1. Computational Radiology Laboratory Harvard Medical School www.crl.med.harvard.edu Brigham and Women’s Hospital Children’s Hospital Boston Massachusetts A validation framework for brain tumor segmentation Neculai Archip, Ph.D. Harvard Medical School

2. Computational Radiology Laboratory. Slide 2 Outline Brain image database; Existent segmentation data; STAPLE; How to validate a new algorithm; Performance study.

3. Computational Radiology Laboratory. Slide 3 Macro- pathology Provided by Kate Drummond Surgical hypothesis: Total resection of low grade glioma prevents progression to high grade glioma. Segmentation critical for preoperative planning, intraoperative targeting, and postoperative assessment.

4. Computational Radiology Laboratory. Slide 4 Motivation of Brain Tumor Segmentation: Augmented Visualization in Image Guided Neurosurgery Acquire MRI, DT-MRI, fMRI preoperatively –Plan intervention –Enhance tumor visualization –Better perceive critical healthy structures Align preoperative data with intra-operative configuration of patient

5. Computational Radiology Laboratory. Slide 5 Brain Image database Acquisition information: –10 SPGR T1 –POST GAD resolution: 256x256x124 –pixel size: 0.9375 x 0.9375 mm –slice thickness: 1.5 mm –slice gap: 0.0 mm –acquisition order: LR case tumorlocation slice 1 meningioma left frontal 44 2 meningiomaleft parasellar 58 3 meningiomaright parietal 78 4 low grade gliomaleft frontal 35 5 astrocytomaright frontal 92 6 low grade gliomaright frontal 81 7 astrocytomaright frontal 92 8 astrocytomaleft temporal 39 9 astrocytomaleft frontotemporal 31 10 low grade gliomaleft temporal 35

6. Computational Radiology Laboratory. Slide 6 Existent segmentation data Manual segmentation performed by 4 independent experts low grade glioma Expert 1Expert 2 Expert 3 Expert 4 Original Image

7. Computational Radiology Laboratory. Slide 7 One automatic segmentation algorithm Kaus et al. – “Adaptive Template Moderated Brain Tumor Segmentation in MRI”, Radiology. 2001;218:586-591 Segmented images Registration Statistical Classification Template Distance Transforms Brain atlas Grey value images Original tumor image Tumor segmentation performed by Kaus’ method

8. Computational Radiology Laboratory. Slide 8 Validation of Image Segmentation Spectrum of accuracy versus realism in reference standard. Digital phantoms. –Ground truth known accurately. –Not so realistic. Acquisitions and careful segmentation. –Some uncertainty in ground truth. –More realistic. Autopsy/histopathology. –Addresses pathology directly; resolution. Clinical data ? –Hard to know ground truth. –Most realistic model.

9. Computational Radiology Laboratory. Slide 9 Validation of Image Segmentation Comparison to digital and physical phantoms: –Excellent for testing the anatomy, noise and artifact which is modeled. –Typically lacks range of normal or pathological variability encountered in practice.

10. Computational Radiology Laboratory. Slide 10 Comparison To Higher Resolution MRIPhotographMRI Provided by Peter Ratiu and Florin Talos.

11. Computational Radiology Laboratory. Slide 11 Validation of Image Segmentation Comparison to expert performance; to other algorithms: What is the appropriate measure for such comparisons ? Our new approach: Simultaneous estimation of hidden ``ground truth’’ and expert performance. Enables comparison between and to experts. Can be easily applied to clinical data exhibiting range of normal and pathological variability.

12. Computational Radiology Laboratory. Slide 12 STAPLE STAPLE (Simultaneous Truth and Performance Level Estimation): –An algorithm for estimating performance and ground truth from a collection of independent segmentations. –Warfield, Zou, Wells MICCAI 2002. –Warfield, Zou, Wells, IEEE TMI 2004.

13. Computational Radiology Laboratory. Slide 13 Estimation Problem Complete data density: Binary ground truth T i for each voxel i. Expert j makes segmentation decisions D ij. Expert performance characterized by sensitivity p and specificity q. –We observe expert decisions D. If we knew ground truth T, we could construct maximum likelihood estimates for each expert’s sensitivity (true positive fraction) and specificity (true negative fraction):

14. Computational Radiology Laboratory. Slide 14 Expectation-Maximization Since we don’t know ground truth T, treat T as a random variable, and solve for the expert performance parameters that maximize: Parameter values θ j =[p j q j ] T that maximize the conditional expectation of the log-likelihood function are found by iterating two steps: –E-step: Estimate probability of hidden ground truth T given a previous estimate of the expert quality parameters, and take expectation. –M-step: Estimate expert performance parameters by comparing D to the current estimate of T.

15. Computational Radiology Laboratory. Slide 15 Validation of a new algorithm 4 manual segmentations 1 automatic segmentation STAPLE Output of a new segmentation algorithm Performance assessment + Ground truth

16. Computational Radiology Laboratory. Slide 16 A new algorithm Spectral clustering algorithms: –Shi and Malik 2000 NCUT criterion –Ng, Jordan and Weiss 2002 Supervised clustering using k eigenvectors –Miela and Shi 2002 Supervised clustering – connection with Markov Chains –Fowlkes, Belongie, Chung, Malik 2004 Nyström method – spine segmentation from MRI Fiedler eigenvector based segmentation: –Archip et al. 2005. Related approached used in seriation and the consecutive ones problems.

17. Computational Radiology Laboratory. Slide 17 Segmentation as weighted graph partitioning Pixels i I = vertices of graph G Edges ij = pixel pairs with S ij > 0 Similarity matrix S = [ S ij ] Given a partition (A,B) of the vertex set V

18. Computational Radiology Laboratory. Slide 18 Optimize NCUT an approximation is obtained by solving the generalized eigenvalue problem for the second smallest generalized eigenvector.

19. Computational Radiology Laboratory. Slide 19 The algorithm P = D-S P sparse Py= λy Lanczos used for efficiency λ1, λ2 first 2 eigenvalues –λ1 =1; use λ2 instead y1,y2 first 2 eigenvectors –y2 – Fiedler eigenvector

20. Computational Radiology Laboratory. Slide 20 Use Fiedler eigenvector to segment the image Sort Fiedler eigenvector with the permutation Apply to the image pixels vector The new image vector Split into compact blocks s.t. components similarity Complete segmentation – interactively select the cluster of interest.

21. Computational Radiology Laboratory. Slide 21 Tumor Segmentation Evaluation 1234Kaus Fiedler based pj 0.8670.9780.9710.9080.9780.956 qj 0.9991.0000.9980.9991.0000.998 Tumor region Experts STAPLE Kaus Fiedler based

22. Computational Radiology Laboratory. Slide 22 Conclusions Framework for the validation of brain tumor segmentation: image + software. STAPLE public available. Image and segmentation data will be made public available. Existent data to be added to the image database.

23. Computational Radiology Laboratory. Slide 23 Acknowledgements Simon K. Warfield. Peter M. Black. Alexandra Golby. Ferenc A. Jolesz. Ron Kikinis. Lawrence Panych. Kelly H. Zou. Steve Haker. Vicente Grau-Colomer. Olivier Clatz Herve Delingette Nicholas Ayache Martha Shenton. Clare Tempany. Carl Winalski. Michael Kaus. William M. Wells. Andrea Mewes. Heidelise Als. Petra Huppi. Terrie Inder. Contributors to this research: www.crl.med.harvard.edu