S fStress analysis of cerebral aneurysms

Madhavan Lakshmi Raghavan Ph DMadhavan Lakshmi Raghavan, Ph.D.Biomedical Engineering

BioMOST division Center for Computer Aided DesignBioMOST division, Center for Computer-Aided DesignUniversity of Iowa

Aneurysm size and shape metricsAneurysm size and shape metrics

Shape Index Low Medium High

Undulation index (UI) ( )

Aspect ratio (AR)

lli i i i dEllipticity index (EI)

Non-sphericity index (NSI)

oror

oror

Ratio of surface area t l

Conicity parameter (CP)

B ttl k f t

to volume

Bottleneck factor (BF)

Raghavan at al., J Neurosurg, 2005

Quantifying aneurysm shapeQuantifying aneurysm shape

3D i t i Dia NSI UI• 3D size metrics– Volume– surface area

‘diameter’

Dia(mm)

NSI UI

7.0 0.07 0.02Patient 1– diameter– ‘height’

3D h h t i 5.0 0.18 0.12Patient 2

Patient 1

• 3D shape shape metrics– Non-sphericity index (NSI)

Undulation index (UI)

5.0 0.18 0.12

3.1 0.17 0.03Patient 3

Patient 2

– Undulation index (UI)– Ellipticity index– Bottleneck factor

5.5 0.05 0.00Spherical

4.5 0.16 0.00Elliptical

Ma at al., J Neurosurg, 2005

Size and shape metrics on rupture statusSize and shape metrics on rupture status

R t d (N 9) t d (N 18)Ruptured (N=9) versus unruptured (N=18)

Unruptured Ruptured Unruptured Ruptured

Hemodynamic metrics of morphologyHemodynamic metrics of morphology

Path lines @ t=0 2T• Hemodynamics metrics Path lines @ t=0.2T(Circle of Willis)

• Hemodynamics metrics– Incorporates the role played by vessels

leading upto and beyond the sacM t i

Velocity (idealized ACOM model)

• Metrics– Shear stress, residence times, energy loss

Baoshun Ma, PhD Dis, Iowa, 2004

Why compute stress in aneurysm wall?Why compute stress in aneurysm wall?

• Blood pressure induces normal stress in the aneurysmal wallN l t i d f it d l• Normal stress is orders of magnitude larger than shear stressHigh stress maybe correlated to rupture risk• High stress maybe correlated to rupture risk

• Stress is affected by morphology – may serve as a quantified proxy for morphologyas a quantified proxy for morphology

Peak stress in aortic aneurysmPeak stress in aortic aneurysm

R t d AAA C t l AAARuptured AAAdia = 5.6 cm

BP=158 mmHg

Control AAAdia = 6.7 cm

BP=130 mmHg

Vorp Lab, University of Pittsburgh- Raghavan et al, ABME 1996- Vorp et al, JVS 1998- Raghavan et al., JVS 2000- Raghavan and Vorp, JVS 2000

Predictability of stress versus diameterPredictability of stress versus diameter

ROC curveROC curve• Prospective unruptured

untreated cohort followed for average of 1 year

103 AAA ti t f ll d• 103 AAA patients followed; • 42 no intervention;• 39 electively repaired;• 22 ruptured (8 symptomatic)p ( y p )

• Diameter criterion 73% right• Tension criterion 85% right

• Tension essentially lumps size and shape into a single

b i h i itiFillinger lab, Dartmouth College

- Fillinger JVS 2002number in a physics-sensitive manner

Fillinger, JVS 2002- Fillinger, JVS 2003- Raghavan, JBME 2005- Raghavan, ABME 2007

Cerebral aneurysm tissue mechanicsCerebral aneurysm tissue mechanics

• Structure: Multiple layers of collagen fibers;Structure: Multiple layers of collagen fibers; no elastin (Canham, 1998)

• Thin wall (80-200μm)( μ )

• Membrane-like

• Pulsation may exist, but not measurablePulsation may exist, but not measurable

• Inflation experiments (N=2) with specimens (Humphrey, 2000)– Modeled as Fung-Orthotropic

