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Fisher-Rao Regularized Transport Analysis of the Glymphatic System and Waste Drainage

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Medical Image Computing and Computer Assisted Intervention – MICCAI 2020 (MICCAI 2020)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12267))

Abstract

In this work, a unified representation of all the time-varying dynamics is accomplished with a Lagrangian framework for analyzing Fisher-Rao regularized dynamical optimal mass transport (OMT) derived flows. While formally equivalent to the Eulerian based Schrödinger bridge OMT regularization scheme, the Fisher-Rao approach allows a simple and interpretable methodology for studying the flows of interest in the present work. The advantage of the proposed Lagrangian technique is that the time-varying particle trajectories and attributes are displayed in a single visualization. This provides a natural capability to identify and distinguish flows under different conditions. The Lagrangian analysis applied to the glymphatic system (brain waste removal pathway associated with Alzheimer’s Disease) successfully captures known flows and distinguishes between flow patterns under two different anesthetics, providing deeper insights into altered states of waste drainage.

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References

  1. Benamou, J.D., Brenier, Y.: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numerische Math. 84, 375–393 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Benveniste, H., et al.: Anesthesia with dexmedetomidine and low-dose isoflurane increases solute transport via the glymphatic pathway in rat brain when compared with high-dose isoflurane. Anesthesiol.: J. Am. Soc. Anesthesiol. 127(6), 976–988 (2017)

    Article  Google Scholar 

  3. Buttazzo, G., Jimenez, C., Oudet, E.: An optimization problem for mass transportation with congested dynamics. SIAM J. Control Optim. 48(3), 1961–1976 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, Y., Georgiou, T.T., Pavon, M.: On the relation between optimal transport and Schrödinger bridges: a stochastic control viewpoint. J. Optim. Theory Appl. 169(2), 671–691 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chizat, L., Peyré, G., Schmitzer, B., Vialard, F.X.: Unbalanced optimal transport: dynamic and Kantorovich formulations. J. Funct. Anal. 274(11), 3090–3123 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cuturi, M.: Sinkhorn distances: lightspeed computation of optimal transport. In: Advances in Neural Information Processing Systems, pp. 2292–2300 (2013)

    Google Scholar 

  7. Elkin, R., et al.: GlymphVIS: visualizing glymphatic transport pathways using regularized optimal transport. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11070, pp. 844–852. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00928-1_95

    Chapter  Google Scholar 

  8. Elkin, R., et al.: Optimal mass transport kinetic modeling for head and neck DCE-MRI: initial analysis. Magn. Reson. Med. 82(6), 2314–2325 (2019)

    Article  Google Scholar 

  9. Feydy, J., Charlier, B., Vialard, F.-X., Peyré, G.: Optimal transport for diffeomorphic registration. In: Descoteaux, M., Maier-Hein, L., Franz, A., Jannin, P., Collins, D.L., Duchesne, S. (eds.) MICCAI 2017. LNCS, vol. 10433, pp. 291–299. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66182-7_34

    Chapter  Google Scholar 

  10. Garyfallidis, E., Brett, M., Correia, M.M., Williams, G.B., Nimmo-Smith, I.: Quickbundles, a method for tractography simplification. Front. Neurosci. 6, 175 (2012)

    Article  Google Scholar 

  11. Gerber, S., Niethammer, M., Styner, M., Aylward, S.: Exploratory population analysis with unbalanced optimal transport. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11072, pp. 464–472. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00931-1_53

    Chapter  Google Scholar 

  12. Haker, S., Zhu, L., Tannenbaum, A., Angenent, S.: Optimal mass transport for registration and warping. Int. J. Comput. Vis. 60(3), 225–240 (2004)

    Article  Google Scholar 

  13. Iliff, J.J., et al.: Brain-wide pathway for waste clearance captured by contrast-enhanced MRI. J. Clin. Investig. 123(3), 1299–1309 (2013)

    Article  Google Scholar 

  14. Iliff, J.J., et al.: A paravascular pathway facilitates CSF flow through the brain parenchyma and the clearance of interstitial solutes, including amyloid \(\beta \). Sci. Transl. Med. 4(147), 147ra111 (2012)

    Google Scholar 

  15. Jiang, Q., et al.: Impairment of the glymphatic system after diabetes. J. Cereb. Blood Flow Metab. 37(4), 1326–1337 (2017)

