Cerebral Aneurysms

33 Pages·2008·3.11 MB·English

Milano, 11 Marzo 2008
Functional Data Analysis of the Geometrical
Features of the Internal Carotid Artery
Laura Maria SANGALLI
Piercesare SECCHI
Simone VANTINI
Alessandro VENEZIANI
The ANEURISK Project
2
We don’t know what to say to people
with cerebral aneurysms.
Choosing between treating or not
can be a matter of choosing
between Life and Death.
Dr E. Boccardi
Statistics
Computer fluid dynamics
Structure Mechanics
Neuroradiology
Medical Imaging
Neurosurgery
SANGALLI, SECCHI, VANTINI, VENEZIANI
Cerebral Aneurysms
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• Cerebral aneurysms: malformations of cerebral arteries,
in particular of arteries belonging to or connected to the
Circle of Willis.
EPIDEMIOLOGICAL STATISTICS
• Incidence rate of cerebral aneurysms:
1/20 people
• Incidence rate of ruptured cerebral aneurysms per year:
1/10000 people per year
• Mortality due to a ruptured aneurysm:
> 50%: Out of 9 patients with a ruptured aneurysm:
(cid:1)
3 are expected to die before arriving at the hospital
(cid:1)
2 to die after having arrived at the hospital
(cid:1)
2 to survive with permanent cerebral damages
(cid:1)
2 to survive without permanent cerebral damages
SANGALLI, SECCHI, VANTINI, VENEZIANI
Cerebral Aneurysms
4
A CONJECTURE
Onset, development and rupture of cerebral
aneurysms are conditioned by the
geometry of the vessel through its effects
on blood fluid dynamics
Is there a relationship between
the geometrical features of the distal part of the ICA and
the onset of cerebral aneurysms in the arterial district
downstream of the ICA?
SANGALLI, SECCHI, VANTINI, VENEZIANI
3D Angiographies
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Observational Study conducted at Ospedale Ca’ Granda Niguarda – Milano
relative to 65 patients hospitalized from September 2002 to October 2005.
Without
With Cerebral
Cerebral
Aneurysm
Aneurysm
On Willis On ICA
7
33 25
SANGALLI, SECCHI, VANTINI, VENEZIANI
3D Angiographies
6
Observational Study conducted relative to 65 patients hospitalized
at Ospedale Niguarda Ca’ Granda Milano from September 2002 to October 2005.
Without
With Cerebral
Cerebral
Aneurysm
Aneurysm
On Willis On ICA
7
33 25
SANGALLI, SECCHI, VANTINI, VENEZIANI
From 3D Angiographies to Discrete Data
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IMAGE RECONSTRUCTION by L. Antiga, M. Piccinelli, Mario Negri-Bergamo
3D-arrays of Vessel Lumen (volume occupied by blood flow)
gray scaled pixels identified by Centerlines and MISR’s
x Right-Left
ELICITATION OF: ij
y Top-Down
ij
1) Centerline coordinates
z Front-Back
(centers of MIS) ij
R MISR
2) Vessel width ij
t Abscissa
(Radius of MIS)
ij
SANGALLI, SECCHI, VANTINI, VENEZIANI
From Discrete Data to Functional Data
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Free Knot Regression Splines
Discrete Points Functional Expression
of the Centerline For each of the Centerline
patient
x Left-Right x(s) Left-Right
ij i
y Top-Down y(s) Top-Down
ij i
z Front-Back z(s) Front-Back
ij i
Why?
• To Match Data
Data Registration
• To Estimate Derivatives
Curvature Profiles
• To Reduce Dimensionality
SANGALLI, SECCHI, VANTINI, VENEZIANI
From Discrete Data to Functional Data
9
Free Knot Regression Splines
Discrete Points Functional Expression
of the Centerline For each of the Centerline
patient
x Left-Right x(s) Left-Right
ij i
y Top-Down y(s) Top-Down
ij i
z Front-Back z(s) Front-Back
ij i
by minimizing through an iterative algorithm:
Fixed:
Spline Order Regularity of Functional Data
Not Fixed:
Number and Position of Knots Spatial Variability
Sum of Squared Residuals Complexity
SANGALLI, SECCHI, VANTINI, VENEZIANI
From Discrete Data to Functional Data
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Free Knot Regression Splines
a
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SANGALLI, SECCHI, VANTINI, VENEZIANI