Linear regression of ln(concentration) versus time (slope = -k)

Q12. How does increased plasma protein binding generally affect the apparent volume of distribution (Vd) for a drug?

• Increased plasma protein binding increases Vd by promoting tissue uptake
• Increased plasma protein binding decreases Vd by retaining drug in plasma
• Protein binding has no effect on Vd
• Increased protein binding always doubles Vd

Correct Answer: Increased plasma protein binding decreases Vd by retaining drug in plasma

Q13. What is the absolute bioavailability (F) for an IV bolus dose?

• 0% (F = 0)
• 50% (F = 0.5)
• 100% (F = 1)
• Cannot be determined for IV dosing

Correct Answer: 100% (F = 1)

Q14. How is AUC0-∞ commonly calculated from observed data when the last measurable concentration is Clast?

• AUC0-∞ = AUC0-tlast – (Clast / k)
• AUC0-∞ = AUC0-tlast + (Clast / k)
• AUC0-∞ = AUC0-tlast × (Clast × k)
• AUC0-∞ = Clast / AUMC

Correct Answer: AUC0-∞ = AUC0-tlast + (Clast / k)

Q15. Which statement best describes first-order elimination kinetics?

• The rate of elimination is constant regardless of concentration
• The amount eliminated per unit time is proportional to the drug concentration
• Elimination follows zero-order kinetics only at low concentrations
• Elimination is independent of clearance

Correct Answer: The amount eliminated per unit time is proportional to the drug concentration

Q16. For multiple IV bolus dosing at fixed interval τ in a one-compartment model, which expression gives the accumulation factor R for peak concentration at steady state?

• R = 1 – e^-kτ
• R = 1 / (1 – e^-kτ)
• R = e^-kτ / (1 – e^-kτ)
• R = k × τ

Correct Answer: R = 1 / (1 – e^-kτ)

Q17. On a semi-log plot of concentration versus time, what does the slope of the terminal phase represent?

• The slope equals +k
• The slope equals -k
• The slope equals CL / Vd
• The slope equals AUC

Correct Answer: The slope equals -k

Q18. If clearance (CL) doubles for a drug given as a fixed IV bolus dose, what happens to AUC0-∞ (all else equal)?

• AUC doubles
• AUC remains unchanged
• AUC is halved
• AUC increases by a factor of four

Correct Answer: AUC is halved

Q19. Given Vd = 50 L and k = 0.1 h^-1 for a one-compartment IV bolus drug, what is the clearance (CL)?

• 0.2 L/h
• 5 L/h
• 500 L/h
• 0.005 L/h

Correct Answer: 5 L/h

Q20. In linear (dose-proportional) pharmacokinetics for a one-compartment IV bolus drug, which parameter is directly proportional to dose (i.e., dose-dependent)?

• Elimination half-life (t1/2)
• Clearance (CL)
• Area under the curve (AUC)
• Elimination rate constant (k)

Correct Answer: Area under the curve (AUC)

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