# Some key elements for exploring the complexity of brain

Michel Dojat

► To cite this version:

Michel Dojat. Some key elements for exploring the complexity of brain. Complex Days 2026, Université Côte d'Azur, Feb 2026, Nice, France. hal-05507537

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Submitted on 12 Feb 2026

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# Some key elements for exploring the complexity of brain

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Michel DOJAT

Research Director Inserm

Deputy Scientific Director Inria

michel.dojat@inria.fr

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I declare relationships with the company Pixyl, Gleamer group (pixyl.ai)

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RESEARCH TOPICS AND EXPERIMENTAL APPROACHES

<figure><img src="image_9.png" /><figcaption>/ Fundamental neurosciences</figcaption></figure>

Cytoskeleton, Intracellular traffic, Synaptic plasticity, Mechanisms studied in normal and pathological conditions (neurobiological diseases, neurodegenerative diseases, myopathies)

<figure><img src="image_10.png" /><figcaption>/ Pre-clinical and clinical research</figcaption></figure>

Developing tools and concepts
Close links with networks such as GREEN, Neuropsynov, NeuroCoG...

<figure><img src="image_11.png" /><figcaption>/ Innovative technologies and treatments</figcaption></figure>

Multidisciplinary approaches including human social sciences, and methodological developments (optogenetics, reconstruction of neural networks, electrophysiology...)

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My main collaborators

<figure><img src="image_21.png" /><figcaption>Benjamin Lambert</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>Arturo Cabrera Vazquez</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Florence Forbes</figcaption></figure>

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Veronica Munoz-Ramirez Lambert

<figure><img src="image_25.png" /><figcaption>Lucrezia Carboni</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>Geoffroy Oudoumanessah</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>Sophie Achard</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>Carole Lartizien</figcaption></figure>

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MARCH 2023: IMAGING AI IN PRACTICE • VOLUME 4 NUMBER 2 • RADIOLOGY-AIDHA.ORG

Kw: « Deep Learning » and « Medical Image Analysis »

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# Automatic analysis of medical images

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NEJM
AI

NEJM AI is a journal exploring cutting-edge research and applications of artificial intelligence in clinical medicine.

Radiology
Artificial Intelligence

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MARCH 2023: IMAGING AI IN PRACTICE • VOLUME 4 NUMBER 2 • RADIOLYSIS-ALBHA.ORG

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# Some Key Elements (I)

- Good for triage

- Gross anomalies

- Hyper-intensities

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Subtle anomalies
detection
unistic detection

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# Some Key Elements (I)

- Good for triage

- Gross anomalies

- Hyper-intensities

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Subtle anomalies
detection
 Old fashion statistical methods

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- DL is data hungry

- Few examples available in medical domain

- Few annotated examples

- Costly

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Unsupervised ML

Old fashion statistical
methods

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# Some Key Elements (II)

- Know-it-All

- Black Box

- Not trustable

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Uncertainty quantification

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110 mL
[90-130]

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# Some Key Elements (III)

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# Some Key Elements (IV)

- Need for specific infrastructures

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10 HUBS for gathering
40 platforms with 160
in vivo imaging systems

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Some Key Elements (I)

Unsupervised ML

Old fashion
statistical methods

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# Anomalies detection: Normal vs Pathologic

## Our method:

- choose a normality model

### I Reference Model

♦ Set of healthy voxel $V_H$

♦ Set of healthy modalities $Y_H = \{y_v | v \in V_H\}$

♦ Mixture model $f_H(y_v, \Theta_H) = \sum_{1 \le k \le K} \pi_k f_k(y_v, \Theta_k)$

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## Our method:

- choose a normality model

### I Reference Model

* Set of healthy voxels $V_H$

* Set of healthy modalities $Y_H = \{y_v | v \in V_H\}$

* Mixture model $f_H(y_v, \Theta_H) = \sum_{1 \le k \le K} \pi_k f_k(y_v, \theta_k)$

