# From Group to Patient-Specific Analysis of Brain Function in Arterial Spin Labelling and BOLD Functional MRI

Camille Maumet

<figure><img src="image_1.png" /></figure>

## To cite this version:

Camille Maumet. From Group to Patient-Specific Analysis of Brain Function in Arterial Spin Labelling and BOLD Functional MRI. PhD Defense, May 2013, Rennes, France. 2013. [hal-04091256](https:// HAL Id: hal-04091256 )

Submitted on 7 May 2023

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Distributed under a Creative Commons Attribution 4.0 International License
# From Group to Patient-Specific Analysis of Brain Function in Arterial Spin Labelling and BOLD Functional MRI

Camille Maumet

PhD Defense, May 29th, 2013

University of Rennes 1, Faculty of medecine, F-35043 Rennes, France

INSERM, U746, F-35042 Rennes, France

CNRS, IRISA, UMR 6074, F-35042 Rennes, France

Inria, VISAGES project-team, F-35042 Rennes, France

Director: Christian Barillot, Co-director: Pierre Maurel

<figure><img src="image_3.png" /></figure>

Inserm

Institut national
de la santé et de la recherche médicale

UNIVERSITE DE
RENNES

CHU
Rennes

VisAGES
Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic

GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion
<figure><img src="image_4.png" /></figure>
# Brain function

## Two views of brain function:

<figure><img src="image_5.png" /><figcaption>Task-evoked activity</figcaption></figure>

<figure><img src="image_6.png" /></figure>

Activation

<figure><img src="image_7.png" /></figure>

Brain function ?

[Raichle 2010]
# Brain function

## Two views of brain function:

From Group to
Patient-Specific
Analysis of Brain
Function

Camille Maumet

Context

### Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic
GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion

### Task-evoked activity

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

Activation

<figure><img src="image_10.png" /></figure>

### Brain function ?

### Intrinsic brain function

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

Metabolic activity

<figure><img src="image_13.png" /></figure>

Perfusion

<figure><img src="image_14.png" /></figure>

Connectivity

<figure><img src="image_15.png" /></figure>

Electrical activity

[Raichle 2010]
# Brain function

## Two views of brain function:

From Group to
Patient-Specific
Analysis of Brain
Function

Camille Maumet

Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic

GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion

Task-evoked activity

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

Activation

<figure><img src="image_18.png" /></figure>

Brain function ?

Intrinsic brain function

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

Metabolic activity

<figure><img src="image_21.png" /></figure>

Perfusion

<figure><img src="image_22.png" /></figure>

Connectivity

<figure><img src="image_23.png" /></figure>

Electrical activity

[Raichle 2010]
# Brain perfusion

<figure><img src="image_24.png" /></figure>

Blood supply to the brain

**Brain perfusion** is the biological process that ensures the delivery of oxygen and nutrients to the cerebral tissues by means of microcirculation.

<figure><img src="image_25.png" /></figure>

Example of perfusion parameters
<figure><img src="image_26.png" /></figure>

Labelling

[Detre et al., MRM 1992]
<figure><img src="image_27.png" /><figcaption>Labelling</figcaption></figure>

