NMD-18

Collimator resolution

Rc = d (Leff + z) / Leff. Hole diameter d, effective length Leff, distance z.

Reading speed

Gamma cameraCollimator resolution

Governing equation

R_c=d\,(L_{\mathrm{eff}}+z)/L_{\mathrm{eff}}

$z \in \left[10, 300\right]$

where

d: Hole diameter (mm)
L_{eff}: Effective length (mm)
z: Source distance (mm)
R_c: Collimator FWHM (mm)

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

R_c=d\,(L_{\mathrm{eff}}+z)/L_{\mathrm{eff}}

$z \in \left[10, 300\right]$

$z = 10$ $R_c = 2.125$

Along the curve

②

Domain of the variable — blue

z_{\min} = 10,\quad z_{\max} = 300

$z \in \left[10, 300\right]$

$z = 10$ $z = 10$

Along the curve

③

Response curve — green

R_c=d\,(L_{\mathrm{eff}}+z)/L_{\mathrm{eff}}

$z \in \left[10, 300\right]$

$z = 10$ $R_c = 2.125$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}R_c}{\mathrm{d}z}

$z \in \left[10, 300\right]$

$z = 11.82$ $R_c^{\prime} = 0.062$

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-18 — Collimator resolution) is the form associated with Collimator resolution. Working symbols: $d$ , $L_{eff}$ , $z$ $\rightarrow$ $R_c$ . Leff = L − 2/μ accounts for septal penetration. Resolution degrades linearly with distance.

Purpose

Purpose: compute

R_c

from

d

L_{eff}

z

in Nuclear medicine via

R_c=d\,(L_{\mathrm{eff}}+z)/L_{\mathrm{eff}}

Rc = d (Leff + z) / Leff. Hole diameter d, effective length Leff, distance z. 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

d = 1.500\,\mathrm{mm}

L_{eff} = 24.000\,\mathrm{mm}

z = 100.000\,\mathrm{mm}

, the governing relation

R_c=d\,(L_{\mathrm{eff}}+z)/L_{\mathrm{eff}}

yields

R_c = 7.75\,\mathrm{mm}

. A hole looking at a point a distance z away. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Hole diameter d1.5 mmEffective length L_{eff}24 mmSource distance z100 mm

Outputs

Collimator FWHM R_c7.75 mm

Reading speed

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Narration of this film

A hole looking at a point a distance z away.

Leff = L − 2/μ accounts for septal penetration. Resolution degrades linearly with distance.

Reading speed

Watch on YouTube