**T-distribution as a Gaussian Scale Mixture**

$$t_M(y; \mu, \Sigma, \nu) = \int_0^\infty \mathcal{N}_M(y; \mu, \Sigma/w) \mathcal{G}(w; \nu/2, \nu/2) dw$$

* $\mu$ is the mean

* $\Sigma$ Scale matrix

* $\nu$ degree of freedom

Trained on the set of healthy voxels

$$Y_H = \{y_v, v \in V_H\}$$

Mixture model of multiple scale t-distributions $\text{MST}$ [X]

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$$f_H(y_v; \Theta_H) = \sum_{k=1}^{K} \pi_k f(y_v; \theta_k)$$

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# Anomalies detection: Normal vs Pathologic

## Our method:

- choose a normality model

- find a metric: score of pathology

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# Anomalies detection: Normal vs Pathologic

Our method:

- choose a normality model

- find a metric: score of pathology

**Proximity measure:** quantify the proximity of an observation towards the reference model

$$ \tilde{w}_m^{\mathbf{y}_v} = \mathbb{E}[W_m | \mathbf{Y} = \mathbf{y}_v] \propto \left( \frac{\nu_m}{2} + \frac{[\mathbf{D}^T(\mathbf{y}_v - \boldsymbol{\mu})]_m^2}{2A_m} \right)^{-1} $$

$$ r(\mathbf{y}_v, \mathbf{\Theta}) = \max_{m=1:M} \tilde{w}_m^{\mathbf{y}_v} $$

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## Our method:

- choose a normality model

- find a metric: score of pathology

- find a decision rule

### Decision Rule

Choose an appropriate False Positive Rate and compute the empirical
quantile

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Comparison with standard NN (AE & VAE)

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N. Pinon, G. Oudoumanessah, R. Trombetta, M. Dojat, F. Forbes, C. Lartizien.
Brain subtle anomaly detection based on Auto-Encoders latent space analysis:
Application to de novo Parkinson patients, IEEE International Symposium on
Biomedical Imaging (ISBI) 2023,

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Results

Parkinson Progression Marker Initiative [Marek et al, 2018]

PPMI dataset

**2 modalities:** T1w, DTI
extraction of FA/MD from
DTI

108 healthy subjects

531 de novo Parkinsonian
patients

Hoehn & Yahr scale severity
scores that spreads between 1 or
2 [Hoehn, Yahr, 1967]

Registration: intra-subject on the T1w

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Comparison between de novo Parkinsonian patient
and control subject

Model selection: K

K: Slope heuristic [Baudry et
al, 2010]

K = 14 for GMM and K = 8
for MMST

mini-batch size: 2048

Epoch: 1

Step-size: γ_r = (1 - ε)r⁻⁰.⁵⁻ᶜ

UAD

False Positive Rate: $\alpha = 2\%$

Computing percentage of abnormalities
per structure

Using ROC to discriminate controls/
patients over their % of abnormalities

Evaluation with g-mean:

$$
\sqrt{\text{sensitivity} \times \text{sensitivity}}
$$

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Parkinson Progression Marker Initiative [Marek et al, 2018]

PPMI dataset

2 modalities: T1w, DTI
extraction of FA/MD from
DTI

108 healthy subjects

531 de novo Parkinsonian
patients

Hoehn & Yahr scale severity
scores that spreads between 1 or
2 [Hoehn, Yahr, 1967]

Registration: intra-subject on the T1w

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Comparison between de novo Parkinsonian patient
and control subject

Model selection: K

K: Slope heuristic [Baudry et
al, 2010]

