Transcript Document

6th Russian workshop
on mathematical models and numerical methods in biomathematics
Numerical modelling of
affected zone for
cerebral aneurysm
A.A.Cherevko, A.P.Chupakhin, A.L.Krivoshapkin, A.K.Khe,
K.Y.Orlov, P.A.Seleznev
Lavrentyev Institute of Hydrodynamics SB RAS
Meshalkin Novosibirsk Scientific Research Institute of Circulation Pathology
Outline
•
•
•
•
•
Purposes and stages of work
Medical information
3D-reconstruction of the cerebral vascular system
Hemodynamic modeling
Assessment of the region of influence of the
aneurysm on hydrodynamic characteristics
• Determination of influence on the aneurysm high
blood pressure ( Hypertension) and low blood
pressure (Hypotension)
Purposes
Assessment of the region of influence of the aneurysm on
hydrodynamic characteristics.
Determination of pressure’s influence on the aneurysm
(high blood pressure and low blood pressure)
Stages of work
3D- geometric reconstruction of circulation of the cerebral
vascular system with and without aneurysm based on
tomograms (data from Meshalkin Novosibirsk Scientific
Research Institute of Circulation Pathology)
Hemodynamic modeling based on the software package
ANSYS-CFX using the 3D- geometric reconstruction
An aneurysm is a weak area
in the wall of a blood vessel that causes
the blood vessel to bulge or balloon out.
• Locations of aneurysm’s appearance :arterial
bifurcations, space of anatomical changes of vessel’s
structure, arteriovenous malformations.
• The major factors: structural changes in the arteries,
hemodynamics, wall biomechanics.
• A person may have an aneurysm without having any
symptoms
• Symptoms : double vision,loss of vision,headaches,eye
pain,neck pain,stiff neck
• Repair an aneurysm:
Clipping and endovascular repair is most often done.
It usually involves a "coil" or coiling,
this is a less invasive way to treat some aneurysms.
3D-reconstruction
Reconstruction of two models of the cerebral vascular system with aneurysm on
• Middle cerebral artery(model А)
• Anterior communicating artery’s bifurcation(model В).
Size of each aneurysm is about 4 mm.
Benchmark data –
Computed tomography (CT) and magnetic resonance imaging (MRI) scans of the brain
Thickness- 0.8 mm, amount of scans-150 for each model
Seg3D и ITK-SNAP
RESAMPLE tool to change
and improve the
resolution of the
tomograms in SEG 3D
program
ITK-Snap program to build
3D-geometry of the cerebral
vascular system with
aneurysms
ITK-SNAP
• The methodology behind SNAP is called snake evolution. The term snake is used to
refer to a closed curve (or surface in 3D) that represents a segmentation. In snake
evolution methods, the snake evolves from a very rough estimate of the anatomical
structure of interest to a very close approximation of the structure, as illustrated in
the figure below
Уравнение построения фронта(змеи):
,where
α –propagation coefficient
β – curvature coefficient
к - curvature
- luminance
- velocity of spreading
Reconstructed 3D-Model before
smoothing
Specific layered features.
Possibly presence of artifacts – excess parts which are not vessels
and also splicing of vessels
Final 3D-Model with aneurysm
Model A
Aneurysm on
the
Middle cerebral
artery
Model B
Aneurysm on the
Anterior
communicating
artery’s
bifurcation
Final 3D-Model without aneurysm
Model A
Without
Aneurysm on
the
Middle cerebral
artery
Model B
Without
Aneurysm on the
Anterior
communicating
artery’s
bifurcation
Hemodynamic modeling. ANSYS-CFX
The main stage of work- hydrodynamic calculation - ANSYS CFX
software which consists of six components that take a geometry
and mesh and pass the information required to perform a
hydrodynamic analysis
Mesh generation with aneurysm
CFX — Meshing (ANSYS ICEM CFD)
A
B
The mesh consists of tetrahedrons.
The mesh is automatically refined based on geometry curvature. This will
result in larger elements on flat planar surfaces and smaller elements in areas of
high curvature.
