Margulies Lab Seminar

1. Kazuya Horibe (twitter: @khoribe3)
Graduate School of Engineering Science, Osaka University
Long association fibers
emerge from minimizing connectivity
on the geometry of the human fetal brain
1
2022.06.14 Margulies Lab Seminar

2. 2
About Me
Research background
・Ph.D student in Theoretical Biology lab. 2018-2021.6 @Osaka Uni.
・Visiting Ph.D. student @IT University of Copenhagen 2019.10-2020.4
Biophysics, Computational Biology, Developmental Biology
Arti
fi
cial Life, Soft robots
・Postdoc @ Osaka University 2021.7-
Human-Agent Interaction, Arti
fi
cial Life
From Intelligent Robotics Lab home page

3. Kazuya Horibe (twitter: @khoribe3)
Graduate School of Engineering Science, Osaka University
Long association fibers
emerge from minimizing connectivity
on the geometry of the human fetal brain
3
2022.06.14 Margulies Lab Seminar

4. 4
Background
Association fibers connect different regions of the same
cerebral hemisphere over long distances.
Copyright © 2018-2021 BrainKart.com
The mechanism about when and where association
fi
ber wiring occur is still unknown.

5. 5
Human association fiber is initially developed at
fetal period in the subplate layer.
Background
Tangentially continuous tissue throughout the
cerebral hemispheres
Green : Connexin 36
Subplate neurons are locally connected to
each other forming gap junctions and
chemical synapse.
[Molnár+ 2020 Science]
[Moore et al., 2014, PNAS]
Subplate appears only during fetal period
(from 8 to 33 GW)
[Kostović+2019, NeuroImage]
Subplate replaces cortical plate.
Subplate is a continuous tissue of uniformly distributed neurons with physical
connections between local neurons development of cortical plate.

6. 6
Subplate neurons show local and global neural activity
before development of cortical plate.
Background
Subplate nexus hypothesis: The subplate layer as a uniform continuum tangentially
across the cerebral hemispheres provides the ``weak'' nerve
fi
bers underlying
association
fi
bers.
Local neural activity:
Traveling waves of neural activity
occur in the visual cortex
[Keunen+ 2017 NeuroImage]
Global neural activity:
Global functional network across the
whole brain can be observed.
Human, fMRI
[Kilb+ 2011 European Journal of Neuroscience]
Rabit, V1
How to organize long range nerve
fi
bers in the subplate?

7. 7
Neural activity in the subplate layer would be involved in
the wiring of local nerve fibers.
Hypothesis
It is speculated that local
fi
bers are driven by neural activity and multiple connections are
made to form long-range
fi
bers.
How can we estimate long-range neural activity propagation?
Neural propagation through
gap junction
Global tangential connectivity
in the subplate (Sky blue)
Local tangential connectivity
in the subplate (Sky blue)
[Kostović 2020 Progress in Neurobiology]

8. 8
Theoretical studies have shown that neuronal activity
propagates through the shortest paths (geodesic) on
curved surfaces such as the cortex.
Background
[Horibe+ 2019 Chaos ]
Sky blue: shortest paths of each initial position.
Red: Traveling wave front
Brain surface Components surfaces
Decompose into repeated
component surfaces.
[Tallinen+ 2015 Phys Rev E]
Question: How are the shortest paths on the cortical surface geometry
spatially distributed on the fetal brain?

9. 9
Compute shortest paths on curved surface geometry using
Fast Marching Method.
Method1
Tutorial on Fast Marching Method by Clement Petres
Distance potential function
Geodesic
Initial point
End point

10. 10
Method1
Compute exhaustively the shortest paths on
the fetal cortical surface.
Data from [Garcia+2018 PNAS]
Draw the shortest paths with random
starting and ending points.
(Corresponding to random neural activities)
Fast Marching Method [Sethian1996 PNAS]
Repeat 50,000 times to fully
cover the surface.
Calculate the passage frequency at
each position.
0.3
0.2
0.1 0.15
0 1

11. 11
Result1
The shortest paths are spatially localized at characteristic
anatomical region.
Hot spots (red, high density) are located around endpoint of sulci
Cold region (blue, low density) are located at pole
Central sulcus
Insula
Sylvian sulcus
where has negative Gaussian curvature.
where has positive Gaussian curvature.