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

[Detre et al., MRM 1992]
<figure><img src="image_29.png" /></figure>

Labelling

<figure><img src="image_30.png" /></figure>

Delay

<figure><img src="image_31.png" /></figure>

Readout

[Detre et al., MRM 1992]
<figure><img src="image_32.png" /></figure>

Labelling

<figure><img src="image_33.png" /></figure>

Delay

<figure><img src="image_34.png" /></figure>

Readout

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>

Label

[Detre et al., MRM 1992]
<figure><img src="image_37.png" /></figure>

Labelling

<figure><img src="image_38.png" /></figure>

Delay

<figure><img src="image_39.png" /></figure>

Readout

<figure><img src="image_40.png" /></figure>

<figure><img src="image_41.png" /></figure>

Label

<figure><img src="image_42.png" /></figure>

Readout

[Detre et al., MRM 1992]
<figure><img src="image_43.png" /></figure>

Labelling

<figure><img src="image_44.png" /></figure>

Delay

<figure><img src="image_45.png" /></figure>

Readout

<figure><img src="image_46.png" /></figure>

<figure><img src="image_47.png" /></figure>

Label

<figure><img src="image_48.png" /></figure>

Readout

<figure><img src="image_49.png" /></figure>

<figure><img src="image_50.png" /></figure>

Control
<figure><img src="image_51.png" /></figure>

Labelling

<figure><img src="image_52.png" /></figure>

Delay

<figure><img src="image_53.png" /></figure>

Readout

<figure><img src="image_54.png" /></figure>

<figure><img src="image_55.png" /></figure>

Label

<figure><img src="image_56.png" /></figure>

Readout

<figure><img src="image_57.png" /></figure>

<figure><img src="image_58.png" /></figure>

Control

<figure><img src="image_59.png" /></figure>

Control

<figure><img src="image_60.png" /></figure>

Label

<figure><img src="image_61.png" /></figure>

<figure><img src="image_62.png" /></figure>

Difference

1 pair
<figure><img src="image_63.png" /></figure>

Labelling

<figure><img src="image_64.png" /></figure>

Delay

<figure><img src="image_65.png" /></figure>

Readout

<figure><img src="image_66.png" /></figure>

<figure><img src="image_67.png" /></figure>

Label

<figure><img src="image_68.png" /></figure>

Readout

<figure><img src="image_69.png" /></figure>

<figure><img src="image_70.png" /></figure>

Control

<figure><img src="image_71.png" /></figure>

Control

<figure><img src="image_72.png" /></figure>

Label

<figure><img src="image_73.png" /></figure>

<figure><img src="image_74.png" /></figure>

Difference

1 pair

<figure><img src="image_75.png" /></figure>

Difference

60 pairs
# Group analyses: definition (1/2)

<figure><img src="image_76.png" /></figure>
Group analyses: definition (1/2)

**Within-group** analyses identify common patterns across a group of subjects.

<figure><img src="image_77.png" /></figure>
# Group analyses: definition (1/2)

**Within-group** analyses identify common patterns across a group of subjects.

<figure><img src="image_78.png" /></figure>

## Examples

<figure><img src="image_79.png" /></figure>

Group activation for a language task.

<figure><img src="image_80.png" /></figure>

Group cerebral blood flow.
# Group analyses: definition (2/2)

<figure><img src="image_81.png" /></figure>

<figure><img src="image_82.png" /></figure>
# Group analyses: definition (2/2)

**Between-group** analyses identify differences at the group level.

<figure><img src="image_83.png" /></figure>
Group analyses: definition (2/2)

**Between-group** analyses identify differences at the group level.

<figure><img src="image_84.png" /></figure>

Example

<figure><img src="image_85.png" /></figure>

Differences of activation between a group of children diagnosed with specific language impairment and a control group during a language task.

* Hyperactivation.

* Hypoactivation.
Group analyses

<figure><img src="image_86.png" /></figure>

<figure><img src="image_87.png" /></figure>

<figure><img src="image_88.png" /></figure>

<figure><img src="image_89.png" /></figure>

Neuroimaging **group analyses**

* focus on the general patterns of brain function observed in the typical or pathological brain.

* are the most widespread type of statistical analysis.
# Patient-specific analyses: definition (1/2)

<figure><img src="image_90.png" /></figure>
Patient-specific analyses: definition (1/2)

**Patient-specific** analyses identify patterns of brain function in a single subject.

<figure><img src="image_91.png" /></figure>
# Patient-specific analyses: definition (1/2)

**Patient-specific** analyses identify patterns of brain function in a single subject.

<figure><img src="image_92.png" /></figure>

## Examples

<figure><img src="image_93.png" /></figure>

Subject activation for a language task.

<figure><img src="image_94.png" /></figure>

Cerebral blood flow.
<figure><img src="image_95.png" /></figure>

<figure><img src="image_96.png" /></figure>

<figure><img src="image_97.png" /></figure>

<figure><img src="image_98.png" /></figure>
# Patient-specific analyses: definition (2/2)

Patient-specific analyses can also identify deviation
from normality in a single subject.

<figure><img src="image_99.png" /></figure>
# Patient-specific analyses: definition (2/2)

Patient-specific analyses can also identify deviation
from normality in a single subject.

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

## Examples

<figure><img src="image_101.png" /></figure>

Hyper- and hypo-perfusions in a patient diagnosed with brain tumour.
# Patient-specific analyses

From Group to
Patient-Specific
Analysis of Brain
Function

Camille Maumet

<figure><img src="image_102.png" /></figure>

<figure><img src="image_103.png" /></figure>

Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic

GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion

Neuroimaging **patient-specific** analyses

* focus on the specific patterns of brain function observed in a single brain.

