Not so tangled - !!the geometric structure of the brain!

!!!!!!!!Van J Wedeen, MD

UCLA LINT NITP

Does cerebral connectivity have a particular shape?!

?!

SLF3!seed!

In tracer studies and their MRI analogs, paths appear to be isolated structures.!Can we ask what other paths are near to a given path - its path neighborhood?!

All paths crossing SLF3. Astonishingly, they all form a single 2D sheet!

Wedeen et al Science 2012!

collossal paths! cingulum bundles left and right !

Rhesus callosum and longitudinal pathways form a 2D sheet and grid!

SLF1 left and right!

Wedeen et al Science 2012!

Crossing fiber pathways of the brain are interwoven, forming 2D sheets !This is overwhelmingly non-random !

A little math - why observing sheet structure is non-trivial typically, crossings would not be sheets occur only if a specific 3D relation expected to form sheets holds between paths

Myocardial fibers and sheets !not foliate or interwoven!Generic!prior probability ≈ 1!

Brain path crosings: !foliate and interwoven!Highly exceptional:!prior probability ≈ 0.!

Grid structure is 3D!!occipital white matter rhesus !

R arcuate sulcus ! ! corpus callosum, SLF1 ! ! L central sulcus !

rostral <-----> caudal !

callosun, SLF1!

L central sulcus !

R arcuate sulcus!

L <-

---->

R !

Rhesus frontal pathways form a continuous grid

Wedeen Science 2012!

Macaque frontal lobe ortholinear structure - deep white matter fiber pathways follow body axes - longitudinal, transverse, AP - with non-euclidean deformations!

CB!

SLF1!FOF!

SLF2!

SLF3!

CC

MB!

SLF3!

SLF3!

SLF2!

MB!

PP!

Fig. 3c!

rostral ! ! ! ! ! ! ! ! !caudal !

PP!

FX!

FX!

Rhesus

Rhesus brainstem - three principal axes express the three primordial concentration gradients and natural coordinate system of the bilaterian body plan

cor

sag

Commenting in Science 9.28.12, Catani, suggest that HARDI of the corticospinal - callosal merging contradicts the grid thesis. We replied that this picture is in error…

T T

A

Grid structure reduces axon path-finding to a 6 letter code - Up, Down, Left, Right, Front, Back

Wendell Krieg 1953 - Corticospinal axons sharply turn from effective transverse T to axial A

T T

A

T

20X Rosene, Motazavi, BU 2012 100X

4X

Tracer injection to rhesus motor cortex – the corticospinal tract turns transverse-to-axial mostly or entirely via microscopic branches and turns of axons between the two directions

100X

Deep white matter known woven structure !courtesy Prof. Almut Schuz, Tubingen!

Jacobson 1959 in Katz Lasek Nauta 1980 -!!Axon tract precursor fields of the neural plate!

Morphogenesis – from pathways substrate precursor fields to mature CNS

Burnside & Jacobsen, 1968

Nieuwenhuys 1992 – !!fiber pathways are parallel or perpendicular to!!developmental segment and column boundaries!

Having a CNS is one aspect of the bilaterian design

Hejnol, Martindate Phil Trans R Soc B 383, 149 (2010) Swanson Brain Maps Elsevier 2004

juvenile acoelomate worm rat nervous system "flatmap"

MGH-UCLA HCP Immediate goal: map human connectivity

Long-term goal: objective mental health care

3T Connectom DSI bmax 15000 s/mm^2 Gmax 300 mT/m Left hemisphere (below) and crossing of SLF and internal capsule, right per Science 362; 1628 (2012)

functional coherence plasticity evolution

The structure and function of the brain must change gradually and together for learning and plasticity, development and evolution. This requires connectivity to be continuous and homogeneous

Specialization and hierarchy of cortical function follow the grid structure of connectivity Cortical areas checkerboard, hierarchic from front to back

Badre & D'Esposito Nature Reviews Neuroscience 2009

Geometric theory of mind and brain!!placazoan (pre-bilaterian pancake animal) -!breaking symmetry to forage !

human -!abstraction and the future!

Partial summary and some implications –!!

!• The brain expresses, or is, a natural 3D Cartesian grid and coordinate system!!!!• this grid system may hold throughout gray matter as well as white matter, !! !over 4 – 6 orders of scale!

!!• this design is unified with similar the bilaterian body plan!

!!• Pathways may use 3D “turn-by-turn navigation” - a 3 axis 6-direction code!

!!• Brain pathways form a continuum; this naturally supports coherence, plasticity, ! !and evolution!

!!• This structure raises new challenges, and opportunities, for MRI of connectivity! !and brain mapping!

Supported by NIH 1 R01 MH64044 NSF PHY 0855161 P41 RR-023953 P41 RR-14075 NIH U01 MH093765 Blueprint "Human Connectome Project"

And Thank You!