Samuel Deslauriers-Gauthier

The challenge of mapping the human connectome based on diffusion tractography

Tractography based on non-invasive diffusion imaging is central to the study of human brain connectivity. To date, the approach has not been systematically validated in ground truth studies. Based on a simulated human brain data set with ground truth tracts, we organized an open international tractography challenge, which resulted in 96 distinct submissions from 20 research groups. Here, we report the encouraging finding that most state-of-the-art algorithms produce tractograms containing 90% of the ground truth bundles (to at least some extent). However, the same tractograms contain many more invalid than valid bundles, and half of these invalid bundles occur systematically across research groups. Taken together, our results demonstrate and confirm fundamental ambiguities inherent in tract reconstruction based on orientation information alone, which need to be considered when interpreting tractography and connectivity results. Our approach provides a novel framework for estimating reliability of tractography and encourages innovation to address its current limitations.Though tractography is widely used, it has not been systematically validated. Here, authors report results from 20 groups showing that many tractography algorithms produce both valid and invalid bundles.

Tractography-based connectomes are dominated by false-positive connections

Fiber tractography based on non-invasive diffusion imaging is at the heart of connectivity studies of the human brain. To date, the approach has not been systematically validated in ground truth studies. Based on a simulated human brain dataset with ground truth white matter tracts, we organized an open international tractography challenge, which resulted in 96 distinct submissions from 20 research groups. While most state-of-the-art algorithms reconstructed 90% of ground truth bundles to at least some extent, on average they produced four times more invalid than valid bundles. About half of the invalid bundles occurred systematically in the majority of submissions. Our results demonstrate fundamental ambiguities inherent to tract reconstruction methods based on diffusion orientation information, with critical consequences for the approach of diffusion tractography in particular and human connectivity studies in general.

Sparse Reconstruction Challenge for diffusion MRI: Validation on a physical phantom to determine which acquisition scheme and analysis method to use?

Diffusion magnetic resonance imaging (dMRI) is the modality of choice for investigating in-vivo white matter connectivity and neural tissue architecture of the brain. The diffusion-weighted signal in dMRI reflects the diffusivity of water molecules in brain tissue and can be utilized to produce image-based biomarkers for clinical research. Due to the constraints on scanning time, a limited number of measurements can be acquired within a clinically feasible scan time. In order to reconstruct the dMRI signal from a discrete set of measurements, a large number of algorithms have been proposed in recent years in conjunction with varying sampling schemes, i.e., with varying b-values and gradient directions. Thus, it is imperative to compare the performance of these reconstruction methods on a single data set to provide appropriate guidelines to neuroscientists on making an informed decision while designing their acquisition protocols. For this purpose, the SPArse Reconstruction Challenge (SPARC) was held along with the workshop on Computational Diffusion MRI (at MICCAI 2014) to validate the performance of multiple reconstruction methods using data acquired from a physical phantom. A total of 16 reconstruction algorithms (9 teams) participated in this community challenge. The goal was to reconstruct single b-value and/or multiple b-value data from a sparse set of measurements. In particular, the aim was to determine an appropriate acquisition protocol (in terms of the number of measurements, b-values) and the analysis method to use for a neuroimaging study. The challenge did not delve on the accuracy of these methods in estimating model specific measures such as fractional anisotropy (FA) or mean diffusivity, but on the accuracy of these methods to fit the data. This paper presents several quantitative results pertaining to each reconstruction algorithm. The conclusions in this paper provide a valuable guideline for choosing a suitable algorithm and the corresponding data-sampling scheme for clinical neuroscience applications.

Sampling Signals With a Finite Rate of Innovation on the Sphere

The state of the art in sampling theory now contains several theorems for signals that are non-bandlimited. For signals on the sphere however, most theorems still require the assumptions of bandlimitedness. In this work we show that a particular class of non-bandlimited signals, which have a finite rate of innovation, can be exactly recovered using a finite number of samples. We consider a sampling scheme where K weighted Diracs are convolved with a kernel on the rotation group. We prove that if the sampling kernel has a bandlimit L = 2K then (2K - 1)(4K - 1) + 1 equiangular samples are sufficient for exact reconstruction. If the samples are uniformly distributed on the sphere, we argue that the signal can be accurately reconstructed using 4K2 samples and validate our claim through numerical simulations. To further reduce the number of samples required, we design an optimal sampling kernel that achieves accurate reconstruction of the signal using only 3K samples, the number of parameters of the weighted Diracs. In addition to weighted Diracs, we show that our results can be extended to sample Diracs integrated along the azimuth. Finally, we consider kernels with antipodal symmetry which are common in applications such as diffusion magnetic resonance imaging.

Spherical finite rate of innovation theory for the recovery of fiber orientations

In this paper, we investigate the reconstruction of a signal defined as the sum of orientations from samples taken with a kernel defined on the 3D rotation group. A potential application is the recovery of fiber orientations in diffusion magnetic resonance imaging. We propose an exact reconstruction algorithm based on the finite rate of innovation theory that makes use of the spherical harmonics representation of the signal. The number of measurements needed for perfect recovery, which may be as low as 3K, depends only on the number of orientations and the bandwidth of the kernel used. Furthermore, the angular resolution of our method does not depend on the number of available measurements. We illustrate the performance of the algorithm using several simulations.