* perform based either on a single subject dataset or on a subject and a group of controls.
Contributions: overview

<table><thead><tr><th></th><th>Group analysis</th><th>Patient-specific analysis</th></tr></thead><tbody><tr><th>Within</th><td></td><td></td></tr><tr><th>Between</th><td></td><td></td></tr></tbody></table>

<figure><img src="image_104.png" /></figure>

<figure><img src="image_105.png" /></figure>

<figure><img src="image_106.png" /></figure>

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

<figure><img src="image_108.png" /></figure>

<figure><img src="image_109.png" /></figure>

<figure><img src="image_110.png" /></figure>

<figure><img src="image_111.png" /></figure>
Contributions: overview

<table><thead><tr><th></th><th>Group analysis</th><th>Patient-specific analysis</th></tr></thead><tbody><tr><th>Within</th><td></td><td></td></tr><tr><th>Between</th><td></td><td></td></tr></tbody></table>

<figure><img src="image_112.png" /></figure>

<figure><img src="image_113.png" /></figure>

<figure><img src="image_114.png" /></figure>

<figure><img src="image_115.png" /></figure>

A panel of 4 fMRI tasks for language mapping in children.

<table><thead><tr><th></th><th>Stimulus presentation</th><th>Category</th><th>Stimulus presentation</th><th>Definition</th></tr></thead><tbody><tr><th>Phon-diff</th><td></td><td></td><td></td><td></td></tr><tr><th>Phon-seg</th><td></td><td></td><td></td><td></td></tr></tbody></table>

<table><thead><tr><th>Category</th></tr></thead><tbody><tr><td>Definition</td></tr></tbody></table>

<table><thead><tr><th>Category</th></tr></thead><tbody><tr><td>Phon-diff</td></tr></tbody></table>

<table><thead><tr><th>Category</th></tr></thead><tbody><tr><td>Phon-seg</td></tr></tbody></table>

<table><thead><tr><th>Category</th></tr></thead><tbody><tr><td>Phon-seg</td></tr></tbody></table>

<figure><img src="image_116.png" /></figure>
Contributions: overview

<table><thead><tr><th></th><th>Group analysis</th><th>Patient-specific analysis</th></tr></thead><tbody><tr><th>Within</th><td></td><td></td></tr><tr><th>Between</th><td></td><td></td></tr></tbody></table>

Atypical activity and lateralisation of brain function in children diagnosed with typical specific language impairment.

<figure><img src="image_117.png" /><figcaption>Definition task (Control > T-SLI)</figcaption></figure>

<figure><img src="image_118.png" /><figcaption>PhonDiff task (T-SLI > Control)</figcaption></figure>

<figure><img src="image_119.png" /></figure>

<figure><img src="image_120.png" /><figcaption>Combined Tasks</figcaption></figure>

<figure><img src="image_121.png" /></figure>
Contributions: overview

<figure><img src="image_122.png" /></figure>

Robust Estimation of the Cerebral Blood Flow in Arterial Spin Labelling.

<figure><img src="image_123.png" /></figure>
Contributions: overview

<table><thead><tr><th></th><th>Group analysis</th><th>Patient-specific analysis</th></tr></thead><tbody><tr><th>Within</th><td></td><td></td></tr><tr><th>Between</th><td></td><td></td></tr></tbody></table>

Objective: Quantitative identification of voxelwise patient-specific perfusion abnormalities.

<figure><img src="image_124.png" /></figure>
# Contributions: overview

<table><thead><tr><th></th><th>Group analysis</th><th>Patient-specific analysis</th></tr></thead><tbody><tr><th>Within</th><td></td><td></td></tr><tr><th>Between</th><td>↔</td><td>↔</td></tr></tbody></table>

Objective: Quantitative identification of voxelwise patient-specific perfusion abnormalities.

<figure><img src="image_125.png" /></figure>
25 patients diagnosed with brain tumours and 61 control subjects participated in this study.

