NMD-32

Partial-volume mixing

C_app = RC C_true + (1−RC) C_bg. Spill-in plus spill-out.

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QuantificationPartial volume

Governing equation

C_{\mathrm{app}}=RC\,C_{\mathrm{true}}+(1-RC)C_{\mathrm{bg}}

$RC \in \left[0.05, 1\right]$

where

RC: Recovery coefficient (—)
C_{true}: True concentration (kBq/ml)
C_{bg}: Background (kBq/ml)
C_{app}: Apparent concentration (kBq/ml)

The figure, part by part

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①

Governing law — red

C_{\mathrm{app}}=RC\,C_{\mathrm{true}}+(1-RC)C_{\mathrm{bg}}

$RC \in \left[0.05, 1\right]$

$RC = 0.05$ $C_{app} = 4.8$

Along the curve

②

Domain of the variable — blue

RC_{\min} = 0.05,\quad RC_{\max} = 1

$RC \in \left[0.05, 1\right]$

$RC = 0.05$ $RC = 0.05$

Along the curve

③

Response curve — green

C_{\mathrm{app}}=RC\,C_{\mathrm{true}}+(1-RC)C_{\mathrm{bg}}

$RC \in \left[0.05, 1\right]$

$RC = 0.05$ $C_{app} = 4.8$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}C_{app}}{\mathrm{d}RC}

$RC \in \left[0.05, 1\right]$

$RC = 0.056$ $C_{app}^{\prime} = 16$

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-32 — Partial-volume mixing) is the form associated with Partial volume. Working symbols: $RC$ , $C_{true}$ , $C_{bg}$ $\rightarrow$ $C_{app}$ . A hot lesion on a warm background is pulled toward C_bg. Recovery correction inverts this mixing.

Purpose

Purpose: compute

C_{app}

from

RC

C_{true}

C_{bg}

in Nuclear medicine via

C_{\mathrm{app}}=RC\,C_{\mathrm{true}}+(1-RC)C_{\mathrm{bg}}

C_app = RC C_true + (1−RC) C_bg. Spill-in plus spill-out. 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

RC = 0.600\,\mathrm{—}

C_{true} = 20.000\,\mathrm{kBq/ml}

C_{bg} = 4.000\,\mathrm{kBq/ml}

, the governing relation

C_{\mathrm{app}}=RC\,C_{\mathrm{true}}+(1-RC)C_{\mathrm{bg}}

yields

C_{app} = 13.60\,\mathrm{kBq/ml}

. A sphere, a background, a mixed mean. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Recovery coefficient RC0.6 —True concentration C_{true}20 kBq/mlBackground C_{bg}4 kBq/ml

Outputs

Apparent concentration C_{app}13.60 kBq/ml

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Narration of this film

A sphere, a background, a mixed mean.

A hot lesion on a warm background is pulled toward C_bg. Recovery correction inverts this mixing.

Reading speed

Watch on YouTube