1. Developing Anatomically Realistic Biomechanical Models of the Breast: Tracking Breast Cancer Across Medical Images Presenting Author: V. Rajagopal Auckland Bioengineering Institute University of Auckland, NZ BMSW 2008, Bangalore, India

2. Overview  Why study breast biomechanics?  Challenges in modelling breast biomechanics.  Our modelling framework  Testing the modeling framework o Controlled Validation: Silicon gel studies o Clinical Validation: Tracking tissue deformation across breast MRI  Conclusions and ongoing work

3. Why model breast biomechanics?  “Mammograms: Room for Improvement Cited” – American Cancer Society (11/06/2004)  Interpretation of mammograms  Mammograms miss up to 17% of tumours  Experience an important factor  Move towards imaging using many modalities.

4. Why study breast biomechanics?  Breast in different positions under varying degrees of compression in different modalities.  Map between modalities to use information from all these images.  Individual-specific finite element breast models will aid the information fusion process. CC View MLO View

5. Challenges in modelling breast biomechanics  Determining the reference state. o Accurate representation of reference state is essential for prediction of gravity loaded deformations. o All images of the breast taken under some kind of loading condition.  Characterization of mechanical properties. o Skin, fat, fibro-glandular tissue, Cooper’s ligaments  Boundary conditions. o Need to determine how the breast tissue is attached to the muscle and ribs  Loading conditions. o Gravity (for MR imaging and biopsies) o Mammographic compression o Indentation (for ultrasound)

6. Our Modelling Framework  Open source modelling software, CMISS 1.  Individual-specific breast geometries using slope continuous (cubic-Hermite) basis functions.  Large deformation finite elasticity theory.  Individual-specific biomechanical properties o Regional variation of mechanical properties 1.CMISS website: www.cmiss.orgwww.cmiss.org

7.  The main question:  How accurately can a patient-specific finite element model of the breast predict tissue movement?  Complex interactions between various parameters of a finite element model make it difficult to perform controlled experiments for systematic validation.  Gel phantoms allow us to validate specific modelling features in a controlled manner:  A custom designed mould used to make the gel, provides us with an accurate representation of the reference state.  We can design the phantom to have a specific set of boundary conditions.  We can design the phantom to have varying degrees of in- homogeneity.  We can impose a known set of loading conditions  Can we accurately predict the deformed state of a homogeneous body? Controlled Validation: Silicon gel studies

8. Can we model a homogeneous body?  Homogeneous gel was created with six polyethylene markers positioned inside the gel.  The gel was imaged using MRI while still in the mould. This gave coordinates of markers in undeformed state.  The gel was then MR imaged while positioned on its flat end (supine) and then at a 20 degree angle to the base (20 SI). Locations of the markers in these deformed state were recorded. supine 20 SI undeformed Supero-inferior direction (SI) Medio-lateral direction through the slide (ML)

9. Can we model a homogeneous body? 10 SI 30 SI 5 ML 10 ML  The gel surface at six different orientations (two of them being the MR imaged orientations) were laser scanned.  The neo-Hookean constitutive relation can be used to model the silicon gel: W = c 1 (I 1 -3). I 1 is an invariant measure of strain.  We can find the optimal value of c 1 that minimises the error between predicted surface deformation and experimentally measured gravity loaded deformed surface scan.  30 SI deformed state was used to estimate the mechanical properties of the gel.

10. Can we model a homogeneous body? Surface RMS error in predicting deformed state with strain energy function W = c 1 (I1- 3) for c 1 =0.6 kPa ranged between 1.2 mm and 1.7 mm. Distances between predicted location of internal markers and actual location were on average 0.44 mm (supine) and 1.9 mm (20 SI). Figure on right shows predicted locations (brown) next to actual (blue). Yes we can model the deformations of a homogeneous gel.

11. Clinical Validation: Tracking tissue deformation across breast MRI  Pilot study to assess predictions of breast shape in the prone orientation under gravity using MR images o Addressed two aspects of model development in this study:  Determining the unloaded configuration.  Obtaining individual-specific biomechanical properties.

