A Continuous Model of Cortical Connectivity

Abstract

We present a continuous model for structural brain connectivity based on the Poisson point process. The model treats each stream-line curve in a tractography as an observed event in connectome space, here a product space of cortical white matter boundaries. We approximate the model parameter via kernel density estimation. To deal with the heavy computational burden, we develop a fast parameter estimation method by pre-computing associated Legendre products of the data, leveraging properties of the spherical heat kernel. We show how our approach can be used to assess the quality of cortical parcellations with respect to connectivty. We further present empirical results that suggest the "discrete" connectomes derived from our model have substantially higher test-retest reliability compared to standard methods.

Keywords: Diffusion MRI; Human Connectome; Non-Parametric Estimation.

Fig. 1

A visualization of the ICC scores for connectivity to Brodmann Area 45 (Destrieux region 14) for the Count connectomes (left) and the proposed Integrated Intensity connectomes (right). Blue denotes a higher score.

Fig. 2

A visualization of the marginal connectivity $M(x)={\displaystyle {\int }_{E_i}\widehat{\lambda }(x,y)dy}$ for the Left Post-central Gyrus region of the DK atlas (Region 57). The region is shown in blue on the inset. Red denotes higher connectivity regions with the blue region.