    Article  Google Scholar 

  16. Koundal, S., et al.: Optimal mass transport with Lagrangian workflow reveals advective and diffusion driven solute transport in the glymphatic system. Sci. Rep. 10(1), 1–18 (2020)

    Article  MathSciNet  Google Scholar 

  17. Lee, H., et al.: The effect of body posture on brain glymphatic transport. J. Neurosci. 35(31), 11034–11044 (2015)

    Article  Google Scholar 

  18. Li, W., Yin, P., Osher, S.: Computations of optimal transport distance with fisher information regularization. J. Sci. Comput. 75(3), 1581–1595 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  19. Liero, M., Mielke, A., Savaré, G.: Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves. SIAM J. Math. Anal. 48(4), 2869–2911 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  20. Otto, F.: The geometry of dissipative evolution equations: the porous medium equation. Communications in Partial Differential Equations (2001)

    Google Scholar 

  21. Papadakis, N., Peyré, G., Oudet, E.: Optimal transport with proximal splitting. SIAM J. Imaging Sci. 7(1), 212–238 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Peng, W., et al.: Suppression of glymphatic fluid transport in a mouse model of Alzheimer’s disease. Neurobiol. Dis. 93, 215–225 (2016)

    Article  Google Scholar 

  23. Ratner, V., et al.: Cerebrospinal and interstitial fluid transport via the glymphatic pathway modeled by optimal mass transport. Neuroimage 152, 530–537 (2017)

    Article  Google Scholar 

  24. Shokri-Kojori, E., et al.: \(\beta \)-amyloid accumulation in the human brain after one night of sleep deprivation. Proc. Natl. Acad. Sci. 115(17), 4483–4488 (2018)

    Google Scholar 

  25. Steklova, K., Haber, E.: Joint hydrogeophysical inversion: state estimation for seawater intrusion models in 3D. Comput. Geosci. 21(1), 75–94 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  26. Villani, C.: Topics in Optimal Transportation No. 58. American Mathematical Society, Providence (2003)

    MATH  Google Scholar 

  27. Villani, C.: Optimal Transport: Old and New, vol. 338. Springer, Cham (2008). https://doi.org/10.1007/978-3-540-71050-9

    Book  MATH  Google Scholar 

  28. Xie, L., et al.: Sleep drives metabolite clearance from the adult brain. Science 342(6156), 373–377 (2013)

    Article  Google Scholar 

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Acknowledgements

This study was supported by AFOSR grants (FA9550-17-1-0435, FA9550-20-1-0029), a grant from National Institutes of Health (R01-AG048769, RF1-AG053991), MSK Cancer Center Support Grant/Core Grant (P30 CA008748), and a grant from Breast Cancer Research Foundation (BCRF-17-193).

Author information

Authors and Affiliations

  1. Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, NY, 10065, USA

    Rena Elkin & Saad Nadeem

  2. Department of Anesthesiology, Yale School of Medicine, New Haven, CT, 06519, USA

    Hedok Lee & Helene Benveniste

  3. Departments of Computer Science and Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY, 11794, USA

    Allen Tannenbaum

Authors
  1. Rena Elkin
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  2. Saad Nadeem
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  3. Hedok Lee
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  4. Helene Benveniste
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  5. Allen Tannenbaum
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Corresponding author

Correspondence to Saad Nadeem .

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Editors and Affiliations

  1. University of Toronto, Toronto, ON, Canada

    Anne L. Martel

  2. The University of British Columbia, Vancouver, BC, Canada

    Purang Abolmaesumi

  3. University College London, London, UK

    Danail Stoyanov

  4. École Centrale de Nantes, Nantes, France

    Diana Mateus

  5. EURECOM, Biot, France

    Maria A. Zuluaga

  6. Chinese Academy of Sciences, Beijing, China

    S. Kevin Zhou

  7. Sorbonne University, Paris, France

    Daniel Racoceanu

  8. The Hebrew University of Jerusalem, Jerusalem, Israel

    Leo Joskowicz

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Elkin, R., Nadeem, S., Lee, H., Benveniste, H., Tannenbaum, A. (2020). Fisher-Rao Regularized Transport Analysis of the Glymphatic System and Waste Drainage. In: Martel, A.L., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2020. MICCAI 2020. Lecture Notes in Computer Science(), vol 12267. Springer, Cham. https://doi.org/10.1007/978-3-030-59728-3_56

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  • DOI: https://doi.org/10.1007/978-3-030-59728-3_56

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