Sections

Example

<sec id="bk978-0-7503-3071-8ch2s2-2">
  <label>2.2</label>
  <title>…particle tracking</title>
  <p>Once we have, as described in the preceding section, created from one of the
  particles in our system a non-invasive ‘tracer particle’, we can place this
  particle back in the system, and begin to track its motion (see figure <xref ref-type="fig" rid="bk978-0-7503-3071-8ch2fig3">2.3</xref>). To do so, we
  must firstly place our system, with its newly-reintroduced tracer particle,
  within the field of view of a suitable detector system, often referred to as
  a ‘gamma camera’ or ‘positron camera’ (see figure <xref ref-type="fig" rid="bk978-0-7503-3071-8ch2fig3">2.3</xref>(a)). Detailed descriptions of
  the various types of gamma camera which may be used to perform PEPT, as well
  as the physics underlying these systems, can be found in chapter <xref ref-type="book-part" rid="bk978-0-7503-3071-8ch5">5</xref>. For now, it
suffices for us to know that, if a gamma photon of a suitable energy
interacts with one of the gamma camera’s detectors, it is able to record the
position of this interaction—i.e. where the photon ‘hit’ the camera. If two
gamma photons hit the detector system within a very short timing window
(typically of the order of nanoseconds), it is assumed that the two photons
were produced simultaneously—i.e. they both originated from a positron
annihilation event within our tracer particle. The registering of two
consecutive photons within the aforementioned timing window is known as a
‘coincidence event’.</p>
  <fig id="bk978-0-7503-3071-8ch2fig3" orientation="portrait" position="float">
    <label>Figure 2.3.</label>
    <caption>
      <p>Schematic diagrams showing an idealised representation of the manner
    in which PEPT may be used to locate a static tracer. (a) The tracer
    emits a pair of back-to-back gamma rays produced by the annihilation
    of a positron. (b) The coordinates at which the gamma rays hit the
    detector are recorded, allowing their trajectory to be recorded. (c)
    Multiple recorded trajectories (lines of response) can be used to
    triangulate the position of the tracer.</p>
    </caption>
    <graphic content-type="print" id="bk978-0-7503-3071-8ch2f3_eps" orientation="portrait" position="float" xlink:href="bk978-0-7503-3071-8ch2f3_pr.tif" xlink:type="simple"/>
    <graphic content-type="online" id="bk978-0-7503-3071-8ch2f3_online" orientation="portrait" position="float" xlink:href="bk978-0-7503-3071-8ch2f3_online.jpg" xlink:type="simple"/>
    <graphic content-type="high" id="bk978-0-7503-3071-8ch2f3_hr" orientation="portrait" position="float" xlink:href="bk978-0-7503-3071-8ch2f3_hr.jpg" xlink:type="simple"/>
  </fig>
  <p>From the previous section, we know that any pair of electrons produced by
  such an event follow a collinear, antiparallel trajectory—in other words, if
  both members of the pair interact with our detector system we must, by
  definition, be able to connect the two recorded points by a straight line
  (see figure <xref ref-type="fig" rid="bk978-0-7503-3071-8ch2fig3">2.3</xref>(b)). Further, we know that this straight line must pass through
(or at least near) the source of these positron annihilation events—i.e. our
tracer particle. Our gamma camera system will record the locations of all
detected photon pairs, allowing it to store and later ‘reconstruct’ these
straight line trajectories, which are typically referred to as ‘lines of
response’ or ‘LoRs’.</p>
  <p>Let us consider first, for simplicity, the case of a static tracer. As the <inline-formula>
    <tex-math>
      <?CDATA ${}^{18}{\rm{F}}$?>
    </tex-math>
    <mml:math overflow="scroll">
      <mml:mrow>
        <mml:msup>
          <mml:mrow/>
          <mml:mrow>
            <mml:mn>18</mml:mn>
          </mml:mrow>
        </mml:msup>
        <mml:mi mathvariant="normal">F</mml:mi>
      </mml:mrow>
    </mml:math>
    <inline-graphic xlink:href="bk978-0-7503-3071-8ch2ieqn17.gif" xlink:type="simple"/>
  </inline-formula> nuclei within the tracer decay, the particle will emit
  multiple pairs of gamma photons, of which a fraction will interact with the
  detector system, and have their trajectories recorded as LoRs. Clearly, if
  we know the point of intersection of these LoRs, then we can triangulate the
  position of our tracer (see figure <xref ref-type="fig" rid="bk978-0-7503-3071-8ch2fig3">2.3</xref>(c)).</p>
  <p>If the tracer particle is adequately active—i.e. produces a large enough
number of positrons per second—it is also possible to track its motion
through three-dimensional space by regularly triangulating its position.</p>
  <sec id="bk978-0-7503-3071-8ch2s2-2-1">
    <label>2.2.1</label>
    <title>Interactive example: PEPT—an idealised case</title>
    <p>The notebook files accompanying this section are available in the
    supplementary data online at <ext-link ext-link-type="uri" xlink:href="https://iopscience.iop.org/book/978-0-7503-3071-8/" xlink:type="simple">https://iopscience.iop.org/book/978-0-7503-3071-8</ext-link>.</p>
  </sec>
</sec>