# Fundamental limits of positron emission mammography Page: 3 of 5

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Accepted by Nuclear Instruments and Methods

Front View Top View

Plane 1 c

Plane 1 A B C A

PlaneP2

Plane 2 Ac C

B"

Plane 3P

C/ B Ak Plane 3

B

Figure 5. In focal plane tomography, lines are drawn between the

interaction points of coincident events in the camera (such as

lines AA, BB, and CC at the left). The intersection point of these

lines with multiple imaging planes (Planes 1-3) is computed and

the pixel value at these points are incremented, as shown on the

right (points A, B, and C in each of the three planes). The image

will be "in-focus" on planes that intersect the source, and

progressively "out-of-focus" for planes at increasing distance

from the source.

rectangular camera, as it is able to acquire projection data at

these angles.

V. RECONSTRUCTION ALGORITHMS

Because of these large gaps in the angular coverage, most

parallel plane PEM cameras do not use the reconstruction

techniques that are standard for conventional PET cameras

(such as Fourier-based filtered backprojection), but instead use

a technique known as focal plane tomography [14]. With this

technique, several imaginary imaging planes are placed in the

field of view. Whenever a pair of coincident 511 keV gamma

rays are detected, a line is drawn connecting the interaction

points and the point of intersection of this line with each of

the imaging planes is computed. The intensity at this point on

the imaging plane (i.e. the pixel value of the image) is then

increased, usually by an amount proportional to the inverse of

the detection efficiency for a point source placed at this

location [15]. Figure 5 shows that a point source placed close

to an imaging plane will yield an excellent image in that plane

(where it is "in focus"), but will yield much poorer images in

imaging planes that are farther away (where it is "out of

focus"). The advantages of this method are that it is simple to

implement and very rapid to compute (real-time reconstruction

is possible). The main disadvantage is that the algorithm

places activity in every plane, even though the event originated

in (or near) a single plane. Even though this mis-placed

activity many be diffuse, it builds up rapidly when distributed

sources are imaged, forming a broad background that

significantly reduces image contrast.

The same raw data sets used by the focal plane tomography

algorithm can also be reconstructed using iterative

reconstruction algorithms similar to those used in

"conventional" PET [16, 17]. The general concept behind such

algorithms is relatively simple: an estimate of the 3-

dimensional activity distribution is assumed, a mathematical

model of the camera response is used to simulate the pattern of

coincident event detections that the camera would observe withLBNL-48131

this activity distribution, and the pattern of "detected" events

derived from the estimated activity distribution is compared to

the measured pattern of events. The differences are noted, used

to revise the estimated activity distribution, and the process

repeated until the agreement cannot be improved. Excellent

image quality is possible, as this method can accurately model

the statistical noise and camera response. The advantage of

such algorithms is that they attempt to place activity only in

the plane that the event originated in, and thus give a truer (and

potentially quantitative) representation of the activity

distribution. The main disadvantage is that they are

computationally intensive and can take several hours to

converge (depending on data set size).

We use Monte Carlo simulation to compare the images

produced by the two geometries (planar and rectangular) and

two reconstruction algorithm types (focal plane tomography

and iterative) for a simple phantom. The iterative

reconstruction algorithm used is the maximum likelihood

algorithm followed by post-reconstruction spatial filtering

[18]. The phantom simulated consists of a uniform activity

concentration that fills the 7.5 cm x 7.5 cm x 10 cm field of

view. In this volume there are seven spheres, each 8 mm in

diameter and each filled with three times the activity

concentration of the uniform background. One sphere is located

at the center of the camera (0, 0, 0) and the other six are placed

along the three axes half way between the camera center and

the edge of the field of view (i.e. at ( 1.875 cm, 0, 0), at (0,

2.5 cm, 0), and at (0, 0, 1.875 cm) ).

Images are reconstructed with the parallel plane camera

using focal plane tomography, the parallel plane camera using

iterative reconstruction, and the rectangular camera using itera-

tive reconstruction. Attenuation is included in the simulation,

but Compton scatter and random coincidences are not simu-

lated. While the number of detected events is different for the

rectangular and parallel plane geometries, both have the same

number of annihilations generated; this number is chosen to

yield the signal to noise ratio (when random and scattered

events are included) that is expected for a 10 min. acquisition

following a 1 mCi whole body injection into a 75 kg patient.

Figure 6 shows a horizontal (z=0) plane of each of the

three 3-dimensional images reconstructed in these simulations.

Figure 7 shows profiles along the x-axis of these three

images; the x-axes would appear as vertical lines bisecting

each of the images in Figure 6. Vertical (x=0) planes of the

same three 3-dimensional data sets that produced Figure 6 are

shown in Figure 8, and their profiles along the z-axis (which

would appear as vertical lines bisecting the images in

Figure 8) are shown in Figure 9. Both Figures 6 & 8 show

that the reconstruction with the focal plane tomography has

significantly less contrast than the two iterative

reconstructions, as expected, and the focal plane reconstruction

has some blurring in the z-direction in Figure 8 that is not

observed with the iterative reconstruction. The profiles in

Figures 7 & 9 show that there is indeed significantly less

contrast (i.e., peak to valley ratio) in the images obtained with

focal plane tomography compared to the two iterative

reconstructions.

The difference between the two iterative reconstructions is

less significant. Figures 6 & 8 show slightly more

background noise in the planar camera images than for the

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Moses, William W. & Qi, Jinyi. Fundamental limits of positron emission mammography, article, June 1, 2001; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc786686/m1/3/: accessed February 19, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.