NMD-02

Decay in vivo

A = A0 e^{−λt}. Activity remaining after physical decay.

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DecayIn-vivo decay

Governing equation

A=A_0 e^{-\lambda t}

$t \in \left[0, 72\right]$

where

A_0: Initial activity (MBq)
\lambda: Decay constant (1/h)
t: Time (h)
A: Remaining activity (MBq)

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

A=A_0 e^{-\lambda t}

$t \in \left[0, 72\right]$

$t = 0$ $A = 370$

Along the curve

②

Domain of the variable — blue

t_{\min} = 0,\quad t_{\max} = 72

$t \in \left[0, 72\right]$

$t = 0$ $t = 0$

Along the curve

③

Response curve — green

A=A_0 e^{-\lambda t}

$t \in \left[0, 72\right]$

$t = 0$ $A = 370$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}A}{\mathrm{d}t}

$t \in \left[0, 72\right]$

$t = 0.453$ $A^{\prime} = -40.41$

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-02 — Decay in vivo) is the form associated with In-vivo decay. Working symbols: $A_0$ , $\lambda$ , $t$ $\rightarrow$ $A$ . In the body the biological clearance adds a second exponential. Here λ is physical only.

Purpose

Purpose: compute

A

from

A_0

\lambda

t

in Nuclear medicine via

A=A_0 e^{-\lambda t}

A = A0 e^{−λt}. Activity remaining after physical decay. 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}

\lambda = 0.115\,\mathrm{1/h}

t = 6.000\,\mathrm{h}

, the governing relation

A=A_0 e^{-\lambda t}

yields

A = 185.58\,\mathrm{MBq}

. A decaying activity curve. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Initial activity A_0370 MBqDecay constant \lambda0.115 1/hTime t6 h

Outputs

Remaining activity A185.58 MBq

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Narration of this film

A decaying activity curve.

In the body the biological clearance adds a second exponential. Here λ is physical only.

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