## Imaging protocol:

* PICORE Q2TIPS Pulsed ASL, 60 repetitions

* MPRAGE T1 3D

* T2 FLAIR

## For the patients only:

* T1 3D Gadolinium

* Dynamic Susceptibility Contrast imaging (DSC)
# Validation: Ground Truth

## 1. Segmentation of the tumour:

<figure><img src="image_126.png" /></figure>

## 2. Combination with T2 perfusion information:

<figure><img src="image_127.png" /></figure>

## 3. Visual assessment and manual corrections by a clinician.
State of the art

<figure><img src="image_128.png" /></figure>
State of the art

From Group to
Patient-Specific
Analysis of Brain
Function

Camille Maumet

Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic

GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion

<figure><img src="image_129.png" /></figure>

<figure><img src="image_130.png" /></figure>

<figure><img src="image_131.png" /></figure>
<figure><img src="image_132.png" /></figure>
State of the art

Massively univariate approaches:

<figure><img src="image_133.png" /></figure>
State of the art

**Massively univariate approaches:**

<figure><img src="image_134.png" /></figure>
# State of the art

Massively univariate approaches:

<figure><img src="image_135.png" /></figure>
# State of the art

Massively univariate approaches:

<figure><img src="image_136.png" /></figure>

<figure><img src="image_137.png" /></figure>

<figure><img src="image_138.png" /></figure>

<figure><img src="image_139.png" /></figure>

<figure><img src="image_140.png" /></figure>

✓ The standard approach, e.g. [Holmes 1998, Beckmann 2003].

✓ Computationally efficient.

X No integration of information cross-voxels (pre-smoothing).
<figure><img src="image_141.png" /></figure>

<figure><img src="image_142.png" /></figure>

<figure><img src="image_143.png" /></figure>

<figure><img src="image_144.png" /></figure>
# State of the art

## Locally multivariate approaches:

<figure><img src="image_145.png" /></figure>
# State of the art

## Locally multivariate approaches:

<figure><img src="image_146.png" /></figure>
# State of the art

## Locally multivariate approaches:

<figure><img src="image_147.png" /></figure>
# State of the art

## Locally multivariate approaches:

<figure><img src="image_148.png" /></figure>

<figure><img src="image_149.png" /></figure>

<figure><img src="image_150.png" /></figure>

<figure><img src="image_151.png" /></figure>

* ✓ Combination of local voxel information (no smoothing), e.g. [Kriegeskorte 2006].

* ✓ Standard statistics or machine learning.

* ✓ Less time consuming than full brain.

* × Can still be time consuming (machine learning).

* × Only local information is combined.
Univariate / Multivariate - overview

<table><thead><tr><th></th><th>Massively univariate</th><th>Locally multivariate</th><th>Multivariate</th></tr></thead><tbody><tr><td>Context</td><td></td><td></td><td></td></tr><tr><td>Brain function</td><td></td><td></td><td></td></tr><tr><td>From group to patient-specific analyses</td><td></td><td></td><td></td></tr><tr><td>Contributions</td><td></td><td></td><td></td></tr><tr><td>Overview</td><td></td><td></td><td></td></tr><tr><td>Materials</td><td></td><td></td><td></td></tr><tr><td>Imaging protocol</td><td></td><td></td><td></td></tr><tr><td>Validation</td><td></td><td></td><td></td></tr><tr><td>State of the art</td><td></td><td></td><td></td></tr><tr><td>Heteroscedastic GLM</td><td></td><td></td><td></td></tr><tr><td>Methods</td><td></td><td></td><td></td></tr><tr><td>Results</td><td></td><td></td><td></td></tr><tr><td>A contrario</td><td></td><td></td><td></td></tr><tr><td>Methods</td><td></td><td></td><td></td></tr><tr><td>Results</td><td></td><td></td><td></td></tr><tr><td>Conclusions and future work</td><td></td><td></td><td></td></tr><tr><td>Contributions</td><td></td><td></td><td></td></tr><tr><td>Discussion</td><td></td><td></td><td></td></tr></tbody></table>

<figure><img src="image_152.png" /></figure>

<figure><img src="image_153.png" /></figure>

<figure><img src="image_154.png" /></figure>

<figure><img src="image_155.png" /></figure>

<figure><img src="image_156.png" /></figure>

<figure><img src="image_157.png" /></figure>

<figure><img src="image_158.png" /></figure>

<figure><img src="image_159.png" /></figure>

<figure><img src="image_160.png" /></figure>
Univariate / Multivariate - overview

Massively univariate

Locally multivariate

Multivariate

<figure><img src="image_161.png" /></figure>

<figure><img src="image_162.png" /></figure>

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

Comput.
efficiency

++

+ / -

-

Cross-
voxels
info.

-

+

++

1. The massively univariate GLM: **homoscedastic** and **heteroscedastic** models.
Univariate / Multivariate - overview

<figure><img src="image_164.png" /></figure>

<figure><img src="image_165.png" /></figure>

<figure><img src="image_166.png" /></figure>

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

Comput.
efficiency

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

<figure><img src="image_169.png" /></figure>

<figure><img src="image_170.png" /></figure>

Cross-
voxels
info.

