# Basic Physics of Nuclear Medicine/Three-Dimensional Visualization Techniques

## Introduction

This is a developing chapter of a wikibook entitled Basic Physics of
Nuclear Medicine.

Three-dimensional visualization techniques are used to integrate a
series of tomographic slices into a form which is often easier to
interpret than the slices on their own. An overview of the major
visualization techniques used in medical imaging is presented in this
chapter. We\'ll start with the integration of two-dimensional (2D) axial
images before considering various three-dimensional (3D) image
presentation methods.

The following set of images will be used to help us with our task. They
consist of a SPECT lung-ventilation study, illustrated by the animated
sequence on the left, a SPECT lung-perfusion study, in the middle, and a
CT pulmonary angiogram (CTPA) from the same patient on the right:

  -------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- -- -- -------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- -- -- ----------------------------------------------------------------------------------------------------------------------------------------------
  !Animated sequence from a patient\'s SPECT lung-ventilation study.{width="256"}            !Animated sequence from the patient\'s SPECT lung-perfusion study.{width="256"}            !Animated sequence from the patient\'s X-ray CTPA study.{width="256"}
                                                                                                                                                                                                                                                                                                                                                              
  -------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- -- -- -------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- -- -- ----------------------------------------------------------------------------------------------------------------------------------------------

We\'ll use these image sets at various stages in this chapter so as to
provide examples which will help with demonstrating the essence of the
techniques we\'ll consider. Acquisition factors for the image sets
include 128 x 128 pixel slices each of thickness 4.8 mm for the SPECT
studies and 512 x 512 pixel contiguous slices of thickness 1.5 mm for
the axial images reconstructed from the CTPA helical scan. In addition,
the lung-perfusion scan was acquired immediately following the
ventilation scan, so that residual activity from the latter is present
in the former at a level of about 20%.

Its helpful, before proceeding, to consider the axial slices, be they
SPECT or CT, stacked one behind the other, as illustrated below:

!A stack of SPECT tomograms from a perfusion study of a patient\'s
lungs.

Notice that the figure illustrates each image as a thin slice when the
data represents in reality a slice wide enough to fill the gap between
it and the next slice, so that the image data can be considered to be a
matrix of volume elements -- called voxels for
short.

A convention applied in medical imaging is to display axial image stacks
with the axes oriented as shown in the following figure:

!Labels for the axial imaging
space.

So the left side of an axial scan represents the patient\'s right side
viewed from below, with their anterior surface at the top of the image.
A modification of a little ditty by Spike
Milligan might help you remember this
perspective:

  -----------------------------------------------------------------
  `<i>`{=html}I\'d love to be a fish,`</i>`{=html}
  `<i>`{=html}Who could swim beneath the ice,`</i>`{=html}
  `<i>`{=html}And look up at all the people skating,`</i>`{=html}
  `<i>`{=html}Oh wouldn\'t it be nice!`</i>`{=html}
  -----------------------------------------------------------------

You\'re likely to find that its a good idea to experience the real thing
when reading this chapter so as to help overcome the abstract nature of
many of the topics we\'ll encounter, as well as the limitations of using
a 2D medium (i.e. this webpage) to communicate 3D visualization
concepts. Numerous open source 3D programs and image libraries are
available via the World Wide Web. The
software used to generate images in this chapter, for instance, includes
OsiriX (MacOS X only),
Madena and
ImageJ (multi-platform).

## Axial Projection

The first technique we\'ll consider is a relatively simple one called
**Axial Projection**. It involves integrating a number of axial images
to display a composite which presents a three-dimensional impression of
that volume of image data. The technique is sometimes referred to as
**Thick Slab** or **Z-Projection**.

The figure below illustrates the outcome of a range of z-projection
methods, with a single slice shown in the bottom right hand corner for
reference purposes. The first image in the top left shows the result of
summing 16 slices, and the other two images on that row show the results
of computing the mean and median of these slices.

!A range of z-projections of 16 axial slices from the CT scan, with a
reference, single slice shown in the bottom right
corner.

The first two images in the second row show the result of what are
called a **Maximum Intensity Projection**
(MIP) and a **Minimum
Intensity Projection** (MinIP), respectively. A MIP evaluates each voxel
along each line of voxels through the volume to determine the maximum
voxel value and forms an image using the values so determined for each
line. A MinIP uses the minimum voxel values, as illustrated in the
following figure:

!A single line of voxels through eight axial slices illustrating the
determination of the maximum voxel value for MIPs on the left, and the
minimum value for MinIPs on the
right.

