Geometric influences on the regional organization of the mammalian brain

1997 

Abstract Submission 

James Pang¹, Peter Robinson², Kevin Aquino³, Priscila Levi¹, Ru Kong⁴, B. T. Thomas Yeo⁴, Michael Breakspear⁵, Alex Fornito¹

¹Monash University, Melbourne, Australia, ²University of Sydney, Sydney, Australia, ³Brain Key Incorporated, San Francisco, USA, ⁴National University of Singapore, Singapore, Singapore, ⁵University of Newcastle, Newcastle, Australia

James Pang, PhD  
Monash University
Melbourne, Australia

Peter Robinson  
University of Sydney
Sydney, Australia

Kevin Aquino, PhD  
Brain Key Incorporated
San Francisco, USA

Priscila Levi  
Monash University
Melbourne, Australia

Ruby Kong  
National University of Singapore
Singapore, Singapore

B. T. Thomas Yeo  
National University of Singapore
Singapore, Singapore

Michael Breakspear  
University of Newcastle
Newcastle, Australia

Alex Fornito  
Monash University
Melbourne, Australia

Since Brodmann's seminal work [1], studies have aimed to divide the brain into spatially contiguous areas or parcels that are functionally or anatomically homogeneous. These parcellations have historically been based on histology, but recent works have derived them by combining neuroimaging with sophisticated algorithms [2,3]. However, current approaches are not generalizable and offer no insight into the generative mechanisms that may have shaped the regional organization of the brain.

Here, we draw on evidence that regional patterning in the brain is strongly shaped by geometrically constrained gradients of gene expression [4] to develop a novel parcellation approach using the eigenmodes of brain geometry [5]. We show that the resulting geometry-derived parcellations are more homogeneous across hundreds of diverse anatomical, functional, cellular, and molecular properties than many existing parcellations of human, non-human primate, and mouse brains.

Figure 1A shows the steps to construct a geometric parcellation of the human cortical surface modeled by a triangular mesh derived from T1w-MRI. The mesh is used to solve the eigenvalue problem [5]: Δψ= -λψ, where Δ is the Laplace-Beltrami operator, which captures the mesh's geometry, and ψ are the geometric eigenmodes with eigenvalues λ. We use the zero-crossings (i.e., white areas in Fig. 1A) of the first non-constant geometric eigenmode (i.e., anterior-posterior mode) to divide the cortex into two regions. We repeat the process hierarchically, subdividing the regions from the previous iteration, and use the eigenvalues to define cut-offs for constructing parcellations with an arbitrary number of parcels. We apply this method to parcellate human, macaque, and marmoset cortices (Fig. 1B). We also apply it to 7 human subcortical nuclei (e.g., hippocampus, thalamus) and mouse isocortex in volumetric rather than in surface space (Fig. 1C).

We evaluated our geometric parcellations against 53 other parcellations, based on different approaches, in human, macaque, marmoset, and mouse. Performance was evaluated using regional homogeneity [6], estimated from 342 different maps capturing brain function, microstructural, cellular, molecular, and genetic properties. We matched the number of regions of our and each comparison parcellations and controlled for parcel size in the homogeneity calculations.

In human cortex, our parcellations were more homogeneous in >70% of 245 brain maps relative to 17 of 18 benchmark parcellations (Fig. 2A). In the subcortex, our parcellations had similar or greater homogeneity than other nucleus-specific parcellations (Fig. 2B). In macaque, our parcellations were more homogeneous in all 3 brain maps relative to 7 of 10 benchmark parcellations (Fig. 2C). In marmoset, our parcellations were always more homogeneous relative to 4 benchmark parcellations. In mouse, our parcellation was more homogeneous than the Allen brain atlas in >86% of 88 brain maps. We further verified that our approach can be generalized to other mammalian species (e.g., chimpanzee, squirrel, guinea pig) for which no parcellations and minimal imaging data exist.

Finally, we simulated a reaction-diffusion model [7] with chemical sources at the poles of the anterior-posterior axis, consistent with evidence that patterning genes are expressed along this axis [4]. We found that the model generated parcellations matching our simple geometric approximations (data not shown), suggesting its plausibility as a generative mechanism of our approach.

We introduce a new geometric approach for brain parcellation that is highly generalizable and can be applied to both the cortex and subcortex of any species, obtaining a reasonable first approximation of regional organization. The strong performance of the approach in obtaining highly homogeneous regions across diverse anatomical and functional properties emphasizes a fundamental role of geometry in shaping the regional organization of the mammalian brain.

Methods Development

Segmentation and Parcellation ¹

Anatomy and Functional Systems

Cortical Anatomy and Brain Mapping ²

Brain Atlases

Atlasing

Cortex

Segmentation

STRUCTURAL MRI

Sub-Cortical

Other - brain geometry; brain parcellation