Simulating Brain Aneurysms with HPC · RISC Software GmbH –Johannes Kepler University Linz ©...

RISC Software GmbH – Johannes Kepler University Linz © 2014 11.04.2014 | 1

Simulating Brain Aneurysms with HPC

RISC Software GmbH

Softwarepark 35, 4232 Hagenberg, Austria


Outline

Medical background

Blood flow simulation (MEDVIS 3D)

– FEM, CFD, CSD, FSI

– Workflow

– Results

Real-time surgery simulation (Virtual Aneurysm)

– Fast FEM

– Collision detection

– Treatment quality assessment


RISC – Unit Medical Informatics

Virtual Patient

• Surface area measurement on 3D models

• Medical documentation and expert systems

Biomechanical Simulation

• Simulation of ocular misalignments and their surgical correction

• Blood flow simulation

Medical Image Processing

• Vessel reconstruction

• Reconstruction of eye muscles and nerves


Medical Motivation

Aneurysms

– Balloon-like dilation of vessel wall with risk to rupture → bleeding into surounding brain tissue (hemorrhage)

– Often at bifurcations of the aorta and brain arteries

– Incidence: 5-8% of population

– Growth/rupture processes of aneurysms still mostly unknown

– Influence parameters:

• Size, location and shape

• Individual blood flow patterns

• Mechanical stresses along the vessel wall


Medical Motivation

Therapies:

Minimally invasive:Stenting + Coiling Surgical Clipping


Medical Motivation

Diagnosis Support Tool (MEDVIS 3D) providing

– 3D reconstruction of vessel morphology

– Automatic mesh generation

– Predefined material parameters and boundary conditions

– Numerical simulation of flow and wall movement

– Interactive visualization of results in 3D

– Low hardware requirements (GPU or GRID connection)

and license cost


Incompressible Navier-Stokes equationfor pressure p and velocity v

Blood ≈ Newtonian fluid (constant viscosity)

r = 1.05 g/cm3, m = 3.85 cP

Laminar flow (no turbulence)

Numerical solution using Finite Element Method(FEM)

𝜌𝜕𝒗

𝜕𝑡+ 𝒗 ∙ 𝛻 𝒗 − 𝜇𝛻2𝒗 + 𝛻𝑝 = 0

𝛻 ∙ 𝒗 = 0

Blood flow: Computational Fluid Dynamics


Finite Element Method (FEM)

Spatial discretization of PDE

Computational domain divided in

mesh of (tetrahedral) elements

Linear PDE → linear equation system

System matrix: dimension up to 107

→ solve by iteration: Conjugate Gradient (CG), Algebraic Multigrid (AMG)

Navier-Stokes Eq. is nonlinear and asymmetric→ need to split p and v

Linear solver: Parallel Toolbox (KFU Graz)


Velocity + pressure fields

Streamlines + Pathlines

Wall shear stress (WSS)

Oscillatory Shear Index (OSI)

Stress tensor

Traction acting on wall

OSI =1

21 −

0𝑇 𝜏𝑊𝑑𝑡

0𝑇 𝜏𝑊 𝑑𝑡

∈ 0,0.5 , 0 ≤ 𝑡 ≤ 𝑇…cardiac cycle

𝜏𝑊 = 𝜏𝑊 = 𝜇 𝛻𝒗 ∙ 𝒏

𝒕 = 𝒏 ∙ 𝜎

𝜎 = 𝜇 𝛻𝒗 + 𝛻𝒗 𝑇 − 𝑝𝕀

Important Results


Blood pressure and flow induce force on vessel wall

→ wall deformation

→ blood surface displacement

→ blood pressure + flow change

Solve by iteration

Convergence criterion: Mechanical equilibrium

Fluid-Structure Interaction (FSI)


Blood surface changes → Mesh needs adaptation

Update of inner mesh nodes necessary

Additional PDE with new surface coordinates as BC

Mesh velocity in Navier-Stokes equation

ALE Method (Arbitrary Lagrangian Eulerian)

