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Placental Vessel Extraction with Shearlets, Laplacian Eigenmaps, and a Conditional Generative Adversarial Network

  • Catalina AnghelEmail author
  • Kellie Archer
  • Jen-Mei Chang
  • Amy Cochran
  • Anca Radulescu
  • Carolyn M. Salafia
  • Rebecca Turner
  • Karamatou Yacoubou Djima
  • Lan Zhong
Chapter
Part of the Association for Women in Mathematics Series book series (AWMS, volume 14)

Abstract

The placenta is the key organ of maternal–fetal interactions, where nutrient, oxygen, and waste transfer take place. Differences in the morphology of the placental chorionic surface vascular network (PCSVN) have been associated with developmental disorders such as autism, hinting that the PCSVN could potentially serve as a biomarker for early diagnosis and treatment of autism. Studying PCSVN features in large cohorts requires a reliable and automated mechanism to extract the vascular networks. This paper presents two distinct methods for PCSVN enhancement and extraction. Our first algorithm, which builds upon a directional multiscale mathematical framework based on a combination of shearlets and Laplacian eigenmaps, is able to intensify the appearance of vessels with high success in high-contrast images such as those produced in CT scans. Our second algorithm, which applies a conditional generative adversarial neural network (cGAN), was trained to simulate a human-traced PCSVN given a digital photograph of the placental chorionic surface. This method surpasses any existing automated PCSVN extraction methods reported on digital photographs of placentas. We hypothesize that a suitable combination of the two methods could further improve PCSVN extraction results and should be studied in the future.

Keywords

Placenta Autism Vascular networks Shearlets Wavelets Laplacian eigenmaps Neural networks Deep learning cGAN Generative models 

Notes

Acknowledgements

The project was part of the MBI Women Advancing Mathematical Biology: Understanding Complex Biological Systems with Mathematics 2017 Workshop organized by the Association for Women in Mathematics. Funding for the workshop was provided by MBI, NSF ADVANCE “Career Advancement for Women Through Research-Focused Networks” (NSF-HRD 1500481), Society for Mathematical Biology, and Microsoft Research.

Over the course of the project, we received biology expertise and support from Drs. Ruchit Shah, George Merz, and Richard K. Miller.

The authors also wish to thank the following people who contributed to the collection of the placentas in the National Children’s Study Placenta Consortium: C.J. Stodgell, L. Salamone, L.I. Ruffolo, A. Penmetsa, P. Weidenborner (University of Rochester), J. Culhane, S. Wadlinger, M. Pacholski, M.A. Kent, L. Green (University of Pennsylvania), R. Wapner, C. Torres, J. Perou (Columbia University), P. Landrigan, J. Chen, L. Lambertini, L. Littman, P. Sheffield, A. Golden, J. Gilbert, C. Lendor, S. Allen, K. Mantilla, Y. Ma (Ichan School of Medicine), S. Leuthner, S. Szabo (Medical College of Wisconsin), J.L. Dalton, D. Misra (Placental Analytics), N. Thiex, K.Gutzman, A. Martin, B. Specker (South Dakota University), J. Swanson, C. Holliday, J. Butler (University of California at Irvine), A. Li, R.M.A.P.S. Dassanayake, J. Nanes, Y. Xia (University of Illinois at Chicago), J.C. Murray, T.D. Busch, J. Rigdon (University of Iowa), Kjersti Aagaard, A. Harris (Baylor College of Medicine), T.H. Darrah, E. Campbell (Boston University), N. Dole, J. Thorp, B. Eucker, C. Bell (University of North Carolina at Chapel Hill), E.B. Clark, M.W. Varner, E. Taggart, J. Billy, S. Stradling, J. Leavitt, W. Bell, S. Waterfall (University of Utah), B. O’Brien, M. Layton, D. Todd, K. Wilson, M.S. Durkin, M.-N. Sandoval (Westat, Inc).

Most importantly, we thank the study participants who donated their placentas.

