NMD-34

Effective decay

Clearance plus physics.

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Nuclear medicineeffective λ

Governing equation

\\lambda_e=\\lambda_p+\\lambda_b

$\lambda_b \in \left[0, 1\right]$

where

\lambda_p: Physical (1/h)
\lambda_b: Biological (1/h)
\lambda_e: λe (1/h)

The figure, part by part

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①

Governing law — red

\\lambda_e=\\lambda_p+\\lambda_b

$\lambda_b \in \left[0, 1\right]$

$\lambda_b = 0$ $\lambda_e = 0.115$

Along the curve

②

Domain of the variable — blue

\lambda_b_{\min} = 0,\quad \lambda_b_{\max} = 1

$\lambda_b \in \left[0, 1\right]$

$\lambda_b = 0$ $\lambda_b = 0$

Along the curve

③

Response curve — green

\\lambda_e=\\lambda_p+\\lambda_b

$\lambda_b \in \left[0, 1\right]$

$\lambda_b = 0$ $\lambda_e = 0.115$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\lambda_e}{\mathrm{d}\lambda_b}

$\lambda_b \in \left[0, 1\right]$

$\lambda_b = 0.006$ $\lambda_e^{\prime} = 1$

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-34 — Effective decay) is the form associated with effective λ. Working symbols: $\lambda_p$ , $\lambda_b$ $\rightarrow$ $\lambda_e$ . Clearance plus physics.

Purpose

Purpose: compute

\lambda_e

from

\lambda_p

\lambda_b

in Nuclear medicine via

\\lambda_e=\\lambda_p+\\lambda_b

Clearance plus physics. 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

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

\lambda_b = 0.050\,\mathrm{1/h}

, the governing relation

\\lambda_e=\\lambda_p+\\lambda_b

yields

\lambda_e = 0.1650\,\mathrm{1/h}

. Clearance plus physics. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Physical \lambda_p0.115 1/hBiological \lambda_b0.05 1/h

Outputs

λe \lambda_e0.1650 1/h

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Narration of this film

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