Skip to main content
SpringerLink
Log in
Book cover

International Conference on Large-Scale Scientific Computing

LSSC 2011: Large-Scale Scientific Computing pp 131–138Cite as

Optimal Mass Transportation-Based Models for Neuronal Fibers

  • Conference paper

  • 1922 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7116))

Abstract

Diffusion Magnetic Resonance Imaging (MRI) is used to (non-invasively) study neuronal fibers in the brain white matter. Reconstructing fiber paths from such data (tractography problem) is relevant in particular to study the connectivity between two given cerebral regions. By considering the fiber paths between two given areas as geodesics of a suitable well-posed optimal control problem (related to optimal mass transportation), we are able to provide a quantitative criterion to estimate the connectivity between two given cerebral regions, and to recover the actual distribution of neuronal fibers between them.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agrachev, A., Lee, P.: Optimal transportation under nonholonomic constraints. Trans. Amer. Math. Soc. 361(11), 6019–6047 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bardi, M., Capuzzo-Dolcetta, I.: Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser Boston, Boston (1997)

    Book  MATH  Google Scholar 

  3. Bernard, P., Buffoni, B.: Optimal mass transportation and Mather theory. J. Eur. Math. Soc. (JEMS) 9(1), 85–121 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Clarke, F.H., Ledyaev, Y.S., Stern, R.J., Wolenski, P.R.: Nonsmooth analysis and control theory. Graduate Texts in Mathematics, vol. 178. Springer, New York (1998)

    MATH  Google Scholar 

  5. Cannarsa, P., Sinestrari, C.: Semiconcave functions, Hamilton-Jacobi equations, and optimal control. Birkhäuser Boston, Boston (2004)

    MATH  Google Scholar 

  6. Pichon, E., Westin, C.-F., Tannenbaum, A.: A Hamilton-Jacobi-Bellman Approach to High Angular Resolution Diffusion Tractography. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 180–187. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Siconolfi, A.: Metric character of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 355(5), 1987–2009 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Villani, C.: Topics in optimal transportation. Graduate Studies in Mathematics, vol. 58. American Mathematical Society, Providence (2003)

    MATH  Google Scholar 

  9. Villani, C.: Optimal transport old and new. Grundlehren der Mathematischen Wissenschaften, vol. 338. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Sciences, University of Verona, Strada Le Grazie 15, I-37134, Verona, Italy

    Antonio Marigonda & Giandomenico Orlandi

Authors
  1. Antonio Marigonda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giandomenico Orlandi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Block 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov  & Svetozar Margenov  & 

  2. Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads, Building 321,, 2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Marigonda, A., Orlandi, G. (2012). Optimal Mass Transportation-Based Models for Neuronal Fibers. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29843-1_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29842-4

  • Online ISBN: 978-3-642-29843-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation