NMD-21

Thyroid uptake

U% = 100 (Neck − Thigh)/Std × e^{λt}. Probe uptake with background and decay.

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UptakeThyroid uptake

Governing equation

U_{\%}=100\,(N-B)/S\,e^{\lambda t}

$N \in \left[10, 5000\right]$

where

N: Neck counts (cps)
B: Thigh background (cps)
S: Standard counts (cps)
\lambda: Decay constant (1/h)
t: Time since standard (h)
U: Thyroid uptake (%)

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

U_{\%}=100\,(N-B)/S\,e^{\lambda t}

$N \in \left[10, 5000\right]$

$N = 10$ $U = 0$

Along the curve

②

Domain of the variable — blue

N_{\min} = 10,\quad N_{\max} = 5000

$N \in \left[10, 5000\right]$

$N = 10$ $N = 10$

Along the curve

③

Response curve — green

U_{\%}=100\,(N-B)/S\,e^{\lambda t}

$N \in \left[10, 5000\right]$

$N = 10$ $U = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}U}{\mathrm{d}N}

$N \in \left[10, 5000\right]$

$N = 41.38$ $U^{\prime} = 0$

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-21 — Thyroid uptake) is the form associated with Thyroid uptake. Working symbols: $N$ , $B$ , $S$ , $\lambda$ , $t$ $\rightarrow$ $U$ . 24 h uptake is 10–30 % in euthyroid patients on iodine-123 or 131. Neck minus thigh removes extra-thyroidal counts.

Purpose

Purpose: compute

U

from

N

B

S

\lambda

t

in Nuclear medicine via

U_{\%}=100\,(N-B)/S\,e^{\lambda t}

U% = 100 (Neck − Thigh)/Std × e^{λt}. Probe uptake with background and 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

N = 800.000\,\mathrm{cps}

B = 80.000\,\mathrm{cps}

S = 2500.000\,\mathrm{cps}

\lambda = 0.005\,\mathrm{1/h}

t = 24.000\,\mathrm{h}

, the governing relation

U_{\%}=100\,(N-B)/S\,e^{\lambda t}

yields

U = 32.63\,\mathrm{%}

. A neck probe, a thigh background, a standard. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Neck counts N800 cpsThigh background B80 cpsStandard counts S2500 cpsDecay constant \lambda0.0052 1/hTime since standard t24 h

Outputs

Thyroid uptake U32.63 %

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Narration of this film

A neck probe, a thigh background, a standard.

24 h uptake is 10–30 % in euthyroid patients on iodine-123 or 131. Neck minus thigh removes extra-thyroidal counts.

Reading speed

Watch on YouTube