Simulating Human Aorta Material Behavior Using a GPU ...on-demand.gputechconf.com/gtc/2016/presentation/s6475-vukasin... · Simulating Human Aorta Material Behavior Using a GPU Explicit

Simulating Human Aorta Material Behavior

Using a GPU Explicit Finite Element Solver

Vukasin Strbac†, David M. Pierce‡, Jos Vander Sloten†, Nele Famaey†

†Biomechanics Section, Mechanical Engineering,

KULeuven, Leuven, BE

‡Mechanical Engineering, Biomedical Engineering,

Mathematics, Interdisciplinary Mechanics Lab

University of Connecticut, Storrs, CT, US

Vukasin Strbac GTC2016

Introduction: general biomech. motivation

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Accelerating FE analysis provides new clinical opportunities: pre-operative (e.g. faster custom stent design)

intra-operative stress monitoring

post-operative damage monitoring/fatigue estimation at lower cost

Ever-advancing capabilities of modern hardware, e.g. GPGPUs, offer

opportunities to accelerate established algorithms

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angioplasty stenting heterogeneous composition, aorta tissue behavior

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Introduction: core facts

Explicit FE is pleasingly parallel (for the most part)

Explicit FE is sensitive to material and geometric parameters

Complex material model is necessary for accurate results

GPUs are sensitive to floating point precision used

What can we expect? How does anisotropy affect GPU explicit FE?

How do hexahedral element formulations affect GPU explicit FE? Particularly in terms of Gaussian integration schemes

How does that affect our research?


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Nonlinear, explicit, large strain, central differences

Trilinear hexahedral elements, unstructured grid

Templated single/double precision, textures, output, etc..

Boundary conditions: kinematic, constant force, pressure

Materials – following slides (linear, nonlinear)

Pre-processing Custom input file structure for geometry, material and BCs

Post-processing Binary .vtu files + Paraview

Real-time rendering

Validated against

- Abaqus (Dassault Systèmes) and

- FEAP(University of California, Berkeley)


Introduction: GPU-based FE solver

End

Compute stress

Integrate stress

Assemble global

internal force

vector

Forward time-

marching step

Co

nv?

Check energy

balance

y

n

Assign Boundary

Conditions

𝑴 {𝒖} + 𝑐𝑑[𝑴]{𝒖 } + {𝑭 𝒖 } = [𝑹]

per node

per element

Element technology: Biofidelic materials

• Nonlinear elastic, anisotropic (fiber-reinforced arterial tissue model [Gasser et al., 2006])

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• Linear elastic model (Hookean)

𝜎𝑖𝑗 = 𝑓 𝜖𝑖𝑗 = λ𝛿𝑖𝑗𝜖𝑖𝑗 + 2𝜇𝜖𝑖𝑗 = Cε

• Nonlinear elastic model, isotropic (neo-Hookean)

𝜎 = 𝑓(𝜕Ψ

𝜕𝑭)

Anisotropic constituent

[Weisbecker et al., 2012]

Compute stress

Integrate stress

NH

GHO

H

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Element technology: Gaussian integration

Under-integration -Fast -Inaccurate -Hourglassing -No volumetric locking -No shear locking

Full integration (FI) -Slow -Very accurate -Volumetric locking -Shear locking

Selective reduced (SR) -Very slow -Very accurate -No volumetric locking -Shear locking

ξ

µ

ζ

(Not appropriate for anisotropic materials with low mesh density)

ξ

µ

ζ

ξ

µ

ζ

1x 1x

~8x ~3x

~9x ~4x

Arithmetic expense

Memory expense


Compute stress

Integrate stress

UI

FI

SR

Ideal case: extension-inflation test

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Extension 5% + systolic pressure

Reference solutions FEAP & ABAQUS

We implement the same materials in all solvers

We solve using 3 different generations: Fermi,

Kepler and Maxwell (no optimization)

GHO material (+neo-Hooke for ref.)

Scaling

Convergence criteria based on

reference solutions RMS < 0.0005mm

deltaRMS < 0.0001mm


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Under-integration

Full integration

Selective-reduced integration

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FERMI (C2075)

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KEPLER (K20c)

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MAXWELL (GTX980)

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Anisotropy cost (GHO/NH)

Integration cost (SR/UI)

Ideal case: conclusions

Speed-ups are considerable

Difficult to say exactly why one GPU is faster in a specific scenario

No architecture-specific considerations are employed, speedup is free

Useful for Parameter-fitting and geometry identification

Sensitivity analyses

…anything made possible by large numbers of FE simulations

Not a clinically accurate scenario


Near incompressibility and floating point precision


MPa

Single

precision

Double

precision

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Double

Single


FI UI SR

Clinically relevant test case: AAA inflation


p1 p2 p3 p4 p5

Patient-specific FE meshes of abdominal aortic aneurysms [Tarjuelo-Gutierrez et al., 2014]

The ‘silent killer’

Peak Wall Stress (PWS) estimate needed

Thrombus: Separation

Different material

Layer specific material properties

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thrombus

aorta

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FEAP[h] 21.12 22.79 21.01 21.52 21.86

CUDA[h] 2.93 1.22 2.75 3.03 1.31

factor x7.2 x18.7 x7.6 x7.1 x16.8


p1 p2 p3 p4 p5

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Poisson = 0.4995


Conclusion

We maintain significant speedup even using state-of-the-art materials, high-

order integration and double precision on GPUs, with no compromise

whatsoever on accuracy. Even for less than ideal meshes.

Single precision becomes ineffective quickly, and depends on Poisson ratio.

Double precision is necessary.

Practical opportunities, enabling technology: FE sensitivity analysis

Inverse FE simulations

Indications of clinical use

Generally: Memory-bound algorithm

Lots of random reads and atomic writes due to unstructured grid

For details on implementation/optimization see: S4497, Strbac GTC2014


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Thank you for your attention.

Questions?


Documents

Simulating Human Aorta Material Behavior Using a GPU ...on-demand.gputechconf.com/gtc/2016/presentation/s6475-vukasin... · Simulating Human Aorta Material Behavior Using a GPU Explicit