Mathematics and Computer Science Division, Argonne National Laboratory Biofluid Dynamics qMotivation q Objective q Challenges q Proposed timeline qTechnical

Mathematics and Computer Science Division, Argonne National Laboratory

Biofluid Dynamics

Motivation Objective Challenges Proposed timeline

Technical Procedure U of C’s role (Bassiouny) UIC’s role (Loth) ANL’s role (Fischer)

Personnel: Francis Loth, UIC (S. Lee, W. Kalata, N. Arsalan, …) Hisham Bassiouny, U of C (O. Bick, … ) Paul Fischer, (L. Freitag, G. Leaf, B. Smith,... )


Turbulence in Biofluid Dynamics

Cardiovascular simulations AV-graft failure - close to a billion dollar annual economic impact

importance of hemodynamic forces (shear, pressure, vibration) in disease progression

Stenosed carotid arteries - $60 B annual turbulence a distinguishing feature of severely stenosed (constricted) arteries high wall-shear (mean and oscillatory) can possibly lead to

embolisms (plaque break-off) thrombis formation (clotting)

Turbulence computations 1-3 orders of magnitude more difficult than laminar (healthy) case No numerical simulations of turbulence in carotids or grafts in current literature


Biofluid Dynamics

Clinical Objective (3-5 years out): rapid (24 hour) quantification of wall shear in stenosed arteries from

in vivo MR / CT images, color Doppler ultrasound velocity measurements, and computational fluid dynamics (CFD).

Technical Challenges: image translation (expert systems?) robust automated meshing (tetrahedra, hexahedra, optimization) role of wall motion (fluid-structure interaction)

CFD parallel computing ( ~120 days on 32 processors, brute force) high-order, adaptive numerical methods, improved algorithms


Timeline for Planned NIH Patient-Specific Proposal

Yr. 1 (now) -- complete 1-2 turbulent cases (feasibility)

Yr. 2-3 -- quantify 6-12 patients

Yr. 3-5 -- track 50-100 patients ( 24 hour turn-around, routine )

Bassiouny ( U of C ) -- track biological/chemical factors Loth (UIC) / MCS -- quantify hemodynamic forces (space and time)


Extra-Procedural Commitment of Surgical Team (Bassiouny, U of C)

Patient-specific timeline: Color Doppler ultrasound:

Severe stenoses identified (patient is enrolled in Loth/Bassiouny study) Flow rate measured in common, internal, and/or external carotid

CT-scan imaging (Dr. O. Bick, Head of CT) Fine resolution image is taken (1.25 mm axial, 0.25 mm planar) Imaging time is $400 / patient Images released to biomechanics team at UIC (image transfer process)

U of C Team personnel on board: ultrasound technician CT-scan technician radiologist

(identifies carotid from CT images, Bick)


Color Doppler Ultrasound -- Flow Rate Information

Provides gross flow rate characterstics Stenosis identified by turbulence

Availability U of C -- 7 units in clinic (700 patients/year) UIC -- 1 unit, biomechanics lab of Loth


Extra-Procedural Commitment of Surgical Team (Bassiouny, U of C)

Patient-specific timeline: Color Doppler ultrasound:

Severe stenoses identified (patient is enrolled in Loth/Bassiouny study) Flow rate measured in common, internal, and/or external carotid

CT-scan imaging (Dr. O. Bick, Head of CT) Fine resolution image is taken (1.25 mm axial, 0.25 mm planar) Imaging time is $400 / patient Images released to biomechanics team at UIC (image transfer process)

U of C Team personnel on board: ultrasound technician CT-scan technician radiologist

(identifies carotid from CT images, Bick)


CT Image to Mesh Translation

CT Scan -- stack of 2D images Mimics/Fortran software used to produce RP data file (Loth et al.)

Currently, image translation & feature identification a bit of an art

(W. Kalata ANL/UIC)

Fourier Smoothing


Fourier-Based Contour Reconstruction

CT/MR output is generally rough due to pixelation. Standard (local) smoothers are not guaranteed to preserve macroscopic

contour features (area, moments, etc.), and often suffer from shrinkage, though nonshrinking variants do exist (Taubin 95).

In any slice, lumen surface is a closed contour Fourier bases are a natural choice:

stable C - continuous macroscopic features built-in z-smoothing applied to Fourier coefficients


Basic Meshing Mechanism

(S.E. Lee ANL/UIC)


Other Examples

Arterio-VenousGraft

AneurismicAbdominal

Aorta

Pig AV Graft


Mesh generation difficulties...

Surface smoothing Mesh topology Interior mesh geometry (Freitag)

etc.

