# Multicomponent and Longitudinal Imaging Seen as a Communication Channel—An Application to Stroke

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Modeling a Shannon-Like Communication Channel for Multicomponent and Longitudinal Biomedical Imaging Studies

#### 2.2. Multicomponent and Longitudinal Imaging Studies in Stroke

#### 2.2.1. Gain of Predictability with Multicomponent Integration

#### 2.2.2. Optimal Observation Scale for Tissue Fate Prediction

#### 2.2.3. Impact of Noise on Tissue Fate Prediction Accuracy

Algorithm 1: Pseudo-algorithm for the introduction of noise in a reference mask M. The inside contour is composed of all the voxels which belong to the segmented region and are in contact with its boundary. The outside contour is composed of all the voxels which do not belong to the segmented region but are in contact with its boundary. The optimum values for $\delta $ and $\alpha $, the two parameters of the algorithm, are application-dependent. Here, they were set to $\delta =5$ and $\alpha =10$. In any case, we should have $\alpha >1$ and $\delta $ odd $\ge 3$. |

## 3. Material

#### 3.1. Clinical Data for Tissue Fate Prediction

#### 3.2. Impact of Noise on Tissue Fate Prediction Accuracy

## 4. Results

#### 4.1. Gain of Predictability with Multicomponent Integration

#### 4.2. Optimal Observation Scale for Tissue Fate Prediction

#### 4.3. Impact of Noise on Tissue Fate Prediction Accuracy

## 5. Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**General Shannon-like communication channel for multicomponent and longitudinal biomedical imaging studies. The imaging process is not deterministic, and the input and output are perturbed by noise.

**Figure 2.**Illustration of the binary mask of a cytotoxic edema (

**c**) segmented from the diffusion-weighted imaging of a patient in acute stage (

**a**); (

**b**) show the superposition of the affected area on the image used for the segmentation.

**Figure 3.**Illustration of the evolution of the labels in an image component as the observation scale N is increased.

**Figure 4.**Illustration of the processing pipeline proposed for the study of the gain in predictability from observation scale optimization in tissue fate prediction studies for stroke. The study of the gain in predictability from component integration presented in Section 2.2.1 corresponds to the specific case where the observation scale equals 1 and the encoded images are thus exactly the same as the binary masks.

**Figure 5.**(

**a**–

**d**): illustration of segmentation masks of a same image (

**a**) when segmented by three different experts (

**b**–

**d**). One can see that the small affected area segmented by the experts in masks (

**b**,

**d**), was not segmented by the expert on mask (

**c**). In addition, one can clearly see differences between masks (

**b**–

**d**) around the border of the largest affected area. (

**e**,

**f**): illustration of noisy masks simulated from the segmentation mask (

**b**) with Algorithm 1.

**Figure 6.**Histogram of the susceptibility factor of the final lesion masks for a cohort of 42 patients, with the red lines corresponding (from left to right) to the first, second and third quartiles, respectively.

**Figure 7.**Evolution of the predictive power as the number of components in the communication channel input is increased.

**Figure 8.**Evolution of the predictive power as a function of the proportion of error (

**a**) or corresponding error rate introduced (

**b**), in red for the mask representative of the first quartile (${M}_{Q1}$), in orange for the mask representative of the second quartile (${M}_{Q2}$) and in purple for the mask representative of the third quartile (${M}_{Q3}$) of the susceptibility factor distribution. The points correspond to the mean values, the line to the median values and the dotted lines to the first and third quartiles values obtained over 30 noise realizations for each value of the proportion of error tested.

**Table 1.**Six-label encoding for binary masks taking into account, for each voxel, the state of the voxels in its $N\times N$ neighborhood.

Label | Voxel in Affected Area | % Of Neighboring Voxels in Affected Area |
---|---|---|

0 | no | $[0,25]$ |

1 | no | $(25,75)$ |

2 | no | $[75,100]$ |

3 | yes | $[0,25]$ |

4 | yes | $(25,75)$ |

5 | yes | $[75,100]$ |

**Table 2.**Predictive power obtained for real data ± mean predictive power of noise evaluated over 100 noise realizations. ${C}_{n}$ = optimum combination of n predictor variables. N = observation scale for the voxel neighborhood.

N | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ | ${\mathit{C}}_{4}$ | ${\mathit{C}}_{5}$ | ${\mathit{C}}_{6}$ |
---|---|---|---|---|---|---|

1 | 37.4508 ± 0.0004 | 43.1119 ± 0.0009 | 44.475 ± 0.002 | 45.669 ± 0.005 | 46.108 ± 0.001 | 46.31 ± 0.02 |

3 | 42.294 ± 0.002 | 48.46 ± 0.01 | 49.90 ± 0.06 | 51.5 ± 0.2 | 52.7 ± 0.8 | 54 ± 2 |

5 | 44.903 ± 0.002 | 51.40 ± 0.01 | 52.93 ± 0.06 | 54.6 ± 0.3 | 56 ± 1 | 58 ± 3 |

7 | 46.846 ± 0.002 | 53.48 ± 0.01 | 55.10 ± 0.06 | 56.9 ± 0.3 | 58 ± 1 | 60 ± 3 |

9 | 48.206 ± 0.002 | 54.95 ± 0.01 | 56.60 ± 0.07 | 58.5 ± 0.3 | 60 ± 1 | 62 ± 4 |

11 | 49.103 ± 0.002 | 55.94 ± 0.01 | 57.59 ± 0.07 | 59.6 ± 0.3 | 61 ± 1 | 63 ± 4 |

13 | 49.668 ± 0.002 | 56.57 ± 0.01 | 58.33 ± 0.07 | 60.4 ± 0.3 | 62 ± 1 | 64 ± 4 |

15 | 50.101 ± 0.002 | 56.92 ± 0.01 | 58.78 ± 0.07 | 60.9 ± 0.3 | 63 ± 1 | 65 ± 4 |

17 | 50.437 ± 0.002 | 57.29 ± 0.01 | 59.23 ± 0.07 | 61.4 ± 0.3 | 63 ± 1 | 65 ± 4 |

19 | 50.558 ± 0.002 | 57.55 ± 0.01 | 59.50 ± 0.07 | 61.8 ± 0.3 | 64 ± 1 | 65 ± 4 |

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**MDPI and ACS Style**

Giacalone, M.; Frindel, C.; Grenier, E.; Rousseau, D. Multicomponent and Longitudinal Imaging Seen as a Communication Channel—An Application to Stroke. *Entropy* **2017**, *19*, 187.
https://doi.org/10.3390/e19050187

**AMA Style**

Giacalone M, Frindel C, Grenier E, Rousseau D. Multicomponent and Longitudinal Imaging Seen as a Communication Channel—An Application to Stroke. *Entropy*. 2017; 19(5):187.
https://doi.org/10.3390/e19050187

**Chicago/Turabian Style**

Giacalone, Mathilde, Carole Frindel, Emmanuel Grenier, and David Rousseau. 2017. "Multicomponent and Longitudinal Imaging Seen as a Communication Channel—An Application to Stroke" *Entropy* 19, no. 5: 187.
https://doi.org/10.3390/e19050187