K = 14 for GMM and K = 8
for MMST

mini-batch size: 2048

Epoch: 1

Step-size: γ_r = (1 - ε)r⁻⁰.⁵⁻ε

UAD

False Positive Rate: $\alpha = 2\%$

Computing percentage of abnormalities
per structure

Using ROC to discriminate controls/
patients over their % of abnormalities

Evaluation with g-mean:

$$
\sqrt{\text{sensitivity} \times \text{sensitivity}}
$$

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Results

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<table><thead><tr><th rowspan="2"></th><th rowspan="2">Method</th><th rowspan="2">Backend</th><th rowspan="2">Time</th><th colspan="2">Training</th><th colspan="3">Inference</th><th rowspan="2">Gmean</th><th rowspan="2">Trainable parameters</th></tr><tr><th>Consumption</th><th>DRAM peak</th><th>Time</th><th>Consumption</th><th>DRAM peak</th></tr></thead><tbody><tr><td rowspan="2">Online Mixtures</td><td>Gaussian</td><td>CPU</td><td>50s</td><td>85 kJ</td><td>494 MB</td><td>17min</td><td>23 kJ</td><td>92 MB</td><td>0.65</td><td>140</td></tr><tr><td>MST</td><td>CPU</td><td>1min20</td><td>153 kJ</td><td>958 MB</td><td>18min</td><td>32 kJ</td><td>96 MB</td><td><strong>0.67</strong></td><td>128</td></tr><tr><td rowspan="2">Lightweight AE</td><td>Reconstruction error</td><td>GPU</td><td>1h26</td><td>5040 kJ</td><td>26 GB</td><td>3h30</td><td>8350 kJ</td><td>22 GB</td><td>0.61</td><td>5266</td></tr><tr><td>FastFlow</td><td>GPU</td><td>4h</td><td>6854 kJ</td><td>27 GB</td><td>3h53</td><td>13158 kJ</td><td>27 GB</td><td>0.55</td><td>1520</td></tr><tr><td rowspan="2">ResNet-18</td><td>Reconstruction error</td><td>GPU</td><td>17h40</td><td>53213 kJ</td><td>26 GB</td><td>59h</td><td>108593 kJ</td><td>28 GB</td><td>0,64</td><td>23730218</td></tr><tr><td>FastFlow</td><td>GPU</td><td>4h10</td><td>7234 kJ</td><td>28 GB</td><td>19h45</td><td>18481 kJ</td><td>28 GB</td><td>0,61</td><td>1520</td></tr></tbody></table>

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Discussion

- Good performances on brain scans

- Simple architecture

- Low cost model that is competitive with more complex, costly and less interpretable NN-based models

- Easier integration in clinical routine

- Frugal AI is not a bargain AI but and AI optimized and centered on medical needs

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Some Key Elements (II)

Uncertainty Quantification

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# The curse of the Black-Box

## Standard Deep Learning approach

<figure><img src="image_98.png" /><figcaption>Input MRI</figcaption></figure>

<figure><img src="image_99.png" /><figcaption>Trained Network</figcaption></figure>

<figure><img src="image_100.png" /><figcaption>Prediction</figcaption></figure>

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Standard Deep Learning approach

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<figure><img src="image_106.png" /><figcaption>Trained Network</figcaption></figure>

<figure><img src="image_107.png" /><figcaption>Prediction</figcaption></figure>

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Explainability
Interpretability

For who?
About what?
What contents?

...

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# The curse of the Black-Box

<figure><img src="image_112.png" /><figcaption>Standard Deep Learning approach</figcaption></figure>

Explainability
Interpretability

For who?
About what?
What contents?

...

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G. Hinton [In response to how do we trust systems?] **You should regulate them based on how they perform.**

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# Uncertainty Quantification
in NN decision

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# Where is uncertainty (UC) hidden?

