Finite Element Modeling of the Human Foot and Footwear Man Cheung - PowerPoint PPT Presentation

Finite Element Modeling of the Human Foot and Footwear Man Cheung 1,2 1,2 , Ph.D. Jason Tak Tak- -Man Cheung , Ph.D. Jason 1 , Ph.D. Ming Zhang 1 , Ph.D. Ming Zhang 1 Department of Health Technology & Informatics, The Hong Kong Polytechnic University, Hong Kong, China 2 Human Performance Laboratory, University of Calgary, Calgary, Alberta, Canada 醫療科技及資訊學系 Department of Health Technology and Informatics

Common Foot Problems Hammertoe Hammertoe Plantar Fasciitis Plantar Fasciitis Achilles Achilles Tendonitis Tendonitis Heel Spurs Heel Spurs Claw Toe Claw Toe Calluses Calluses Corns Corns Mallet Toe Mallet Toe Bunions Bunions Metatarsalgia Metatarsalgia http://www.foot.com http://www.foot.com

Why Finite Element (FE) Approach? • Experimental measurements of the biomechanical variables such as joint motion and load distribution are costly and difficult for the ankle-foot complex. • Finite element method allows – predictions of joint motion, load distribution between the foot and supports and in bony and soft tissue structures. – efficient parametrical analyses of loading conditions, structural and material variables.

Summary on FE Analysis on Foot & Footwear Previous FE foot models • have shown the contributions to the understanding of biomechanics of the foot and footwear • were developed under certain simplifications (Simplified or partial foot structures, assumptions of linear material properties, simplified loading and boundary conditions). Bandak et al (2001), Camacho et al (2002), Chen et al (2003), Chu et al (1995), Erdemir et al (2005), Gefen et al (2000), Goske et al (2005), Jacob & Patil (1999), Lemmon et al (1997), Shiang (1997).

Objectives • To develop a comprehensive 3D FE model to quantify the biomechanical response of the human foot and ankle ( joint motion, load distribution of bony and soft tissue structures and foot-support interface) . • To provide a systematic tool for the parametric analyses of different foot structures, surgical and footwear performances.

Development of the Finite Element Model • Coronal MR images of 2mm intervals obtained from the right foot of a healthy male subject in unloaded, neutral position

3D Reconstruction of Foot Structures Segmentation (Mimics v7.10, Materialise.) Boundaries for Foot Bones Boundary for Soft Tissue Surface Model Solid Model (SolidWorks v2001, SolidWorks Corp.)

Finite Element Mesh of Bony and Soft Tissue Structures Automatic mesh creation in ABAQUS v6.4, HKS.

Anatomical References of the Ligaments Interactive Foot & Ankle, Ver.1.0.0, Primal Picture Ltd. Interactive Foot & Ankle, Ver.1.0.0, Primal Picture Ltd.

Structural Components of the FE Model • 28 bones embedded in a volume of soft tissue (Tetrahedral elements) • 72 associated ligaments (excluding the ligaments between the toes) and the plantar fascia (Tension-only truss elements)

Joint Articulations of the Model • The phalanges were connected together using 2 mm thick structural elements to simulate the connections. • The interaction between the metatarsals, cuneiforms, cuboid, navicular, talus, calcaneus, tibia and fibula were defined by contact surfaces with a prescribed contacting stiffness of articular cartilage to allow relative bone movement.

Material Properties of Ankle-Foot Model Encapsulated soft tissue (Hyperelastic) Bony & ligamentous structures (Homogeneous, Linearly elastic ) Young’s Modulus Poisson’s Ratio Cross-sectional Area Component Element Type ν E (MPa) (mm 2 ) Bony Structures 3D-Tetrahedra 7,300 0.3 - Soft Tissue 3D-Tetrahedra Hyperelastic - - Cartilage 3D-Tetrahedra 1 0.4 - Ligaments Tension-only Truss 260 - 18.4 Fascia Tension-only Truss 350 - 58.6 Nakamura et al., 1981 (Bone); Lemmon et al., 1997 (soft tissue); Athanasiou et al., 1998 (Cartilage); Siegler et al., 1988 (ligaments); Wright and Rennels, 1964 (Plantar Fascia).

Hyperelastic Material Model for Soft Tissue 2 2 __ __ 1 ∑ ∑ = − − + − 2 C U 3 ) 3 1 ) i j i J ( 1 ( 2 ) ( I I e D i j l + = = 1 1 i j i i where U is the second-order strain energy per unit of reference volume; C ij and D i are material parameters; __ __ and are the first and second deviatoric strain invariants: I 2 I 1 2 2 2 __ __ __ __ = λ + λ + λ 1 I 1 2 3 − − − ( 2 ) ( 2 ) ( 2 ) __ __ __ __ = λ + λ + λ 2 I 1 2 3 __ -1/3 λ i ; λ with the deviatoric stretches = J el i J el and λ i are the elastic volume ratio & the principal stretches. ABAQUS v6.4, Hibbitt, Karlsson & Sorensen, Inc.

