M-RBM: A Spatially Informed Model for Individual Brain Parcellation

1548 

Abstract Submission 

Da Zhi¹, Ladan Shahshahani², Caroline Nettekoven³, Ana Luisa Pinho⁴, Danilo Bzdok⁵, Jörn Diedrichsen⁶

¹University of Western Ontario, London, Ontario, ²Brown University, Providence, RI, ³University of Western Ontario, London, MT, ⁴Western University, London, Ontario, ⁵McConnell Brain Imaging Centre (BIC), Montreal Neurol, McGill Universityogical Institute (MNI), Montreal, Quebec, ⁶The Brain and Mind Institute, University of Western Ontario, London, Ontario

Da Zhi  
University of Western Ontario
London, Ontario

Ladan Shahshahani  
Brown University
Providence, RI

Caroline Nettekoven  
University of Western Ontario
London, MT

Ana Luisa Pinho  
Western University
London, Ontario

Danilo Bzdok  
McConnell Brain Imaging Centre (BIC), Montreal Neurol, McGill Universityogical Institute (MNI)
Montreal, Quebec

Jörn Diedrichsen  
The Brain and Mind Institute, University of Western Ontario
London, Ontario

Understanding individual variability becomes a significant challenge in brain parcellation studies. A major concern for building accurate individual parcellation is the intrinsic spatial dependence between nearby brain locations, which are more likely connected to each other than far-away ones. As a consequence, the neighboring brain locations tend to exhibit a higher functional similarity. However, most parcellation methods do not utilize this intrinsic smoothness, which leads to a poor and noisy reconstruction. Here, we present a new computational model, multinomial-restricted Boltzmann machine (m-RBM), that models the spatial co-dependency between brain locations. We then integrated this model into our Bayesian parcellation framework (Zhi et al., 2023) to learn individual cortical parcellations. The experiments on both synthetic and task-based fMRI data show the performance of individual parcellations derived by m-RBM model are improved compared to the ones by spatially independent model.

The m-RBM model imposes spatial dependence between brain locations (voxels) on the group probability measure p(U), which defines how likely a certain location belongs to a functional region across population. This was modeled through a modified three-layer RBM parameterized by a connectivity weights w_(i,j) connecting the parcellation layer U with the hidden layer H, and a temperature parameters θ_w to control the overall strength of this connection (Fig. 1). Compared to Markov Random Fields (Ryali et al., 2013; Schaefer et al., 2018), the new model is computationally faster, using layer-wise Gibbs sampling and variational approximation. In contrast to traditional RBMs, the units in each layer of the m-RBM model are now multinomial variables, rather than binary Bernoulli variables, thereby making it possible to learn the parcellation into K regions.
The individual parcellations (for each subject s) are then estimated by integrating the spatially informed group map p(U) with data likelihood of the observed data given the individual parcellation p(Y^s│U^s) under the Bayesian framework (Zhi et al., 2023). Here, we applied a stochastic maximum likelihood algorithm with mini-batch learning to train the m-RBM model. The parameters update then follow the gradients of the un-normalized likelihood calculated by contrastive divergence between positive and negative phase.
We first validate this new model on an exhaustive simulation. Then, we applied this new model to a task-based dataset that covers many functional domains (Pinho et al., 2018) to generate individual cortical atlas. We evaluated the parcellations using the distance-controlled boundary coefficient (DCBC, Zhi et al., 2022).

We first ran a simulation by training either a m-RBM or a spatially independent model on a synthetic dataset with true spatial dependence (Fig. 2a). The evaluation on three evaluation metrics showed that the m-RBM model was able to reconstruct the true individual parcellation better than the spatially independent model (Fig 2b,c,d).
We then estimate individual parcellations using the m-RBM model on real task fMRI data (Pinho et al., 2018) with different connection strength θ_w within range 0.1 to 5. We then tested the performance of the resultant maps on test set, and found that the individual parcellations from m-RBM model with θ_w between 2 to 4 show significant better performance than the ones trained by the independent model (Fig. 2e).

In this work, we proposed a novel computational architecture, called m-RBM, which is designed to capture the intrinsic spatial dependence between brain locations while accounting for individual variations. Both simulation and real data results showed the m-RBM model has significant advantages in estimating individual parcellations in the presence of spatial dependencies. Altogether, the proposed model may have promising applications in understanding variations of brain functional organizations by accurate individual parcellations.

Activation (eg. BOLD task-fMRI)

Bayesian Modeling ²

Connectivity (eg. functional, effective, structural) ¹

fMRI Connectivity and Network Modeling

Methods Development

Computational Neuroscience

Data analysis

Modeling

Source Localization