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[Kendall & Gal 2017 Adv Neural Inf Process Syst]

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# The multi-dimensional aspect of uncertainty

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# Consensus meeting

## Definition of ground truth

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## Inter-expert variability

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[Commowick et al NeuroImage 2021]

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# Voxel level UQ: Ensembling

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Entropy (C: number of classes, M: number of models)

$$H(p) = - \sum_{c=1}^{C} \frac{1}{M} \sum_{m=1}^{M} p_{c,m} \log(\frac{1}{M} \sum_{m=1}^{M} p_{c,m})$$

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# Voxel level UQ: Ensembling

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# Lesion level UQ

## Goal: Identify FP

## Estimate $P_{FP}$: proba that the lesion is FP using an
auxillary classifier

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## Note: Lesion are highly variable in **shape**

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and **position**

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# Lesions as Graphs

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## Training to separate
True and False Positive lesions

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Lambert B et al. Beyond Voxel Prediction Uncertainty: Identifying brain lesions you can trust 2022, LNCS 13611 pp. 61-70.

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# The Graph Isomorphism Network

Deep Ensemble (5 models)

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Multicentric, 3 Tesla

MSSEG 2016 - ISBI 2015 - WMH 2017
(N = 219)

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10775 identified lesions (9050 TP / 1725 FP)

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FC: Fully-connected layer. BN: Batch Normalization. ReLU: Rectified Linear Unit. Parameters: 26 700

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# The Graph Isomorphism Network

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# The Graph Isomorphism Network

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Slight gain over the baseline

Score easily interpretable

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# The multi-dimensional aspect of uncertainty

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# Predictive intervals in volumetry

## Definition

* $X \in \mathbb{R}^{N-1}$ are estimates of the true volumes $Y \in \mathbb{R}^{N-1}$, obtained from the segmentation.

* A predictive interval $\Gamma_{\alpha}(X)$ is a range of values intended to encompass $Y$ with a specified degree of confidence $1 - \alpha$ (e.g. 90%, 95%), so that $P(Y \in \Gamma_{\alpha}(X)) \ge 1 - \alpha$

## Sampling-based approaches

* Sample a set of estimated volumes $X_1, ..., X_K$ for the given image.

* Estimate the mean $\mu(X)$ and standard deviation $\sigma(X)$.

* Assuming $Y|X \sim N(\mu(X), \sigma(X))$:

$$ \Gamma_{\alpha}(X) = [\mu(X) - z\sigma(X), \mu(X) + z\sigma(X)] \quad (1) $$

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# Predictive intervals in volumetry

## Definition

* $X \in \mathbb{R}^{N-1}$ are estimates of the true volumes $Y \in \mathbb{R}^{N-1}$, obtained from the segmentation.

* A predictive interval $\Gamma_{\alpha}(X)$ is a range of values intended to encompass $Y$ with a specified degree of confidence $1 - \alpha$ (e.g. 90%, 95%), so that $P(Y \in \Gamma_{\alpha}(X)) \ge 1 - \alpha$.

## Sampling-based approaches

* Sample a set of estimated volumes $X_1, ..., X_K$ for the given image.

* Estimate the mean $\mu(X)$ and standard deviation $\sigma(X)$.

* Assuming $Y|X \sim N(\mu(X), \sigma(X))$,
  $\Gamma_{\alpha}(X) = [\mu(X) - z_{\sigma(X)}\sigma(X), \mu(X) + z_{\sigma(X)}\sigma(X)]$

## Limitations

* **Inference time**, due to the sampling procedure.

* **The normality assumption**, which may not always hold.

* **Lack of flexibility**, as intervals are symmetrical by design.

<figure><img src="image_162.png" /></figure>
# Predictive intervals in volumetry

## Definition

* $X \in \mathbb{R}^{N-1}$ are estimates of the true volumes $Y \in \mathbb{R}^{N-1}$, obtained from the segmentation.

* A predictive interval $\Gamma_{\alpha}(X)$ is a range of values intended to encompass $Y$ with a specified degree of confidence $1 - \alpha$ (e.g. 90%, 95%), so that $P(Y \in \Gamma_{\alpha}(X)) \ge 1 - \alpha$.

## Sampling-based approaches

* Sample a set of estimated volumes $X_1, ..., X_K$ for the given image.

* Estimate the mean $\mu(X)$ and standard deviation $\sigma(X)$.