References

  1. 1.
    N. Almoussa, B. Dutra, B. Lampe, P. Getreuer, T. Wittman, C. Salafia, L. Vese, Automated vasculature extraction from placenta images, in Proceedings of SPIE Medical Imaging Conference, vol. 7962, 2011Google Scholar
  2. 2.
    M. Belkin, P. Niyogi, Laplacian Eigenmaps for dimensionality reduction and data representation. Neural Comput. 15, 1373–1396 (2002)CrossRefGoogle Scholar
  3. 3.
    P. Burt, E. Adelson, The Laplacian pyramid as a compact image code. IEEE Trans. Commun. 31, 532–540 (1983)CrossRefGoogle Scholar
  4. 4.
    E. Candès, L. Demanet, D. Donoho, L. Ying, Fast discrete curvelet transforms. Multiscale Model. Simul. 5(3), 861–899 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    J.-M. Chang, N. Huynh, M. Vasquez, C. Salafia, Vessel enhancement with multi-scale and curvilinear filer matching for placenta images, in Proceeding of the 2013 20th International Conference on Systems, Signals and Image Processing (IWSSIP), 2013, pp. 125–128Google Scholar
  6. 6.
    J.-M. Chang, H. Zeng, Y.-M. Chang, R. Shah, C. Salafia, C. Newschaffer, R. Miller, P. Katzman, M.-F. Moye, C. Walker, L. Croen, Autism risk classification using placental chorionic surface vascular network features. BMC Med. Inform. Decis. Mak. 17(1), 162 (2017)Google Scholar
  7. 7.
    F.R.K. Chung, Spectral Graph Theory (American Mathematical Society, Providence, 1997)zbMATHGoogle Scholar
  8. 8.
    R. Coifman, Y. Meyer, V. Wickerhauser, Adapted wave form analysis, wavelet-packets and applications, in Proceedings of the second International Conference on Industrial and Applied Mathematics, ICIAM 91 (Society for Industrial and Applied Mathematics, Philadelphia, 1992), pp. 41–50Google Scholar
  9. 9.
    W. Czaja, M. Ehler, Schrödinger Eigenmaps for the analysis of bio-medical data. CoRR, abs/1102.4086, 2011Google Scholar
  10. 10.
    I. Daubechies, Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41(7), 909–996 (1988)MathSciNetCrossRefGoogle Scholar
  11. 11.
    M. Do, M. Vetterli, Contourlets: a directional multiresolution image representation, in ICIP (1), 2002, pp. 357–360Google Scholar
  12. 12.
    M. Egbor, T. Ansari, N. Morris, C.J. Green, P.D. Sibbons, Morphometric placental villous and vascular abnormalities in early- and late-onset pre-eclampsia with and without fetal growth restriction. J. Obstet. Gynecol. 113(5), 580–589 (2006)Google Scholar
  13. 13.
    E. Farnell, S. Farnell, J.-M. Chang, M. Hoffman, R. Belton, K. Keaty, S. Lederman, C. Salafia, A shape-context model for matching placental chorionic surface vascular networks. Image Anal. Stenogr. 37(1), 55–62 (2018)MathSciNetCrossRefGoogle Scholar
  14. 14.
    A.F. Frangi, W.J. Niessen, K.L. Vincken, M.A. Viergever, Multiscale Vessel Enhancement Filtering (Springer, Berlin, 1998)CrossRefGoogle Scholar
  15. 15.
    I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y. Bengio, Generative adversarial nets, in Advances in Neural Information Processing Systems, vol. 27, ed. by Z. Ghahramani, M. Welling, C. Cortes, N.D. Lawrence, K.Q. Weinberger (Curran Associates, Inc., Red Hook, 2014), pp. 2672–2680Google Scholar
  16. 16.
    I. Goodfellow, Y. Bengio, A. Courville, Deep Learning (MIT press, Cambridge, 2016)zbMATHGoogle Scholar
  17. 17.
    K. Guo, D. Labate, Optimally sparse multidimensional representation using shearlets. SIAM J. Math. Anal. 39(1), 298–318 (2007)MathSciNetCrossRefGoogle Scholar
  18. 18.
    E. Haeussner, C. Schmitz, H.G. Frank, F.E. von Koch, Novel 3D light microscopic analysis of IUGR placentas points to a morphological correlate of compensated ischemic placental disease in humans. Sci. Rep. 6, 24004 (2016)CrossRefGoogle Scholar
  19. 19.
    J. Ham, D. Lee, S. Mika, B. Schölkopf, A kernel view of the dimensionality reduction of manifolds, in Proceedings of the Twenty-first International Conference on Machine Learning, ICML ’04 (ACM, New York, 2004), pp. 47–55Google Scholar
  20. 20.
    S. Ioffe, C. Szegedy, Batch normalization: accelerating deep network training by reducing internal covariate shift, in International Conference on Machine Learning, 2015, pp. 448–456Google Scholar