<figure><img src="image_171.png" /></figure>

<figure><img src="image_172.png" /></figure>

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

Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic
GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion

1. The **massively univariate GLM: homoscedastic and heteroscedastic models.**

2. The **a contrario approach** as a new locally multivariate procedure.
Univariate / Multivariate - overview

Massively univariate

Locally multivariate

Multivariate

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

<figure><img src="image_175.png" /></figure>

<figure><img src="image_176.png" /></figure>

Comput.
efficiency

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

<figure><img src="image_178.png" /></figure>

<figure><img src="image_179.png" /></figure>

Cross-
voxels
info.

<figure><img src="image_180.png" /></figure>

<figure><img src="image_181.png" /></figure>

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

1. The **massively univariate GLM: homoscedastic and heteroscedastic models.**

2. The *a contrario* approach as a new locally multivariate procedure.
# Standard statistics: overview

<figure><img src="image_183.png" /></figure>
# Standard statistics: overview

<figure><img src="image_184.png" /></figure>
# Modelling: subject level

## General Linear Model: subject level

<figure><img src="image_185.png" /></figure>

Repetition 1

<figure><img src="image_186.png" /></figure>

Repetition 2

...

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

Repetition r
<figure><img src="image_188.png" /></figure>

Repetition 1

<figure><img src="image_189.png" /></figure>

Repetition 2

...

<figure><img src="image_190.png" /></figure>

Repetition r

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

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

Perfusion
estimate in
subject 1: $\beta_1$
# Modelling: subject level

## General Linear Model: subject level

<figure><img src="image_193.png" /></figure>
# Modelling: subject level

## General Linear Model: subject level

### Context

Brain function

From group to
patient-specific
analyses

### Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic
GLM

### Methods

Results

A contrario

### Methods

Results

### Conclusions and
future work

Contributions

### Discussion

<figure><img src="image_194.png" /></figure>
Modelling: group level

General Linear Model: group level.

<figure><img src="image_195.png" /></figure>

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

<figure><img src="image_197.png" /></figure>

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

Two sources of variation: the **between-subject** variance and the **within-subject** variance.
Modelling: group level

General Linear Model: group level.

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

Two sources of variation: the **between-subject** variance
and the **within-subject** variance.
Modelling: group level

General Linear Model: group level.

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

Two sources of variation: the **between-subject** variance
and the **within-subject** variance.
Modelling: group level

General Linear Model: group level. The **homoscedastic model**:

Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic
GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion

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

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

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

<figure><img src="image_224.png" /></figure>

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

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

Two sources of variation: the **between-subject variance** and the **within-subject variance**.
Modelling: group level

General Linear Model: group level. The heteroscedastic model:

<figure><img src="image_227.png" /></figure>

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

Two sources of variation: the **between-subject** variance and the **within-subject** variance.
The **homoscedastic model assumes** that the
**within-subject variance** is:

► **negligible** by comparison to the between-subject variance; or

► **roughly constant** across subjects.
In functional MRI there is no consensus:

► Superiority of the heteroscedastic model, [Beckmann 2003, Mumford 2006, Thirion 2007].

► Validity of the homoscedastic model for one-sample t-tests in BOLD fMRI, [Mumford 2009].

► Invalidity of the homoscedastic model [Chen 2012].

Both approaches are in use in the neuroimaging
community:

► The homoscedastic approach (SPM<fnref n="1" />)

► The heteroscedastic approach (FSL<fnref n="2" />, AFNI<fnref n="3" />).

<footnote n="1">¹www.fil.ion.ucl.ac.uk/spm/</footnote>

<footnote n="2">²fsl.fmrib.ox.ac.uk/fsl/fslwiki/</footnote>

<footnote n="3">³afni.nimh.nih.gov/afni/</footnote>
# Standard statistics: overview

<figure><img src="image_229.png" /></figure>
# Standard statistics: overview

From Group to
Patient-Specific
Analysis of Brain
Function

Camille Maumet

## Context

Brain function

From group to
patient-specific
analyses

## Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic

GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion

<figure><img src="image_230.png" /></figure>
# Results: Perfusion in the control group

## Mean estimate

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

## Standard deviation estimates

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

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

<figure><img src="image_234.png" /></figure>
# Results: Perfusion in the control group

## Mean estimate

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

## Standard deviation estimates

<figure><img src="image_236.png" /><figcaption>Between-subject standard deviation (heteroscedastic model)</figcaption></figure>

<figure><img src="image_237.png" /><figcaption>Root-square of the average within-subject variance (heteroscedastic model)</figcaption></figure>

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

<figure><img src="image_239.png" /><figcaption>Brain arteries</figcaption></figure>

<figure><img src="image_240.png" /><figcaption>Brain veins</figcaption></figure>
# Assumptions of the homoscedastic model

* Assumption 1: Within-subject variance negligible by comparison to the between-subject variance.

