CPET - Reconstruction Filters, Image Resolution, ROI size, etc.*

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Measured image resolution for various reconstruction filters

The following graphs plot the "x" dimension Full Width Half Maximum (FWHM) and Full Width Tenth Maximum (FWTM) values of image activity intensity distributions measured for a point source imaged on our Siemens ECAT 951/31-R PET Camera. A general guideline for resolving two distinct objects is that they must be separated by at least twice the FWHM resolution value of the image.

Method:

Graphs (resolution and c(f)):

In the functional descriptions of the filters below, f = frequency and F = cutoff frequency. (Functional forms from Siemens Operating Instructions ECAT Scanner Software, Sept. 1991, section 13, page 34).

BUTTERWORTH measured resolution

HAMM measured resolution

HANN measured resolution

PARZEN measured resolution

RAMP measured resolution

SHEPP measured resolution

Effects of Finite Image Resolution and ROI size/placement

Visual Aid - (13,202 bytes) - view this while reading the material discussed below

Solid and dotted lines

Actual Phantom

Imagine a phantom (container) to be imaged which consists of a hollowed out square bar, 5[cm] on a side, filled with activity and imaged in a PET camera. If you were to examine one of the resulting images, and plot a line profile of activity vs. distance for an arbitrary horizontal row of pixels passing through the phantom, scaled so that the maximum activity reported was 1.0, what you would hope to see is a graph which looks like the solid line labeled "Actual Phantom".

Point Spread Function

Unfortunately, the PET camera is limited in terms of its resolution, due to both finite detector size and the filter/cutoff frequency chosen in filtered backprojection for image reconstruction. If you were to put a point source in the center of the camera and image it, what you would see is a profile response in the reconstructed image representing the Point Spread Function (PSF). Even though there'd only be real activity at the exact center of the camera (X=0), because of the finite camera resolution your image would have an activity profile which looked similar to the PSF shown. This PSF has a Full Width Half Maximum (FWHM) value of 0.5[cm].

Reconstructed Image

The effects of finite image resolution are reflected in the solid line plotting the "Reconstructed Image" activity profile. Just as with the point source, near the edges of the phantom, activity from inside the phantom is spread to areas outside the phantom - giving us signal where there is none (spillover effect) - and areas just outside the phantom contribute "non-signal" to regions just inside the phantom thus lowering the activity profile inside the phantom at its edges (partial volume effect).

You can think of the PSF as a smoothing filter. The actual phantom profile, smoothed (convolved) with the PSF during data acquisition and image reconstruction, results in the reconstructed image profile. At this point, this profile represents what the output image will look like given the PSF shown. You never get to see an image the is identical to the actual source distribution. The only control you have over this type of information degradation is to try and reduce the FWHM of the PSF by varying the filter type and its cutoff frequency in the image reconstruction process. Conversely, increasing the FWHM of the PSF makes the effect more dramatic and extend farther inside and outside from the phantom's edge.

ROI Size/Placement considerations

Up to this point we've examined the activity profiles pixel by pixel. However, when data is taken from an image, it is traditionally done by drawing a region of interest (ROI) on the image and reporting the average value of all pixels contained in the ROI. If the ROI is larger than one pixel in size, then it too can be though of as smoothing the image in a way that is identical to the way our PSF smoothed the image. The same relationships hold here as in the PSF. The narrower you can make the smoothing function (in this case the ROI width), the smaller its smoothing effect will be.

Five ROIs of varying widths are shown. The edge-to-edge size of the ROIs have been defined as multiples of the PSF FWHM value. N=1 is an ROI whose width is identical to the PSF FWHM, N=2 is an ROI whose width is twice the PSF FWHM, etc. These ROIs are drawn inside the phantom and plotted at arbitrary heights to give you a feel for how big (x-dimension) they are relative to the actual phantom.

The dotted lines associated with these ROIs represent what you get when the reconstructed image is further smoothed by the ROI's finite size. If you pick a location on the x-axis, the y-value of the dotted line above (associated with a particular ROI) represents the average pixel value which would be reported for that ROI. It is easy to see from the graph that as the ROI gets bigger, the area along the x-axis where it will report the 'correct' value of activity=1.0 becomes smaller and smaller. If the ROI were the same size as the original source, no matter where you placed the ROI, it would underestimate the actual amount of activity present because it would always include the activity of some pixels from outside the source. However, as long as we draw our ROI the same size or smaller than the width of the source's 100% level in the reconstructed image, the ROI will correctly reflect the original source's activity (note that the size of this 100% region in the reconstructed image is always smaller than the actual dimensions of the original source).