Volume rendered projections are shown in the first two images along the
bottom row of our collection of example axial projections. This image
compositing method involves applying an opacity function to the voxel
data as well as a recursive addition of the resulting data. An equation
of the form:

```{=html}
<div class="center">
```
`<span style="color:red;">`{=html}`<big>`{=html}C~n~ = A~n~ +
B~n~`</big>`{=html}`</span>`{=html}

```{=html}
</div>
```
where

:   

    :   `<span style="color:red;">`{=html}A~n~ = (α).(Voxel Value of
        voxel, n)`</span>`{=html},
    :    
    :   `<span style="color:red;">`{=html}B~n~ = (1-α).(Voxel Value of
        voxel, n-1)`</span>`{=html}, and
    :    
    :   `<span style="color:red;">`{=html} α = opacity`</span>`{=html},
        in the range `<span style="color:red;">`{=html}0`</span>`{=html}
        (i.e. fully transparent) to
        `<span style="color:red;">`{=html}1`</span>`{=html} (i.e. fully
        opaque),
    :    

is applied to each line of voxels as illustrated in the following
figure:

!Illustration of the volume rendering
technique.

The figure shows the line of voxels we\'ve used previously with an
opacity table in the top right corner. The opacity function shown is one
where a zero opacity is applied to voxel values below a threshold level,
a linear increase in opacity is applied to an intermediate range of
voxel values and maximum opacity applied to high voxel values. The
opacity table is somewhat like the look-up table used for greyscale
windowing which we\'ve described
earlier,
with the function applied to the opacity of voxel values instead of to
their grey levels. Note that more complex opacity tables to the one used
in our figure above can be also applied, e.g. logarithmic and
exponential functions.

The bottom half of the figure shows the steps involved in calculating
the volume rendered value of the composited voxel. Voxel values are
shown on the top row with opacity values, derived from a crude opacity
table, for each voxel shown on the second row. The third, fourth and
fifth rows detail the values of
`<span style="color:red;">`{=html}A`</span>`{=html},
`<span style="color:red;">`{=html}B`</span>`{=html} and
`<span style="color:red;">`{=html}C`</span>`{=html}, calculated using
our volume rendering equation above. The final voxel value is obtained
by summing the bottom row, and normalizing the result to, say, a 256
level grey scale.

The outcome of this form of processing is the generation of an image
which includes visual depth cues on the basis that similar voxel values
will be displayed with a similar transparency and those closest to the
reference slice having a stronger contribution than those from more
distal slices. Further, note that all voxel values in each line
contribute to the rendered image, in contrast to the limited number of
voxels that contribute to a MIP or a MinIP image. A 3D effect results
from volume rendering, as illustrated in the images above.

Notice that volume rendering can be applied from distal to proximal
slices, as illustrated in our figure, as well as in the opposite
direction, i.e. from proximal to distal slices. Hence the terms **Volume
Rendering Up** and **Volume Rendering Down** used in our set of nine
example images above.

The type of axial projection method appropriate to an individual patient
study is dependent on the anatomical and/or functional information of
relevance to the diagnostic process. Let\'s take the case of imaging
contrast-filled blood vessels, for example, in our nine example images
above. Note that a MIP can be used to give a visually-stunning
impression of the vessel bed in the patient\'s lungs. There\'s little
depth information in this projection, however, so that overlapping and
underlying vessels can obscure lesions that might be present in blood
vessels of interest. The application of this form of axial projection to
angiography is therefore limited to studies where vessel overlap isn\'t
an issue. The inclusion of voxel transparency and depth weighting in
volume rendered images addresses this limitation of MIP processing.

A final point to note is that this form of image projection can also be
applied to multi-planar reconstructions of axial slices, which we\'ll
consider next\.....

## Multi-Planar Reconstruction

In the simplest case, multi-planar reconstruction (MPR) involves
generating perspectives at right
angles to a stack of axial
slices so that coronal and sagittal images can be generated. We\'ll
start this section by describing these orthogonal projections before
considering their synchronized composite display. We\'ll also describe
three variants on this theme: oblique reconstruction, curved
reconstruction and integrated three-dimensional presentation.

-   `<big>`{=html}Coronal Reconstruction`</big>`{=html}

:   

    :   Here the image stack is rotated so that the z-axis becomes the
        vertical and a stack of images is reconstructed using parallel
        planes of voxels arranged from the patient\'s anterior to
        posterior surface, as illustrated in the following figure:

!Labels for the coronal image
space.