* Assumption 2: Within-subject variance roughly constant across subjects.

From Group to
Patient-Specific
Analysis of Brain
Function

Camille Maumet

Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic

GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion
# Assumptions of the homoscedastic model

* **Assumption 1: Within-subject variance negligible by comparison to the between-subject variance.**

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

* **Assumption 2: Within-subject variance roughly constant across subjects.**
# Assumptions of the homoscedastic model

* **Assumption 1: Within-subject variance negligible by comparison to the between-subject variance.**

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

× not verified

* **Assumption 2: Within-subject variance roughly constant across subjects.**
# Assumptions of the homoscedastic model

* **Assumption 1: Within-subject variance negligible by comparison to the between-subject variance.**

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

× not verified

* **Assumption 2: Within-subject variance roughly constant across subjects.**

Within-subject standard deviation in two control subjects:

<figure><img src="image_244.png" /></figure>
# Assumptions of the homoscedastic model

* **Assumption 1: Within-subject variance negligible by comparison to the between-subject variance.**

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

× not verified

* **Assumption 2: Within-subject variance roughly constant across subjects.**

Within-subject standard deviation in two control subjects:

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

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

Using a metric from [Mumford 2009].
# Assumptions of the homoscedastic model

* **Assumption 1: Within-subject variance negligible by comparison to the between-subject variance.**

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

not verified

* **Assumption 2: Within-subject variance roughly constant across subjects.**

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

not verified

Using a metric from [Mumford 2009].
# Results: homoscedastic versus heteroscedastic GLM

From Group to
Patient-Specific
Analysis of Brain
Function

Camille Maumet

Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic
GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion

<figure><img src="image_250.png" /></figure>
# Results: homoscedastic versus heteroscedastic GLM

<figure><img src="image_251.png" /><figcaption>ROC curves for perfusion abnormality detections.</figcaption></figure>

<table><thead><tr><th></th><th colspan="6">Homoscedastic model</th></tr><tr><th></th><th>0</th><th>4</th><th>6</th><th>8</th><th>10</th><th>12</th></tr></thead><tbody><tr><th>FWHM (mm³)</th><td>0</td><td>4</td><td>6</td><td>8</td><td>10</td><td>12</td></tr><tr><th>ROC Area</th><td>0.46</td><td><strong>0.49</strong></td><td><strong>0.49</strong></td><td><strong>0.49</strong></td><td>0.48</td><td>0.48</td></tr></tbody></table>

<table><thead><tr><th></th><th colspan="6">Heteroscedastic model</th></tr><tr><th></th><th>0</th><th>4</th><th>6</th><th>8</th><th>10</th><th>12</th></tr></thead><tbody><tr><th>FWHM (mm³)</th><td>0</td><td>4</td><td>6</td><td>8</td><td>10</td><td>12</td></tr><tr><th>ROC Area</th><td>0.63</td><td>0.70</td><td><strong>0.72</strong></td><td><strong>0.72</strong></td><td>0.69</td><td>0.65</td></tr></tbody></table>

Area under the ROC curve.
# Conclusion: homoscedastic versus heteroscedastic GLM

* The assumption of homoscedasticity is violated in ASL studies.

* Modelling heteroscedasticity is essential in the detection of patient-specific perfusion abnormalities with ASL.