<figure><img src="image_163.png" /></figure>

## Direct approaches

* Directly estimate the quantiles $\hat{t}_{\alpha/2}(X)$ and $\hat{t}_{1-\alpha/2}(X)$.

* The PI is computed as:

$$ \Gamma_{\alpha}(X) = [\hat{t}_{\alpha/2}(X), \hat{t}_{1-\alpha/2}(X)] \quad (2) $$

Conformal prediction

<figure><img src="image_164.png" /></figure>
# The TriadNet approach

$$T_{\gamma,\beta} \approx 1 - \frac{TP}{TP + \gamma FP + \beta FN}$$

$$\text{TriadLoss} = T_{0.8,0.2}(p_{\text{lower},y}) + T_{0.5,0.5}(p_{\text{mean},y}) + T_{0.2,0.8}(p_{\text{upper},y})$$

<figure><img src="image_165.png" /><figcaption>The Tversky loss (Salehi et al. 2017)</figcaption></figure>

[B. Lambert et al. (2023). “TriadNet: Sampling-Free Predictive Intervals for Lesional Volume in 3D Brain MR Images”. In: UNSURE 2023, LNCS 14291, pp. 32–41]

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TriadNet predictions

<figure><img src="image_167.png" /></figure>

<figure><img src="image_168.png" /></figure>

Input sequences

Segmentation

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Predictive Intervals

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# Tumor volume estimation

## Glioblastoma

- 679 subjects for training, 227 for calibration, and 227 for testing (BraTS 2023 dataset)

- Intervals calibrated for a target coverage of 90%.

### Necrosis:

- MAE: 3.10 ± 0.46mL

- Coverage: 90.78 ± 2.71%

<figure><img src="image_173.png" /></figure>

### Edema:

- MAE: 8.22 ± 0.57mL

- Coverage: 90.76 ± 2.70%

<figure><img src="image_174.png" /></figure>

### Enhancing tumor:

- MAE: 1.73 ± 0.19mL

- Coverage: 90.79 ± 2.71%

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# The multi-dimensional aspect of uncertainty

<figure><img src="image_177.png" /></figure>

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<figure><img src="image_179.png" /></figure>
DLL trained for Gioblastoma detection on T1w

<figure><img src="image_180.png" /><figcaption>Artefacted T1w</figcaption></figure>

<figure><img src="image_181.png" /><figcaption>Healthy subject</figcaption></figure>

<figure><img src="image_182.png" /><figcaption>FLAIR</figcaption></figure>

<figure><img src="image_183.png" /><figcaption>Abdominal T1w</figcaption></figure>

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DLL trained for Gioblastoma segmentation on T1w

<figure><img src="image_185.png" /><figcaption>Artefacted T1w</figcaption></figure>

<figure><img src="image_186.png" /><figcaption>Healthy subject</figcaption></figure>

<figure><img src="image_187.png" /><figcaption>FLAIR</figcaption></figure>

<figure><img src="image_188.png" /><figcaption>Abdominal T1w</figcaption></figure>

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<figure><img src="image_191.png" /></figure>

<figure><img src="image_192.png" /></figure>

<figure><img src="image_193.png" /></figure>
Input Quality Control

DLL trained for Gioblastoma segmentation on T1w

<figure><img src="image_194.png" /><figcaption>Artefacted T1w</figcaption></figure>

<figure><img src="image_195.png" /><figcaption>Healthy subject</figcaption></figure>

<figure><img src="image_196.png" /><figcaption>FLAIR</figcaption></figure>

<figure><img src="image_197.png" /><figcaption>Abdominal T1w</figcaption></figure>

<figure><img src="image_198.png" /></figure>

<figure><img src="image_199.png" /></figure>

<figure><img src="image_200.png" /></figure>

<figure><img src="image_201.png" /></figure>

Images far from the training image distribution
(OOD) should be detected

<figure><img src="image_202.png" /></figure>

<figure><img src="image_203.png" /></figure>
# Why an image is OOD?