Fluid-Structure Interaction (FSI)


Vessel wall: isotropic, linear elastic structure

Lamé-Navier equation for displacement d

l, m ... Elasticity parameters

Stress tensor s, strain tensor e→ effective (von Mises) stress sVM

Solution using FEM + CG solver

Computational Structure Dynamics (CSD)

𝜌𝜕2𝒅

𝜕𝑡2− 𝛻𝜎 = 𝒇

𝜎 = 𝜆 tr 𝜀 𝕀 + 2𝜇𝜀

𝜀 = 1 2 𝛻𝒅 + 𝛻𝒅 𝑇


Solve CFD Traction forces f

CSD with f as BC Displacement d

Mesh Updatewith d as BC

Mesh converged?

t < tmax ? Endnoyes

no

yes

FSI Iteratio

nSubcycling

t = t + dtf

Solve CFDt = t + dtf

Dt = Dt + dtf

Dt = dts ?

Dt = 0

yes

no

Start

FSI Algorithm


OpenMP:

– Simple implementation

– Calculation of element matrices/vectors, accumulation

MPI:

– Supported by AMG solver

– External solver call

– Additional mesh partitioning necessary (METIS)

CUDA/OpenCL:

– Supported by AMG solver (CUDA)

– Calculation of element matrices/vectors, accumulation

– Complex to implement (avoid CPU-GPU data transfers)

Parallelization Approaches


Test Systems: – Intel Core i7 3930K (6 cores)– NVIDIA Geforce GTX 580, NVIDIA Tesla M2090

CFD Benchmark

660

324.3

264.6

45.84 40.23 30.64

0

100

200

300

400

500

600

700

Single Core OpenMP OpenMP + MPI OpenCL (GTX) CUDA (Tesla) CUDA (GTX)

Calculation time for 500 steps (s)

Up to 21.5x speedup


2D medical image data (X-Ray angiography, CT)

Workflow in MEDVIS 3D


3D reconstruction of vascular geometry (voxel data)



Segmentation of aneurysm



Removal of artifacts, noise



Skeleton calculation (homotopic thinning)



Definition of inlet + outlets



Vessel detection



Aneurysm measurement(diameters, volume)



Blood mesh generation

1. Choose intensity threshold

2. Advanced Skeleton Climbing → Isosurface mesh

3. Taubin mesh smoothing

4. Remeshing of isosurface with arbitrary resolution

5. Mesh cutting at inlet/outlet planes

6. Meshing of cut areas

7. Volume Meshing (Netgen/Tetgen)



Blood Mesh Generation



Resolution: 0.2 mm68,000 nodes 378,000 elements


Definition of aneurysm surface



Simplest method: Extrusion of all surface nodes innormal direction → intersecting elements in case of high concave curvature and thick wall→ FEM does not converge

Wall Mesh Generation


Extrusion along stream lines of a calculated vector field → no intersection

Identical to normal vectorsclose to blood surface

Gradient Vector Flow (GVF) used in image processing

𝜇𝛻2𝒗 − 𝒗 − 𝛻𝑓 𝛻𝑓 2 = 0

edge map 𝑓 = 𝛻𝐼 2

Vector Field Method


Create voxel volume with minimum distance to blood surface as intensity

Generate isosurface from volume with thickness as threshold → outer wall surface

Fill intermediate space with volume mesh

Thickness variation by weighting the distance

Works with any geometry

Distance Field Method


Extrusion in normal direction

Extrusion along GVF field

Distance Field Meshing



40,000 nodes

120,000 elements

Ends are fixed

r = 1 g/cm3

E ≈ 1 MPa

n = 0.45

dts = 10 ms= 500 dtf




Varying thickness:Artery: 0.4 mmAneurysm: 0.2 mm


vinlet

Pulse 1s, time step dtf = 0.02 ms

Choose systolic/diastolic pressure + inlet curve

poutlet

Boundary Conditions

vinlet


Computation time (1 pulse cycle): 1 hour (GPU)

