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Statistical analysis of neuronal
connectivity in patients with
Gilles de la Tourette syndrome
Pietro GORI
Stanley DURRLEMAN, Olivier COLLIOT, Nicholas AYACHE
Aramis project-team (CRICM - CNRS - INSERM - INRIA), Paris, France
Asclepios project-team, Sophia Antipolis, France
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Purpose of the Project
Worbe et al. – Distinct
structural changes… - Brain -
2010
2
Study differences concerning shape and organization between
cerebral anatomical configurations of 27 controls and 47 patients
subject to Gilles de la Tourette syndrome in order to test the
hypothesis presented in Worbe et al.
Pietro Gori – Aramis team
Gilles de la Tourette syndrome:
• Multiple motor tics and at least one vocal tic.
• Tics occur many times everyday for at least one year.
• Onset before 18 years old.
• No drugs or any other general medical condition.
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Purpose of the Project
Alexander et al. – Parallel
organization of functionally…
- Ann. Rev. Neurosci.- 1986
3
Multiple inputs from several
functionally related cortical areas
(A,B,C) are "funneled“ back
through the basal ganglia and
thalamus to a particular area of the
cortical surface.
Pietro Gori – Aramis team
Worbe’s hypothesis: “Gilles de la Tourette syndrome is associated
with dysfunctions of the cortico-striato-thalamo-cortical circuits.”
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Purpose of the Project
Krack et al. – Deep brain
stimulation… - Trends in
Neuroscience - 2010
4 Pietro Gori – Aramis team
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Gilles de la Tourette syndrome
Pietro Gori – Aramis team 5
Sub-cortical Structures Cortical Surface Fiber bundles
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Atlas Construction
Pietro Gori – Aramis team 6
𝑿𝟏 𝑿𝟐
𝑿𝟒 𝑿𝟑
𝝓𝟏 𝑻 𝝓𝟐 𝑻
𝝓𝟑 𝑻 𝝓𝟒 𝑻
𝑿𝒔 = 𝝓𝒔 𝑻 + 𝝐𝒔
𝑻
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Atlas Construction
Pietro Gori – Aramis team 7
𝐸 𝑻, {𝜙𝑠} = 1
2𝜎𝜖2 𝐷 𝜙𝑠 𝑻 ,𝑿𝑠 + 𝑅𝑒𝑔(𝜙𝑠)
𝑁
𝑠=1
• Template
• Deformations
• Dissimilarity measure
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𝑿𝟐
𝑿𝟑 𝑿𝟒 𝑿𝟒 𝑿𝟑
𝑿𝟐 𝑿𝟏
Dissimilarity measure
Pietro Gori – Aramis team 8
𝑿𝟏
𝑻
𝝓𝟏 𝑻 𝝓𝟐 𝑻
𝝓𝟑 𝑻 𝝓𝟒 𝑻
𝑿𝒔 = 𝝓𝒔 𝑻 + 𝝐𝒔
𝑻
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1. For both surfaces and curves
2. No need of point or fiber
correspondences
3. Robust to different sampling
4. Global geometrical
differences
Currents
Dissimilarity measure
Pietro Gori – Aramis team 9
𝑿𝟏
𝝓𝟏 𝑻
Glaunès et al. –
Surface matching via currents –
IPMI - (2006)
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Dissimilarity measure
Pietro Gori – Aramis team 10
The framework of Currents can represent both curves and
surfaces and it doesn’t need point or fiber correspondence.
