NMD-08

Residence time

τ = Ã / A0. Hours of cumulated activity per unit injected.

Reading speed

Internal dosimetryMIRD residence

Governing equation

\tau=\tilde A/A_0

$\tilde A \in \left[1, 5000\right]$

where

\tilde A: Cumulated activity (MBq·h)
A_0: Injected activity (MBq)
\tau: Residence time (h)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\tau=\tilde A/A_0

$\tilde A \in \left[1, 5000\right]$

$\tilde A = 1$ $\tau = 0.003$

Along the curve

②

Domain of the variable — blue

\tilde A_{\min} = 1,\quad \tilde A_{\max} = 5000

$\tilde A \in \left[1, 5000\right]$

$\tilde A = 1$ $\tilde A = 1$

Along the curve

③

Response curve — green

\tau=\tilde A/A_0

$\tilde A \in \left[1, 5000\right]$

$\tilde A = 1$ $\tau = 0.003$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\tau}{\mathrm{d}\tilde A}

$\tilde A \in \left[1, 5000\right]$

$\tilde A = 32.44$ $\tau^{\prime} = 0.003$

Along the curve

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-08 — Residence time) is the form associated with MIRD residence. Working symbols: $\tilde A$ , $A_0$ $\rightarrow$ $\tau$ . For a single exponential τ = 1.443 Teff. Multi-compartment τ is the area under A(t)/A0.

Purpose

Purpose: compute

\tau

from

\tilde A

A_0

in Nuclear medicine via

\tau=\tilde A/A_0

τ = Ã / A0. Hours of cumulated activity per unit injected. 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

\tilde A = 200.000\,\mathrm{MBq·h}

A_0 = 370.000\,\mathrm{MBq}

, the governing relation

\tau=\tilde A/A_0

yields

\tau = 0.541\,\mathrm{h}

. An activity curve and the area that is Ã. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Cumulated activity \tilde A200 MBq·hInjected activity A_0370 MBq

Outputs

Residence time \tau0.541 h

Reading speed

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Narration of this film

An activity curve and the area that is Ã.

For a single exponential τ = 1.443 Teff. Multi-compartment τ is the area under A(t)/A0.

Reading speed

Watch on YouTube