in vivo identification of soft tissue mechanical properties: indentation experiments and inverse...

In Vivo Identification of Soft Tissue Mechanical

Properties: Indentation Experiments and Inverse Finite Element Method

Ergin TönükMiddle East Technical University

Department of Mechanical Engineering

Outline

• Biomechanics Research at the Mechanical Engineering Department, METU– KISS Motion and Gait Analysis System– Soft Tissue Testing System– Collaborations

• Mechanics and Biomechanics• Deformable Solid Biomechanics• Biological Material Identification

– Indenter Tests– Inverse Finite Element Method– Questions to be Answered

Biomechanics Research at Mechanical Engineering Department, METU

KISS Motion and Gait Analysis System (1/5)

• KISS (Kinematic Support System/Kas İskelet Sistemi) is the first gait analysis system in Turkey

• It is the only system developed by local people• Besides performing referred patient

experiments we work on – developing new gait analysis protocols,– developing new mechanical models for gait and

other motion, – analyze gait patterns of various pathologies with

clinicans,– work on different joint models.



• Motion of the subject is captured by six cameras following the trajectories of retro-reflective markers on the subject’s anatomical landmarks (kinematic data collection)



• Ground reaction forces (force components in three orthogonal directions and moment components about these force components) of the subject are measured by two force-plates



• With the help of mathematical models anatomical joint angles, the joint reaction moments and mechanical power are calculated and presented in the form of graphs

• Example: Calcaneus fracture with conservative treatment compared with a normal subject.

Fracture Normal

Joint moment

Joint power



• We can also conduct other sorts of human motion analyses:– Archery shooting,– Sacro-lumbar force estimation during weight

lifting,– Jumping and falling analysis of male and

female volleyball players,– Human shoulder joint motion analysis,– Wheelchair propulsion analysis,– Simple human posture analysis.


In-Vivo Soft Tissue Testing System

• For accurate computer modeling of soft tissue mechanical behavior we need to perform “materal testing” on living soft tissues.

• We have developed a soft tissue indenter to perform tests on soft tissues in vivo.


Collaboration• Ankara University, Faculty of Medicine, Department of Anatomy,• Ankara University, Faculty of Medicine, Department of Physical

Medicine and Rehabilitation, • Ankara Atatürk Education and Research Hospital, Orthopeady and

Traumatology Clinics,• Ankara Dışkapı Education and Research Hospital, Orthopeady and

Traumatology Clinics,• Gülhane Military Medical Academy, Department of Orthopeady and

Traumatology and Laboratory of Prosthesis and Orthosis• Hacettepe University, Faculty of Dentistry, Department of

Prosthodontics,• BİAS Mühendislik, Teknokent, ODTÜ,• TÜBİTAK-UZAY (formerly TÜBİTAK-BİLTEN),• Middle East Techical University, Department of Sports,• Middle East Technical University, Department of Engineering Science.

Mechanics (1/2)

• It is the physical science that deals with the behavior of materials under the action of forces.

• Materials may either move or deform (or do both) if subjected to forces.

Mechanics (2/2)

• For rigid body motion, laws of dynamics are well established and there are techniques available for analyzing multibody dynamics.

• For deformation, ranging from strength of materials or elementary fluid mechanics to continuum mechanics and various advanced numerical solution techniques (like finite element analysis) are available.

Biomechanics

• Application of principles of mechanics to biological systems in order to– Understand what is going on in detail– Predict what might happen under

predefined conditions– Use computer models to perform tests

which are hard do realize physically

Deformable Solid Mechanics

• In engineering we have very powerful tools (like finite element or boundary element modeling techniques) that help engineers to predict the internal force intensities (i. e. stresses) and measures of deformations (i. e. strains).

Deformable Solid Biomechanics

• This powerful tool of engineering is not that powerful in biomechanics because engineering materials are mostly linear elastic.

• Further, engineering materials are mostly subjected to small strains which can be well approximated with infinitesimal strain theory.


• For conventional engineering materials, to identify the material properties one may perform extensive material tests.

• For many common engineering materials these mechanical properties are already tabulated.


• For biological materials, performing material tests is more complicated due to:– Large physiological strains commonly

encountered– Nonlinear and non-elastic material

behavior– Maintaining physiological conditions

and homeostasis during experiments


• Result:– Improperly identified or over-

simplified material models used in the powerful tool of engineering

– Non-realistic and non-predictive computer models

• Finite element or boundary element techniques found limited use in biomechanics.

