1. 1/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Optimum Topology Design of an Interbody Fusion Implant for Lumbar Spine Fixation Andrés Tovar John E. Renaud University of Notre Dame Department of Aerospace and Mechanical Engineering Design Automation Laboratory Optimum Design of Mechanical Elements April the 1 st, 2003

2. 2/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Content Finite Element-Based Optimization The Spinal Column Topology Optimization Shape Optmization Results and Conclusion

3. 3/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Finite Element-Based Optimization Mr. Lucien A. Schmit Jr. Rockwell Professor of Aerospace Engineering, Emeritus University of California, Los Angeles (Retired). National Academy of Engineering Election Citation (1985): For pioneering work in structural synthesis, combining finite element analysis and nonlinear programming algorithms to create a powerful class of modern structural design methods (in 1960’s).

4. 4/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Finite Element-Based Optimization The Optimization Problem minF(x 1,x 2,…,x n ) s.t.g j (x 1,x 2,…x n )  0; j=1,m x il  x i  x iu ; i=1,n where, F: objective function g j : constraints x i : design variables x il, x iu : side constraints

5. 5/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Finite Element-Based Optimization Sizing (or Parameter) Optimization x i : cross-sectional dimension A2A2 A1A1 I yy =112*B*H^3 A=B*H The mesh is unchanged.

6. 6/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Finite Element-Based Optimization Shape Optimization x i : perturbation vector In continuum, the genus of the body is unchanged.

7. 7/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Finite Element-Based Optimization Topology Optimization x i : element relative density Reduces and redistributes material by deletion / creation of elements.

8. 8/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant The Spinal Column

9. 9/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant The Spinal Column Disc Problems

10. 10/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant 1. Artificial Disc2. Interbody Fusion The Spinal Column Classical Surgery Procedures

11. 11/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant The Spinal Column New Surgery Procedure Implant Vertebra Implant Bond Graft

12. 12/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant The Spinal Column Implant candidates HybridLeafIbeamClover

13. 13/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant 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

14. 14/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Topology Design of an Intervertebral Implant Optimization Problem minF(x) = U T K U =  u i k i u i : strain energy s.t.M / M 0  MF: mass fraction x il  x i  x iu where, k i = (x i ) p k 0 : stiffness of an element p = 2 ~ 3 : penalty factor  i = x i  0 : density of an element x il = 0.001 x iu = 1

15. 15/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Topology Design of an Intervertebral Implant Compression – model 1 Distributed 400 N compression load s.t. 40 and 20 % of mass fraction

16. 16/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Topology Design of an Intervertebral Implant Flexion / extension – model 1 Flexion / extension 7.5 Nm moment s.t. 20 and 10 % of mass fraction 20% MF10% MF

17. 17/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Topology Design of an Intervertebral Implant Lateral bending – model 1 Lateral bending 7.5 Nm moment s.t. 20 and 10 % of mass fraction 20% MF10% MF

18. 18/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Topology Design of an Intervertebral Implant Topologies – model 1 Superimposed Topologies Candidate geometry

19. 19/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Topology Design of an Intervertebral Implant Model 2

20. 20/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Topology Design of an Intervertebral Implant Model 3 Cortical bone Cancellous bone Cartilage Implant

21. 21/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Topology Design of an Intervertebral Implant Model 3

22. 22/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Topology Design of an Intervertebral Implant Model 3

23. 23/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Shape Optimization minMF =  i : mass fraction s.t.  max  Sf: von Mises stress x il  x i  x iu where,  i = x i  0 : density of an element Sf = 7.5 MPa: fatigue stress limit x il = 0.001 x iu = 1

24. 24/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Shape Optimization

25. 25/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant Shape Optimization

26. 26/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant The Spinal Column Disc 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]

27. 27/27Optimum DesignOptimum Topology Design of an Interbody Fusion Implant 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.