Learning to estimate the fiber orientation distribution function from diffusion-weighted MRI

Abstract

Estimation of white matter fiber orientation distribution function (fODF) is the essential first step for reliable brain tractography and connectivity analysis. Most of the existing fODF estimation methods rely on sub-optimal physical models of the diffusion signal or mathematical simplifications, which can impact the estimation accuracy. In this paper, we propose a data-driven method that avoids some of these pitfalls. Our proposed method is based on a multilayer perceptron that learns to map the diffusion-weighted measurements, interpolated onto a fixed spherical grid in the q space, to the target fODF. Importantly, we also propose methods for synthesizing reliable simulated training data. We show that the model can be effectively trained with simulated or real training data. Our phantom experiments show that the proposed method results in more accurate fODF estimation and tractography than several competing methods including the multi-tensor model, Bayesian estimation, spherical deconvolution, and two other machine learning techniques. On real data, we compare our method with other techniques in terms of accuracy of estimating the ground-truth fODF. The results show that our method is more accurate than other methods, and that it performs better than the competing methods when applied to under-sampled diffusion measurements. We also compare our method with the Sparse Fascicle Model in terms of expert ratings of the accuracy of reconstruction of several commissural, projection, association, and cerebellar tracts. The results show that the tracts reconstructed with the proposed method are rated significantly higher by three independent experts. Our study demonstrates the potential of data-driven methods for improving the accuracy and robustness of fODF estimation.

GORDA: Graph-Based Orientation Distribution Analysis of SLI Scatterometry Patterns of Nerve Fibres

“…The mapping from the measurement to the sphere is calculated as φ = arctan( ∆x ∆y ) and θ = arctan( d H ∆x 2 + ∆y 2 ). We interpolate the values from the measurement sphere to the HEALPix sphere using the angular distance between the surface of the spheres as described in [14].…”

Atlas-powered deep learning (ADL) -- application to diffusion weighted MRI

“…To select the 6 measurements, similar to [34,19], we considered the 6 optimal diffusion gradient directions proposed in [32] and chose the measurements that were closest to those directions. To select the 12 measurements, we selected these measurements to be close to uniformly spread on the sphere, as suggested in [18,20].…”

“…Here, we choose either 6 and 15 measurements from each of the b = 1000 and b = 2600 shells, for a total of 12 and 30 measurements, which represent downsampling factors of approximately 24 and 10, respectively. We selected these measurements to be close to uniformly spread on the sphere, using an approach similar to [20]. For a fair comparison, for both FA and OD we used the same down-sampled datasets for our method and for all competing techniques.…”

“…Rather than solving the inverse problem directly, DL methods aim to learn the complex relation between the dMRI signal and the parameter of interest from a set of training data. Recent studies have used DL models for estimating diffusion tensor, diffusion kurtosis, multi-compartment models, and fiber orientation distribution, to name just a few [12,11,20,34,24]. They have shown that DL methods can accurately estimate dMRI biomarkers using far fewer measurements than optimization-based techniques.…”

ConvTract: A Convolutional-based Framework for Tractography

“…The model was tested using simulated and in vivo datasets and demonstrated superior performance over the MSMT-CSD algorithm. More recently, a CNN model was introduced to predict precise fODF that can be utilized for brain tractography as well as connectivity analysis [49]. Extensive experiments were carried out to assess the framework performance in comparison to classical and data-driven approaches using weighted average angular error (WAAE) and Jensen-Shannon divergence (JSD) metrics as well as evaluating the accuracy of fiber tract reconstruction by expert ratings.…”