12. The Unloaded Configuration  Previous studies typically used prone gravity-loaded configuration as the reference state. o May lead to large errors in simulation predictions  The unloaded state is also ideal to assimilate information from different imaging modalities.  Can be obtained in two ways: o Experimentally by immersing the breast in a liquid that has a similar density. o Computationally from a given set of loading conditions and deformed configurations.

13. Neutral Buoyancy Imaging  We have developed a computational technique 1 to compute the unloaded state.  We obtained images of the breast immersed in water as an estimate of the reference state.  These images are useful to validate the computation technique and assess the importance of the reference state 2. 1.Rajagopal, V., et al.: In IJNME 2.Rajagopal, V. et al: In MICCAI 2007 Workshop on Computational Biomechanics in Medicine. 44.8 mm 61.7 mm

14. Individual-Specific Breast Geometry Code 1 developed to create individual-specific breast finite element geometries. 1. Rajagopal, V.: PhD thesis, University of Auckland (2007) RMS Errors: 0.78 mm in fitting skin contour 1.20 mm in fitting muscle contour

15. Loading and Boundary Conditions  Gravity loading was applied to the neutral buoyancy model to predict prone configuration.  Breast was assumed to be firmly attached to the chest wall.  Simulations driven mostly by the loading conditions alone.

16. Individual-Specific Mechanical Properties  Following previous studies 1, breast was assumed to be homogeneous, incompressible and isotropic.  Stress-strain relation modelled by neo-Hookean relation: W = c 1 (I 1 -3).  Breast tissue mechanical properties vary significantly between individuals 2.  Used material parameter optimization techniques 3 to estimate the value of c 1. 1.Ruiter, N., Stotzka, R.: In IEEE Trans. on Nucl. Sci. 53(1), 204–211 (2006) 2.Sarvazyan, A., et al: In Acous Imag. 21, 223–240 (1995) 3.Rajagopal, V.: PhD thesis, University of Auckland (2007)

17. Predicting the Prone Gravity-Loaded Configuration – Volunteer No. 1 Tissue region1234 Displacement (mm)5.0620.4719.021.7 Euclidean error (mm)1.564.824.513.97 C 1 Value = 0.08 kPa, 4.2 mm RMS error in predicting skin configuration

18. Predicting the Prone Gravity-Loaded Configuration – Volunteer No. 2 Tissue region1234 Displacement (mm)22.315.115.026.3 Euclidean error (mm)4.33.664.336.55 C 1 Value = 0.13 kPa, 3.6 mm RMS error in predicting skin configuration

19. Conclusions and ongoing work  Our modelling framework uses individual-specific biomechanical properties and breast geometries.  First estimates of the unloaded state.  Gross characteristics of the deformed configuration are captured.  Boundary conditions and heterogeneity of breast tissues must be further investigated for improving accuracy.

20. Conclusions and ongoing work  Simulation of breast deformation under mammographic compression 1,2 1.Chung, J., et al: In: Proceedings of SPIE (Medical Imaging). Volume 5746. (2005) 817-824 2.Chung, J., et al.: In: Biomech. Model. Mechanobiol.

21. Application to Image Warping

23. Ongoing work  Assess ability of our FE model to match internal deformations using image comparison metrics  Develop techniques to customise the geometry and material properties of the inhomogeneous breast tissues  Incorporate images from mammography and ultrasound into the biophysically based model of the breast  Develop techniques to enable images from multiple modalities to be viewed and interpreted in a common unloaded state with the finite element model

24. Acknowledgments Auckland Bioengineering Institute, NZ Angela LeeA/Prof Poul NielsenA/Prof Martyn Nash Jae-Hoon Chung Dr Ruth Warren Addenbrooke’s Hospital, Cambridge, UK Highnam Associates Ltd, NZ UCL Center for Image Computing, UK Dr Ralph Highnam Prof. David Hawkes

25. Acknowledgments Our Website: http://www.bioeng.auckland.ac.nz/projects/breast-mechanics