𝑇1 𝑤 = 𝑤 𝑡𝑇𝛼 𝑡 𝑑𝑡
𝑇1
𝑤 𝑥𝑖 = 𝐾𝑊 𝑥𝑖 , 𝑦𝑗 𝛽𝑗
𝑘
𝑇1, 𝑇2 𝑊∗ = 𝛽𝑗𝑇𝐾𝑊 𝑦𝑗 , 𝑥𝑖 𝛼𝑖
𝑗𝑖
Characterize an object via its
response to probing vector field
∼ 𝑤 𝑥𝑖𝑇𝛼𝑖
𝑖
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𝑻
Template Initialization
Pietro Gori – Aramis team 11
𝑿𝟏 𝑿𝟐
𝑿𝟒 𝑿𝟑
𝝓𝟏 𝑻 𝝓𝟐 𝑻
𝝓𝟑 𝑻 𝝓𝟒 𝑻
𝐸 𝑻, {𝜙𝑠} = 1
2𝜎𝜖2 𝐷 𝜙𝑠 𝑻 , 𝑿𝑠 + 𝑅𝑒𝑔(𝜙𝑠)
𝑁
𝑠=1
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Template Initialization
Pietro Gori – Aramis team 12
𝑿𝟏 𝑿𝟐
𝑿𝟑 𝑿𝟒
Durrleman et al. – Topology
Preserving Atlas Construction… -
MICCAI 2012 (2012)
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Template Initialization
Pietro Gori – Aramis team 13
𝑿𝟏 𝑿𝟐
𝑿𝟑 𝑿𝟒
Gori et al. – Towards joint
morphometry… - OHBM -
2013
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Template Initialization
Pietro Gori – Aramis team 14
𝑻
𝑰𝟏 𝑰𝟐 𝑰𝟒 … 𝑰𝟑
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Template Initialization
Pietro Gori – Aramis team 15
𝐼∗ = argmin𝐼𝑘
𝑇 − 𝐼𝑘 𝑊∗2
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Template Initialization
Pietro Gori – Aramis team 16
𝐼∗ = argmin𝐼𝑘
𝑇 − 𝐼𝑘 𝑊∗2
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Deformations
Pietro Gori – Aramis team 17
𝑿𝟏 𝑿𝟐
𝑿𝟒 𝑿𝟑
𝝓𝟏 𝑻 𝝓𝟐 𝑻
𝝓𝟑 𝑻 𝝓𝟒 𝑻
𝐸 𝑻, {𝜙𝑠} = 1
2𝜎𝜖2 𝐷 𝜙𝑠 𝑻 , 𝑿𝑠 + 𝑅𝑒𝑔(𝜙𝑠)
𝑁
𝑠=1
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Deformations
Pietro Gori – Aramis team 18
• Low dimension parameterization
Durrleman et al. – Topology
Preserving Atlas Construction… -
MICCAI 2012 (2012)
• Enables a global description of the whole brain preserving the
underlying organization of structures
• Captures local non-linear variations
One single diffeomorphism for the whole 3D space
Framework of diffeomorphism
New control point formulation
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Deformations
Pietro Gori – Aramis team 19
The whole 3D space is deformed by a single diffeomorphism
𝑣𝑡 𝑥(𝑡) = 𝐾 𝑥 𝑡 , 𝑐𝑝 𝑡 𝛼𝑝𝑖 (𝑡)
𝐶𝑝
𝑝=1
Control point
Momenta
𝜙𝑡 𝑥 = 𝑥 + 𝑣𝑠 𝜙𝑠 𝑥 𝑑𝑠𝑡
0
Position of point
x at time t
time-varying vector field
{𝜶𝒊(𝟎)} Deformation
parameters
Linear
Statistics
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Deformations
Pietro Gori – Aramis team 20
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𝑿𝟏 𝑿𝟐
𝑿𝟒 𝑿𝟑
Deformations
Pietro Gori – Aramis team 21
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PCA – first mode
Pietro Gori – Aramis team 22
- 2σ Updated template + 2σ
P
A
T
I
E
N
T
S
C
O
N
T
R
O
L
S
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First mode
Pietro Gori – Aramis team 23
- 2σ Updated template + 2σ
P
A
T
I
E
N
T
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C
O
N
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O
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Conclusions
Pietro Gori – Aramis team 24
• New multi-object atlas construction method based on
currents for shape complexes
• Joint analysis of white matter tracts and gray matter
surfaces preserving spatial organization of the
structures
• Fiber bundles template with anatomically correct
topology
• Limited number of deformation parameters well
suited for linear statistical analysis
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Perspectives
Pietro Gori – Aramis team 25
• Include the cortical surface into our analysis
• Decrease the computational time of the process
using a GPU-CUDA code
• Find a suitable statistical test to highlight few
important differences between the two populations
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Deformetrica
Pietro Gori – Aramis team 26
• Software for the statistical analysis of 2D and 3D shape data:
curves, surfaces, images, point clouds
• Multi-object registration and atlas construction
• Different kinds of deformation: rigid, affine, diffeomorphism
• Longitudinal analysis
• GPU implementation (under construction, Alexandre Routier)
• Bayesian Framework (under construction, Pietro Gori)
• Multi-scale analysis (under construction, Barbara Gris)
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Acknowledgments
Pietro Gori – Aramis team 27
• Alexandre Routier
• Dr Linda Marrakchi-Kacem (PhD)
• Dr Yulia Worbe (PhD, MD)
• Dr Cyril Poupon (PhD)
• Professor Andreas Hartmann (MD)
• Dr Olivier Colliot (PhD)
• Professor Nicholas Ayache (PhD)
• Dr Stanley Durrleman (PhD)
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Pietro Gori – Aramis team 28
P
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E
N
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- 2σ Updated template + 2σ
P
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N
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Thank You for your attention!