Stress analysis of cerebral aneurysms

Transcription

1 Stress analysis of cerebral aneurysms Madhavan Lakshmi Raghavan, Ph.D. Biomedical Engineering BioMOST division, Center for Computer-Aided Design University of Iowa

2 Aneurysm size and shape metrics Shape Index Low Medium High Undulation index (UI) Aspect ratio (AR) Ellipticity i i index (EI) or or Non-sphericity index (NSI) Conicity parameter (CP) or or Ratio of surface area to volume Bottleneck factor (BF) Raghavan at al., J Neurosurg, 2005

3 Quantifying aneurysm shape 3D size metrics Dia NSI UI Volume surface area diameter height Patient 1 (mm) D shape shape metrics ti Non-sphericity index (NSI) Undulation index (UI) Ellipticity index Bottleneck factor Ma at al., J Neurosurg, 2005 Patient 2 Patient 3 Spherical Elliptical

4 Size and shape metrics on rupture status Ruptured (N=9) versus unruptured (N=18) Unruptured Ruptured Unruptured Ruptured

5 Hemodynamic metrics of morphology Hemodynamics metrics Path t=0.2t Incorporates the role played by vessels leading upto and beyond the sac Metrics Shear stress, residence times, energy loss Velocity (idealized ACOM model) Path t=0 2T (Circle of Willis) Baoshun Ma, PhD Dis, Iowa, 2004

6 Why compute stress in aneurysm wall? Blood pressure induces normal stress in the aneurysmal wall Normal stress is orders of magnitude larger than shear stress High stress maybe correlated to rupture risk Stress is affected by morphology may serve as a quantified proxy for morphology

7 Peak stress in aortic aneurysm Ruptured AAA Control AAA dia = 5.6 cm dia = 6.7 cm BP=158 mmhg BP=130 mmhg Vorp Lab, University of Pittsburgh - Raghavan et al, ABME Vorp et al, JVS Raghavan et al., JVS Raghavan and Vorp, JVS 2000

8 Predictability of stress versus diameter Prospective unruptured untreated cohort followed for average of 1 year 103 AAA patients t followed; 42 no intervention; 39 electively repaired; 22 ruptured (8 symptomatic) ROC curve Diameter criterion 73% right Tension criterion 85% right Tension essentially lumps size and shape into a single number in a physics-sensitive iti manner Fillinger lab, Dartmouth College - Fillinger, JVS Fillinger, JVS Raghavan, JBME Raghavan, ABME 2007

9 Cerebral aneurysm tissue mechanics Structure: Multiple layers of collagen fibers; no elastin (Canham, 1998) Thin wall (80-200μm) μ Membrane-like Pulsation may exist, but not measurable Inflation experiments (N=2) with specimens (Humphrey, 2000) Modeled as Fung-Orthotropic W = ½ c(e Q 1) where, Q = c 1 E c 2 E c 3 E 11 E 22

10 Patient-specific geometries CTA, MRA-contrast, MRA- TOF, and 3DRA 3D reconstruction ti Mimics, VMTK Non-shrinking surface smoothing Isolation of the aneurysm

11 Finite element analysis Shell element wall of uniform thickness (80 μm) Forward formulation Fung model (literature) Material fiber directions along principal curvature directions Uniform systolic pressure Studied d normal stress along stiff and weak fiber directions So its not stress, but stress resultant

12 Biomechanics based indices Principal i curvature directions Principal curvature, k 1

13 Regional fiber orientation and stress Material fiber directions Sensitivity studies suggest that t total t strain energy stored during pressureinduced deformation is minimized when the material fiber directions coincide with principal curvature directions ic strain energ gy (J) Total elasti 5.5E E E-08 40E08 4.0E E E-08 Sensitivity to Fiber Directions Perturbation from optimum direction (degree) Ma et al, 2007 Stiffer fiber direction along max prin. curvature dir Stiffer fiber direction along min prin. curvature dir

14 Finite element analysis Shell element wall of uniform thickness (80 μm) Fung model (literature) Material fiber directions along principal curvature directions Uniform systolic pressure Forward formulation Studied normal stress along stiff and weak fiber directions Ma et al, 2007

15 Stress distribution in realistic model Stress along stiff fiber direction Animation Top view

16 Tension and rupture status

17 Inverse formulation Avoid assumption that in vivo geometry is stress free Formulate solution in inverse Solve for in vivo stress and stress-free configuration CTA-based in vivo geometry; assumed to be under mean-arterial pressure Backward displacement method or Inverse elastostatics div σ = 0 Apply systolic pr. Div P = 0 Lu et al, 2007, 2009 Zhou et al., 2010 Predicted zero-pr. geometry Predicted systolic pr. geometry

18 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 modeling choices? Material behavior Forward versus inverse solution schemes Computational domain Others

19 Role of modeling choices? The true goal Stress is really used here as a proxy for geometry Geometry is the only patient-specific, t ifi measured information True stress distribution is a lofty goal anyway. ay Too many intractable issues Wall thickness Failure strength Contact constraints

20 Ongoing study Longitudinal study of 200 unruptured intracranial aneurysms over time Question: Do morphological and biomechanical indices distinguish the many that remain stable from the few that do not (grow or rupture)?

21 Acknowledgements Students and staff Baoshun Ma; Manasi Ramachandran; Dave Welch; Rohini Retarekar; Ben Berkowitz; Ben Dickerhoff; Tatiana Correa-Leibfried; i Steve Lin; Shouhua h Hu Faculty Robert Harbaugh; Jia Lu; Robert Rosenwasser; Chris Ogilvy; David Hasan; James Torner; Aki Laakso Funding NHLBI #R01 HL A2 01A2 (MLR); NHLBI #3R01HL S1 (MLR) Thank you!