Conformal multi-material mesh generation from labelled medical volumes (Dec 2012)

1 Challenge the future

Conformal multi-material mesh generation from labelled medical volumes


Introduction

• Generation of volume meshes for FEA

• Particular use case: hip prostheses analysis

• Typical pipeline:

Segmentation from patient’s CT-scan (a) to labelled volume image (b). Volume Meshing (c) of the image and FEA for stress-strain results (d,[Dick2011]).


Introduction

• Mesh requirements:

• precise meshes

• segmentation-conform

• minimal mesh element number feature-adaptive


Related Work

Weighted Delaunay Tetrahedralization refinement [Boltcheva2009]

Dynamic Particle System Meshing [Meyer2007]

Multi-labelled volumes meshes with particle systems [Meyer2008]


Challenges

• long computation time • oversampling of edges and corners • no sharp-feature recreation ε-sample requirement

wrong topology, bad

reconstruction

too many samples


Contribution

• Application of Integer Medial Axis (IMA) as fast, discrete

medial axis scheme

• proposal of local surface triangulation scheme for volume

images


Integer Medial Axis - Analysis


Integer Medial Axis - Idea

BioMesh3D – Centres of

maximal spheres

IMA – shortest path in feature

transform


Integer Medial Axis – Results

Runtime

dataset BioMesh3D DeVIDE FE-Mesher

artificial 26 min 0.1 sec

Tooth 1h 41 min 1 sec

real femur 14h 11 min 2 sec



Quality

Tooth # Tetra 142795 DeVIDE FE-Mesher

Max. Min. Avg. Variance # bad

Tetra

%

bad

Aspect

Ratio

119.69 1.01 1.94 1.00 9282 6.50

Radius

Ratio

105.43 1.00 1.69 0.83 6736 4.72

Volume 272.34 0.0 2.96 21.74 0 0.0

Tooth # Tetra 118110 Simpleware FE+

Max. Min. Avg. Variance # bad

Tetra

%

bad

Aspect

Ratio

44.59 1.02 1.54 0.16 816 0.69

Radius

Ratio

921.55 1.00 1.37 7.92 997 0.84

Volume 46.68 0.0 3.41 14.24 0 0.0



Precision


Minimal Sample for accurate Meshing Concept

• ε-sampling:

• ensures topologic conformity

• applies to dense and sparse

samples

• Loss of sharp features

• only applies for 3D meshes

without additional information

• our idea:

• mesh surface locally

• take surface mesh to

generate volume mesh

0,, xxBESx


Minimal Sample for accurate Meshing Concept

1. Get TBN-Matrix per sample

vertex

2. Get Neighbourhood per

vertex

3. re-project points in

tangent plane

4. mesh via Local Delaunay

Triangulation tangent

plane neighbourhood

5. use established

connections in 3D


Minimal Sample for accurate Meshing Results

VTK CGAL – no constraint CGAL – Convex Hull constraint

formation of holes due unsuitable Neighbourhood determination


Conclusion and Future Work

• Improved runtime behaviour due to Medial Axis Transform

Algorithm change

• Local Triangulation in tangent space not ε-sample bound, but

dependent on Neighbourhood operation

• k-Nearest Neighbour not suitable for non-uniformal, sparse

samples

• In future: usage of natural neighbours for neighbourhood

determination

Science

Conformal multi-material mesh generation from labelled medical volumes (Dec 2012)