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Proof of concept studies for surface-based mechanical property reconstruction

Proof of concept studies for surface-based mechanical property reconstruction. Ashton Peters 1 , Lawrence A. Ray 2 , J. Geoffrey Chase 1 , Elijah E.W. Van Houten 1. 1. University of Canterbury, Christchurch, NZ 2. Eastman Kodak Company, Rochester, NY, USA. Introduction. Motivation.

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Proof of concept studies for surface-based mechanical property reconstruction

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  1. Proof of concept studies for surface-based mechanical property reconstruction Ashton Peters1, Lawrence A. Ray2, J. Geoffrey Chase1, Elijah E.W. Van Houten1 1. University of Canterbury, Christchurch, NZ 2. Eastman Kodak Company, Rochester, NY, USA

  2. Introduction Motivation • Breast cancer the most common cause of female cancer death in 1999[1] [1] NZ Ministry of Health, 2002

  3. Introduction Motivation • Breast cancer the most common cause of female cancer death in 1999[1] • Local stage diagnosis can increase survival rate to over 95%[2] [1] NZ Ministry of Health, 2002 [2] American Cancer Society, 2004

  4. Introduction Motivation • Breast cancer the most common cause of female cancer death in 1999[1] • Local stage diagnosis can increase survival rate to over 95%[2] • Current screening and diagnosis techniques • Mammography • Ultrasound • Magnetic Resonance (MR) Scanning [1] NZ Ministry of Health, 2002 [2] American Cancer Society, 2004

  5. Introduction Tissue Elastography • Krouskop et al. (1998) and Samani et al. (2003) found invasive ductal carcinoma to be stiffer than healthy breast tissue

  6. Introduction Tissue Elastography • Krouskop et al. (1998) and Samani et al. (2003) found invasive ductal carcinoma to be stiffer than healthy breast tissue • Elastography has basis in these findings

  7. Introduction Tissue Elastography • Krouskop et al. (1998) and Samani et al. (2003) found invasive ductal carcinoma to be stiffer than healthy breast tissue • Elastography has basis in these findings • Several novel methods currently being developed to take advantage of this contrast • MR Elastography • Ultrasound Elastography • Digital Image-based Elasto-Tomography (DIET)

  8. Introduction The DIET Process • DIET as a complete imaging solution

  9. Introduction The DIET Process • DIET as a complete imaging solution • Steps involved in the system

  10. Introduction The DIET Process • DIET as a complete imaging solution • Steps involved in the system • Actuate breast surface

  11. Introduction The DIET Process • DIET as a complete imaging solution • Steps involved in the system • Actuate breast surface • Capture surface images

  12. Introduction The DIET Process • DIET as a complete imaging solution • Steps involved in the system • Actuate breast surface • Capture surface images • Process to obtain surface motion

  13. Introduction The DIET Process • DIET as a complete imaging solution • Steps involved in the system • Actuate breast surface • Capture surface images • Process to obtain surface motion • Reconstruct internal stiffness

  14. Introduction The DIET Process • DIET as a complete imaging solution • Steps involved in the system • Actuate breast surface • Capture surface images • Process to obtain surface motion • Reconstruct internal stiffness • Lack of clinical data creates need for simulation

  15. Simulation of Clinical Data Finite Element Model • Finite Element Methods (FEM) used for simulation

  16. Simulation of Clinical Data Finite Element Model • Finite Element Methods (FEM) used for simulation • Current Model • Geometry • Material properties

  17. Simulation of Clinical Data Finite Element Model • Finite Element Methods (FEM) used for simulation • Current Model • Geometry • Material properties • Model Creation • Create geometry • Mesh model • Convert output to useable format

  18. Simulation of Clinical Data Computer Model cont.

  19. Simulation of Clinical Data Computer Model cont. • Boundary conditions • Chest wall • Internal faces • Actuation

  20. Simulation of Clinical Data Computer Model cont. • Boundary conditions • Chest wall • Internal faces • Actuation • Variations in model geometry • Tumor stiffness • Tumor location • Tumor size