<figure><img src="image_204.png" /></figure>

* In-distribution ↔ training distribution (T1 MRI of Adult glioblastoma patients)

* Are out-of-distribution:

* Images corrupted with artifacts.

* Shifts in the imaged population.

* Shifts in image modality.

* Diseases not present in the training set.

* Incorrect organs.

<figure><img src="image_205.png" /></figure>

<figure><img src="image_206.png" /></figure>

<figure><img src="image_207.png" /></figure>
The latent-space distance

<figure><img src="image_208.png" /></figure>

OOD activation

<figure><img src="image_209.png" /></figure>

<figure><img src="image_210.png" /></figure>
# Input Quality Control

## The latent-space distance

<figure><img src="image_211.png" /></figure>

multivariate
Gaussian
distribution

OOD activation

<figure><img src="image_212.png" /></figure>

Computed with Mahalanobis distance
(MD)

$$ \mu = \frac{1}{N} \sum_{i=1}^{N} x_i $$

$$ \Sigma = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)(x_i - \mu)^T $$

$$ \text{MD}(x_{\text{test}}; \mu, \Sigma) = (x_{\text{test}} - \mu)^T \Sigma^{-1} (x_{\text{test}} - \mu) $$
A multi-layer aggregation of MD

<figure><img src="image_213.png" /></figure>

[B. Lambert et al. (2023). “Multi-layer Aggregation as a key to feature-based OOD detection”. In: UNSURE 2023, Held in Conjunction with MICCAI 2023. LNCS 14291, pp. 104–114]

<figure><img src="image_214.png" /></figure>
Input Quality Control

Brats: 876 subjects for training,
30 for validation,
227 for in-distribution testing

Dynamic U-Net

<figure><img src="image_215.png" /></figure>

The optimal layer for OOD detection depends on the segmentation architecture.

<figure><img src="image_216.png" /></figure>

<figure><img src="image_217.png" /></figure>
Input Quality Control

The multi-layer scores (**Mean** and **Max**) provide high detection accuracy.

<figure><img src="image_218.png" /></figure>

Latent-space distances efficient in detecting images far from the training distribution.

<figure><img src="image_219.png" /></figure>
Output Quality Control

Goal: estimate the true segmentation accuracy.

How: Measure the segmentation variability among models.

<figure><img src="image_220.png" /></figure>

We note $S_k$ the individual segmentations and *MV* the majority vote segmentation
Ensemble Prediction Agreement (EPA): $EPA = \frac{1}{K} \sum_{i=1}^{K} Dice(S_k, MV)$

[B. Lambert et al. (2024) "From Out-of-distribution detection to Quality Control".
In: Trustworthy AI in Medical Imaging, MICCAI book series]

<figure><img src="image_221.png" /></figure>
Unified Input-Output control

<figure><img src="image_222.png" /></figure>

<figure><img src="image_223.png" /></figure>

<figure><img src="image_224.png" /></figure>
Unified Input-Output control

<figure><img src="image_225.png" /></figure>

<figure><img src="image_226.png" /></figure>

<figure><img src="image_227.png" /></figure>
Unified Input-Output control

5 Dynamic U-Nets are trained to segment gliomas.

QC scores computed for 874 test subjects with variable difficulty.

thresholds fixed on a validation dataset (N=30).

<figure><img src="image_228.png" /></figure>

<figure><img src="image_229.png" /></figure>

<figure><img src="image_230.png" /></figure>
# Take home messages

* ✓ Confidence is central for AI deployment

* ✓ Uncertainty quantification improves user's confidence

* ✓ Uncertainty is multidimensional

Lesion uncertainty scores

Predictive volume intervals

Unified input & output controls

<figure><img src="image_231.png" /></figure>

uncertainty quantification

for trusted AI

<figure><img src="image_232.png" /></figure>

for AI penetration in clinical

routine

<figure><img src="image_233.png" /></figure>

<figure><img src="image_234.png" /></figure>
What is the added-value
in clinical routine applications?