Not yet automated…

Interior element distribution can have a huge impact on matrix conditioning and iteration counts


Numerical Simulation

Spectral element method (SEM) High-order ( > ~8 ) -- minimal numerical dissipation, dispersion General geometries

Very efficient (locally structured -- hex) vector parallel (1000s of processors)

Ideal for weakly turbulent (transitional) flows

A significant competitive advantage for diseased cases.


Why high-order methods?

Transitional flows are sensitive to a small amount of viscosity (.001-.0001) Require numerical dissipation/dispersion to be small ( << .001 ) Four-fold savings in 1D translates into 64-fold savings in 3D

Error for 1D Convection Example -- t=10

For .5% error, 8th order requires 64 pts., vs. 256 pts for quadratic

Solution

(E,N) = (256,1),

at t=10.

Solution

(E,N) = (256,1),

at t=0.


Initial steady flow results for healthy carotid artery

Re=542 Experimental ResultsRe=377Prof. Francis Loth, UICEmil Ghengeaua, UIC

Spectral element mesh, Seung Lee, UICPaul Fischer, MCS/ANL


Arterio-venous Graft Simulations

PTFE plastic tubing surgically attached from artery to vein (short-circuit)

Provides a port for dialysis patients, to avoid repeated vessel injury

Failure often results after 3 months from occlusion forming immediately downstream of attachment to vein, where flow is turbulent (Re ~ D-1)


Comparison of LDA (experimental) and SEM (numerical) results

Re=1060 (laminar) Re=1820 (weakly turbulent)

<u>

<u’>

<v’>


Turbulent Structures in AV-Graft


AV Graft -- Re=1820


Validation: Arterio-Venous Graft Studies(Arsalan, Lee, Loth - UIC, Fischer - ANL)

AV Graft - Re=1820


Summary -- Turbulent Simulations in Vascular Flows

Impact quality of life economic

Timeliness availability of imaging technology cost/performance of commodity-based parallel computers physician acceptance of simulation as a diagnostic tool NIH, DOE funding appears to be increasing

Technical Challenges image analysis meshing (construction, optimization) CFD vessel wall response (fluid-structure interaction)



Opportunities in Biofluid Dynamics

Currently focusing on vascular geometries: grafts and diseased arteries

Simulation has the opportunity to play a role in surgical decisions Can provide more detailed diagnoses of hemodynamical forces in the

vessel than inspection of vessel geometry or flow rates alone.

Medical treatment for diseased carotid arteries is estimated to cost $60 billion annually. Arteriovenous graft (for dialysis patients) costs are estimated at $1 billion annually.


Opportunities in Biofluid Dynamics

5-year Mission: provide physicians with patient-specific wall-shear stress and pressure distributions within 24 hours of MRI scan.

Near term mission: compute wall shear for turbulent flow in AV-graft model compute turbulent flow in a stenosed (blocked) carotid artery (take course on how to handle medical data….)

Mid-term mission: (2-3 years)

Get NIH funding for 100-patient study


Numerical Issues

geometry geometry geometry translation of images to meshes

2D surface in R3

image smoothing feature identification

surface smoothing mesh optimization

turbulence commonly found in diseased arteries and vascular grafts much harder to simulate than laminar case

moving walls non-Newtonian fluid


Capabilities within MCS

In a unique position w.r.t. turbulence we have a high-order spectral element code for complex 3D geometries high-order codes are optimal for this regime

minimal numerical dissipation which otherwise overwhelms physical viscosity minimal dispersion estimate 8-fold reduction in number of gridpoints for reasonable accuracy

significant parallel computing resources

Behind w.r.t. image translation / mesh generation Roughly 20 groups working in vascular simulations (others in closely related

cardiac and neuro areas) most are using low-order tetrahedra, significant simplifications in meshing

Efficient implementation of high-order methods requires hexahedra (bricks)

Optimal hexahedral meshing poses many interesting CS/math issues.




Mathematics and Computer Science Division - ANL

Biofluid Dynamics

Paul Fischer - MCS

Prof. Francis Loth, Ph.D., UIC

Prof. Hashim Bassiouny, M.D., U of C

[email protected]/~fischer


Advanced CFD: State of the art

Quarteroni, Formaggia (EPFL) fluid structure interactions with ALE finite element code coupling of 3D models with 1D models for impedence matching low Reynolds numbers

Pedley (Cambridge) fundamental and applied fluid dynamics relating to biology

Peskin (Courant) immersed boundary method

Perktold, (Graz) SUPG FEM code, moving meshes, grid generation

Kamm (MIT) experimental biofluids


Biofluid dynamics: Research Challenges

For AV-graft simulations having Re > 2500, nonconforming meshing will provide an order of magnitude reduction in computational cost, due to locality of coherent structures in the flow field.