Sampling great circles at their rate of innovation

In this work, we show that great circles, the intersection of a plane through the origin and a sphere centered at the origin, can be perfectly recovered at their rate of innovation. Specifically, we show that 4K(8K − 7) + 7 samples are sufficient to perfectly recover K great circles, given an appropriate sampling scheme. Moreover, we argue that the number of samples can be reduced to 2K(4K − 1) while maintaining accurate results. This argument is supported by our numerical results. To improve the robustness to noise of our approach, we propose a modification that uses all the available information, instead of the critical amount. The increase in accuracy is demonstrated using numerical simulations.

Magnetic resonance image reconstruction using the annihilating filter method

Compressed sensing reconstruction algorithms exploit the sparsity of MRI images to significantly undersample the k-space. However, these algorithms are computationally expensive, may be slow to converge, and perform best when the samples are randomly selected. We propose a new sparse reconstruction algorithm based on the annihilating filter method to palliate these issues. This new method is non iterative and does not require random sampling. We demonstrate that our technique outperforms the basis pursuit theoretical limit for very sparse signals. As an application, we show clinical MRI images reconstructed using our method.

The association between white matter and sleep spindles differs in young and older individuals

Study Objectives Sleep is a reliable indicator of cognitive health in older individuals. Sleep spindles (SS) are non-rapid eye movement (NREM) sleep oscillations implicated in sleep-dependent learning. Their generation imply a complex activation of the thalamo-cortico-thalamic loop. Since SS require neuronal synchrony, the integrity of the white matter (WM) underlying these connections is of major importance. During aging, both SS and WM undergo important changes. The goal of this study was to investigate whether WM integrity could predict the age-related reductions in SS characteristics. Methods Thirty young and 31 older participants underwent a night of polysomnographic recording and a 3T magnetic resonance imaging acquisition including a diffusion sequence. SS were detected in NREM sleep and EEG spectral analysis was performed for the sigma frequency band. WM diffusion metrics were computed in a voxelwise design of analysis. Results Compared to young participants, older individuals showed lower SS density, amplitude, and sigma power. Diffusion metrics were correlated with SS amplitude and sigma power in tracts connecting the thalamus to the frontal cortex for the young but not for the older group, suggesting a moderation effect. Moderation analyses showed that diffusion metrics explained between 14% and 39% of SS amplitude and sigma power variance in the young participants only. Conclusion Our results indicate that WM underlying the thalamo-cortico-thalamic loop predicts SS characteristics in young individuals, but does not explain age-related changes in SS. Other neurophysiological factors could better explain the effect of age on SS characteristics.

Inference and Visualization of Information Flow in the Visual Pathway using dMRI and EEG

We propose a method to visualize information flow in the visual pathway following a visual stimulus. Our method estimates structural connections using diffusion magnetic resonance imaging and functional connections using electroencephalography. First, a Bayesian network which represents the cortical regions of the brain and their connections is built from the structural connections. Next, the functional information is added as evidence into the network and the posterior probability of activation is inferred using a maximum entropy on the mean approach. Finally, projecting these posterior probabilities back onto streamlines generates a visual depiction of pathways used in the network. We first show the effect of noise in a simulated phantom dataset. We then present the results obtained from left and right visual stimuli which show expected information flow traveling from eyes to the lateral geniculate nucleus and to the visual cortex. Information flow visualization along white matter pathways has potential to explore the brain dynamics in novel ways.

The application of a new sampling theorem for non-bandlimited signals on the sphere: Improving the recovery of crossing fibers for low b-value acquisitions

Recent development in sampling theory now allows the sampling and reconstruction of certain non-bandlimited functions on the sphere, namely a sum of weighted Diracs. Because the signal acquired in diffusion Magnetic Resonance Imaging (dMRI) can be modeled as the convolution between a sampling kernel and two dimensional Diracs defined on the sphere, these advances have great potential in dMRI. In this work, we introduce a local reconstruction method for dMRI based on a new sampling theorem for non-bandlimited signals on the sphere. This new algorithm, named Spherical Finite Rate of Innovation (SFRI), is able to recover fibers crossing at very narrow angles with little dependence on the b-value. Because of its parametric formulation, SFRI can distinguish crossing fibers even when using a DTI-like acquisition (≈32 directions). This opens new perspective for low b-value and low number of gradient directions diffusion acquisitions and tractography studies. We evaluate the angular resolution of SFRI using state of the art synthetic data and compare its performance using in-vivo data. Our results show that, at low b-values, SFRI recovers crossing fibers not identified by constrained spherical deconvolution. We also show that low b-value results obtained using SFRI are similar to those obtained with constrained spherical deconvolution at a higher b-value.