NMD-16

Non-paralysable dead time

n = m / (1 − m τ). True rate from observed rate and dead time τ.

Reading speed

CountingDead time

Governing equation

n=m/(1-m\tau)

$m \in \left[1, 400\right]$

where

m: Observed rate (kcps)
\tau: Dead time τ (µs)
n: True rate (kcps)

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

n=m/(1-m\tau)

$m \in \left[1, 400\right]$

$m = 1$ $n = 1.002$

Along the curve

②

Domain of the variable — blue

m_{\min} = 1,\quad m_{\max} = 400

$m \in \left[1, 400\right]$

$m = 1$ $m = 1$

Along the curve

③

Response curve — green

n=m/(1-m\tau)

$m \in \left[1, 400\right]$

$m = 1$ $n = 1.002$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}n}{\mathrm{d}m}

$m \in \left[1, 400\right]$

$m = 3.509$ $n^{\prime} = 1.014$

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-16 — Non-paralysable dead time) is the form associated with Dead time. Working symbols: $m$ , $\tau$ $\rightarrow$ $n$ . Paralysable: m = n e^{−nτ}. Cameras mix both. Typical τ is 1–5 μs per event.

Purpose

Purpose: compute

n

from

m

\tau

in Nuclear medicine via

n=m/(1-m\tau)

n = m / (1 − m τ). True rate from observed rate and dead time τ. 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

m = 80.000\,\mathrm{kcps}

\tau = 2.000\,\mathrm{\mu s}

, the governing relation

n=m/(1-m\tau)

yields

n = 95.24\,\mathrm{kcps}

. A pulse train with forbidden gaps of length τ. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Observed rate m80 kcpsDead time τ \tau2 µs

Outputs

True rate n95.24 kcps

Reading speed

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Narration of this film

A pulse train with forbidden gaps of length τ.

Paralysable: m = n e^{−nτ}. Cameras mix both. Typical τ is 1–5 μs per event.

Reading speed

Watch on YouTube