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

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

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

 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 Introduction Motivation [1] NZ Ministry of Health, 2002 [2] American Cancer Society, 2004

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

 DIET as a complete imaging solution Introduction The DIET Process

 DIET as a complete imaging solution  Steps involved in the system Introduction The DIET Process

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

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

 Finite Element Methods (FEM) used for simulation Simulation of Clinical Data Finite Element Model

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

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

Simulation of Clinical Data Computer Model cont.

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

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

 Using standard Finite Element techniques for forward solution Simulation of Clinical Data Forward Solution

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

Simulation of Clinical Data Motion Sampling

 Surface motion sampling schemes Simulation of Clinical Data Motion Sampling  Random selection  All surface nodes

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

 Requirement for reduced number of solution parameters Parameter Reconstruction Dual Resolution

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

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

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

 Nonlinear elastic property reconstruction Parameter Reconstruction Background Theory

 Nonlinear elastic property reconstruction  Error term Parameter Reconstruction Background Theory

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

 Using Gauss-Newton based iteration to solve Parameter Reconstruction Iterative Solution

 Using Gauss-Newton based iteration to solve  Expanding gives the full iterative formulation 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) Parameter Reconstruction Iterative Solution

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

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

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

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

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

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

 Simple region-based geometric property assignment Results Three-Region Model

 Simple region-based geometric property assignment  Reconstructed results Results Three-Region Model

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

 Same surface motion as three-region model Results 20-Region Model

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

 Increasing coarse mesh resolution Results More Recent Cases

 Increasing coarse mesh resolution  Problems with accuracy of model emerging Results More Recent Cases

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

 Increasing coarse mesh resolution  Problems with accuracy of model emerging Results More Recent Cases  Possibly effects of borderline stability in mathematics  Compressibility of model becoming important

 Rewrite Fortran code in parallel for Beowulf cluster Conclusion Current Challenges

 Rewrite Fortran code in parallel for Beowulf cluster  Availability of real world data sets Conclusion Current Challenges

 Rewrite Fortran code in parallel for Beowulf cluster  Availability of real world data sets  Radius-based and other methods of regularisation Conclusion Current Challenges

 Rewrite Fortran code in parallel for Beowulf cluster  Availability of real world data sets  Radius-based and other methods of regularisation  Investigation of incompressible finite element model Conclusion Current Challenges

 Rewrite Fortran code in parallel for Beowulf cluster  Availability of real world data sets  Radius-based and other methods of regularisation  Investigation of incompressible finite element model  Acknowledgements Conclusion Current Challenges