Application of Loading and Boundary Conditions Connector Elements Fixed Surfaces for Muscles Force Application Moving Support for Foot-Insole Interface and Ground Reaction Force Application

References for Muscular Insertion Points Interactive Foot & Ankle, Ver.1.0.0, Primal Picture Ltd., UK, 1999

Muscles and Ground Reaction Forces for Standing and Midstance Simulation Tendon/External Forces Standing Midstance Achilles 175N 750 Tibialis Posterior - 70N Flexor Hallucis Longus - 35N Flexor Digitorum Longus - 40N Peroneus Brevis - 40N Peroneus Longus - 35N Reaction of Lateral Retinaculum - 50N Reaction of Medial Retinaculum - 60N Vertical Ground Reaction 350N 550N The active extrinsic muscles forces during midstance were estimated from normalized EMG data using a constant muscle gain and cross-sectional area relationship (Dul, 1983; Kim et al., 2001; Perry, 1992).

Simulation of Midstance Contact Degrees 10

Plantar Pressure F-scan Measurement FE Prediction MPa MPa Contact Contact Area Area 68.8 cm 2 68.3 cm 2

Predicted Von Mises Stress of Bony and Ligamentous Structures MPa Plantar View Dorsal View

Parametrical Studies • Effect of plantar fascia stiffness (E = 0 to 700 MPa). • Effect of plantar soft tissue stiffness. • Effect of Achilles tendon loading. • Effect of posterior tibial tendon dysfunction. • Effect of different parametrical design of foot orthoses.

The Plantar Fascia and Plantar Ligaments Long Spring lig. plantar lig. Short Plantar plantar lig. fascia

Effect of varying Young’s modulus of fascia on arch height and arch length 44 149 148 43 Arch Length, mm Arch Height, mm 147 42 146 41 145 Arch Length 40 Arch Height 144 39 143 38 142 37 141 0 175 350 525 700 0 175 350 525 700 Young's Modulus of Fascia, MPa Young's Modulus of Fascia, MPa Deformed Arch Height Unloaded Arch Height (42.5 mm) FE (52.5 mm) (44 mm) Measured

Effect of varying Young’s modulus of fascia on the tensions of the ligamentous structures 150 200 Ligament Tension, N Fascia Tension, N Long Plantar Lig. 150 100 Short Plantar Lig. Spring Lig. Total Tension 100 50 50 0 0 0 175 350 525 700 0 175 350 525 700 Young's Modulus of Fascia, MPa Young's Modulus of Fascia, MPa Plantar fascia – Major arch-supporting ligamentous structure sustaining tension ~45% of applied body weight Tension of plantar ligaments With Fasciotomy short plantar lig. > long plantar lig. > spring lig.

Clinical Implications • The plantar fascia is one of the major stabilizers of the longitudinal arch of the foot. • Laceration or surgical dissection of plantar fascia may induce excessive loading in the ligamentous and bony structures. • Surgical release of the plantar fascia should be well- planned to minimize the effect on its structural integrity to reduce the risk of possible post-operative complications.

Parametrical Studies • Effect of plantar fascia stiffness. • Effect of plantar soft tissue stiffening (Up to 5 times). • Effect of Achilles tendon loading. • Effect of posterior tibial tendon dysfunction. • Effect of different parametrical design of foot orthoses.

Simulation of Stiffened Soft Tissue 0.5 F5 0.4 F3 Stress (MPa) F2 0.3 Normal 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 Strain Nonlinear compressive stress-strain response of plantar soft tissue was adopted from the in-vivo measurements (Lemmon et al., 2002). F2, F3 and F5 correspond to simulations of two, three and five times the stiffness of normal tissue. Pathologically stiffened tissue with increasing stages of diabetic neuropathy (Klaesner et al., 2002; Gefen et al., 2001).

Effect of Soft Tissue Stiffening on Plantar Pressure Distribution Normal 3 Times 5 Times 2 Times MPa MPa MPa MPa Peak Peak Peak Peak 0.306 MPa 0.291 MPa 0.230 MPa 0.263 MPa Increasing Soft Tissue Stiffness

Effect of Soft Tissue Stiffening on Peak Plantar Pressure and Contact Area 0.4 80 Peak Pressure (MPa) 0.3 2 ) 60 Contact Area (cm ForeFoot ForeFoot MidFoot 0.2 MidFoot 40 RearFoot WholeFoot RearFoot 0.1 20 0 0 1 2 3 4 5 1 2 3 4 5 Factor of Soft Tissue Stiffening Factor of Soft Tissue Stiffening Five times Heel (33%), Forefoot (35%) 47% Soft tissue stiffness Peak Plantar Pressure Contact Area