X-ray micro-CT based 3D structure Semester project Final - - PowerPoint PPT Presentation

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X-ray micro-CT based 3D structure Semester project Final - - PowerPoint PPT Presentation

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Modelling the deformation of an X-ray micro-CT based 3D structure Semester project Final presentation Olivier Schpfer EPFL GC MA3 Project objective From an existing sample to a numerical model to use with the software

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Modelling the deformation of an X-ray micro-CT based 3D structure

Semester project – Final presentation

Olivier Schöpfer – EPFL – GC MA3

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Project objective

  • From an existing sample
  • to a numerical model
  • to use with the software “Akantu”

from the EPFL LSMS lab

  • in order to perform numerical testing of the sample

2

[1]

14.01.2019 Olivier Schöpfer - EPFL - GC MA3

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X-ray micro-CT : What is it?

  • CT : Computed tomography
  • Before the X-ray CT, the slices had to be taken manually and examined

by hand, one by one

  • Very long
  • Sample destroyed
  • Produces images similar to an X-ray, but in 3D
  • Non destructive
  • High resolution
  • Fast + no sample preparation needed
  • Automated

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X-ray micro-CT : How does it work?

  • Procedure:

4

2D 3D [2] [3]

14.01.2019 Olivier Schöpfer - EPFL - GC MA3

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X-ray micro-CT : How does it work?

  • The receptor is there to read the intensity of the X-ray in comparison

to the intensity that was emitted

  • The attenuation of the X-ray signal will give an indication on the

material properties

  • Final intensity :

𝐽 = 𝐽0 ∙ exp −𝜈 ∙ 𝑦 𝜈 ∶ attenuatiuon coefficient 𝑦 ∶ length of the x − ray path through the sample

  • The attenuation coefficient depends on material properties

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X-ray micro-CT : How does it work?

  • Need for a good calibration

6

Low energy High energy [4] [5]

14.01.2019 Olivier Schöpfer - EPFL - GC MA3

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Procedure to get a 3D model

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From a stack of slices to a 3D model

  • What comes out of the X-ray CT scan
  • What the 3D model looks like at first

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From a stack of slices to a 3D model

  • What comes out of the X-ray CT scan
  • What the 3D model looks like at first

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From a stack of slices to a 3D model

  • Binarize the slices

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From a stack of slices to a 3D model

  • Binarize the slices

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From a stack of slices to a 3D model

  • Remove Small Spots

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From a stack of slices to a 3D model

  • Remove Small Spots

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From a stack of slices to a 3D model

  • Possible to extract a subvolume to have lower computation

requirements

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From a stack of slices to a 3D model

  • Generate a surface

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From a stack of slices to a 3D model

  • Generate a surface

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From a stack of slices to a 3D model

  • Generate a surface

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From a stack of slices to a 3D model

  • Generate a surface - Constrained Smoothing

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From a stack of slices to a 3D model

  • Generate a surface - Constrained Smoothing

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From a stack of slices to a 3D model

  • Generate a surface - Constrained Smoothing: Problem

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Smoothing set to 1 Smoothing set to 9 [6]

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From a stack of slices to a 3D model

  • Simplify the modelization

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From a stack of slices to a 3D model

  • Simplify the modelization

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30%

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From a stack of slices to a 3D model

  • Test the triangles before going to a tetrahedron model

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From a stack of slices to a 3D model

  • Intersection test

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From a stack of slices to a 3D model

  • Intersection test

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From a stack of slices to a 3D model

  • Intersection test

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From a stack of slices to a 3D model

  • Intersection test

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From a stack of slices to a 3D model

  • Intersection test

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From a stack of slices to a 3D model

  • Aspect Ratio test

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Aspect ratio = 110’053

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From a stack of slices to a 3D model

  • Aspect Ratio test

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Aspect ratio = 50 Aspect ratio = 110’053

14.01.2019 Olivier Schöpfer - EPFL - GC MA3

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From a stack of slices to a 3D model

