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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.
Biomechanics Research at Mechanical Engineering Department, METU
KISS Motion and Gait Analysis System (2/5)
• 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)
Biomechanics Research at Mechanical Engineering Department, METU
KISS Motion and Gait Analysis System (3/5)
• 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
Biomechanics Research at Mechanical Engineering Department, METU
KISS Motion and Gait Analysis System (4/5)
• 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
Biomechanics Research at Mechanical Engineering Department, METU
KISS Motion and Gait Analysis System (5/5)
• 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.
Biomechanics Research at Mechanical Engineering Department, METU
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.
Biomechanics Research at Mechanical Engineering Department, METU
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.
Deformable Solid Biomechanics
• 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.
Deformable Solid Biomechanics
• 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
Deformable Solid Biomechanics
• 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.
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)
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
Inverse Finite Element Method
• Geometry is known• Boundary conditions are known• Material constants (and material
constitutive law) are unknown• System response is known
Inverse Finite Element Method
• 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
Inverse Finite Element Method
[-]
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
Inverse Finite Element Method
[-]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
Inverse Finite Element Method
[-]
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
Inverse Finite Element Method
[-]
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