:   

    :   Example coronal reconstructions from our image sets are shown
        below:

  ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- -- -- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  !Animated sequence of reconstructed coronal slices from a SPECT lung-perfusion study.            !Animated sequence of reconstructed coronal slices from a CT pulmonary angiography (CTPA) study. study.")
                                                                                                                                                                                                             
  ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- -- -- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

:   

    :   Here the reconstructed slices are typically displayed from the
        patient\'s anterior to their posterior surface with the
        patient\'s head towards the top of the slices and their right
        hand side on the left of the slices.

-   `<big>`{=html}Sagittal Reconstruction`</big>`{=html}

:   

    :   Sagittal reconstructions are possible through additional
        rotations of the image stack so that a patient\'s left-to-right
        slice sequence can be generated as illustrated in the following
        figure:

!Labels for the sagittal image
space.

:   

    :   Example sagittal reconstructions from our image sets are shown
        below:

  ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- -- -- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  !Animated sequence of reconstructed (left-to-right) sagittal slices from a SPECT lung-perfusion study. sagittal slices from a SPECT lung-perfusion study.")            !Animated sequence of reconstructed (left-to-right) sagittal slices from a CT pulmonary angiography (CTPA) study. sagittal slices from a CT pulmonary angiography (CTPA) study.")
                                                                                                                                                                                                                                               
  ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- -- -- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

:   

    :   Here the reconstructed slices are typically displayed from the
        patient\'s left to right side, with their head towards the top
        and their anterior surface towards the left of the slices. Note
        that a right-to-left sagittal stack can also be generated using
        additional geometric transformation of the data.

-   `<big>`{=html}Composite MPR Display`</big>`{=html}

:   

    :   Coronal and sagittal reconstructions are referred to as
        Orthogonal MPRs because the perspectives generated are from
        planes of image data which are at right angles to each other.
        Composite MPR displays can be generated so that linked cursors
        or crosshairs can be used to locate a point of interest from all
        three perspectives, as illustrated in these images:

  ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  !A composite orthogonal MPR display with linked cursors on the axial and sagittal images.   !A composite orthogonal MPR display with linked crosshairs on all three images.
                                                                                                                                                                                                          
  ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

:   

    :   This form of image presentation is sometimes referred to as a
        **TCS** display -- implying the viewing of
        _T_ransaxial,
        _C_oronal and
        _S_agittal slices. It can be combined
        with the slice projection methods we discussed earlier, as
        illustrated in the two sets of images below, where the blue
        lines highlight the limits of the coronal projections:

!Axial and sagittal reconstructions from the SPECT lung-perfusion study
with various coronal
projections.

!Axial and sagittal reconstructions from the CT study with a coronal
MIP.

-   `<big>`{=html}Oblique Reconstruction`</big>`{=html}

:   

    :   Oblique MPRs are possible by defining angled planes through the
        voxel data , as illustrated in the following figure:

!CT MPR incorporating an oblique
MIP.

:   

    :   Here the plane can be defined in, say, the axial images (red
        line, top left) and a maximum intensity projection (the limits
        used are highlighted by the blue lines), for example, can be
        displayed for the reconstructed plane (right). This technique is
        useful when attempting to generate perspectives in cases where
        the visualization of three-dimensional structures is complicated
        by overlapping anatomical detail.

-   `<big>`{=html}Curved Reconstruction`</big>`{=html}

:   

    :   Curved MPRs can be used for the reconstruction of more complex
        perspectives, as illustrated in the next figure:

!An axial slice from the CT scan on the left with a curve (highlighted
in green) which is used to define the reconstruction on the
right. which is used to define the reconstruction on the right.")

:   

    :   Here a curve (highlighted in green) can been positioned in the
        axial images (left panel) to define a curved surface which
        extends through the voxel data in the z-direction, and voxels
        from this data can be reconstructed into a two-dimensional image
        (right panel). Note that more complex curves than the one
        illustrated can be generated so that, for instance, the
        three-dimensional course of a major blood vessel can be
        isolated, or CT head scans can be *planarized* for orthodontic
        applications.

-   `<big>`{=html}3D Multi-Planar Reconstruction`</big>`{=html}

:   

    :   A final variant on the MPR theme is the generation of a
        three-dimensional display showing all three orthogonal
        projections combined so that a defined point of interest locates
        the intersection of the planes, as illustrated in the following
        figure:

!3D Orthogonal MPR rotating
sequence.