12. 12
Whether dose the bundles of the shortest paths further
correspond to major association tracts mediating the regions?
Method2
AND ( HS2, HS3 )
“AND” takes the logical product of the set of shortest paths at each of the two regions.
“OR” takes the logical sum of the set of shortest paths at each of the two regions.
OR ( Dorsal points in HR, Ventoral points in HR)
We compare the position and direction between these bundles
and main
fi
ve association
fi
bers.

13. 13
The position and direction of the obtained shortest paths’ s
bundle delineates association fibers.
High density: Bundles of shortest paths passing through the HSs
HS1-HS2-HS3: Accurate fasciculus
Result2
The bundle between the HS1 and HS3 traveled along the
anterior-posterior direction over the hot link of the frontal and
parietal regions.
Many paths passing through HS2 curved towards the temporal
lobes, forming a large arc on the perisylvian cortex
[Mori et al. 2005 MRI Atlas ofHuman White Matter]
HR: Cingulum
The circular bundle passing through anterior cingulate,
isthmus cingulate, posterior cingulate, and parahippocampal
gyrus
The bundle extends toward HS5 along the parieto-occipital
fi
ssure and a hot rergion along the calcarine
fi
ssure

14. 14
Result2
The shape and trajectory of the obtained shortest paths’ s
bundle delineates association fibers.
Long distance: Bundles of long range shortest paths for each pole
CR1-CR2: Uncinate faciculus
Passing through a narrow part of HS4
CR1-CR3: Inferior front-occipital fasciculus
The ones connecting the inferior part of the frontal cortex and
the inferior and medial occipital cortex passed through a
narrow part of HS4 on the insula cortex and the hot regions on
the medial occipito-temporal cortex.
CR2-CR3: Inferior longitudinal fasciculus
Many paths passed through the ventro-medial hot regions on
the occipito-temporal cortex

15. 15
• The macro geometry of fetal cortex constrains generation of
fi
bers with the shortest path
connecting two points on the surface.
• In particular, saddle points with negative Gaussian curvature bundle
fi
bers and a
ff
ect overall
patterns of network.
• The generated pattern of bundles showed distinct spatial features for the
fi
ve major association
tracts of the cortex.
Summary
Summary
New hypothesis: Under the geometric constraints of the cortical surface, the
shortest path determines the position and orientation of the association
fi
bers.
Development

16. 16
Discussion
How valid is it to compare the location of three-dimensional
association fibers with the bundles of shortest pathways on
the cortical surface?
The
fi
ve association
fi
bers compared to the shortest pathway are arranged in
the following order from lateral to medial: arcuate fasciculus, inferior
longitudinal fasciculus, uncinate, inferior fronto-occipital fasciculus, cimgulum
[Mori+. 2005 MRI Atlas ofHuman White Matter]
[Catani+ 2008 Cortex]
Surface Depth
The prototype of association
fi
bers may be formed under geometrical constraints in the
subplate and may migrate into the interior during development.

17. 17
Future Plan
Development
33 GW 38 GW
28 GW
Analyze shortest paths for multiple growth stages (especially faster stages) and compare the localization
patterns of shortest paths and the order of development of association
fi
bers.
Investigate the relationship between time evolution of localization patterns of the shortest path and tissue
folding.
Evolution
[Rilling+2008, Nat Neurosci]
The arch bundle is particularly well developed in humans and is a major factor in language function. Analysis
of the shortest pathways on the brain surface of apes (e.g., chimpanzees) may provide insight into the
evolutionary origins of the arch bundle