Hierarchical modelling of crossing fibres in the white matter

1592 

Abstract Submission 

Hossein Rafipoor¹, Frederik Lange¹, Christoph Arthofer¹, Michiel Cottaar¹, Saad Jbabdi¹

¹Oxford University, Oxford, United Kingdom

Hossein Rafipoor  
Oxford University
Oxford, United Kingdom

Frederik Lange  
Oxford University
Oxford, United Kingdom

Christoph Arthofer  
Oxford University
Oxford, United Kingdom

Michiel Cottaar  
Oxford University
Oxford, United Kingdom

Saad Jbabdi  
Oxford University
Oxford, United Kingdom

Fixel-based analyses aim to extract fibre-specific parameters from single voxels using diffusion MRI data. To compare fibre-specific parameters across subjects, it is necessary to identify equivalent fibre populations. This task is complicated by variations in the number of crossing fibres and fibre orientations per voxel among subjects. Conventionally, fixel-based analyses resolve these correspondences after fitting crossing fibre models to each individual. In this work, we introduce a hierarchical framework to fit crossing fibre models to diffusion MRI data, ensuring consistent and comparable fibre-specific parameters across subjects. We employ an Expectation-Maximisation (EM) method for scalability. Additionally, we introduce a modified version of Threshold Free Cluster Enhancement (TFCE) applied to fixel data for family-wise error correction. As an example application, we applied our method to the UK biobank dataset to investigate changes in white matter through ageing.

The ball and sticks model posits that the diffusion MRI signal arises from intra-axonal water diffusing along fibres (sticks) and extracellular water diffusing isotropically (ball) (Figure 1A). Traditionally, this model is fitted to single voxels and single subjects independently. Here we extend the model with a hierarchical structure, where we assume that each subject's model parameter is drawn from a population distribution, which ensures consistent fibre labelling across subjects (Figure 1B). Fitting the entire hierarchical model necessitates optimization in a high dimensional space, increasing linearly with the number of subjects. For scalability, we adopt an EM approach. During maximisation, subject parameters are estimated while keeping group parameters fixed, enabling parallel processing across subjects. In the expectation step, subject parameters are fixed while group parameters are estimated. These steps are iterated until convergence. To determine the number of fibres in each voxel, we fit models with one to three fibres. The optimal number is then determined by evaluating the enhancement in the likelihood function upon the addition of extra fibres (Figure 1C). For multiple comparison corrections for fixel statistics, we adjusted the original TFCE approach to accommodate the structure of the fixel neighbourhood (Figure 1D). We employ the Oxford Multimodal (OMM-1) template as the structural reference space. For each voxel within this space, we extract data from the corresponding voxels in each subject's native diffusion space using the nearest neighbour sampling technique, utilising nonlinear transformations created by FSL MMORF.(https://doi.org/10.1101/2023.09.26.559484)

Our EM algorithm was used to create a white matter fibre template using T1 and diffusion images from 100 HCP young adult dataset. (Figure 2A) This template contains the group means and variances for the ball and sticks model parameters within each white matter voxel. Using this template, we fitted the hierarchical model to 400 subjects from the UK biobank dataset and estimated fibre signal fractions to study age-related alterations in white matter. Figure 2B illustrates the resulting t-statistics from the GLM analysis, using fixel signal fractions as the dependent variable and age as the independent variable, while adjusting for head size and sex as confounding variables. We can observe fibre-specific changes in the sample region. Subsequently, our modified TFCE was used to identify fixels with significant age-related changes, set at an alpha threshold of 0.05 after family-wise error correction (Figure 2C).

This work presents a hierarchical Bayesian framework to extract fibre-specific parameters from diffusion MRI data that are comparable across subjects. This facilitates the application of Fixel-Based Analysis techniques for models with a discrete fibre orientation distribution. Such integration can pave the way for fibre-level comparisons of biophysically meaningful parameters.

Bayesian Modeling

Diffusion MRI Modeling and Analysis ¹

Methods Development ²

Data analysis

Machine Learning

Modeling

Open-Source Code

Open-Source Software

Statistical Methods

White Matter

Other - Fixel based analysis