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Using Topological Data Analysis to Study Glandular Architecture Brittany Terese Fasy School of Computing, Montana State University 2 October 2016 TDA-Bio Workshop Seattle, Washington B. Fasy (MSU) TDA for Glandular Architecture 2 October

  1. Using Topological Data Analysis to Study Glandular Architecture Brittany Terese Fasy School of Computing, Montana State University 2 October 2016 TDA-Bio Workshop Seattle, Washington B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 1 / 22

  2. Joint Work With Carola Wenk (Tulane, CS) J. Quincy Brown (Tulane, BME) 0 NSF DMS / NIH Planning Grant: 1557716 (MSU) and 1557750 (Tulane) B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 2 / 22

  3. Joint Work With Carola Wenk (Tulane, CS) J. Quincy Brown (Tulane, BME) Andrew Sholl (Tulane Med) John Sheppard (MSU, CS) Brian Summa (Tulane, CS) 0 NSF DMS / NIH Planning Grant: 1557716 (MSU) and 1557750 (Tulane) B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 2 / 22

  4. Joint Work With Carola Wenk (Tulane, CS) J. Quincy Brown (Tulane, BME) Andrew Sholl (Tulane Med) John Sheppard (MSU, CS) Brian Summa (Tulane, CS) Pete Lawson (Tulane, BME) Eric Berry (MSU, Math) Sush Majhi (Tulane, Math) Alan Cleary (MSU, CS) Sawyer Payne(MSU, CS Undergrad) 0 NSF DMS / NIH Planning Grant: 1557716 (MSU) and 1557750 (Tulane) B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 2 / 22

  5. The Problem: Qualitative Diagnosis and Prognosis Prostate Cancer The Question is Will He Outlive It? More than 225 , 000 cases per year (USA). One is seven men will be diagnosed. Treatments: surgery, chemo, radiation, harmone therapy. Either slowly-growing and benign or fast-growing and dangerous. Surgery / radiation benefits questionable for SG/B. Surgery / radiation side effects not desirable. ... therefore, active surveillance. B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 3 / 22

  6. The Problem: Qualitative Diagnosis and Prognosis Prostate Cancer Diagnosis PCA B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 4 / 22

  7. The Problem: Qualitative Diagnosis and Prognosis Prostate Cancer Diagnosis 2+2 3+3 Surveillance 3+4 PCA 4+3 4+4 Radical 5+4 5+5 B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 4 / 22

  8. The Problem: Qualitative Diagnosis and Prognosis Prostate Cancer Diagnosis 2+2 3+3 Surveillance 2+2 3+4 PCA 3+3 4+3 3+4 4+4 Radical 4+3 5+4 4+4 5+5 5+4 5+5 B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 4 / 22

  9. The Problem: Qualitative Diagnosis and Prognosis Prostate Cancer Diagnosis 2+2 3+3 Surveillance PCA 2+2 3+4 PCA 3+3 4+3 S.M. 3+4 4+4 Radical Other 4+3 5+4 Treatment 4+4 5+5 5+4 Age 5+5 B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 4 / 22

  10. The Problem: Qualitative Diagnosis and Prognosis Biopsy and Prostectmy Slides How to Describe Glandular Architecture B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 5 / 22

  11. The Problem: Qualitative Diagnosis and Prognosis Gleason Grading Grade 1: well-defined, nicely packed Grade 2: larger, more tissue, less uniform Grade 3: less defined glands, some cribriform Grade 4: fused glands, open lumens Grade 5: no glandular definition, sheets of cells 0 Donald Gleason, 1966, image from The Gleason Grading System: A Complete Guide for Pathologist and Clinicians by Eppstein B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 6 / 22

  12. The Problem: Qualitative Diagnosis and Prognosis Gleason Grading Grade 1: well-defined, nicely packed Grade 2: larger, more tissue, less uniform Grade 3: less defined glands Grade 4: fused glands, open lumens, cribriform Grade 5: no glandular definition, sheets of cells 0 2005 Consensus, image from The Gleason Grading System: A Complete Guide for Pathologist and Clinicians by Eppstein B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 6 / 22

  13. The Problem: Qualitative Diagnosis and Prognosis Learning to Grade The Gleason Grading System: A Complete Guide for Pathologists and Clinicians B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 7 / 22

  14. The Problem: Qualitative Diagnosis and Prognosis Glandular Architecture Discrete-vs-Fused Glands Gleason 3 Discrete glands. Gleason 4 Presence of fused glands. 0 Image source: Eppstein, The Gleason Grading System B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 8 / 22

  15. The Problem: Qualitative Diagnosis and Prognosis Glandular Architecture Cribriform Pattern Gleason 4 A gland with numerous small holes. 0 Image source: Eppstein, The Gleason Grading System B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 9 / 22