  21. Simulation of Clinical Data Forward Solution • Using standard Finite Element techniques for forward solution

  22. Simulation of Clinical Data Forward Solution • Using standard Finite Element techniques for forward solution • Symmetrical banded forward solver written in Fortran

  23. Simulation of Clinical Data Forward Solution • Using standard Finite Element techniques for forward solution • Symmetrical banded forward solver written in Fortran • Size limit due to physical computer memory available

  24. Simulation of Clinical Data Motion Sampling

  25. Simulation of Clinical Data Motion Sampling • Surface motion sampling schemes • Random selection • All surface nodes

  26. Simulation of Clinical Data Motion Sampling • Surface motion sampling schemes • Random selection • All surface nodes • Addition of random noise to motion data • Magnitude • Distribution

  27. Parameter Reconstruction Dual Resolution • Requirement for reduced number of solution parameters

  28. Parameter Reconstruction Dual Resolution • Requirement for reduced number of solution parameters • Dual resolution techniques • Region-based assignment • Interpolated properties

  29. Parameter Reconstruction Dual Resolution • Requirement for reduced number of solution parameters • Dual resolution techniques • Region-based assignment • Interpolated properties • Coarse mesh details

  30. Parameter Reconstruction Dual Resolution • Requirement for reduced number of solution parameters • Dual resolution techniques • Region-based assignment • Interpolated properties • Coarse mesh details

  31. Parameter Reconstruction Background Theory • Nonlinear elastic property reconstruction

  32. Parameter Reconstruction Background Theory • Nonlinear elastic property reconstruction • Error term

  33. Parameter Reconstruction Background Theory • Nonlinear elastic property reconstruction • Error term • Reformulate as non-linear system of equations in order to minimise error term

  34. Parameter Reconstruction Iterative Solution • Using Gauss-Newton based iteration to solve

  35. Parameter Reconstruction Iterative Solution • Using Gauss-Newton based iteration to solve • Expanding gives the full iterative formulation

  36. Parameter Reconstruction Iterative Solution • Using Gauss-Newton based iteration to solve • Expanding gives the full iterative formulation • Regularisation applied to aid matrix inversion • Marquardt (1963) with modification • Joachimowicz et al. (1991)

  37. Parameter Reconstruction Algorithm Structure Capture real surface motion of breast (simulated)

  38. Parameter Reconstruction Algorithm Structure Guess the elastic properties within the breast volume Capture real surface motion of breast (simulated)

  39. Parameter Reconstruction Algorithm Structure Guess the elastic properties within the breast volume Capture real surface motion of breast (simulated) Simulate breast actuation and solve forward FE problem to output surface motions

  40. Parameter Reconstruction Algorithm Structure Guess the elastic properties within the breast volume Capture real surface motion of breast (simulated) Simulate breast actuation and solve forward FE problem to output surface motions Compare this motion with actual surface motion. Is the error small enough?

  41. Parameter Reconstruction Algorithm Structure Guess the elastic properties within the breast volume Capture real surface motion of breast (simulated) Simulate breast actuation and solve forward FE problem to output surface motions Compare this motion with actual surface motion. Is the error small enough? Update the internal elastic property guess using error between current and actual motion.

  42. Parameter Reconstruction Algorithm Structure Guess the elastic properties within the breast volume Capture real surface motion of breast (simulated) Simulate breast actuation and solve forward FE problem to output surface motions Compare this motion with actual surface motion. Is the error small enough? Update the internal elastic property guess using error between current and actual motion. SOLVED

  43. Results Three-Region Model • Simple region-based geometric property assignment

  44. Results Three-Region Model • Simple region-based geometric property assignment • Reconstructed results

  45. Results Three-Region Model • Simple region-based geometric property assignment • Reconstructed results • Limitations of reconstructive model

  46. Results 20-Region Model • Same surface motion as three-region model

  47. Results 20-Region Model • Same surface motion as three-region model • More freedom within reconstructive model

  48. Results More Recent Cases • Increasing coarse mesh resolution

  49. Results More Recent Cases • Increasing coarse mesh resolution • Problems with accuracy of model emerging

  50. Results More Recent Cases • Increasing coarse mesh resolution • Problems with accuracy of model emerging • Possibly effects of borderline stability in mathematics

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