NMD-09

Cumulated activity

Ã = 1.443 Teff A0. Area under a single-exponential A(t).

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Internal dosimetryCumulated activity

Governing equation

\tilde A=1.443\,T_{\mathrm{eff}}A_0

where

A_0: Initial activity (MBq)
T_{eff}: Effective half-life (h)
\tilde A: Cumulated activity (MBq·h)

Lecture brief

Historical brief

MIRD schema, in-vivo decay, uptake fractions and PET coincidence turned unsealed sources into organ dose. The sheets compute activity, residence and well-counter geometry. This sheet (NMD-09 — Cumulated activity) is the form associated with Cumulated activity. Working symbols: $A_0$ , $T_{eff}$ $\rightarrow$ $\tilde A$ . Ã = ∫_0^∞ A0 e^{−λe t} dt = A0 / λe. 1.443 = 1/ln2 converts half-life to 1/λ.

Purpose

Purpose: compute

\tilde A

from

A_0

T_{eff}

in Nuclear medicine via

\tilde A=1.443\,T_{\mathrm{eff}}A_0

Ã = 1.443 Teff A0. Area under a single-exponential A(t). Use it when a real nuclear medicine question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

A_0 = 370.000\,\mathrm{MBq}

T_{eff} = 4.000\,\mathrm{h}

, the governing relation

\tilde A=1.443\,T_{\mathrm{eff}}A_0

yields

\tilde A = 2135.2\,\mathrm{MBq·h}

. An exponential dying away and the area under it. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Initial activity A_0370 MBqEffective half-life T_{eff}4 h

Outputs

Cumulated activity \tilde A2135.2 MBq·h

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Narration of this film

An exponential dying away and the area under it.

Ã = ∫_0^∞ A0 e^{−λe t} dt = A0 / λe. 1.443 = 1/ln2 converts half-life to 1/λ.

Reading speed

Watch on YouTube