Source Size / Image Resolution (PSF) / ROI Size & Placement

These graphs illustrate the effects of ROI and Source size relative to the size of the PSF FWHM.

Cases where the adjacent regions contain activity

In the examples above, both regions adjacent to the uniform source were set up to contain no activity. What happens when this is not the case? Suppose the regions on either side of our uniform source region also contain activity. In this case, the same graphs can be used, but you must consider their y-values in a slightly different way. In the examples, the uniform source region was defined as having an arbitrary activity level of 1.0. Looking at things this way, the y-values represented actual activity levels one would see in the "reconstructed image" or in a ROI of a given size.

Another, more useful, way of looking at these values is to consider them as representing the fractional contribution (Fc) that activity from within the uniform source region will make to a pixel or ROI centroid at a given location (x-value). When viewed this way, a value of 1.0 on the "reconstructed image" or "ROI" curves means that 100% of the activity being used to come up with the activity level for that pixel is coming from within the uniform source region. When the value is 1.0, partial volume and spillover are not a problem. A value of 0.25, on the other hand, means that only 25% of the activity inside the uniform source region is contributing to the activity value at that pixel whereas 1.0-0.25=0.75 or 75% of the activity in the pixel is coming from a location outside of the uniform source region. If the uniform region had an activity level of 0.2[µCi/cc], and the adjacent area had an activity level of 0.4[µCi/cc], then the pixel with a Fc of 0.25 would report an activity level of 0.25*0.2[µCi/cc] + 0.75*0.4[µCi/cc] = 0.35[µCi/cc].

Of course this generalization only holds providing the source region on the outside of the central uniform source region in the example plots is also uniform and of large extent relative to the PSF FWHM and ROI size. For an arbitrary source distribution, the Fc curve of the reconstructed image is found by convolving the original source distribution with the PSF. Convolving this result, in turn, with the ROI distribution then results in the Fc curve for that particular ROI.

Multiple Sources (12,268 bytes) - In this example, multiple sources are present and "reconstructed image" as well as ROI reported values for various sized ROIs are presented. Note that there is only one location on the entire graph where the activity in a pixel for the reconstructed image matches the activity actually present in the source (at x=-0.5). Similarly, for each sized ROI, there is only one pixel where the reported ROI activity matches that of the original source, and the location of the ROI centroid where this condition occurs is in a different place for each ROI. For any other pixel in this generated image, the activity levels reported never match those in the original image; of course this effect was simple to achieve by simply constructing all the sources to have widths which were less than or equal to twice the PSF FWHM value.

Take Home Messages

Note: Everything discussed so far deals only with within plane resolution. Between plane resolution considerations are similar (except that traditionally, ROIs have not been drawn across planes).

  1. If the size of the source you want to image is smaller than 3x the PSF FWHM then it is impossible to correctly determine the actual activity in the source because no pixel in the reconstructed image will contain activity that comes from that source alone.
  2. The size of the source in the image, based on edges obtained by thresholding at 100% of the source's actual activity level, will always be SMALLER than the size of the actual source. This effect becomes more pronounced as the PSF FWHM increases. It is a reasonable generalization to say that the edges of the source obtained this way - as seen in the image - will be about one PSF FWHM inside the edges of the actual source. Another way to say this is: EXTENT(image) ~= EXTENT(actual)-2*FWHM(psf); any time this value becomes negative, no portion of the image will accurately reflect the source activity alone.
  3. Drawing ROIs can be thought of as adding a second smoothing to the image. However, as long as the edges of the ROI remain within the 100% level region of the source as seen on the image, they will correctly report the source's activity levels (provided the PSF FWHM meets the criteria in [1]). Of course things become more complex when your source is surrounded by other sources of activity since they may artificially extend what you think is the 100% level region if their activity levels are the same as those of your target source.
  4. If a large PSF FWHM is so evil, why shouldn't you always reconstruct with a filter that reduces it to the smallest possible value? That's another discussion, but the short answer is that as you do less smoothing, the images become noisier; as this happens, it becomes more difficult for the human eye to distinguish between structures. So, although any given pixel will be less contaminated with the activity of other pixels when the PSF FWHM is reduced, humans have a difficult time interpreting the resulting images. In practice then (for visual interpretation) you want to choose a filter with the smallest PSF FWHM that still permits humans to feel comfortable when viewing the image.
    1. This suggests one possible approach to take when drawing ROIs: Reconstruct you image with two filters. The first filter will be your "visual interpretation" filter. It's PSF FWHM will be chosen as suggested above - as high as possible but still permitting visual identification of structure. ROIs would be drawn on this image. A second image would be reconstructed with the smallest PSF FWHM possible. ROIs from the 1st image would be retrieved and then computed (after some possible enlargement) on this second "computational" image. In theory this would permit you to draw larger ROIs encompassing true source activity levels. In practice, it is not clear that the slight improvement in your activity values would be worth the extra work. The one exception to this would be when you knew the PSF FWHM of your "visual interpretation" image was larger than 1/3 the source size whereas the PSF FWHM of your "computational" image was < 1/3 of the source size. In this situation, if you couldn't draw ROIs on the "computational" image because of noise, this two-image approach may be the only way to properly retrieve correct ROI values.
  5. Drawing high percentage (say 95-105% of region maximum) isocontour ROIs in homogeneous tissue regions is perhaps the best way of ensuring thay you are using activity values from only the 100% recovery zone of that region in a given tissue (again, provided the criteria in [1] is met to insure that the center of a region actually does represent 100% of activity from that region). This technique only works, of course, when you can a-priori identify the "center" of the target (homogeneous) tissue region.