  • Aspect Ratio test

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Aspect ratio = 50 Aspect ratio = 15 Aspect ratio = 110’053

14.01.2019 Olivier Schöpfer - EPFL - GC MA3

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From a stack of slices to a 3D model

  • Aspect ratio – autofix : “Prepare generate tetra grid”
  • Will fix most of the aspect ratio errors
  • Remaining errors have to be corrected

manually

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From a stack of slices to a 3D model

  • Aspect ratio – autofix : “Prepare generate tetra grid”
  • Will fix most of the aspect ratio errors
  • Remaining errors have to be corrected

manually

33 14.01.2019 Olivier Schöpfer - EPFL - GC MA3

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From a stack of slices to a 3D model

  • Aspect ratio – autofix : “Prepare generate tetra grid”
  • Will fix most of the aspect ratio errors
  • Remaining errors have to be corrected

manually

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From a stack of slices to a 3D model

  • Orientation test

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From a stack of slices to a 3D model

  • Orientation test

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From a stack of slices to a 3D model

  • Remesh the surface before creating the tetrahedron model to have a

simpler model and better triangles

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From a stack of slices to a 3D model

  • Remesh the surface before creating the tetrahedron model to have a

simpler model and better triangles

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From a stack of slices to a 3D model

  • Remesh the surface before creating the tetrahedron model to have a

simpler model and better triangles

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From a stack of slices to a 3D model

  • Remesh the surface before creating the tetrahedron model to have a

simpler model and better triangles

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From a stack of slices to a 3D model

  • Generate Tetra Grid

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From a stack of slices to a 3D model

  • Generate Tetra Grid

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From a stack of slices to a 3D model

  • Export for Akantu

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From a stack of slices to a 3D model

  • Size of the model

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Units Editor Data Parameter Editor

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Traction test

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Bone material

  • Variable properties depending on :
  • Species (Human, Cow, Rat, etc…)
  • Age (Young, Old)
  • Health (Bone disease, Calcium levels, etc…)
  • Bone (Femur, Tibia, etc…)
  • Part of the bone (Cortical, Trabecular)
  • “Freshness” of the sample and is it conserved wet?

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[7]

14.01.2019 Olivier Schöpfer - EPFL - GC MA3

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Bone material – Mechanical properties, example

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  • Typical intervals for human trabecular bone
  • Young modulus : can vary from 10 to 3000 [MPa]
  • Ultimate strain : typically between 1.0 and 2.5%
  • Poisson’s Ratio : between 0.03 and 0.6
  • We should probably use a visco elastic constitutive law

(Keaveny, Morgan and Yeh, 2004, p. 8.15) [8]

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Bone material – Mechanical properties – Young Modulus

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  • Traction test on a bone sample
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Bone material – Mechanical properties – Young Modulus

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  • Traction test on a bone sample

𝐹𝑓𝑚𝑏𝑡𝑢𝑗𝑑 = 3060 𝑁𝑄𝑏

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Bone material – Mechanical properties – Young Modulus

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  • How to get the effective modulus

𝑐𝑝𝑜𝑓 bone + 𝑤𝑝𝑗𝑒

𝑢𝑝𝑢

= σ𝑗

𝑜

𝑐𝑝𝑜𝑓 bone + 𝑤𝑝𝑗𝑒 𝑗 𝑜 = 0.3424 = 34.2% 𝑐𝑝𝑜𝑓

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Simple traction test with Akantu

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  • Input:
  • E = 1000 [MPa]
  • 𝜉 = 0.25
  • Tests:
  • 3 Displacement controlled : x, y, z
  • 3 Force controlled : x, y, z
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Simple traction test with Akantu

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  • Displacement controlled
  • 𝜗𝑗 = 1%, i = x, y, z
  • Young modulus calculation for x
  • 𝐹𝑦 =