Model A: quantity of nodes- 195226, quantity of elements– 1019089.
Model B: quantity of nodes - 208691, quantity of elements - 1070303.
Mesh generation without aneurysm
CFX — Meshing (ANSYS ICEM CFD)
B
Model A : quantity of nodes - 18754 , quantity of elements - 990567
Model B : quantity of nodes -196536, quantity of elements-1006249,
Mathematical Statement
of the Problem
Blood flow described by the Navier-Stokes equations for three-dimensional motion of
an incompressible, viscous Newtonian fluid
where v - velocity, p - pressure, ν - the kinematic viscosity, Ω - the internal volume of
the computational domain, including the configuration of the vessels in the form
of the tee and the aneurysm. γ = ∂ Ω - boundary wall of the vessel. Boundary
conditions:
Where
and
- velocity and pressure
-
Computational area. Steady State
ANSYS CFX — Pre. Model А
Diameter of the biggest vessel is 5 mm (Input),
Diameter of the smallest - 1,02 mm (Output2)
Boundary Conditions:
V=100 cm/s on Input,
P=40 mmHg on Output(3,5), P=35 mmHg on Output4, P=30 mmHg on Output(1,2).
Computational area. Steady State
ANSYS CFX — Pre. Model В
Diameter of the biggest vessel is 4,87 mm (InputRight),
Diameter of the smallest - 0,412 mm (OutputRight2).
Boundary Conditions: v=100 cm/s on InputLeft, InputRight,
P=40mmHg on OutputLeft1, OutputRight1, P=35mmHg on OutputLeft(2,31,31),
OutputRight(2,3), P=30mmHg on OutputLeft4, OutputRight4
Assessment of the
area of influence
of the aneurysm on
hydrodynamic characteristics
Comparative analysis
Allocation of pressure for Model A
Variations in the
pressure are not
observed(1,19%
with respect to
maximum value).
Point of max value
moves on 2,6 mm,
min – 2.8 mm
Comparative analysis
Allocation of pressure for Model B
Variations ~2%,
point of max value
moves on 3 mm,
min – 2.4 mm
Comparative analysis
Allocation of velocity for Model A
Variations - 20 cm/s
(6% with respect to
maximum value) in the
region of the location
of the aneurysm.
Point of max value
moves on 4.6 mm, min
– 1.4 mm
Comparative analysis
Allocation of velocity for Model B
Variations in velocity
is small (4% with
respect to maximum
value), point of max
value moves on 5.1
mm, point of min
value remains at the
same location
Comparative analysis
Allocation of wall shear stress (WSS) for Model A
Little changes
(≈6%) about 0-0,2
mm Hg.
Point of max value
moves on 5.2 mm,
min – 4.6 mm
Comparative analysis
Allocation of wall shear stress (WSS) for Model B
Changes are not
observed, point of
max value move
on 5.7 mm, min 5 mm
Changes for max and min values in the cerebral
vascular system with and without aneurysm
Model A
∆max
Distance(mm)
Pressure
mm Hg
1.2365 (1,19%)
2.6345
Velocity
cm/s
16.904 (5,5%)
4.6423
WSS
mm Hg
0.03 (0,96%)
5.2397
∆min
Distance(mm)
Pressure
mm Hg
2.8991 (2,81%)
2.8523
Velocity
cm/s
2.68359 (0,88%)
1.4523
WSS
mm Hg
0.07 (2,25%)
4.6324
Distance is length between points with max value (or min value) on
the cerebral vascular system with and without aneurysm
Model B
∆max
Distance(mm)
Pressure
mm Hg
1.5207 (1,83%)
2.9944
Velocity
cm/s
14.811 (4,61%)
5.1318
WSS
mm Hg
0.05 (2,9%)
5.6795
∆min
Distance(mm)
Pressure
mm Hg
0.9074 (1,09%)
2.493
Velocity
cm/s
6.48087 (1,99%)
0.7345
WSS
mm Hg
0.02 (1,17%)
5.0148
Pressure
Velocity
WSS
Distance is
length
between
points with
max value (or
min value) on
the cerebral
vascular
system with
and without
aneurysm
Summary points
• Uniform pressure distribution for models with aneurysm;
• Velocity and pressure don’t change in the transition from the
model with aneurysm to the model without aneurysm;
• Influence of the aneurysm on hydrodynamic characteristics is
local;
• Aneurysm affects locally, in the future we can restrict by the
area of influence of the aneurysm, which extends to 25 mm
along the vessel on both sides of the aneurysm (outside the
"zone of influence" of data changes are small).
