What is the effective half-life and how do you compute it from physical and biological half-lives?

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Multiple Choice

What is the effective half-life and how do you compute it from physical and biological half-lives?

Explanation:
Two processes remove radiopharmaceutical activity at the same time: physical decay and biological clearance. They act as parallel first-order processes, so their rates add rather than their times. Each process has a decay constant λ = ln2 / T1/2. The combined rate is λ_eff = λ_phys + λ_bio = ln2(1/T1/2,phys + 1/T1/2,bio). The effective half-life is then T1/2,eff = ln2 / λ_eff, which simplifies to T1/2,eff = 1 / (1/T1/2,phys + 1/T1/2,bio). This is the correct way to account for both decay and clearance together. It also explains why the other forms don’t match: adding the half-lives directly (instead of their rates) or using a geometric mean or the minimum would not reflect how the two first-order processes combine. For example, if one half-life is much shorter, it dominates the effective half-life, since its higher decay rate drives the overall decrease.

Two processes remove radiopharmaceutical activity at the same time: physical decay and biological clearance. They act as parallel first-order processes, so their rates add rather than their times. Each process has a decay constant λ = ln2 / T1/2. The combined rate is λ_eff = λ_phys + λ_bio = ln2(1/T1/2,phys + 1/T1/2,bio). The effective half-life is then T1/2,eff = ln2 / λ_eff, which simplifies to T1/2,eff = 1 / (1/T1/2,phys + 1/T1/2,bio).

This is the correct way to account for both decay and clearance together. It also explains why the other forms don’t match: adding the half-lives directly (instead of their rates) or using a geometric mean or the minimum would not reflect how the two first-order processes combine. For example, if one half-life is much shorter, it dominates the effective half-life, since its higher decay rate drives the overall decrease.

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