Effects on values computed from images

Standard Uptake Values (SUVs)

Standard Uptake Values (SUVs) represent a quasi-quantitative way of categorizing tracer uptake in tissue. They are computed by dividing the activity per unit mass in some target tissue by the injected activity normalized to body weight: (activity in tissue/mass of tissue)/(activity injected/body mass). Assuming the tracer is accumulated in tissue (as is 18-FDG), the SUV is a simplistic way of attempting to derive some number which can be compared across patients to give an indication of how much/rapidly the tracer is taken up in any given tissue. SUVs are used when more rigorous quantitation, e.g. determination of metabolic rates in the tissue, are not employed.

There are a number of technical limitations in the determination of any values obtained from regions of interest (ROIs) including placement of the ROI, size of the ROI relative to the structure you're obtaining data from, assuring the ROI is completely in the structure (both transaxially and axially), and partial volume effects contributed by intrinsic camera resolution and reconstruction filter resolution determined by the filter type and cutoff frequency.

The effects of reconstruction filters in filtered back projection can be thought of in terms of the amount of spatial smoothing they introduce into the image. For a given filter, the higher the cutoff frequency (in cycles/pixel), the less spatial smoothing the filter introduces into the image. For a given region where you want to determine the average activity level within that region, e.g. that represented by an ROI drawn over the tumor, the effect of smoothing is to bring activity level contributions from tissue voxels physically adjacent but outside the ROI into voxels which fall within the bounds of the ROI. If one has a large, homogeneous tumor on which one can place an ROI well within the boundaries of the tumor, then spatial smoothing will have little effect since the voxel activity levels of tissue surrounding the ROI are the same as those of tissues within the ROI - thus the averaging effect of spatial smoothing does not really affect measured ROI activity values. On the other hand, if the ROI includes the effective edge of the tumor or regions outside the tumor (which lies within the physical boundary of the tumor and ROI due to spatial smoothing), and the tissue surrounding the tumor has activity levels different than those inside the tumor, then SUV values are going to be dramatically affected by the activity averaging effect of spatial smoothing.

In the following two oncology subjects, a single ROI was drawn over what, by inspection, was considered to be the centroid of a tumor and the location of this ROI was saved to a file. The same raw camera data were then reconstructed into image sets using a variety of reconstruction filters and cutoff frequencies. The single saved ROI was then retrieved onto the various images and SUV values were computed for the ROI. The following graphs demonstrate the wide variation in SUV values. Variations within an image plane across filters are due solely to varying the cutoff frequency and filter specified during image reconstruction. Variations across image planes for a given filter are due solely to the ROI being placed over different sections of the tumor where differences can be due to both variations in tumor tissue tracer uptake, and variations in the amount of non-tumor tissue brought into the ROI by spatial smoothing. The original ROI was drawn in either plane 4 or plane 5.

General recommendations for filter cutoff and ROI placement in determining tumor SUV values that are minimally influenced by tissue outside the tumor.

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Last update: September 23, 2005