# Information Capacity of Positron Emission Tomography Scanners

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}). Conclusions: The upper bound of the image information content of PET scanners can be fully characterized and further improved by investigating the imaging chain components through MC methods.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Modeled PET System Geometry

_{3}:Ce or YAP, QDE = 0.75) [36,43,44], lutetium orthoaluminate perovskite LuAlO

_{3}:Ce or LuAP:Ce, lutetium yttrium orthoaluminate perovskite ((LuY)AlO

_{3}:Ce or LuYAP:Ce, QDE = 0.90) with 70% lutetium (Lu) atomic fraction, LuYAP:Ce with 80% Lu atomic fraction (QDE = 0.91) [44,46], lutetium oxyorthosilicate (Lu

_{2}SiO

_{5}:Ce or LSO, QDE = 0.93) [46,47,48,49,50], and gadolinium oxyorthosilicate (Gd

_{2}SiO

_{5}:Ce or GSO, QDE = 0.88) [43,44,51] crystals with dimensions equal to those of BGO (QDE = 0.94) (6.3 × 6.3 × 30 mm) in the tangential, axial, and radial directions, respectively.

#### 2.2. Software Customization and Plane Source Test Object

^{3}) [40]. The dimensions of the TLC plate were 5 × 10 cm and it was simulated to be immersed in 18F-FDG bath solution (1 MBq), corresponding to radioactivity of 200 Bq/mm

^{2}. The plane test object (plane source, i.e., the radioactive plate) was simulated within a phantom, consisting of two semi-cylindrical polyethylene blocks with 20 cm diameter and 70 cm length, in the horizontal and vertical directions for both 2D and 3D data acquisitions [40]. Plane source images were acquired from STIR, after the reconstruction of the arc-corrected sinogram data, with commonly used 2D-filtered back projections (FBP2D) (Ramp filter 0.5) [55], the Kinahan and Rogers [55,56] 3-dimensional filtered back projection re-projection (FPB3DRP) [55] (Colsher filter 0.5) [57] and the maximum likelihood estimation (MLE)-OS-MAP-OSL [55] algorithms.

#### 2.3. Noise Equivalent Quanta

^{2}

_{out}/SNR

^{2}

_{in}) [20] with the input signal (SNR

^{2}

_{in}), defined as the plane source phantom activity (counts/mm

^{2}) incident on the detectors, and can be given as [36,40]:

^{2}

_{in}

#### 2.4. Information Capacity

_{p}log

_{2}N

_{s}, where n

_{p}is the number of image elements (pixels) per unit of area, and N

_{S}is the number of distinguishable signal intensity levels that can be registered in an image element [73]. However, since IC can be expressed as a function of the output SNR squared [14,40], it can written as [19,40]:

## 3. Results

#### 3.1. NEQ

^{2}), incident on the detectors. Results are shown for various combinations of subsets and iterations of the maximum likelihood estimation (MLE)-OS-MAP-OSL algorithm, covering the commonly used range in clinical practice [40]. The shapes of the NEQ curves are affected by both resolution and noise, whereas the amplitude of NEQ is affected by the input plane source phantom activity incident on the detectors. As has been pointed out in a previous study of our group, as the number of iterations increase, the resolution in terms of the MTF is improved, however, with a simultaneous increase of magnitude in image noise (NNPS). However, due to the non-linear nature of the iterative reconstruction algorithms, noise levels tend to fluctuate locally, yielding to peak in different spatial frequencies [40]. Since the improvement of the resolution is restricted up to the 12th iteration and remains almost constant thereafter, whereas noise increases constantly [40], their ratio results in a reduction of the image SNR. In the quest for the maximum available signal-to-noise ratio, per frequency, Figure 1a shows that with one subset and various iterations, higher NEQ values can be preserved in the spatial frequency range up to 0.045 cycles/mm. Afterwards, all NEQ curves show a steep drop-off, due to the excessive increase of noise. In particular, NEQ values of Figure 1a saturate in the range from eight to 14 iterations, with a maximum value (101.92 at 0.038 cycles/mm) for eight iterations, showing that low-contrast objects of large dimensions may be better visualized with this subset and iterations combination. This finding is in close agreement with the IC results that are shown in Table 1. However, NEQ values obtained with one subset practically demonstrate higher values compared to 3, 15, and 21 subsets, as shown in Figure 1b–d, respectively, in the frequency range under investigation. This effect is due to the resolution saturation, which occurs at 12 iterations in combination with the progressive increase in image noise, resulting in a constant reduction in the output signal-to-noise ratio, for higher subsets.