W = ½ c(eQ – 1)where, Q = c1E11

2 + c2E222 + 2c3E11E22

Patient-specific geometriesPatient specific geometries

• CTA, MRA-contrast, MRA-TOF, and 3DRA3D t ti• 3D reconstruction –Mimics, VMTKNon shrinking surface• Non-shrinking surface smoothing

• Isolation of the aneurysm• Isolation of the aneurysm

Finite element analysisFinite element analysis

Sh ll l t ll f if• Shell element wall of uniform thickness (80 μm)

• Forward formulationSo its not stress, b t stressForward formulation

• Fung model (literature)• Material fiber directions along

but stress resultant

gprincipal curvature directions

• Uniform systolic pressureSt di d l t l• Studied normal stress along stiff and weak fiber directions

Biomechanics based indicesBiomechanics based indices

P i i l t di tiPrincipal curvature directions

Principal curvature, k1

Regional fiber orientation and stressRegional fiber orientation and stress

M t i l fib• Material fiber directions– Sensitivity studies

t th t t t l

Sensitivity to Fiber Directions

5.0E-08

5.5E-08

gy (J

)

suggest that total strain energy stored during pressure-induced deformation 4 0E 08

4.5E-08

ic s

train

ene

rgis minimized when the material fiber directions coincide with principal

3.5E-08

4.0E-08

Tota

l ela

sti

with principal curvature directions

3.0E-080 10 20 30 40 50 60 70 80 90

Perturbation from optimum direction (degree)

Stiffer fiber Stiffer fiberStiffer fiber direction along max prin. curvature dir

Stiffer fiber direction along min prin. curvature dir

Ma et al, 2007

Finite element analysisFinite element analysis

Sh ll l t ll f• Shell element wall of uniform thickness (80 μm)

• Fung model (literature)Fung model (literature)• Material fiber directions

along principal curvature directions

• Uniform systolic pressure• Forward formulation• Forward formulation• Studied normal stress

along stiff and weak fiber gdirections

Ma et al, 2007

Stress distribution in realistic modelStress distribution in realistic model

Stress along stiff fiber direction

Animation Top view

Tension and rupture statusTension and rupture status

Inverse formulationInverse formulation

A id ti• Avoid assumption that in vivo geometry is stress free

• Formulate solution in inverse

Inverse

CTA-based in vivo geometry; assumed to be under mean-arterial pressure

Backward or• Solve for in vivo stress and stress-free configuration

elastostatics

Apply systolic pr

div σ = 0displacement

methodor

g

Predicted zero-pr. geometry

Predicted systolic pr. geometry

systolic pr.Div P = 0

L t l 2007 2009 geometry geometryLu et al, 2007, 2009Zhou et al., 2010

Role of modeling choices?Role of modeling choices?

• When the goal is to distinguish the stresses induced in one population of aneurysms from another what is the role of modelinganother, what is the role of modeling choices?– Material behaviorMaterial behavior– Forward versus inverse solution schemes– Computational domain– Others

Role of modeling choices?Role of modeling choices?

• The true goal– Stress is really used here as a proxy for geometry

G t i th l ti t ifi d– Geometry is the only patient-specific, measured information

– True stress distribution is a lofty goal anyway. Too ue s ess d s bu o s a o y goa a y ay oomany intractable issues

• Wall thicknessFailure strength• Failure strength

• Contact constraints

Ongoing studyOngoing study

• Longitudinal study of 200 unruptured intracranial aneurysms over time

• Question:Question:– Do morphological and biomechanical

indices distinguish the many that remain g ystable from the few that do not (grow or rupture)?

AcknowledgementsAcknowledgements

• Students and staff• Students and staff– Baoshun Ma; Manasi Ramachandran;– Dave Welch; Rohini Retarekar; Ben Berkowitz; Ben Dickerhoff;

T ti C L ibf i d St Li Sh h HTatiana Correa-Leibfried; Steve Lin; Shouhua Hu

• Faculty– Robert Harbaugh; Jia Lu; Robert Rosenwasser; Chris Ogilvy; obe a baug ; J a u; obe ose asse ; C s Og y;

David Hasan; James Torner; Aki Laakso

• FundingNHLBI #R01 HL083475 01A2 (MLR);– NHLBI #R01 HL083475-01A2 (MLR);

– NHLBI #3R01HL083475-02S1 (MLR)

Thank you!