Related publication: [Maumet et al., NeuroImage 2013].
# Univariate / Multivariate - overview

<table><thead><tr><th></th><th>Massively univariate</th><th>Locally multivariate</th><th>Multivariate</th></tr></thead><tbody><tr><td></td><td><img src="massively_univariate.png" alt="Massively univariate.png"></td><td><img src="locally_multivariate.png" alt="Locally multivariate.png"></td><td><img src="multivariate.png" alt="Multivariate.png"></td></tr><tr><td>Context</td><td></td><td></td><td></td></tr><tr><td>Brain function</td><td></td><td></td><td></td></tr><tr><td>From group to<br>patient-specific<br>analyses</td><td></td><td></td><td></td></tr><tr><td>Contributions</td><td></td><td></td><td></td></tr><tr><td>Overview</td><td></td><td></td><td></td></tr><tr><td>Materials</td><td></td><td></td><td></td></tr><tr><td>Imaging protocol</td><td></td><td></td><td></td></tr><tr><td>Validation</td><td></td><td></td><td></td></tr><tr><td>State of the art</td><td></td><td></td><td></td></tr><tr><td>Heteroscedastic<br>GLM</td><td></td><td></td><td></td></tr><tr><td>Methods</td><td></td><td></td><td></td></tr><tr><td>Results</td><td></td><td></td><td></td></tr><tr><td>A contrario</td><td></td><td></td><td></td></tr><tr><td>Methods</td><td></td><td></td><td></td></tr><tr><td>Results</td><td></td><td></td><td></td></tr></tbody></table>

<figure><img src="image_252.png" /></figure>

<figure><img src="image_253.png" /></figure>

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

1. The **massively univariate GLM: homoscedastic and heteroscedastic models.**

2. The **a contrario approach** as a new locally multivariate procedure.
A contrario

From the computer vision community [Desolneux 2003].

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

From the computer vision community [Desolneux 2003].

From Group to
Patient-Specific
Analysis of Brain
Function

Camille Maumet

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

Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic
GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion
Rare event count per sphere as region-based statistic:

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

1. Voxel-based
probability
Rare event count per sphere as region-based statistic:

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

1. Voxel-based
probability

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

2. Thresholding

$k_{(v)} = \begin{cases} 1, & \text{if } \pi_v^{GLM} \le p_{PRE}, \\ 0, & \text{otherwise.} \end{cases}$
# A contrario approach

Rare event count per sphere as region-based statistic:

<figure><img src="image_260.png" /><figcaption>1. Voxel-based probability</figcaption></figure>

<figure><img src="image_261.png" /><figcaption>2. Thresholding</figcaption></figure>

<figure><img src="image_262.png" /><figcaption>3. Rare event count per region</figcaption></figure>

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

$$k_{(v)} = \begin{cases} 1, & \text{if } \pi_v^{GLM} \le p_{PRE}, \\ 0, & \text{otherwise.} \end{cases}, \quad l_{(r)} = \sum_{v \in R} k_{(v)}$$
A contrario approach

From the computer vision community [Desloneux 2003].

From Group to
Patient-Specific
Analysis of Brain
Function

Camille Maumet

Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic
GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion

<figure><img src="image_264.png" /></figure>
# A contrario approach

From region-based statistic to region-based probability:

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

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

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

3. Rare event count per region
4. Region-based probability

$$L_{(r)} = \sum_{v \in R} K_{(v)} \quad \text{with} \quad K_{(v)} \sim \text{Bern}(p_{\text{PRE}})$$

The original a contrario approach assumes **white noise**, i.e. the events are **independent**:

$$\pi_{(r)} = \Pr(L_{(r)} \geq l_{(r)}), \text{ where } L_{(r)} \sim \text{B}(e, p_{\text{PRE}}),$$

where *e* is the number of voxel per region.
# A contrario approach

From region-based statistic to region-based probability:

<figure><img src="image_268.png" /><figcaption>3. Rare event count per region
4. Region-based probability</figcaption></figure>

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

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

$$L_{(r)} = \sum_{v \in R} K_{(v)} \quad \text{with} \quad K_{(v)} \sim \text{Bern}(p_{\text{PRE}})$$

In MRI, spatial autocorrelation of the noise has been described (e.g. [Chumbley 2009]) and the independence assumption is therefore questioned.

We proposed a **non-independent probability** based on the joint distribution of a multivariate Gaussian distribution.
A contrario approach

From the computer vision community [Desloneux 2003].

From Group to
Patient-Specific
Analysis of Brain
Function

Camille Maumet

Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic

GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion

<figure><img src="image_271.png" /></figure>
# A contrario approach: thresholding

The correction for multiple testing is usually done by computing the Number of False Alarms:

$$NFA_{(r)} = numReg \pi_{(r)},$$

and the detections are outlined with:

$$NFA_{(r)} < \epsilon.$$

where $\epsilon$, is the average number of false detections that are tolerated.