#### 3.2. Information Capacity

^{2}obtained in this study (Table 1), it is derived, for example, that in a 30 cm × 30 cm PET image, there would be roughly 4.67 × 10

^{5}bits.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**(

**a**) Noise-equivalent quanta from the plane source, obtained using OS-MAP-OSL, one subset combined with 1, 2, 6, 8, 14 and 20 iterations, (

**b**) three subsets combined with 2, 6, 8, 12, 14 and 20 iterations, (

**c**) 15 subsets combined with 2, 6, 8, 10, 14 and 20 iterations, and (

**d**) 21 subsets combined with 2, 4, 6, 12, 14 and 20 iterations.

**Figure 2.**Noise equivalent quanta from the plane source, obtained using (

**a**) FBP 2D, (

**b**) FBP3DRP, and (

**c**) OS-MAP-OSL (15 subsets, three iterations) for various crystals.

Iterations | Subsets | |||
---|---|---|---|---|

1 | 3 | 15 | 21 | |

Information Capacity (bits/mm^{2}) | ||||

1 | 0.0217 | - | - | - |

2 | 0.5577 | 1.3774 | 1.6869 | 1.4100 |

4 | - | - | - | 1.6770 |

6 | 2.2899 | 3.8744 | 1.9202 | 1.7926 |

8 | 2.8716 | 4.5902 | 1.9510 | - |

12 | - | 4.7432 | 2.2109 | 1.7690 |

14 | 3.5305 | 4.7080 | 1.9586 | 1.6097 |

20 | 4.0222 | 5.1947 | 2.1936 | 2.0781 |

PET Module/Scintillating Crystal Combination | Algorithm | ||
---|---|---|---|

FBP2D | FBP3DRP | OS-MAP-OSL | |

Information Capacity (bits/mm^{2}) | |||

BGO | 0.7197 | 2.4829 | 1.6042 |

Gd_{2}SiO_{5}:Ce | 0.2481 | 1.4735 | 0.8864 |

Lu_{2}SiO_{5}:Ce | 0.3215 | 1.7611 | 1.1651 |

LuAP:Ce | 0.8648 | 1.8757 | 0.5875 |

LuYAP:Ce—70% | 0.1242 | 0.9860 | 0.7620 |

LuYAP:Ce—80% | 0.2265 | 1.2798 | 1.4028 |

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Michail, C.; Karpetas, G.; Kalyvas, N.; Valais, I.; Kandarakis, I.; Agavanakis, K.; Panayiotakis, G.; Fountos, G.
Information Capacity of Positron Emission Tomography Scanners. *Crystals* **2018**, *8*, 459.
https://doi.org/10.3390/cryst8120459

**AMA Style**

Michail C, Karpetas G, Kalyvas N, Valais I, Kandarakis I, Agavanakis K, Panayiotakis G, Fountos G.
Information Capacity of Positron Emission Tomography Scanners. *Crystals*. 2018; 8(12):459.
https://doi.org/10.3390/cryst8120459

**Chicago/Turabian Style**

Michail, Christos, George Karpetas, Nektarios Kalyvas, Ioannis Valais, Ioannis Kandarakis, Kyriakos Agavanakis, George Panayiotakis, and George Fountos.
2018. "Information Capacity of Positron Emission Tomography Scanners" *Crystals* 8, no. 12: 459.
https://doi.org/10.3390/cryst8120459