1. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 1 Dynamic Data Driven Finite Element Modeling of Brain Shape Deformation During Neurosurgery A. Majumdar 1, D. Choi 1, P. Krysl 2, S. K. Warfield 3, N. Archip 3, K. Baldridge 1,4 1 San Diego Supercomputer Center & 2 Structural Engineering Dept University of California San Diego 3 Computational Radiology Lab Brigham and Women’s Hospital Harvard Medical School 4 Universität Zürich Grants: NSF: ITR 0427183, 0426558; NIH:P41 RR13218, P01 CA67165, LM0078651, I3 grant (IBM)

2. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 2 Contents of Talk 1.Overview of Image Guided Neurosurgery and Dynamic Data Drive Application System 2.Biomechanical FEM solution 3.Briefly grid scheduling 4.Future : near-continuous DDDAS

3. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 3 1.Overview of Image Guided Neurosurgery and Dynamic Data Drive Application System

4. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 4 Neurosurgery Challenge Challenges : Remove as much tumor tissue as possible Minimize the removal of healthy tissue Avoid the disruption of critical anatomical structures Know when to stop the resection process Pre-op MRI compounded by the intra-operative brain shape deformation as a result of the surgical process Important to quantify and correct for these deformations while surgery is in progress Real-time constraints – provide images ~once/hour within few mins during surgery lasting ~6 hours

5. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 5 Intraoperative MRI Scanner at BWH (0.5 T)

6. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 6 Brain Deformation Before surgery After surgery

7. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 7 Tumor Ventricles Pre-operative Image Intra-operative image, after dura opened and partial tumor resection

8. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 8 Overall Process Before image guided neurosurgery During image guided neurosurgery Segmentation and Visualization Preoperative Planning of Surgical Trajectory Preoperative Data Acquisition Preoperative data Intraoperative MRI SegmentationRegistration Surface matching Solve biomechanical Model for volumetric deformation Visualization Guide surgical process Tetrahedral FE mesh

9. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 9 Timeline of Image Acquisition and Analysis Time (min) Before surgery During surgery 0 10 20 30 40 Preop processes Intraop MRI Segmentation Registration Surface displacement Biomechanical simulation Visualization Surgical progress Action

10. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 10 Current DDDAS ( Dynamic Data Driven Application System) Pre- and Intra-op 3D MRI (once/hr) Pre- and Intra-op 3D MRI (once/hr) Local computer at BWH Crude linear elastic FEM solution Merge pre- and intra-op viz Intra-op surgical decision and steer Segmentation, Registration, Surface Matching for BC Once every hour or two for a 6 hour surgery

11. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 11 Two Research Aspects Parallel solution of the linear elastic biomechanical model for brain shape deformation during surgery Grid Architecture – grid scheduling, on demand remote access to multi-teraflop machines, data transfer/sharing

12. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 12 2. Biomechanical FEM solution

13. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 13 Brief Concept of Biomechanical Model Assuming a linear elastic continuum with no initial stress or strains, the deformation energy of an elastic body submitted to eternally applied forces : F = F(x,y,z) is the vector representing the force applied to the elastic body u = u(x,y,z) is the displacement vector field we want to compute is the strain vector = Lu and the stress vector linked to the strain vector is the strain vector = Lu and the stress vector linked to the strain vector by the material constitutive equation. Linear isotropic elastic brain tissue is modeled with two parameters: Young’s elasticity modulus and Poisson’s ratio. Introducing FE and some analysis, Ku = -F (K is the rigidity matrix) Ku = -F (K is the rigidity matrix) The displacements at the boundary surface nodes are fixed to match those generated by the deformable surface model.

14. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 14 Mesh Model with Brain Segmentation

15. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 15 Current and New Biomechanical Models Current linear elastic material model RTBM Advanced biomechanical model FAMULS (AMR) Advanced model is based on conforming adaptive refinement method Inspired by the theory of wavelets this refinement produces globally compatible meshes by construction Replicate the linear elastic result produced by RTBM using FAMULS

16. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 16 FEM Mesh : FAMULS & RTBM RTBM (Uniform) FAMULS (AMR)

17. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 17 Deformation Simulation After Cut No – AMR FAMULS 3 level AMR FAMULS RTBM

18. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 18 Petsc setup PetscMapCreateMPI(PETSC_COMM_WORLD,PE TSC_DECIDE,n,&map) ; MatCreateMPIAIJ(PETSC_COMM_WORLD,..&K_g lobal) ;

19. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 19 Domain decomposition PetscMapGetLocalRange(map,&Istart,&Iend) for (each elements) {for (each dof in each nodes is in (lstart, lend)) if it is in the rage { ComputeShape(); ComputeBD(); MatSetValues(K_global,..ADD_VALUES); } }

20. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 20 Boundary condition Prescribed forces: VecSetValues(F_global, nodeForces->NIndices, nodeForces- >Indices, nodeForces->Displacements, ADD_VALUES); Prescribed displacements: (displacements on the surface obtained by active surface algorithm) MatZeroRows(K_global,ISBoundaryNodes,&one); VecSetValues(F_global, bc->NIndices,bc->Indices, bc->Displacements,INSERT_VALUES);

21. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 21 KSPCreate(PETSC_COMM_WORLD,&ksp) KSPSetOperators(ksp,K_global,K_global..) KSPGetPC(ksp,&pc) PCSetType(pc,PCBJACOBI) KSPSetTolerances(ksp,1.e-7..) KSPSetFromOptions(ksp) KSPSolve(ksp,F_global,u_displ,&its) Solver setup

22. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 22 Parallel RTBM Performance (214035 tetrahedral elements) - 10.00 20.00 30.00 40.00 50.00 60.00 12481632 # of CPUs Elapsed Time (sec) IBM Power3 IA64 TeraGrid IBM Power4

23. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 23 Advanced Biomechanical Model The current solver is based on small strain isotropic elastic principle New biomechanical model Inhomogeneous scalable non-linear hyper-elastic or visco-elastic model with AMR Increase resolution close to the level of MRI voxels i.e. millions of FEM meshes New high resolution complex model still has to meet the real time constraint of neurosurgery Requires fast access to remote multi-teraflop systems

24. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 24

25. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 25

26. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 26

27. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 27 3. Briefly Grid Scheduling

28. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 28 On-demand Scheduling Experiment on 5 TeraGrid Clusters The real-time constraint of this application requires that data transfer and simulation altogether take about 10 mins, otherwise these results are not of use to surgeons Assume simulation and data transfer (both ways) together takes 10 mins and data transfer takes 4 mins Leaves 6 mins for biomechanical simulation on remote HPC machines Assume biomechanical model is scalable i.e. better results achieved on higher number of processors Objective : Get simulation done in 6 mins Get maximum number of processors available within 6 mins Allow 4 mins to wait in the queue; this leaves 2 mins for actual simulation

29. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 29 Experiment Characteristics Flooding scheduler approach – experiment 1: Simultaneously submit 8, 16, 32, 64, 128 procs jobs to multiple clusters - SDSC DataStar, SDSC TG, NCSA TG, ANL TG, PSC TG When a higher count job starts (at any center) kill all the lower CPU count jobs at all the other centers Results : out of 1464 job submissions over ~7 days, only 6 failed giving success of 99.59%; 128 CPU jobs ran greater than 50% of time; at least 64 CPU jobs ran more than 80% of time Next slide gives time varying behavior with 6 hour intervals for this experiment 4 other experiments were performed by taking out some of the successful clusters as well as taking scheduler cycle time into account on DataStar As number of clusters were reduced, success rate goes down

30. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 30

31. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 31 4. Future : Near-continuous DDDAS

32. Universität Zürich San Diego Supercomputer Center Computational Radiology Laboratory Brigham & Women’s Hospital, Harvard Medical School SIAM PP06 – San Francisco 32 Current DDDAS vs. (future) near-continuous DDDAS Problem of current DDDAS: Using current DDDAS procedure, surgeon does not have near-continuous brain deformation info It takes more than 20 minutes to have whole 3d scan, segmentation, surface matching and FEM solution Solution is to extend to near continuous DDDAS: DDDAS approach to provide near-continuous closed loop registration updates using near-continuous 2D MRI slice scans