  21. 21.
    P. Isola, J.-Y. Zhu, T. Zhou, A.A. Efros, Image-to-image translation with conditional adversarial networks, in CVPR, 2017Google Scholar
  22. 22.
    P. Jarmuzek, M. Wielgos, D.A. Bomba-Opon, Placental pathologic changes in gestational diabetes mellitus. Neuroendocrinol. Lett. 36(2), 101–105 (2015)Google Scholar
  23. 23.
    D. Labate, W.-Q. Lim, G. Kutyniok, G. Weiss, Sparse multidimensional representation using shearlets. Opt. Photon. 2005, 59140U (2005)Google Scholar
  24. 24.
    T.S. Lee, Image representation using 2D Gabor wavelets. IEEE Trans. Pattern Anal. Mach. Intell. 18(10), 959–971 (1996)CrossRefGoogle Scholar
  25. 25.
    J. Lee, M. Verleysen, Nonlinear Dimensionality Reduction, 1st edn. (Springer, New York, 2007)CrossRefGoogle Scholar
  26. 26.
    S. Mallat, A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989)CrossRefGoogle Scholar
  27. 27.
    L. Matelski, J. Van de Water, Risk factors in autism: thinking outside the brain. J. Autoimmun. 67, 1–7 (2016)CrossRefGoogle Scholar
  28. 28.
    A. Modabbernia, E. Velthorst, A. Reichenberg, Environmental risk factors for autism: an evidence-based review of systematic reviews and meta-analyses. Mol. Autism 8, 13 (2017)CrossRefGoogle Scholar
  29. 29.
    C.J. Newschaffer, L.A. Croen, M.D. Fallin, I. Hertz-Picciotto, D.V. Nguyen, N.L. Lee, C.A. Berry, H. Farzadegan, H.N. Hess, R.J. Landa, S.E. Levy, M.L. Massolo, S.C. Meyerer, S.M. Mohammed, M.C. Oliver, S. Ozonoff, J. Pandey, A. Schroeder, K.M. Shedd-Wise, Infant siblings and the investigation of autism risk factors. J. Neurodev. Disord. 4, 1–16 (2012)CrossRefGoogle Scholar
  30. 30.
    H.R. Park, J.M. Lee, H.E. Moon, D.S. Lee, B.N. Kim, J. Kim, D.G. Kim, S.H. Paek, A short review on the current understanding of autism spectrum disorders. Exp. Neurobiol. 25(1), 1–13 (2016)CrossRefGoogle Scholar
  31. 31.
    O. Ronneberger, P. Fischer, T. Brox, U-net: convolutional networks for biomedical image segmentation, in International Conference on Medical Image Computing and Computer-Assisted Intervention (Springer, Berlin, 2015), pp. 234–241Google Scholar
  32. 32.
    C.M. Salafia, C. Platt, T. Girardi, R. Shah, G. Merz, D.P. Misra, Placental structure in ASD: does the placenta mirror the diagnosis? in 2014 International Meeting for Autism Research, page Abstract No. 17578, May 14–17 2014Google Scholar
  33. 33.
    R.G. Shah, C.M. Salafia, T. Girardi, L. Conrad, K. Keaty, A. Bartleotc, Shape matching algorithm to validate the tracing protocol of placental chorionic surface vessel networks. Placenta 36(8), 944–946 (2015)CrossRefGoogle Scholar
  34. 34.
    C.K. Walker, P. Krakowiak, A. Baker, R.L. Hansen, S. Ozonoff, I. Hertz-Picciotto, Preeclampsia, placental insufficiency, and autism spectrum disorder or developmental delay. JAMA Pediatr. 169(2), 154–162 (2015)CrossRefGoogle Scholar
  35. 35.
    K. Yacoubou Djima, L. Simonelli, D. Cunnigham, W. Czaja, Detection of anomaly in human retina using Laplacian Eigenmaps and vectorized matched filtering, in Proceedings of SPIE, vol. 9413, Mar 2015, pp. 94132F-1–94132F-11Google Scholar
  36. 36.
    S.K. Zhou, H. Greenspan, D. Shen, Deep Learning for Medical Image Analysis (Elsevier Science, Amsterdam, 2017)Google Scholar

Copyright information

© The Author(s) and the Association for Women in Mathematics 2018

Authors and Affiliations

  • Catalina Anghel
    • 1
    Email author
  • Kellie Archer
    • 2
  • Jen-Mei Chang
    • 3
  • Amy Cochran
    • 4
  • Anca Radulescu
    • 5
  • Carolyn M. Salafia
    • 6
  • Rebecca Turner
    • 7
  • Karamatou Yacoubou Djima
    • 8
  • Lan Zhong
    • 9
  1. 1.University of California DavisDavisUSA
  2. 2.The Ohio State UniversityColumbusUSA
  3. 3.California State University Long BeachLong BeachUSA
  4. 4.University of WisconsinMadisonUSA
  5. 5.SUNY New PaltzNew PaltzUSA
  6. 6.Placental Analytics, LLC.New RochelleUSA
  7. 7.The University of AucklandAucklandNew Zealand
  8. 8.Amherst CollegeAmherstUSA
  9. 9.University of DelawareNewarkUSA

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