In Vivo Identification of Soft Tissue Mechanical Properties: Indentation Experiments and Inverse Finite Element Method Ergin Tönük Middle 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.

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)

In vivo Indentation Tests Experiment results need further processing

In vivo Indentation Tests

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 DC0~5 V DC 1~1000 Hz USB Step Motor Loadcell Control Box Test Unit Centronix Connector Portable Computer Non-Rotational Bearing Enable& Direction Force Soft Tissue Interface Indenter Test System

 Data Acquisition Card 220 V~ Switching Power Supply 12 V DC Step Motor Driver Card  15 V DC V/F Converter 0-5 V DC0~5 V DC 1~1000 Hz USB Step Motor Loadcell Control Box Test Unit Centronix Connector Portable Computer Non-Rotational Bearing Enable& Direction Force Soft Tissue Interface Indenter Test System

Indentation Test Results 2 mm/s Cyclic Loading Raw Data Preconditioning

Indentation Test Results 2 mm/s Cyclic Loading Processed Data F d

Indentation Test Results Material Behavior ? Inverse Finite Element Method

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

Inverse Finite Element Method

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 , March 2003

Inelastic Material Model Viscoelastic extension of James-Green- Simpson material model * : W 0 : 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 , April 2004.

Inverse Finite Element Method (Relaxation)

Inverse Finite Element Method (Creep)

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! Photo: Ergin Tönük, Sabuncupınar, 18 November