Effects of cortical heterogeneity on the eigenmodes of brain geometry

1892 

Abstract Submission 

Victor Barnes¹, Jace Cruddas¹, Trang Cao², James Pang¹, Alex Fornito³

¹Monash University, Melbourne, Victoria, ²Monash University, Clayton, VIC, ³Monash University, Clayton, Victoria

Victor Barnes  
Monash University
Melbourne, Victoria

Jace Cruddas  
Monash University
Melbourne, Victoria

Trang Cao  
Monash University
Clayton, VIC

James Pang, PhD  
Monash University
Melbourne, Victoria

Alex Fornito  
Monash University
Clayton, Victoria

Brain function is constrained by its underlying structure and anatomy, but explaining the mechanisms behind this link has proven challenging. In many areas of physics and engineering, the dynamics of a system can be understood with respect to the eigenmodes of its structure, representing the fundamental, resonant vibrations of the system. Recent work has shown that a diverse array of functional brain maps derived from task-evoked and resting-state fMRI can be parsimoniously explained as excitations of the eigenmodes of cortical geometry (termed geometric eigenmodes) [1], offering a robust paradigm to explore how the intrinsic geometry of the brain physically constrains emerging dynamics. The success of these geometric eigenmodes is somewhat surprising given that they are estimated using a minimal set of features-simply defining how the shape of the cortex varies through space. However, they treat the cortex as a homogeneous medium, ignoring spatial variations in local cellular and molecular composition (e.g., myelination, cell and neurite density). Here, we developed a framework for deriving geometric eigenmodes that can account for spatial heterogeneities in any arbitrary cortical property.

We derived geometric eigenmodes with and without spatial heterogeneities, which we termed herein as homogeneous and heterogeneous modes, respectively. We derived the modes by using a triangular mesh representation of the cortical surface from a FreeSurfer template [2] and solving the heterogeneous form of the Helmholtz equation:
∇(c_s ²·∇)ψ=-λψ
where ψ are the eigenmodes, λ are the eigenvalues, and c_s is the heterogeneous term describing local variations across the cortical mesh and corresponds to the wave speed of the resulting dynamics, as captured in biophysical models such as neural field theory [3]. We define c_s as a function of a heterogeneity map, ρ, that encodes spatial variations in cortical properties (e.g. myelination), written formally as:
c_s=c_mean+αc_mean(ρ-ρ_mean)
where c_mean=3352.4 mm/s is the mean neural propagation speed taken from physiological estimates [1], ρ is the heterogeneity map normalized between 0 and 1, and α is a free parameter controlling the variance of c_s. As an initial case, we derived heterogeneous modes parameterized by the sensory-association (SA) axis, which differentiates sensory and association areas of the cortex and captures spatial variations in a diverse range of anatomical and other properties [4]. We also derived the classical homogeneous modes by solving the above Helmholtz equation with c_s set to unity, following [1].
The modes form a complete, orthogonal basis set and can thus be used to decompose data. We used this approach to compare the accuracy with which the heterogeneous and homogeneous modes could reconstruct diverse maps of cortical organisation drawn from the neuromaps repository [5].

Figure 1 shows the homogeneous modes and heterogeneous modes parametrized by the SA axis at varying levels of α. We found that higher levels of α significantly changes the structure of the heterogeneous modes in comparison to the homogeneous modes (see low correlations along the diagonal of the correlation matrices). Figure 2 shows the reconstruction accuracies of key brain maps from the neuromaps repository for both the homogeneous modes and the heterogeneous modes (α=0.3). We found that the heterogeneous modes consistently show a higher accuracy at 5 and 10 modes relative to the homogeneous modes, indicating that they have greater flexibility in capturing the very low-frequency content of the neuromaps data.

We show that refining the geometric eigenmode model by incorporating information about spatial heterogeneities in cortical tissue can improve reconstruction of very low-frequency aspects of cortical organization. Future work will explore how these heterogeneities influence dynamics.

Methods Development ¹

Anatomy and Functional Systems ²

Cortical Anatomy and Brain Mapping

Cortical Cyto- and Myeloarchitecture

Anatomical MRI

Computational Neuroscience

Cortex

Modeling

MRI

NORMAL HUMAN

STRUCTURAL MRI

Other - brain geometry; eigenmodes