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Simulations of the Vascular Network Growth Process for Studying Placenta Structure and Function Associated with Autism

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

Abstract

Placenta chorionic surface vascular networks differ in individuals at-risk for autism compared to controls in terms of longer, straighter, thicker vessels; less branching; smaller changes in flow directions; and better coverage to the placental boundary. What mechanism(s) could drive these differences and how these mechanisms would impact blood transport has not been widely investigated. We used a Monte-Carlo simulation to mimic three mechanisms for controlling vascular growth: vessels grow faster and longer, terminate more frequently before branching, and flow directions are more tightly controlled in the at-risk simulations. For each mechanism, we analyzed simulated vascular networks based on structural properties and blood flow, assuming Poiseuille’s law and distensible vessels. Our simulations showed that none of these mechanisms alone could reproduce all structural properties of vascular networks in placentas identified as at-risk for autism. Terminating vessels more frequently or growing longer vessels could each reproduce longer vessels and less branching, but not greater boundary coverage or smaller changes in flow directions. As for their influence on blood flow, longer vessels and less branching have large, opposing effects on network function. Networks with longer vessels are less efficient in terms of slower flow rates and higher total network volume; in contrast, networks with less branching are more efficient. Our results suggest either these mechanisms work together to drive observed differences in vascular networks of at-risk individuals by balancing their impacts on network function; or another mechanism not considered here might drive these differences.

Keywords

Placentas Autism Vascular networks Blood flow Simulations 

Notes

Acknowledgements

The work described in this chapter was initiated during the Association for Women in Mathematics collaborative workshop Women Advancing Mathematical Biology hosted by the Mathematical Biosciences Institute (MBI) at Ohio State University in April 2017. 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.

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Copyright information

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

Authors and Affiliations

  • Catalina Anghel
    • 1
  • Kellie Archer
    • 2
  • Jen-Mei Chang
    • 3
    Email author
  • Amy Cochran
    • 4
  • Anca Radulescu
    • 5
  • Carolyn M. Salafia
    • 6
  • Rebecca Turner
    • 7
  • Yacoubou Djima Karamatou
    • 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.ScionRiccarton, ChristchurchNew Zealand
  8. 8.Amherst CollegeAmherstUSA
  9. 9.University of DelawareNewarkUSA

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