TO BE EVALUATED

<figure><img src="image_235.png" /></figure>

<figure><img src="image_236.png" /></figure>

<figure><img src="image_237.png" /></figure>
# Trustworthy AI in Medical Imaging

<figure><img src="image_238.png" /></figure>

## Trustworthy AI in Medical Imaging

* 1st Edition - December 1, 2024

* Editors: Marco Lorenzi, Maria A Zuluaga

* eBook ISBN: 9780443237607

## Section 1 – Robustness

## Section 2 - Validation, Transparency and Reproducibility

## Section 3 – Bias and Fairness

## Section 4 - Explainability, Interpretability and Causality

## Section 5 - Privacy-preserving ML

## Section 6 - Collaborative Learning

## Section 7 - Beyond the Technical Aspects

<figure><img src="image_239.png" /></figure>

<figure><img src="image_240.png" /></figure>
Some Key Elements (III)

- The use of graphs for brain exploration

<figure><img src="image_241.png" /></figure>

<figure><img src="image_242.png" /></figure>

<figure><img src="image_243.png" /></figure>
<figure><img src="image_244.png" /></figure>

**degree**

<figure><img src="image_245.png" /></figure>

high degree

<figure><img src="image_246.png" /></figure>

low degree

**clustering coefficient**

<figure><img src="image_247.png" /></figure>

high clustering coeff.

<figure><img src="image_248.png" /></figure>

low clustering coeff.

**closeness centrality**

<figure><img src="image_249.png" /></figure>

high closeness c.

<figure><img src="image_250.png" /></figure>

low closeness c.

<figure><img src="image_251.png" /></figure>

<figure><img src="image_252.png" /></figure>
Def. 1 (Graph automorphism)

An automorphism of a graph $\mathcal{G} = (\mathcal{V}, \mathcal{E})$ is a bijection $\pi$ between $\mathcal{G}$ and itself such that:

$$ \forall u, v \in \mathcal{V}, \{u, v\} \in \mathcal{E} \iff \{\pi(u), \pi(v)\} \in \mathcal{E}. $$

Def. 2 (Structural equivalence)

Two nodes $v, u \in \mathcal{V}$ are structurally equivalent or automorphically equivalent $v \equiv u$ if there exists an automorphism $\pi: \mathcal{G} \to \mathcal{G}$ such that $\pi(v) = u$.

Def. 3 (Structural Equivalence associated with the nodal statistics $s$)

$$ v \sim_s u \iff s(u) = s(v). \qquad (1) $$

or when $s(\mathcal{V})$ is dense and continuous subset of $\mathbb{R}$ the equivalence is defined up to a fixed positive small $\epsilon$: $v \sim_s u \iff |s(u) - s(v)| \le \epsilon$

Def. 4 (Structural Equivalence associated with a collection of nodal statistics $S$)

$$ v \sim_S u \iff v \sim_{S_1} u, v \sim_{S_2} u, \dots, v \sim_{S_n} u. \qquad (2) $$

Lucrezia Carboni, Michel Dojat, Sophie Achard (2023). “Nodal-statistics-based equivalence relation for graph collections”. In: Physical Review E 107.1

<figure><img src="image_253.png" /></figure>
# Structural Patterns Comparison

Def. 7 (Correspondence Structural Pattern Score)

$$C(\mathcal{G}, \mathcal{G}') := \max_{\pi \in \Pi} \frac{1}{|\mathcal{V}|} \sum_{i=1}^{|\mathcal{V}|} \chi\left(\pi(c(v_i)) = c'(v_i)\right) \quad (4)$$

where $\Pi$ is the set of all coupling between the elements in $P_S$ and the elements in $P'_S$ and $\chi$ is the indicator function.

<figure><img src="image_254.png" /></figure>

$P_S = [ABEFGH], [L], [CDI], [M]$

<figure><img src="image_255.png" /></figure>

$P'_S = [ABCEFGH], [L], [DIM]$

<figure><img src="image_256.png" /></figure>

$$C(\mathcal{G}, \mathcal{G}') = \frac{1+2+6}{11} = 0.81$$
Neuroinflammation & functional Connectivity

- Traumatic patients

- fMRI & TSPO-Pet

- How to combine ? Which relation ?

<figure><img src="image_257.png" /></figure>

<figure><img src="image_258.png" /></figure>

<figure><img src="image_259.png" /></figure>
# Infrastructure

FLi

<figure><img src="image_260.png" /></figure>

<figure><img src="image_261.png" /><figcaption>Michel Dojat
Scientific Manager</figcaption></figure>

Tools:
SPM, fsl,
Freesurfer
....

**Pipelines execution**

<figure><img src="image_262.png" /><figcaption>Michael Kain
Technical Manager</figcaption></figure>

<figure><img src="image_263.png" /></figure>

Stockage

shancir

in vivo imaging: MRI, CT,...
Nifti, Dicom, Bids
Signal: EEG
Additional: eye-tracking
Neuropsy tests
(.txt, table, ...)

<figure><img src="image_264.png" /></figure>

Centre n

VIP

<figure><img src="image_265.png" /></figure>

<figure><img src="image_266.png" /></figure>

End user

Portal web
(qqueries)

<figure><img src="image_267.png" /></figure>

Tools
catalog

Segmentatio
ndenoising,
...

<figure><img src="image_268.png" /></figure>

docker

A public
data center

<figure><img src="image_269.png" /></figure>

Supported by

<figure><img src="image_270.png" /></figure>

<figure><img src="image_271.png" /></figure>

euris
cloud santé

<figure><img src="image_272.png" /></figure>

<figure><img src="image_273.png" /></figure>

<figure><img src="image_274.png" /></figure>

<figure><img src="image_275.png" /></figure>

A private
data center

<figure><img src="image_276.png" /></figure>
# Deployment in different hospitals

<figure><img src="image_277.png" /></figure>

<figure><img src="image_278.png" /></figure>

<figure><img src="image_279.png" /></figure>
<figure><img src="image_280.png" /></figure>

Open and controlled data access

Data User Agreement

Signed by researchers

"[...] I will not attempt to [...] retrieve the identity of the study participants."

<figure><img src="image_281.png" /></figure>

<figure><img src="image_282.png" /></figure>

3- Access the data

2- Sign the Data User Agreement

<figure><img src="image_283.png" /></figure>

<figure><img src="image_284.png" /></figure>
# Challenges

## The MS-Multi-Spine Challenges

<figure><img src="image_285.png" /><figcaption>PetSeg
MSSEG-1</figcaption></figure>

53 patients
Different patients

<figure><img src="image_286.png" /></figure>

<figure><img src="image_287.png" /><figcaption>Challenges MSSEG-2</figcaption></figure>

100MRI from 100 patients

"Multiple Sclerosis Spinal Cord Lesions Detection from MultiSequence MRIs"

An uncommon but relevant task: spinal cord lesions detection

Multisequences: 4 sequences potentially available with various resolutions

Missing modalities: all four sequences not available for each patient at training and at testing

600 MRI from
100 patients

Empenn
B. Combès

<figure><img src="image_288.png" /></figure>

<figure><img src="image_289.png" /></figure>

<figure><img src="image_290.png" /><figcaption>Sagittal slices from 3 sequences acquired in a given session on patient with MS</figcaption></figure>

<figure><img src="image_291.png" /></figure>

<figure><img src="image_292.png" /></figure>
<figure><img src="image_293.png" /></figure>

The End

<figure><img src="image_294.png" /></figure>

<figure><img src="image_295.png" /></figure>

<figure><img src="image_296.png" /></figure>