### About the Sieman’s Symbia-T

I finally found the name and web page for the machine.
### Terminology

Terminology and history

SPECT Single-photon-emission computed tomography
In this document
Siemans uses “^{99m}Tc MDP bone scintigraphy” to describe one diagnostic procedure performed by their hardware.
This article describes a decay mode for ^{99m}Tc which involves no positron and thus no diametrically opposed gamma rays.
These observations may reduce the following to wishful thinking, or perhaps I have just not found the right system name for it.
I need to track down “gamma cameras”.

### How modern PET scans work

“Bone scan” means pretty much the same as “PET scan”.
I have had two and the 2nd time I figured out the physics and math work which I describe here.
A few hours before the procedure they put some NaF in your blood where some of the F is isotope 18 of Fluorine (^{18}F) whose half life is 110 minutes.
For chemical reasons that I have not explored the fluorine collects in the bones and the doctor uses the PET scan to find out where.
The scan machine looks at first to be a horizontal box about 120 cm long by 70 cm wide.
It is perhaps 20 cm high.
“Siemans” appears prominently on the small end of the box.
You lie down and an operator moves the box over you so that it nearly touches you.
What I did not see the first time is that there is a twin of the box very near beneath you.
What is relevant is that you are between two parallel arrays of gamma ray detectors.
They provide fairly good spatial resolution, perhaps a mm.

When the ^{18}F atom decays it emits a positron which doesn’t get very far in your body before it finds an electron with which to unite and convert their combined masses into the pure energy of two gamma rays moving in opposite directions along a common line.
The system geometry described above means that there is an excellent chance that both the upper and the lower detector arrays will observe simultaneous gamma photons and locate them accurately in their respective arrays.
This determines a line thru your body on which the event very likely occurred.
The parameters of such temporal coincidences are kept as raw observation data.

You move toward your head slowly, about 2mm per second, relative to the boxes.
It takes a while and sometimes they do retakes.

On my 2nd PET scan they briefly rotated the two boxes about the my body axis so that they were no longer horizontal.
Only then did I see the box below.
Without the 2nd box it was all quite mysterious.

### The Math

In 1917 as a pure geometric exercise
Radon considered whether the total masses of a every line thru a bounded 2D distribution determined that distribution.
By mass we mean here the total integral of the distribution along that line.
He showed that it did.
The CAT scan relies on this and sends all possible rays thru a 2D slice of your body and records each attenuation which amounts to measuring the total absorption of the X-ray along that line.
From that may be determined the varying density of the absorbing mass.
The 3D nature of CAT scans arrises from many such 2D slices.
The arithmetic is not trivial!
The PET scan, by contrast, starts from a 4D collection of line segments thru you and concludes where the points are that must have emitted them.
The arithmetic is even harder.

This article describes an older technology that included only ring detectors as in CAT scans.