The NFA is related to Bonferroni correction [Rousseau 2007].
Results: a contrario

From Group to
Patient-Specific
Analysis of Brain
Function

Camille Maumet

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

Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic
GLM

Methods

Results

A contrario

Methods

Results

Conclusions and
future work

Contributions

Discussion
Results: *a contrario*

From Group to
Patient-Specific
Analysis of Brain
Function

Camille Maumet

<figure><img src="image_273.png" /><figcaption>Average ROC curves</figcaption></figure>

Context

Brain function

From group to
patient-specific
analyses

Contributions

Overview

Materials

Imaging protocol

Validation

State of the art

Heteroscedastic

GLM

Methods

Results

A contrario

Methods

Results

GLM

<table><thead><tr><th>w</th><th>0</th><th>2</th><th>4</th><th>6</th><th>8</th><th>10</th><th>12</th></tr></thead><tbody><tr><th>ROC area</th><td>0.63</td><td>0.67</td><td>0.70</td><td>0.72</td><td><strong>0.73</strong></td><td>0.70</td><td>0.65</td></tr></tbody></table>

a contrario

<table><caption>Area under the ROC curves</caption><thead><tr><th rowspan="2">p<sub>PRE</sub></th><th colspan="3">rd = 1</th><th colspan="3">rd = 2</th></tr><tr><th>0.01</th><th>0.005</th><th>0.001</th><th>0.01</th><th>0.005</th><th>0.001</th></tr></thead><tbody><tr><th>ROC area</th><td>0.68</td><td>0.73</td><td>0.79</td><td>0.75</td><td>0.80</td><td><strong>0.87</strong></td></tr></tbody></table>

Conclusions and
future work

Contributions

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

GLM

* Invalidity of the GLM.

* This invalidity was also observed in voxel-based morphometry [Scarpazza 2013, Viviani 2007].
# Results: a contrario

## Checking the test validity

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

A contrario
Conclusion: a contrario

► The *a contrario* approach outperforms the standard General Linear Model.

► Non-independent probabilities provide more valid statistics in the context of MRI data analysis.

Related publications: [Maumet et al., ISBI 2012], [Maumet et al., MICCAI 2012], a journal paper submitted to NeuroImage.
# Contributions(1/2)

## Patient-specific analysis in BOLD fMRI and ASL:

* Comparison of the homoscedastic and heteroscedastic GLM

* Heteroscedasticity of Arterial Spin Labelling data.

* Modelling heteroscedasticity is essential in the detection of patient-specific perfusion abnormalities with ASL.
# Contributions(1/2)

## Patient-specific analysis in BOLD fMRI and ASL:

* Comparison of the homoscedastic and heteroscedastic GLM

* Heteroscedasticity of Arterial Spin Labelling data.

* Modelling heteroscedasticity is essential in the detection of patient-specific perfusion abnormalities with ASL.

* The *a contrario* locally multivariate procedure

* Superiority onto the massively univariate GLM.

* Two applications: the detection of patient-specific perfusion abnormalities and the detection of activation patterns in task-evoked analyses.
# Contributions(1/2)

Patient-specific analysis in BOLD fMRI and ASL:

* Comparison of the homoscedastic and heteroscedastic GLM

* Heteroscedasticity of Arterial Spin Labelling data.

* Modelling heteroscedasticity is essential in the detection of patient-specific perfusion abnormalities with ASL.

* The *a contrario* locally multivariate procedure

* Superiority onto the massively univariate GLM.

* Two applications: the detection of patient-specific perfusion abnormalities and the detection of activation patterns in task-evoked analyses.

* Robust computation (using M-estimators) of cerebral blood flow maps from a series of Arterial Spin Labelling acquisitions.
Group analyses in BOLD functional MRI.

* An original panel of four tasks for language mapping in children.

* Atypical patterns of activity and lateralisation in children diagnosed with specific language impairment.
# Discussion and future work (1/2)

Atypical brain function in specific language impairment:

* Extend the preliminary results of the *a contrario* approach in fMRI to this context.

* Take advantage of ASL sequences.

Robust statistics to compute cerebral blood flow maps:

* Compare current results with other M-estimators and complementary robust approaches.
# Discussion and future work (2/2)

## Arterial Spin Labelling

* More advanced ASL sequences, such as pseudo-continuous ASL with 3D readouts, provide a better signal-to-noise ratio.

* How does the conclusion on heteroscedasticity extend to these datasets ?

## The a contrario approach

* Provide a more thorough validation in BOLD fMRI.

* Extend the approach to group analyses.