:   

    :   The point of intersection is located for illustrative purposes
        at the *centre* of the voxel data in the figure above. It can
        typically be placed at any point in the 3D data using
        interactive controls. In addition, the perspective used for the
        rotating sequence can typically be manipulated interactively to
        improve the visualization of a region of interest. Note that the
        image sequence illustrated above is one from a myriad of
        perspectives that can thus be generated. Note also that slice
        projections (e.g. MIPs) can be combined with this form of
        display to provide additional perspectives on a feature of
        interest.

## Maximum Intensity Projection

We\'ve described the maximum intensity projection (**MIP**) earlier in
the context of axial projection, where the maximum voxel value is
determined for lines running in parallel through the projected slice
thickness. A sequence of such images can be generated when this
computation is applied at successive angles around the voxel data. One
simple sequence is a rotating one for 360 degrees around the horizontal
plane, as illustrated in the left panel of the figure below, where the
maximum intensity is projected for every 9 degrees around the patient
and the resultant 40 images compiled into a repeating, temporal (e.g.
movie) sequence:

!3D MIPs of a CT scan: Horizontal rotating sequences using parallel
projections (left) and perspective projections
(right). and perspective projections (right).")

Notice that the 3D MIP derives its information from the most attenuating
regions of the CT scan (given that the
CT-number
is directly dependent on the linear attenuation coefficient) and hence
portrays bone, contrast media and metal with little information from
surrounding, lower attenuating tissues. Notice also that continued
viewing of the rotating MIP sequence can generate a disturbing effect
where the direction of rotation appears to periodically reverse -- which
may be an aspect of perceptual
oscillation.
The perspective MIP, illustrated in the panel on the right in the above
figure, can reduce this limitation by providing spatial cues which can
be used to guide continued visual inspection.

Perspective projections can be generated by changing from the parallel
lines used to generate the parallel projections to lines of voxels which
diverge from an apparent point behind the volume at a distance such that
the viewer of the display can visualize closer features of the image
data as relatively larger than deeper features -- see the following
figure:

!Illustration of parallel (left) and perspective (right) projections
using conceptualized lateral views of the voxel data and the eye of the
viewer of the projected
image. and perspective (right) projections using conceptualized lateral views of the voxel data and the eye of the viewer of the projected image.")

## Volume Rendering

Volume rendering can be applied to the voxel data in the successive
rotation manner described for MIPs above, as illustrated by the results
in the following figure:

!3D VR: Parallel projection (left) and perspective projection
(right). and perspective projection (right).")

Note that the volume rendering can be contrast enhanced so as to
threshold, for instance, through the voxel values to eliminate low
attenuating surfaces, as illustrated in the following figure:

!3D VR contrast enhancement progressively applied, from top left to
bottom right panels, through the voxel value
range.

Note also that the colour look-up table (CLUT) can be varied to
highlight features of particular interest, as shown in the set of images
below:

!3D volume renderings using four different
CLUTs.

The influence of the opacity table is illustrated in the following
example images:

!3D volume renderings using four different opacity
tables.

The influence on volume rendering of various shading settings is shown
below:

!3D VR shading comparison.

The shading settings used for the above images are as follows:

+-------------+-------------+-------------+-------------+-------------+
| Image       | Ambient     | Diffuse     | Specular    | Specular    |
|             | Coefficient | Coefficient | Coefficient | Power       |
+=============+=============+=============+=============+=============+
| Top Left    | ```{=html}  | ```{=html}  | ```{=html}  | ```{=html}  |
|             | <div clas   | <div clas   | <div clas   | <div clas   |
|             | s="center"> | s="center"> | s="center"> | s="center"> |
|             | ```         | ```         | ```         | ```         |
|             | 0.15        | 0.9         | 0.3         | 15.0        |
|             |             |             |             |             |
|             | ```{=html}  | ```{=html}  | ```{=html}  | ```{=html}  |
|             | </div>      | </div>      | </div>      | </div>      |
|             | ```         | ```         | ```         | ```         |
+-------------+-------------+-------------+-------------+-------------+
| Top Middle  | ```{=html}  | ```{=html}  | ```{=html}  | ```{=html}  |
|             | <div clas   | <div clas   | <div clas   | <div clas   |
|             | s="center"> | s="center"> | s="center"> | s="center"> |
|             | ```         | ```         | ```         | ```         |
|             | `<span sty  | 0.9         | 0.3         | 15.0        |
|             | le="color:r |             |             |             |
|             | ed;">`{=htm | ```{=html}  | ```{=html}  | ```{=html}  |
|             | l}0.75`</sp | </div>      | </div>      | </div>      |
|             | an>`{=html} | ```         | ```         | ```         |
|             |             |             |             |             |
|             | ```{=html}  |             |             |             |
|             | </div>      |             |             |             |
|             | ```         |             |             |             |
+-------------+-------------+-------------+-------------+-------------+
| Top Right   | ```{=html}  | ```{=html}  | ```{=html}  | ```{=html}  |
|             | <div clas   | <div clas   | <div clas   | <div clas   |
|             | s="center"> | s="center"> | s="center"> | s="center"> |
|             | ```         | ```         | ```         | ```         |
|             | 0.15        | `<span st   | 0.3         | 15.0        |
|             |             | yle="color: |             |             |
|             | ```{=html}  | red;">`{=ht | ```{=html}  | ```{=html}  |
|             | </div>      | ml}0.1`</sp | </div>      | </div>      |
|             | ```         | an>`{=html} | ```         | ```         |
|             |             |             |             |             |
|             |             | ```{=html}  |             |             |
|             |             | </div>      |             |             |
|             |             | ```         |             |             |
+-------------+-------------+-------------+-------------+-------------+
| Bottom Left | ```{=html}  | ```{=html}  | ```{=html}  | ```{=html}  |
|             | <div clas   | <div clas   | <div clas   | <div clas   |
|             | s="center"> | s="center"> | s="center"> | s="center"> |
|             | ```         | ```         | ```         | ```         |
|             | 0.15        | 0.9         | `<span st   | 15.0        |
|             |             |             | yle="color: |             |
|             | ```{=html}  | ```{=html}  | red;">`{=ht | ```{=html}  |
|             | </div>      | </div>      | ml}1.2`</sp | </div>      |
|             | ```         | ```         | an>`{=html} | ```         |
|             |             |             |             |             |
|             |             |             | ```{=html}  |             |
|             |             |             | </div>      |             |
|             |             |             | ```         |             |
+-------------+-------------+-------------+-------------+-------------+
| Bottom      | ```{=html}  | ```{=html}  | ```{=html}  | ```{=html}  |
| Middle      | <div clas   | <div clas   | <div clas   | <div clas   |
|             | s="center"> | s="center"> | s="center"> | s="center"> |
|             | ```         | ```         | ```         | ```         |
|             | 0.15        | 0.9         | 0.1         | `<span st   |
|             |             |             |             | yle="color: |
|             | ```{=html}  | ```{=html}  | ```{=html}  | red;">`{=ht |
|             | </div>      | </div>      | </div>      | ml}1.0`</sp |
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|             |             |             |             | </div>      |
|             |             |             |             | ```         |
+-------------+-------------+-------------+-------------+-------------+
| Bottom      | ```{=html}  | ```{=html}  | ```{=html}  | ```{=html}  |
| Right       | <div clas   | <div clas   | <div clas   | <div clas   |
|             | s="center"> | s="center"> | s="center"> | s="center"> |
|             | ```         | ```         | ```         | ```         |
|             | 0.15        | 0.9         | `<span st   | `<span st   |
|             |             |             | yle="color: | yle="color: |
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|             | </div>      | </div>      | ml}0.6`</sp | ml}1.0`</sp |
|             | ```         | ```         | an>`{=html} | an>`{=html} |
|             |             |             |             |             |
|             |             |             | ```{=html}  | ```{=html}  |
|             |             |             | </div>      | </div>      |
|             |             |             | ```         | ```         |
+-------------+-------------+-------------+-------------+-------------+
|             |             |             |             |             |
+-------------+-------------+-------------+-------------+-------------+

A final feature to note about volume rendering is that 3D editing
techniques can be applied so as to exclude unwanted features from the
computations and to expose internal structure. This is illustrated in
the following figure, where planes of an orthogonal frame can be moved
to crop the voxel data from six directions.

!3D volume rendering with cropping frame (left) and cropped, magnified
projection
(right). and cropped, magnified projection (right).")

## Surface Rendering

Surface rendering is also referred to as Shaded Surface Display
(**SSD**) and involves generating
surfaces
from regions with similar voxel values in the 3D data as illustrated by
the SPECT lung-perfusion scan shown in the left panel below:

!3D surface rendering: shaded surface and wireframe
display.