𝜏𝑦𝑦 𝜗

  • 𝜏𝑦𝑦 =

σ𝑗

𝑜 𝜏𝑦𝑦,𝑗

𝑜

  • n = #elements on the considered surface

In Paraview, 𝜏𝑦𝑦 = 𝑡𝑢𝑠𝑓𝑡𝑡: 0 ; 𝜏𝑧𝑧 = 𝑡𝑢𝑠𝑓𝑡𝑡: 4 ; 𝜏𝑨𝑨 = 𝑡𝑢𝑠𝑓𝑡𝑡: 8

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Simple traction test with Akantu

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  • Force controlled
  • 𝐺

𝑗 = 1000 [𝑂], i = 1, 2, …, n

  • n = #vertex at the surface where the force is applied
  • Young modulus calculation for x
  • 𝐹 =

𝜏 𝜗 = 𝐺/𝐵 Δ𝑀/𝑀

  • n = 9247; 𝐺𝑢𝑝𝑢 = 9′247′000 𝑂 ; 𝐵𝑐𝑝𝑜𝑓 = 2.51 𝑛2 ; 𝜏𝑦𝑦 = 3.68 ∙ 106 𝑂/𝑛2
  • Δ𝑀𝑦 =

σ𝑗

𝑜 Δ𝑀𝑦,𝑗

𝑜

= 0.035 [𝑛]; 𝑀𝑦 = 4.57 𝑛 ; 𝜗𝑦𝑦 =

Δ𝑀𝑦 𝑀𝑦 = 7.77 ∙ 10−3

  • 𝐹𝑦 =

𝜏𝑦𝑦 𝜗𝑦𝑦 = 473.7 𝑁𝑄𝑏

In Paraview, Δ𝑀𝑦,𝑗 = 𝑒𝑗𝑡𝑞𝑚𝑏𝑑𝑓𝑛𝑓𝑜𝑢: 0 ; Δ𝑀𝑧,𝑗 = 𝑒𝑗𝑡𝑞𝑚𝑏𝑑𝑓𝑛𝑓𝑜𝑢 ∶ 1 ; Δ𝑀𝑨,𝑗 = 𝑒𝑗𝑡𝑞𝑚𝑏𝑑𝑓𝑛𝑓𝑜𝑢: 2

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Simple traction test with Akantu

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  • Results:
  • Displacement controlled
  • Force controlled
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Simple traction test with Akantu

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  • Graphic representation
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Simple traction test with Akantu

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  • Graphic representation
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Simple traction test with Akantu

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  • Graphic representation
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Simple traction test with Akantu

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  • Graphic representation
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Conclusion

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  • It is possible to create a 3D model, using the X-ray micro-CT scan
  • Go from *.tif to *.inp (ABAQUS Input)
  • Straightforward procedure
  • Limit the size of the model (1-2 million triangles for the surface)
  • Simplify or cut the model if needed and possible
  • The model created can be used for calculations in Akantu
  • The procedure can be used for other projects
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Thank you !

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Sources

  • Picture :
  • [1] taken from : https://actu.epfl.ch/news/akantu-v300-is-out/ (consulted the 05.11.2018)
  • [2], [4], [5] Ketcham, Richard A. and Carlson, William D.. 2001. Acquisition, optimization and

interpretation of X-ray computed tomographic imagery: applications to the geosciences. Computers & Geosciences 27: 381-400.

  • [3] Schoeman, L., Williams, P., Du Plessis, A., Manley, M.. 2016. X-ray micro-computed tomography

(𝜈CT) for non-destructive characterization of food microstructure. Trends in Food Science & Technology 47: 10-24.

  • [6] Konrad-Zuse-Zentrum. 1995-2017. Avizo 9 - Avizo User's Guide. Berlin: Informationstechnik Berlin

(ZIB).

  • [7] taken from : https://en.wikipedia.org/wiki/Bone (Consulted the 07.11.2018)
  • [8] Keaveny, Tony M., Elise F. Morgan, et Oscar C. Yeh. 2004. Standard handbook of biomedical

engineering and design. The McGraw-Hill Companies.

  • Other : Personal pictures and screenshots from Avizo

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