Development of Cerebral Aneurysms. A Prediction Model

Ihor Machyshyn

Dr. Ir. P.M.J. Rongen (Philips Medical Systems)Dr. Ir. A.A.F. van de Ven (TU/e, W&I)Dr. Ir. S.J.L. van Eijndhoven (TU/e, W&I)Prof. Dr. Ir. F.N. van de Vosse (TU/e, BMT)Dr. Ir. P.H.M. Bovendeerd (TU/e, BMT)

Supervisors

3D Rotational Angiography (3D-RA)

Combined X-ray images into a 3D view

dangerous?

safe?

Approaches to assess risk of rupture

• Current clinical practice (based on geometry)

• Mechanical analysis:

– Hemodynamical approach

– Vessel wall mechanics

Stress and strain estimation

Adaptation of the tissue

Rupture criterion

Goal of the project

• Develop a model that uses realistic description of

aneurysmal tissue

• Study growth of cerebral aneurysms

Blood Vessel Histology

Model

elastin

collagen

rec - recruitment

cn - collagen thickness

a - attachment collagen stretch

Collagen

Elastin - elastin (tissue) stretch

Variables

c - collagen stretch

Equations Governing Mechanics

div 0 • Equation of equilibrium:

• Incompressibility equation: det 1F

• Constitutive equation:

1 1 1 2 2 2

1,

2e c f c c f c cp n e e e e I +

( ),e ec B - I 22 2 21 22 1 exp 1 ,fi ci ci cik k

X

x

F =,TB = FFwith

Evolution Equations of Remodeling

( ),recc a

d

dt

( )cc a

dn

dt

with , - rate constants of remodeling

• Equations of remodeling:

• Initial conditions

0 ,0( ) ( ),rec rect t x 0 ,0( )c cn t t n

Healthy State of an Artery

Transition between States

Remodeling to a Healthy State

Visualization of Instability

Stability of Equilibrium ((e)) States

Analysis of Stability of an Equilibrium State of a Thin-walled cylinder. Equations

2

4 2 2 2

( ) cos ( )11 ( ) ,

( ) sin ( ) cos ( )c

f ce

n t R pt

t H c

1 2 1 2( ) ( ) ( ), ( ) ( ) ( )c c c f c f c f ct t t t t t

0( ) ( ) ,c recn t t C

( )( ) ,

( )crec

tt

t

( )( )recc a

d tt

dt

22 2 212( ) 2 1 exp 1f c c c c

e

kk

c

where

Method

( )( ) ( ),et t ( )( ) ( ),e

rec rec rect t ( )( ) ( ),e

c c cn t n n t

( ) ( ) ( ), , ; ( ), ( ), ( )e e erec recn t t n t satisfy equations on the previous slide

const,p

0 state is, ,

0 state isaK p

stable

unstableStability condition:

Result