Geometrical Multiscale Models for the Cardiovascular System I SimpleMinded Models for the Circulatio

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2nd Case Statistical/Numerical Investigations of
Cerebral Aneurysm Risk Development
THE ANEURISK PROJECT (2005-2007)
www2.mate.polimi.it8080/aneurisk
S.Bacigaluppi, E. Boccardi, L. Antiga, B.
Ene-Iordache, M. Piccinelli, A. Remuzzi, G.
Dubini, F. Migliavacca, L. Socci, P. Secchi, S.
Vantini, L. Formaggia, T. Passerini, M.R. De
Luca, A. V. (Coordinator)
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CEREBRAL ANEUSYSMS are lesions arising on
cerebral vessels characterized by a bulge of the
vessel wall. They quite often they are subject
to rupture. This event means cerebral
haemorrhage.
ANEURISK GOAL To highlight the possible
relationships linking vascular morphology and
development/rupture risks in Aneurysms
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STRUCTURE OF THE PROJECT
3D reconstruction and semi-automatic detection of
relevant morphological features
Clinical Data (DICOM)
GEOMETRICAL ANALYSIS
DATA-BASE
NUMERICAL SIMULATIONS
STATISTICAL ANALYSIS
Correlation Analysis, Decision Tree Definition
3D Simulations WSS Computation,
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3D RECONSTRUCTION
Level set is a numerical method for tracking the
evolution of contours and surfaces. The contour
is embedded as the zero-level of a function
evolving under the control of a differential
equation.
Gradient Image
The initial conditions (initial contour) are
given by the user and then it evolves until it
will locate on the regions corresponding to the
steepest change of image intensity across the
vessel wall, which is a robust and objective
criterion.
L. Antiga, M. Piccinelli
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Definition of the region of interest
Initialization
Level Set surface
VTK/ITK based C Code
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PROBLEMS IN 3D RECONSTRUCTION
1) Segmentation and Filtering can be
Operator/Code Dependent
Mimics (Materialize)
Amira (Mercury Inc.)
Level Sets method seem to be more robust and
accurate
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Home
Amira
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2) Variability of Cerebral Vasculature
Internal Carotid Arteries
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Basilar Arteries
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(SEMI-)AUTOMATIC GEOMETRY CHARACTERIZATION

• Decomposition of the vascular structure into
  subdomains on the basis of centerlines
  computation
• Computation of Landmarks parameters on
• Segments, Bifurcations, Aneurysms
• (detected at the previous step)

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Centerline computation and Vascular Structure
Subdivision
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LANDMARKS
SEGMENTS

• Length L
• Min/max/mean Radius R
• Mean curvature
• Torsion
• Toruosity (L/d)
• Stenosis (Boolean)

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LANDMARKS
BIFURCATIONS

• Angles
• Radii

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LANDMARKS
ANEURYSMS

• Presence (Boolean)
• Rupture (Boolean)
• Position
• Inlet Section Area
• Angiographic Volume
• Shape

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PRELIMINAR NUMERICAL RESULTS
Is the blood Newtonian in Aneurysms?
Steady/Unsteady Computation
Newton vs. Casson Rheologies
Boundary Conditions
F. Migliavacca, L. Socci FLUENT
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PRESSURE FIELDS
Casson
Newton
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WALL SHEAR STRESSES
Casson
Newton
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UNSTEADY COMPUTATION
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Is this flow division realistic?
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ANSWER
Integration of 1D/3D/0D Models
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1D REPRESENTATIONS OF THE WILLIS CIRCLE
T. Passerini, M.R. De Luca, A.V.
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1D MATHEMATICAL MODEL OF THE WILLIS CIRCLE
Starting point Euler equations for an arterial
segment
Bi-Trifurcation Modeling Conservation of flow
rates and (total) pressures
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THE SYMMETRIC CASE
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RIGHT CAROTID COMPRESSION TEST
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PCA MISSING (16 PATIENTS)
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CAROTID COMPRESSION ON A PATIENT WITH NO PCA
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Conclusions and Perspectives
1 - Deep understanding of relevant
cerebrovascular pathologies is quite far
mathematical/numerical models can support
investigations and hypotheses validations
2 - Cerebral circulation has specific features to
be considered
Biochemics/Haemodynamics interaction Willis
Circle robustness
3 Integration of different competences is
mandatory
NumericsStatisticsMedical ValidationGeometry
Analysis