The process involves the display of surfaces which might potentially
exist within the 3D voxel data on the basis that the edges of objects
can be expected to have similar voxel values. One approach is to use a
grey-level thresholding technique where voxels are extracted once a
threshold value is encountered in the line of the projection -- see the
following diagram. Triangles are then used to tesselate the extracted
voxels, as shown in the right panel of the figure above -- and the
triangles are filled using a constant value with shading applied on the
basis of simulating the effects of a fixed virtual light source -- as
shown in the left panel above.

!Illustration of surface
rendering.

An opacity table can be applied to the results so that surfaces from
internal features can also be visualized. As an example, two surfaces
have been identified in the following image from the CT scan where voxel
values from bone surfaces are coded in an opaque yellow colour and
tissue surfaces in a transparent shade of red.

!SSD of two surfaces.

A second example of using an opacity table is shown in the following
figure. Here, axial CT data from the patient\'s airways have been
segmented using a region
growth
technique and the result processed using surface rendering, with full
opacity as shown in the left panel and with a reduced opacity (30%) as
shown in the right panel:

!3D SSD: opaque and transparent
display.

Notice that internal features of each lung can be discerned when the
opacity is reduced. Notice also that continued viewing of this type of
transparency display can generate apparent reversal of the image
rotation, similar to that noted for the 3D MIPs above. One method of
overcoming this type of problem is to segment each lung, for instance.
and to blend the results, as illustrated in the following figure:

!3D SSD: blending of each lung following
segmentation.

## subFusion Processing

We\'ll conclude this chapter by considering an application of 3D
visualization which integrates many of the image processing techniques
we\'ve described in this wikibook. We\'ll use the two SPECT scans, from
a patient\'s lung-ventilation (V) and lung-perfusion (Q) studies, in an
attempt to visualize any mismatch(es) characteristic of pulmonary
embolism (PE). The application we\'ll consider is called **subFusion
Processing** because it involves both image subtraction and image fusion
techniques.

Note again that the SPECT studies were generated using a *swamping*
technique where the perfusion scan was acquired immediately following
the ventilation scan using an administered activity which generated a
relative count rate of about 5:1 between scans. The first image
processing step therefore is to correct the perfusion scan for the
*background* ventilation activity.

Since the ventilation tracer in this case was administered using a
aerosol, we can assume for simplicity that its biodistribution is
reasonably identical in the two scans. Further, since the scans were
acquired about 15 minutes apart using the ^99m^Tc radioisotope, we can
assume a negligible effect from radioactive decay. We can simply
therefore subtract the ventilation stack from the perfusion stack, on
the basis of these assumptions, to isolate what we\'ll call the \"pure
perfusion\" scan.

The second step is to normalize the two scans by multiplying the
ventilation stack by a factor such that the mean counts (for example) in
the two stacks are similar.

:   `<span style="color:green;">`{=html}*We can now compare apples with
    apples!*`</span>`{=html}

Since a PE mismatch is likely to arise from regions of the lungs which
contain counts in the ventilation scan and are relatively bereft of such
counts in the perfusion scan, we can subtract the \"pure perfusion\"
stack from the ventilation stack, as a third image processing step, to
isolate any such differences as positively-valued features.

The final image processing step is to volume render this difference
stack along with the \"pure perfusion\" scan and to blend the results,
as illustrated in the following image:

frame\|center\|subFusion processing applied to a SPECT lung
ventilation-perfusion scan: Both lungs of the patient displayed on the
left, with their right lung displayed in the top right and their left
lung below it. The \"pure perfusion\" scan is displayed using a
grey-scale and the difference data using a spectrum CLUT, where large
differences are coded in red with intermediate differences in yellow and
smaller differences in green.

The steps involved are outlined in the following diagram. Note that
minor processes, such as CLUT selection, relative opacity adjustment and
contrast enhancement are omitted from this diagram for the sake of
simplicity. Note also that an image
registration
step may need inclusion at the beginning of the procedure in cases where
patient movement occurs between the two SPECT acquisitions.

!Block diagram of the 3D subFusion
process.

A final point to note is the larger appearance of the patient\'s lungs
in the segmented CTPA images relative to the SPECT images. This arises
because the CTPA study was acquired using a single breath-hold and the
SPECT studies with the patient breathing quietly over the period of
gamma camera rotation. The spatial registration of the three sets of
images is therefore not possible directly, and would require the
application of spatial warping and
other techniques which, unfortunately, are beyond the scope of our
treatment here.