Bottleneck: Material Identification

In vivo Indentation Tests

• In vivo• Easy to perform• Non-invasive• Diverse

– Cyclic loading-unloading at different rates– Relaxation (with different initial rate)– Creep (with different initial rate)


• Experiment results need further processing

Indenter Test Unit

Step Motor

Indenter Tip

Load Cell

Data Acquisition Card

220 V~Switching Power Supply

12 V DC

Step Motor Driver Card

15 V DC

V/F Converter

0-5 V DC 0~5 V DC

1~1000 Hz

USB

Control Box

Centronix Connector

Portable Computer

Enable&Direction

Force

Indenter Test System

Step Motor Driver Card

V/F Converter

0-5 V DC 0~5 V DC

1~1000 Hz

Step Motor

Loadcell

Control Box

Test Unit

Centronix Connector

Portable Computer

Non-Rotational Bearing

Enable&Direction

Soft Tissue Interface

Indenter Test System

Indentation Test Results2 mm/s Cyclic Loading

Raw Data

-10123456789

10111213

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Time [s]

Sof

t Tis

sue

Rea

ctio

n F

orce

[N

]

Preconditioning

Indentation Test Results2 mm/s Cyclic Loading

Processed Data

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8 9 10Displacement [mm]

Sof

t Tis

sue

Rea

ctio

n F

orce

[N

]

Loading Unloading

F

d

Indentation Test ResultsMaterial Behavior

Strain [-]

Str

ess

[Pa] ?F

A

0

InverseFiniteElementMethod

Inverse Finite Element Method

• Geometry is known• Boundary conditions are known• Material constants (and material

constitutive law) are unknown• System response is known


• Construct a finite element model • Apply appropriate boundary conditions• Select a material law (suitable for soft

tissues) and make a guess about material coefficients

• Obtain the response of ‘virtual’ soft tissue and compare it with the experimental one

• Update the material coefficients

Displacement

For

ce

Experimental

FE Trial 1


[-]

Trial C1 C2 C3 NSSE

1 0,001 0,001 0,001 412,28%

[MPa]

Displacement

For

ce

Experimental

FE Trial 1

FE Trial 2


[-]Trial C1 C2 C3 NSSE

1 0,001 0,001 0,001 412,28%2 0,002 0,002 0,002 188,82%

[MPa]

Displacement

For

ce

Experimental

FE Trial 1

FE Trial 2

FE Trial 3


[-]

Trial C1 C2 C3 NSSE

1 0,001 0,001 0,001 412,28%2 0,002 0,002 0,002 188,82%3 0,002 0,01 0,002 24,46%

[MPa]

Displacement

For

ce

Experimental

FE Trial 1

FE Trial 2

FE Trial 3

FE Trial 4


[-]

Trial C1 C2 C3 NSSE

1 0,001 0,001 0,001 412,28%2 0,002 0,002 0,002 188,82%3 0,002 0,01 0,002 24,46%4 0,002 0,015 0,002 0,41%

[MPa]

Elastic Material Model• James-Green-Simpson hyperelastic

material model (modified for axisymmetric loading*):

• W: Strain energy density per unit undeformed volume

• I: Invariant of Green-Lagrange finite strain tensor

* TÖNÜK, E., SILVER-THORN, M. B., “Nonlinear Elastic Material Property Estimation of Lower Extremity Residual Limb Tissues”. IEEE, Transactions on Rehabilitation Engineering Vol 11, No 1, pp. 43-53, March 2003

2 33 1 3I II IIIW C I C I C I

Inelastic Material Model

• Viscoelastic extension of James-Green-Simpson material model*:

• W0: Initial strain energy density per unit undeformed volume

• 1 and 2 short and long term relaxation constants

• 1 and 2 short and long term relaxation magnitudes* TÖNÜK, E., SILVER-THORN, M. B., Nonlinear Viscoelastic Material Property Estimation of Lower Extremity

Residual Limb Tissues, ASME Journal of Biomechanical Engineering v. 126, pp. 289-300, April 2004.

21

t

2

t

10 e1e11WtW

Inverse Finite Element Method (Relaxation)

Time

For

ceExperimental DataFE Trial 1FE Trial 2FE Trial 3

Trial 1 2 SSE

1 0,2997 0,3317 1,05%2 0,31 0,3317 0,23%3 0,32 0,32 0,02%

Inverse Finite Element Method (Creep)

Time

Dis

plac

emen

t

Experimental DataFE Trial 1FE Trial 2FE Trial 3FE Trial 4

Trial 1

2 SSE

1 0.133 0.098 69.50%2 0.3 0.098 9.29%3 0.35 0.098 2.01%4 0.35 0.15 0.27%

Ongoing Research

• Experimental Procedure– Verification of indenter test protocols– Effect of indenter tip geometry– Ways to obtain cleaner data

• Material Model– Different strain energy functions– Different inelastic material models

Goal

• Accurate finite element models of mechanical interaction of soft tissue with its environment

Thank You!Thank You!

Photo: Ergin Tönük, Sabuncupınar, 18 November 2006

http://E40003.me.metu.edu.tr

in vivo identification of soft tissue mechanical properties: indentation experiments and inverse...

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