Determination of influence on the
aneurysm
high blood pressure (hypertension)
and
low blood pressure (hypotension)
Comparative analysis
Allocation of pressure for Model A. Modeling hypertension
(increase of pressure on outlets on 30%)
Pressure
increases
throughout
model. Locally
elevated
pressure is not
observed
Comparative analysis
Allocation of pressure for Model B. Modeling hypertension
(increase of pressure on outlets on 30%)
Pressure
increases
throughout
model. Locally
elevated
pressure is not
observed
Comparative analysis
Allocation of velocity for Model А. Modeling hypertension
(increase of pressure on outlets on 30%)
Flow reconstructs
at a distance 4 cm
(or 10 diameters
of aneurysm)
Comparative analysis
Allocation of velocity for Model B. Modeling hypertension
(increase of pressure on outlets on 30%)
Flow reconstructs
at a distance 2 cm
(or 5 diameters of
aneurysm)
Changes of velocity close to
the aneurysm are 5-10 cm/s
between max values for
each model
Comparative analysis
Allocation of wall shear stress (WSS) for Model А.
Modeling hypertension( increase of pressure on outlets on 30%)
Changes of WSS close
to the aneurysm
are not observed
Comparative analysis
Allocation of wall shear stress (WSS) for Model B.
Modeling hypertension( increase of pressure on outlets on 30%)
Place of locally elevated WSS
near the basis of aneurysm
Essential changes of WSS
-0.2 mm Hg or 27 Pa
(difference 30%)
Values of MAX and MIN of important hemodynamic parameters around the
aneurysm for Model A
Values of basic
parameters around the
aneurysm
Bench
mark
+30% for values of
pressure on outlets
-30% for values of
pressure on outlets
Max WSS (mm Hg)
0,5
0,5
0,4
Min WSS (mm Hg)
0,003
0,004
0,003
Max velocity (cm/s)
130
135
121
Max pressure (mm Hg)
70
80
57
Min pressure (mm Hg)
64
75
52
Values of MAX and MIN of important hemodynamic parameters around the
aneurysm for Model B
Values of basic
parameters around the
aneurysm
Bench
mark
+30% for values of
pressure on outlets
-30% for values of
pressure on outlets
Max WSS (mm Hg)
1,05
0,98
0,9
Min WSS (mm Hg)
0,0018
0,0019
0,0016
Max velocity (cm/s)
146
155
140
Max pressure (mm Hg)
50,3
58
42
Min pressure (mm Hg)
35,5
44
30
Linear changes
Summary points
Modeling of high blood pressure
( Hypertension) and low blood pressure (Hypotension) has shown changes of basic
hemodynamic parameters:
• Little changes of max and min values of WSS
• WSS is locally elevated close to the aneurysm on the arterial
bifurcation
• Linear changes of pressure on walls of vessel close to the
aneurysm (4 mm) and also throughout model
• Linear changes of max velocity values close to the aneurysm
• Reconstruction of flow at the distance 4 cm (or 10 diameters of
aneurysm) for model A and at the distance 2 cm (or 5 diameters
of aneurysm) for model B
Make an assumption that aneurysm on arterial bifurcation could be
more danger than aneurysm on the vessel’s wall. During modeling of
the brain’s vascular system can consider local areas close to the
aneurysm (about 10 diameters of aneurysm)
Thank you for your
attention!
ANSYS Geometry
Model A of the cerebral vascular system consists of two unconnected parts .
It is an anatomical peculiarity of patient .The generate of mesh and the
calculation have performed only for the component with aneurysm.