**Scatter Fraction, Count Losses and Random Measurement**

### General

The scatter of gamma-photons can result falsely located coincidence events. Measuring of the count losses and randoms provides information about the ability of the tomograph for measuring high radioactivity.

### Purpose

The first purpose is to measure the relative system sensitivity to scattered radiation. The scatter radiation is characterized quantitatively by scatter fraction (SF). Further purpose is to measure the effects of the dead-time and randoms. The true event rate is the total event rate minus the scattered event rate and minus the randoms event rate.

### Method

The phantom for this measurement is a solid cylinder composed of polyethylene (gravity: 0.96±0.01 g/cm3). Outside diameter of the phantom is 203±3 mm, length of the phantom is 700±5 mm. There is a hole with a diameter of 6.4±0.2 mm parallel with the axis of the cylinder and the distance of the hole and the center of the cylinder is 45±1 mm. At least 800 mm in length plastic tube shall be placed in the hole. The center 700±5 mm of this plastic tube shall be filled with radioactivity. The inside diameter of the plastic tube is 3.2±0.2 mm, the outside diameter is 4.8±0.2 mm.

Measurement shall be run through some half-lives. To begin the test a relatively high activity shall be chosen. As the activity decreases the tomograph is rather able to collect the true event. If enough time pasts, the tomograph measures only true events. These measures should be extrapolated for the high activities. The difference of measured total event rate and calculated true event rate is the scattered event rate plus random event rate.

1. Radionuclide

18F shall be used for this measure. The activity in the line source shall be placed that way that it can’t be further from the end of the cylinder like 5 mm. The activity should be chosen high, it’s expected, that the vendor offers an initial activity.

2. Source distribution

The cylinder must be placed on the patient table and rotated that the hole is positioned nearest to the patient bed. The phantom shall be centered in the transverse and axial FOV within 5 mm.

3. Data collection

Data collections shall be more frequent than the half of the half-time. And an acquisition-time Tacq,j shall be shorter than the quarter of the half-live. Acquisitions shall be done until the true event losses are less than 1%. Every acquisition shall be have at least 500000 coincidence. It’s expected, that the manufacturer recommends a protocol including starting activity, acquisition time and acquisition durations.

4. Data processing

For tomographs with axial FOV less than 65 cm prompt and random sinograms shall be generated for each acquisition (j) of slice (i). If the tomograph can measure randoms extra, they must be measured extra. Because there are tomographs that can’t measure randoms, in this presentation there are two different data-analysis (for tomograph with and without randoms measurement). For tomographs with an axial FOV greater than 65 cm, only the central 65 cm of the FOV shall be measured. No smooth or filter shall be used for this measure.

### Analysis

For each i. slice of j. acquisition shall be processed:

- Every pixel farther than12 cm from the center of the phantom has 0 value.
- For each projection angle within the sinogram, the location of the center of the line source response shall be determined by finding the pixel having the greatest value. Each projection shall be shifted so that the pixel containing the maximum value is aligned with the central pixel of the sinogram.
- • After the shift a sum projection shall be calculated. The sum projection pixel value is the sum of the pixels in each angular projection having the same radial offset as the pixel in the sum projection:

where, ’r’ the pixel number in a projection, Φ is the projection number in the sinogram, r_{max}(a) refers to the location of the maximum value in projection Φ

- The counts C
_{L,i,j}and C_{R,i,j}the left and right pixel intensities ±20 mm distance from the center of the sinogram. These must be derived from the sum projection. In the distance of exactly 20 mm-s, there will be probably no pixel-center, that’s why the searched pixel intensities shall be calculated by linear interpolation from the neighbor pixels. - The average of C
_{L,i,j}és C_{R,i,j}shall be multiplied the number of pixel between them (including the partial pixel at the ends). This product added to the sum of the counts further than 20 mm yield the number of random plus scatter counts Cr+s,i,j for j. acquisition and i. slice. - The total event count (C
_{TOT,i,j}) is the sum of all pixel value. - The average activity shall be calculated for each j. acquisition.

#### Analysis with randoms estimate

The pixels of every slice of every acquisition located farther than 12 cm from the center of the phantom shall be 0 value. The number of random counts (SF_{i,j}) is the sum of every counts in the sinogram.

1. Scatter fraction

The scatter fraction of every i. slice of j. acqusition shall be calculated as follows:

The scatter fraction of the system is computed:

2. Count rates and NECR

Follows shall be calculated for each acquisition j:

- Total event rate (R
_{TOT,i,j})

- True event rate (R
_{t,i,j})

- Random event rate (R
_{r,i,j})

- Scatter event rate (R
_{s,i,j})

where T_{acq,j} is the acqusition time of acqusition j.

On the systems (except those which are able calculate with direct random substraction) the noise equivalent count rate (R_{NEC,i,j}) shall be computed for each slice I of each acqusition j:

In systems which are able calculate with direct random substraction compute R_{NECi,j}:

The event rates of the total system shall be computed as the sum of the corresponding slice over all slices:

#### Alternative analysis with no randoms estimate

1. Scatter fraction

The final acqusition (j’) shall be used to determine scatter fraction. This acqusition has lower count loss tates and random rates than 1%. For this acqusiton it is said that C_{r+s,i,j} has no random counts and consits only scatter coincidence (because of the low activity) andC_{TOT,i,j} cconsits only of true and scatter counts.

Scatter fraction can be calculated from the last acqusition:

The system scatter fraction is calculated as the count-weighted average of the SFi values:

2. Count rates and NECR''

Follows shall be calculated for each acquisition j:

- Total event rate : R
_{TOT,i,j}

- True event rate: R
_{t,i,j}

- Random event rate : R
_{r,i,j}

- • Scatter event rate : R
_{s,i,j}

where Tacq,j is the acqusition time of acqusition j.

On the systems (except those which are able calculate with direct random substraction) the noise equivalent count rate (RNEC,i,j) shall be computed for each slice I of each acqusition j:

In systems which are able calculate with direct random substraction compute R_{NECi,j}:

The event rates of the total system shall be computed as the sum of the corresponding slice over all slices:

### Report

#### Count rate plot

The following five quantities shall be plotted as a function of the average effective radioactivity concentration (a_{ave,j}) The average effective radioactivity A_{ave,j} can be calculated:

The activitiy concentration is derived by dividing the volume. The volume of this phantom is 22000 cm^{3}).

The following 5 quantitives shall be plotted

- R
_{t,j}: system true event rate - R
_{r,j}: system scatter event rate - R
_{s,j}: system scatter event rate - R
_{NEC,j}: system noise equivalent count rate - R
_{TOT,j}: system total event rate

#### Peak count values

The following values shall be reported, derived from above plot:

- R
_{t,peak}: peak true count rate - R
_{NEC,peak}: peak noise equivalent count rate - a
_{t,peak}: the activity concentraton at which R_{t,peak}is reached - a
_{NEC,peak}: the activity concentraton at which R_{NEC,peak}is reached

#### System scatter fractio

The value of SF at peak noise equivalent count rate shall be reported if the system has randoms estimate. And the scatter fraction of every acquisiton shall be plotted versus a_{ave,j}.

If the system has no randoms estimate report the SF value calculated from the last acquisition.