University of Notre Dame Department of Aerospace and Mechanical Engineering

1. Optimum Topology Design of an Interbody Fusion Implant for Lumbar Spine FixationAndrés TovarJohn E. Renaud University of Notre DameDepartment of Aerospace and Mechanical Engineering Design Automation Laboratory Optimum Design of Mechanical Elements April the 1st, 2003 Optimum Topology Design of an Interbody Fusion Implant

2. Finite Element-Based OptimizationThe Optimization Problem min F(x1,x2,…,xn) s.t. gj(x1,x2,…xn)  0; j=1,m xil  xi  xiu; i=1,n where, F: objective function gj: constraints xi: design variables xil, xiu: side constraints Optimum Topology Design of an Interbody Fusion Implant

3. Finite Element-Based OptimizationSizing (or Parameter) Optimization Iyy=112*B*H^3 A=B*H A2 A1 xi: cross-sectional dimension The mesh is unchanged. Optimum Topology Design of an Interbody Fusion Implant

4. Finite Element-Based OptimizationShape Optimization xi: perturbation vector In continuum, the genus of the body is unchanged. Optimum Topology Design of an Interbody Fusion Implant

5. Finite Element-Based OptimizationTopology Optimization xi: element relative density Reduces and redistributes material by deletion / creation of elements. Optimum Topology Design of an Interbody Fusion Implant

6. The Spinal Column Optimum Topology Design of an Interbody Fusion Implant

7. The Spinal ColumnDisc Problems Optimum Topology Design of an Interbody Fusion Implant

8. The Spinal ColumnClassical Surgery Procedures 1. Artificial Disc 2. Interbody Fusion Optimum Topology Design of an Interbody Fusion Implant

9. The Spinal ColumnNew Surgery Procedure Vertebra Implant Implant Bond Graft Optimum Topology Design of an Interbody Fusion Implant

10. The Spinal ColumnImplant candidates Clover Ibeam Leaf Hybrid Optimum Topology Design of an Interbody Fusion Implant

11. Topology Design of an Intervertebral Implant • Topology optimization software: GENESIS • Implant: 8256 eight-node element CHEXA • Upper vertebra: one rigid element RBE2 • Load cases: • Compression (400 N) • Flexion/extension and lateral bending (7,5 Nm) • Minimize strain energy (maximize stiffness) • Constrained to a maximum mass fraction Optimum Topology Design of an Interbody Fusion Implant

12. Topology Design of an Intervertebral ImplantOptimization Problem min F(x) = UTK U = S ui ki ui : strain energy s.t. M / M0 MF : mass fraction xil  xi  xiu where, ki = (xi)p k0 : stiffness of an element p = 2 ~ 3 : penalty factor ri =xir0 : density of an element xil = 0.001 xiu = 1 Optimum Topology Design of an Interbody Fusion Implant

13. Topology Design of an Intervertebral ImplantCompression – model 1 Distributed 400 N compression load s.t. 40 and 20 % of mass fraction Optimum Topology Design of an Interbody Fusion Implant

14. Topology Design of an Intervertebral ImplantFlexion / extension – model 1 Flexion / extension 7.5 Nm moment s.t. 20 and 10 % of mass fraction 20% MF 10% MF Optimum Topology Design of an Interbody Fusion Implant

15. Topology Design of an Intervertebral ImplantLateral bending – model 1 Lateral bending 7.5 Nm moment s.t. 20 and 10 % of mass fraction 20% MF 10% MF Optimum Topology Design of an Interbody Fusion Implant

16. Topology Design of an Intervertebral ImplantTopologies – model 1 Superimposed Topologies Candidate geometry Optimum Topology Design of an Interbody Fusion Implant

17. Topology Design of an Intervertebral ImplantModel 2 Optimum Topology Design of an Interbody Fusion Implant

18. Topology Design of an Intervertebral ImplantModel 3 Cortical bone Cancellous bone Cartilage Implant Optimum Topology Design of an Interbody Fusion Implant

19. Topology Design of an Intervertebral ImplantModel 3 Optimum Topology Design of an Interbody Fusion Implant

20. Topology Design of an Intervertebral ImplantModel 3 Optimum Topology Design of an Interbody Fusion Implant

21. Shape Optimization min MF = S ri : mass fraction s.t. max Sf : von Mises stress xil  xi  xiu where, ri =xir0 : density of an element Sf = 7.5 MPa: fatigue stress limit xil = 0.001 xiu = 1 Optimum Topology Design of an Interbody Fusion Implant

22. Shape Optimization Optimum Topology Design of an Interbody Fusion Implant

23. Shape Optimization Optimum Topology Design of an Interbody Fusion Implant

24. The Spinal ColumnDisc Problem Facts • Prevalence of disc degeneration [Boden, 1990] • Under 50 years old : 46% • Over 60 years old : 93% • From L1-L2 to L5-S1 in 54 years old mean [Jarvik, 2000] • DDD increases : from 37% to 73% • Dehydration : from 30% to 64% • Bulges : from 18% to 37% • 600,000 spinal surgeries every year [national estimate, 2002] Optimum Topology Design of an Interbody Fusion Implant

25. Conclusions • The optimal topology of the interbody fusion implant is obtained for mass fraction constrained optimization. • The implant will restrain the bone graft material while maintaining proper intervertebral spacing during spinal fusion. • The implant topology is capable of supporting the mechanical loads of the lumbar spine while solid fusion of the vertebral bodies occurs. • The topology can be detailed by shape optimization. Optimum Topology Design of an Interbody Fusion Implant