FSI Results: Velocity + Wall displacement


Streamlines


Pressure distribution at max inflow velocity


Velocity field at max inflow velocity


Time-averaged Wall Shear Stress


Oscillatory Shear Index


Von Mises Stress


Particle Paths


Rupture Odds

Estimation of aneurysm rupture odds [Xiang et al., Stroke 2011, 42:144-152]

WSS: average over the simulation time and aneurysm surface w.r.t. parent vessellow WSS → higher rupture risk

OSI: average over aneurysm surface high OSI → higher rupture risk

𝑝 = 𝑒−0.73∗𝑊𝑆𝑆+2.86∗𝑂𝑆𝐼−0.12


Virtual Aneurysm

Most aneurysms coiled

Only most difficult treated with Clipping→ Training of young surgeons problematic

Synthetic aneurysm models expensive to produce

Project “Virtual Aneurysm”:Haptic Training Simulator for clipping surgeries


Environment

2 haptic input devices(Phantom Omni)

Mount clipping forceps + sensor for opening angle

Stereoscopic display+


New Challenges

Communication with haptic device (OpenHaptics)

Real-time FEM calculation of vessel deformation

Collision detection for deformable objects

3D models obtained from

– MEDVIS 3D (Aneurysm wall)

– Aesculap, Inc. (Forceps + clips)

Assessment of surgery result (blood flow simulation)→ trainee can determine optimal clip type & position for patient-specific geometry


Linear Elasticity

FEM discretization yields linear equation system

K … Stiffness matrix

u … nodal displacements

f … nodal forces

Precalculation of inverse system matrix

109 components ≅ 2 GB memory

Real-time Simulation: Fast Finite Element

𝐾𝒖 = 𝒇

𝒖 = 𝐾−1𝒇


Precalculation slow, but only done once per model

Stationary solution: Sparse force vector f→ fast calculation of multiplication

Matrix condensation: Reduction to visible (outer) degrees of freedom

Boundary conditions prescribed as forces→ conversion of displacements necessary

Parallelization using CUDA



Up to 10,000 nodes (30,000 elements) in real-time with our current hardware



Known problem, e.g. from

– Computer games

– 3D Animation, special effects in movies

Basis: Bullet Physics Library

– Fast

– Open source

– Simple utilization

Problems:

– Deformation of the colliding mesh

– Response (nodal displacement, force feedback)

Real-time Simulation: Collision Detection


Continuously test for collisions between triangular meshes

If collision is found:

– List of positions + penetration vectors→ fixed displacements for nearest nodes

– Obtain boundary forces

– FEM calculation

– Update collision object

– Update visualization

At least 20 timesper second!

Real-time Simulation: Collision Detection


Smooth haptic feedback with 1000 Hz

New contact generates tangential collision plane

– Direction of force normal to plane

– Amount of force proportional to penetration depth

– Multiple collision planes → addition of forces

Real-time Simulation: Force Feedback


Real-time Simulation: Results


Result Assessment

Simulation of blood flow through inner volume

Meshing of interior space of deformed vessel wall

Problem: Self-intersections of interior walls have to be removed and newly meshed


Result Assessment


Outlook

Inclusion of multiple clip types

Forceps + sensor mounted on haptic device

Modeling of surrounding tissue

Simulation of preparation phase

Definition of assessment criteria (scoring)

Future projects:

– Simulation of stenting

– Aortic dissections

– …


www.risc-software.at

Thank You! Castor, 4228mPollux, 4092mzwischenMonte-Rosa-Massiv und Matterhorn

Wallis, Schweiz

Simulating Brain Aneurysms with HPC · RISC Software GmbH –Johannes Kepler University Linz ©...

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