Complex geometry problems require robust mesh generation, smoothing adaptive refinement with load balancing ALE to support flexible walls

Biofluids requires biology and medical experts (team of F. Loth) detailed knowledge of wall material properties


Transitional Flows in Complex Geometries -- Paul Fischer

Biofluid dynamics simulations first known simulations of transitional flow in vascular geometries excellent agreement with experiments for AV-graft and carotid arteries

(AV-graft failure - close to a billion dollar annual economic impact)


Color Doppler Ultrasound -- Flow Rate Information

Provides gross flow rate characterstics Needed for boundary conditions to CFD

Availability U of C -- 7 units in clinic (700 patients/year) UIC -- 1 unit, biomechanics lab of Loth


Biofluid Dynamics: Timeline

Current Status Ph.D. student N. Pearsol will use nek5000 for thesis work on

carotid artery in 2000 Loth, Lee, and Fischer are using nek5000 for steady AV-graft

simulations (NIH grant w/ Bassiouny submitted) Full curved geometry supported

Upgrade Path Nonconforming SEM in production by 8-1-00 (required for

unsteady AV-graft simulations with 1000 < Re < 2600). Mesh smoothing? ALE formulation in place (due to MIT thesis work of L.W. Ho) -

this could be extended/validated by 1-1-01 if necessary.




Advanced CFD: Research Challenges


Biofluid Dynamics: State of the Art within MCS

Parallel spectral element code highly accurate -- excellent agreement with

experimental data for AV-graft model abstract submitted to the Int. Mech. Eng. Cong.,

Orlando, November 2000

Automated mesh generation rapid translation of MR/CT scan images to hex-

based meshes Seung Lee co-op student working for

Fischer/Loth abstract accepted to the World Congress on

Medical Physics and Bioengineering, Chicago, IL, July 23-28, 2000

mesh smoothing technology - Freitag

Wall material properties, solid mechanics T. Canfield

Porcine AV-graft geometry de-veloped by S.E. Lee, UIC/ANL


Biofluid Dynamics: State of the Art within MCS

Accurate parallel spectral element code Excellent agreement with experimental data for

AV-graft model. (Abstract submitted to the Int. Mech. Eng. Cong., Orlando, November 2000)

Excellent agreement with experimental results for human carotid. Superior to commercial package Star-CD.

Automated mesh generation rapid translation of MR/CT scan images to hex-

based meshes Seung Lee co-op student working for

Fischer/Loth paper presented at the World Congress on

Medical Physics and Bioengineering, Chicago, IL, July 23-28, 2000

mesh smoothing technology - Freitag

Wall material properties, solid mechanics future investigation

Porcine AV-graft geometry de-veloped by S.E. Lee, UIC/ANL


Method

Vessel geometry has been shown to strongly affect hemodynamic variables therefore, an accurate representation of the 3D vascular geometry is critical for accurate simulation.

Use MRI or spiral CT scans to get the geometry

MR Images from a volunteer


Objectives

Automated Hexahedral Mesh Generation Technique for Bifurcation Geometries Fast (5 - 10 minutes) Bifurcation specific control parameters for grid refinement Robust (no bad cells)


“Construction of a Physical Model of the Human Carotid Artery Based upon In Vivo Magnetic Resonance Images” R. V. Yedavalli, F. Loth, A. Yardimci, W.F. Pritchard, J.N. Oshinski, L. Sadler, F. Charbel, N. Alperin, accepted as a Technical Brief to the Journal of Biomechanical Engineering.

Use Mimics and Fortran to extract the slice-based data

Create CFD mesh from slice-based data (RP format)


From Slice-based data of carotid bifurcation artery

Pick control points to define three planes

Divide into three parts

Obtain new section slice (angled) from the original slice-based data

Mesh each branch as a "pipe"


Manually pick the points The code determines outline vertices Get new angled section slices

Procedure


Basic Meshing Mechanism


Octagonal box at middle, and arbitrary surface curve around Greater resolution near the wall compared to the middle Smooth transition from polygon to arbitrary curve

Mesh of each cross-section


Three way partition avoids figure '8' cross section


Other Examples

Arterio-VenousGraft

AneurismicAbdominal

Aorta

Pig AV Graft



Mathematics and Computer Science Division - ANL

Biofluid Dynamics

Paul Fischer - MCS

Prof. Francis Loth, Ph.D., UIC

Prof. Hashim Bassiouny, M.D., U of C

[email protected]/~fischer


Documents

Mathematics and Computer Science Division, Argonne National Laboratory Biofluid Dynamics qMotivation q Objective q Challenges q Proposed timeline qTechnical