  16. The Problem: Qualitative Diagnosis and Prognosis Glandular Architecture Glomeruloid Structures Gleason 3,4 Intraluminal cribriform, single point of attachment. 0 Image source: http://www.nature.com/modpathol/journal/v17/n3/fig_tab/3800050f9.html B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 10 / 22

  17. The Problem: Qualitative Diagnosis and Prognosis Glandular Architecture Telescoping Glands Gleason 3 Telescoping (gland in gland) may mimic Glumeroid. Gleason 4 Actual glumeroid pattern. 0 Image source: Eppstein, The Gleason Grading System B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 11 / 22

  18. The Problem: Qualitative Diagnosis and Prognosis Glandular Architecture Distribution of Glandular Shape and Size Gleason 1 Uniform distribution of gland size. Round. Gleason 3 Irregularly separated glands. Gleason 4 Poorly formed glands. 0 Image source: Eppstein, The Gleason Grading System B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 12 / 22

  19. Methods: TDA Persistent Homology ? = B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 13 / 22

  20. Methods: TDA Persistent Homology ? = B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 13 / 22

  21. Methods: TDA Quantifying the Process TDA B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 14 / 22

  22. Methods: TDA Quantifying the Process TDA B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 14 / 22

  23. Methods: TDA Quantifying the Process TDA B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 14 / 22

  24. Methods: TDA Quantifying the Process TDA Death Birth B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 14 / 22

  25. Methods: TDA Quantifying the Process TDA Death Birth B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 14 / 22

  26. Methods: TDA Quantifying the Process TDA Death Death Birth Birth B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 14 / 22

  27. Methods: TDA Quantifying the Process TDA Death Death 100 120 0 20 40 60 80 Birth (Birth + Death)/2 Birth B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 14 / 22

  28. Methods: TDA Functional and Vectorized Summaries Death 100 120 0 20 40 60 80 Birth (Birth + Death)/2 B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 15 / 22

  29. Methods: TDA Aside: Hypothesis Testing Upcoming Paper The Euler Characteristic curve seems to be the most discriminating among the functional summaries when using the Hotelling Test a . a Joint work with Jessi Cisewski, Wojciech Hellwing, Mark Lovell, Alessandro Rinaldo, Larry Wasserman, Mike Wu B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 16 / 22

  30. Methods: TDA Collaboration B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 17 / 22

  31. Results: Towards Classification Comparing Purely Graded Images Initial Results 4 4 0 4 4 4 3 3 3 3 4 4 3 −3 44 3 4 3 3 4 4 3 3 5 −6 4 5 5 55 5 3 5 5 −9 −20 −15 −10 −5 0 5 B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 18 / 22

  32. Other Problems: Analyzing DeBruijn Graphs Joint work with Alan Cleary and Brendan Mumey CTGAACAGCTAGCAGTAGTGTAGGG B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 19 / 22

  33. Other Problems: Analyzing DeBruijn Graphs Joint work with Alan Cleary and Brendan Mumey CTGAACAGCTAGCAGTAGTGTAGGG GTG AGG GGG TAT CTG GTA TGA AGT GAA AAC GCA TAG CAG CTA AGC GCT B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 19 / 22

  34. Other Problems: Analyzing DeBruijn Graphs Joint work with Alan Cleary and Brendan Mumey CTGAACAGCTAGCAGTAGTGTAGGG GTG AGG GGG TAT CTG GTA TGA AGT GAA AAC GCA TAG CAG CTA AGC GCT B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 19 / 22

  35. Other Problems: Analyzing DeBruijn Graphs Joint work with Alan Cleary and Brendan Mumey CTGAACAGCTAGCAGTAGTGTAGGG GTG AGG GGG TAT CTG GTA TGA AGT GAA AAC GCA TAG CAG CTA AGC GCT B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 19 / 22

  36. Other Problems: Analyzing DeBruijn Graphs Joint work with Alan Cleary and Brendan Mumey CTGAACAGCTAGCAGTAGTGTAGGG GTG AGG GGG TAT CTG GTA TGA AGT GAA AAC GCA TAG CAG CTA AGC GCT B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 19 / 22

  37. Other Problems: Analyzing DeBruijn Graphs Joint work with Alan Cleary and Brendan Mumey CTGAACAGCTAGCAGTAGTGTAGGG GTG AGG GGG TAT CTG GTA TGA AGT GAA AAC GCA TAG CAG CTA AGC GCT B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 19 / 22

  38. Other Problems: Analyzing DeBruijn Graphs Joint work with Alan Cleary and Brendan Mumey CTGAACAGCTAGCAGTAGTGTAGGG GTG AGG GGG TAT CTG GTA TGA AGT GAA AAC GCA TAG CAG CTA AGC GCT B. Fasy (MSU) TDA for Glandular Architecture 2 October 2016 19 / 22

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