A program for creating patient-specific Finite Element models of fractured bones fixed with metallic implants Aviv Hurvitz, CAS Laboratory, The Hebrew University Advisor: Prof. Leo Joskowicz

Goals of the project Goals of the project The purpose of our software The purpose of our software Finite Element Modeling - briefly Finite Element Modeling - briefly Our software in detail Our software in detail What we compute What we compute Tools that we use Tools that we use

Hip fracture fixation Images from Wheeless' Textbook of Orthopaedics

Create a mechanical model of the fractured bones along with their fixation Create a mechanical model of the fractured bones along with their fixation Evaluate quality of the various proposed fixation methods Evaluate quality of the various proposed fixation methods Patient specific model Patient specific model Ultimate goal – integrate the tool in the clinical process Ultimate goal – integrate the tool in the clinical process

FEM - Stress and Strain

Finite Element Modeling Represent a system as a set of simple geometrically- similar elements. Represent a system as a set of simple geometrically- similar elements. Each element is equivalent to a spring. Each element is equivalent to a spring. Elements are joined together by frictionless pins. Elements are joined together by frictionless pins.

Finite Element Analysis Each element has a corresponding force-displacement equation: Each element has a corresponding force-displacement equation: Elements that are connected at common joints have compatible displacements. Elements that are connected at common joints have compatible displacements. Each joint is in force equilibrium; internal and external forces sum to zero. Each joint is in force equilibrium; internal and external forces sum to zero.

Finite Element Analysis Combine the equations to get the master stiffness equation: In matrix notation: f = Ku K is a non-invertible matrix. Need boundary conditions to solve the system. [f 1 ] – prescribed forces [u 2 ] – known displacements

Apply boundary conditions Solution: with enough boundary conditions, [K 11 ] is invertible, and the unknown displacements [u 1 ] can be calculated. Post-processing: recover external and internal forces, stresses, strains.

Input data A CT image of the fracture A CT image of the fracture Calibration phantom Calibration phantom

Segmentation

Segmentation

Surface Generation

Surface Simplification

Fracture reduction planning

Fixation method planning

Creating the FE Model Cut the BONE meshes with the IMPLANT meshes Cut the BONE meshes with the IMPLANT meshes Find the contact surfaces between the CUT BONE and the IMPLANT Find the contact surfaces between the CUT BONE and the IMPLANT

Generating tetrahedral grids Quality-conforming meshes Quality-conforming meshes TetGen [Hang Si, WIAS] TetGen [Hang Si, WIAS]

Assigning material properties E – Young’s modulus E – Young’s modulus

Analysis in ABAQUS