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 RASMeshalkin Novosibirsk Scientific Research Institute of Circulation Pathology

6th Russian workshop on mathematical models and numerical methods in biomathematics

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)

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

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)

Purposes

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.

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

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.

3D-reconstruction

Seg3D и ITK-SNAPRESAMPLE 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 coefficientβ – 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 aneurysmModel A

Aneurysm on the

Middle cerebralartery

Model BAneurysm on the

Anteriorcommunicating

artery’s bifurcation

Final 3D-Model without aneurysmModel AWithout

Aneurysm on the

Middle cerebralartery

Model BWithout

Aneurysm on the Anterior

communicating artery’s

bifurcation

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

Hemodynamic modeling. ANSYS-CFX

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 with aneurysm CFX — Meshing (ANSYS ICEM CFD)

A B

Mesh generation without aneurysm CFX — Meshing (ANSYS ICEM CFD)

Model A : quantity of nodes - 18754 , quantity of elements - 990567Model B : quantity of nodes -196536, quantity of elements-1006249,

B

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

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 velocity for Model B

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

Changes are not observed, point of max value move on 5.7 mm, min -

5 mm

Comparative analysis Allocation of wall shear stress (WSS) for Model B

∆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

Model A

Changes for max and min values in the cerebral vascular system with and without aneurysm

Distance is length between points with max value (or min value) on the cerebral vascular system with and without aneurysm

∆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

Model B

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

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)

Comparative analysis

Changes of velocity close to the aneurysm are 5-10 cm/s between max values for each model

Allocation of wall shear stress (WSS) for Model А. Modeling hypertension( increase of pressure on outlets on 30%)

Comparative analysis

Changes of WSS close to the aneurysm are not observed

Allocation of wall shear stress (WSS) for Model B. Modeling hypertension( increase of pressure on outlets on 30%)

Comparative analysis

Place of locally elevated WSSnear 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 theaneurysm

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 theaneurysm

Bench mark

+30% for values of pressure on outlets

-30% for values of pressure on outlets

Max WSS (mm Hg) 1,05 0,98 0,9Min WSS (mm Hg) 0,0018 0,0019 0,0016Max 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

• 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

Modeling of high blood pressure( Hypertension) and low blood pressure (Hypotension) has shown changes of basic

hemodynamic parameters:

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.