Determination of the bulk material properties of sub-dermal soft tissue using digital image correlation and inverse finite element analysis

Kevin M. Moerman 1

, Ciaran K.Simms

1 , Christian M. Kerskens 2 , Cathy A. Holt 3 , Sam L. Evans 3 , Caitríona Lally 4 1 Trinity Centre for Bioengineering, Trinity College Dublin, Ireland 2 Trinity College Institute of Neuroscience, Trinity College Dublin, Dublin, Ireland 3 School of Engineering, Cardiff University, Cardiff, Wales 4 School of Mechanical Manufacturing Engineering, Dublin City University, Dublin, Ireland

Introduction

Project objective: “To use magnetic resonance (MR) imaging and finite element (FE) analysis to non-invasively determine the non-linear material properties of passive living human skeletal muscle tissue”

Anatomy 360 CD-Rom, Version 1.0. Pearson Education, Inc. Benjamin Cummins.

Iteration procedure

Error?

Update Material model Tagged MRI experiment Force, deformation Comparison Iteration Procedure Material parameters Force , deformation FE simulation Initial material parameters

Tagged Magnetic Resonance Imaging In tagged MR imaging, a pattern of saturated parallel planes are temporarily created in the imaged volume. These planes appear as dark bands in the images and are temporarily locked in the tissue and deform with the tissue. By tracking the taglines over time and by combining the information for various imaging planes a continuous 3D displacement field can be reconstructed.

• The imaging and the post-processing of the data is challenging • To date work has mainly focussed on developing validation method, see poster

www_uphs_upenn_edu-radiology-depa-cvrg-index_html

Alternative iterative procedure

Error?

Update Material model Force, deformation Comparison Iteration Procedure Material parameters Force , deformation FE simulation Initial material parameters

Digital Image Correlation

• DIC is an optical method which through tracking and image registration can be used to measure high resolution 3D deformation. • The technique relies on tracking of unique features (such as speckles) within small image subsets which can be imaged from multiple camera angles.

Limess Messtechnik & Software GmbH, Pforzheim, Germany

• Can Digital Image Correlation (DIC) be used in combination with finite element modelling as a method to determine mechanical properties of human soft tissue

in vivo?

• Test suitability using soft tissue phantom with known material properties.

The DIC soft tissue phantom

• A soft tissue phantom was constructed from Sylgard ® 527 (Dow&Corning, MI, USA) • This silicone gel has similar mechanical properties to human tissue and was moulded in a cylindrical container • The surface was speckled using black paint particles (~2mm)

Material modelling of Sylgard

®

527

• Cubic samples (10~14mm) were prepared and subjected to uniaxial compression up to 50% strain. • The material parameters for an incompressible hyperelastic (Neo-Hookean) material model of the gel were determined by regression of the model against the tests data.

Material modelling of Sylgard

®

527

• The compressible form of the Neo-Hookean material model:

Material modelling of Sylgard

®

527

• Regression to experimental data (Prism 4.0, GraphPad Software Inc.) R 2 = 0.9979 Fitted parameters: μ = 1.71 kPa κ = 2500 kPa (κ was constrained with ν=0.4997)

Alternative iterative procedure

DIC on soft tissue phantom

• A two camera DIC configuration (Limess Messtechnik & Software GmbH, Pforzheim, Germany) was then used to calculate the deformation of the top surface of the gel and the indentor displacement.

the gel through the indentor.

DIC on soft tissue phantom

Alternative iterative procedure

FE modelling of DIC experiment

• A 2D axi-symmetric FE model of the gel indentation was created using Abaqus 6.7-1 Implicit (Dessault Systèmes, Suresnes Cedex, France). • The piston was rigid and the gel phantom modelled using a Neo Hookean hyperelastic material model and meshed using 4-node quadrilateral elements.

Alternative iterative procedure

Updating material model

μ: force κ: compressibility and thus the shape (κ so that ν=0.4997) μ=1.80 kPa κ=2666 kPa, (ν=0.4997)

Alternative iterative procedure

Comparing DIC to FE: Deformation • Rotate curve defined by top nodes to obtain 3D surface

Comparing DIC to FE: Deformation Compared to 3D revolved FE data 3D DIC data wrapped to 2D to compare to 2D FE results Nearly incompressible (ν=0.4997) is a good assumption, lowering ν results in divergence from experimental results

DIC and FE: Force

• Regression of uniaxial tests show μ = 1.71 kPa, with ν=0.4997

• To match the experimental force of 11.7N the μ in the FE simulation needs to be raised to 1.8 kPa, with ν=0.4997

Can Digital Image Correlation (DIC) be used in combination with finite element modelling as a method to determine mechanical properties of human soft tissue

in vivo?

• Regression of uniaxial tests: μ = 1.71 kPa, ν=0.4997

• DIC and FE predicts: μ = 1.80 kPa, ν=0.4997 - An FE simulation with μ = 1.71 kPa produces 94% force match. - The force difference (0.4 N=40 gram) is likely due to friction of indentor, this remains to be analyzed

Conclusions

• DIC is capable of measuring high resolution 3D surface deformation • The material properties of a silicone gel soft tissue phantom were determined using DIC and inverse finite element analysis • The predicted material parameters correspond well to material properties determined from regression to uniaxial test data. • The combination of DIC and FE analysis is promising as a method to non-invasively determine the bulk material properties of sub dermal soft tissue

Acknowledgements

Questions?