Brain white matter tractogram analysis

Title : Neural Meta Tracts: parsimonious multi-resolution representations for modeling, visualizing and statistically analyzing brain tractograms
Project coordinator : Pietro Gori
Participants : Jean-Marc Thiery, Damien Rohmer, Isabelle Bloch, Tamy Boubekeur, Marie-Paule Cani and Johan Pallud
Institutions : Télécom Paris, Ecole Polytechnique and St. Anne hospital
Funding: DigiCosme Emergence Project (240 k€)
Period : 2017-2020

Context - Tractography from diffusion MRI is currently the only technique able to non-invasively explore the white matter architecture of the brain. It results in a tractogram, which is a set of 3D polylines (i.e., lists of ordered 3D points), usually called streamlines, which are estimates of the trajectories of large groups of nerves (axons). Indeed, current diffusion MR machines have a spatial resolution in the millimeter (mm) scale, and therefore it’s not possible to perfectly reconstruct each axon, whose diameter is typically in the micrometer (µm) scale. This means that reconstructed streamlines might approximate more than $10^5$ axons in each voxel. Nevertheless, even with such low reconstruction resolution, tractography has proven to be an invaluable tool for clinicians and researchers. It is nowadays used on a daily basis by neurosurgeons for pre-operative planning and during surgical operations. It also offers important information for studying pathological processes in neurological and psychiatric diseases and aging. When visualized, a whole-brain tractogram, namely the estimate of all the nerve streamlines in the white matter of the brain, might seem a highly intricate and complex wiring system, where it’s difficult to recognize specific bundles and a well-structured organization (see figure below). However, thanks to numerous postmortem studies, the white matter architecture of the brain has been deciphered into a set of biologically plausible pathways (also called fasciculi or tracts), that have helped understanding the functional expression of the cerebral activity. Tractogram segmentation can thus be defined as the subdivision of whole-brain tractograms into anatomically relevant and reproducible tracts with well-known structural and diffusion properties.

Example of whole-brain tractogram visualization using streamlines (left) or tubes (right).

Goal: Explore new geometric representations, metrics and deformation models for fast, robust and reliable processing, comparison and visualization of tractograms from diffusion MRI.

Challenges: Recent tractography methods may produce whole-brain tractograms composed of millions of streamlines. This can complicate their visualization and interpretation, thus limiting the aforementioned clinical applications. Furthermore, the considerable number of streamlines can make computationally intractable processes such as segmentation (Delmonte et al., 2019), non-linear registration (Gori et al., 2016) or atlas construction (Gori et al., 2015) (Gori et al., 2017), which are important for research purposes. The presence of spurious streamlines (outliers) and the high inter-subject variability are two other challenges that can make the analysis of tractograms even more complicated. Lastly, the anatomical definition of a tract, as documented in the postmortem studies, is usually qualitative, since it is based on spatial relationships, such as “anterior to” or “close to”, that are difficult to model in a quantitative and accurate way.

Contributions In this project, we proposed four original contributions:

A new parsimonious and multi-resolution geometric representation for tractograms, called Neural Meta Tracts (Mercier et al., 2018)
Qfib, a new compression algorithm well-suited for tractograms (Mercier et al., 2020)
Two fast and scalable methods to automatically segment tractograms, one based on symbolic AI (Delmonte et al., 2019) and one on optimal transport (Feydy et al., 2019)

Press Interview published in the I’MTech, the science and technology news website of the Institut Mines-Telecom: HERE

References

2020

Neuroinformatics

QFib: Fast and Efficient Brain Tractogram Compression

Corentin Mercier, S Rousseau, P Gori, I Bloch, and T Boubekeur

Neuroinformatics, 2020

Abstract Paper Code

Diffusion MRI ﬁber tracking datasets can contain millions of 3D streamlines, and their representation can weight tens of gigabytes of memory. These sets of streamlines are called tractograms and are often used for clinical operations or research. Their size makes them difﬁcult to store, visualize, process or exchange over the network. We propose a new compression algorithm well-suited for tractograms, by taking advantage of the way streamlines are obtained with usual tracking algorithms. Our approach is based on unit vector quantization methods combined with a spatial transformation which results in low compression and decompression times, as well as a high compression ratio. For instance, a 11.5GB tractogram can be compressed to a 1.02GB ﬁle and decompressed in 11.3 seconds. Moreover, our method allows for the compression and decompression of individual streamlines, reducing the need for a costly outof-core algorithm with heavy datasets. Last, we open a way toward on-the-ﬂy compression and decompression for handling larger datasets without needing a load of RAM (i.e. in-core handling), faster network exchanges and faster loading times for visualization or processing.

2019

IEEE ISBI

White Matter Multi-Resolution Segmentation Using Fuzzy Set Theory

A. Delmonte, C. Mercier, J. Pallud, I. Bloch, and Pietro Gori

In IEEE 16th International Symposium on Biomedical Imaging (ISBI), 2019

Abstract DOI Paper Code

The neural architecture of the white matter of the brain, obtained using tractography algorithms, can be divided into different tracts. Their function is, in many cases, still an object of study and might be affected in some syndromes or conditions. Obtaining a reproducible and correct segmentation is therefore crucial both in clinics and in research. However, it is difficult to obtain due to the huge number of fibers and high inter-subject variability. In this paper, we propose to segment and recognize tracts by directly modeling their anatomical definitions, which are usually based on relationships between structures. Since these definitions are mainly qualitative, we propose to model their intrinsic vagueness using fuzzy spatial relations and combine them into a single quantitative score mapped to each fiber. To cope with the high redundancy of tractograms and ease interpretation, we also take advantage of a simplification scheme based on a multi-resolution representation. This allows for an interactive and real-time navigation through different levels of detail. We illustrate our method using the Human Connectome Project dataset and compare it to other well-known white matter segmentation techniques.
MICCAI

Fast and Scalable Optimal Transport for Brain Tractograms

Jean Feydy, Pierre Roussillon, Alain Trouvé, and Pietro Gori

In Medical Image Computing and Computer Assisted Intervention – MICCAI, 2019

Abstract DOI Paper Code

We present a new multiscale algorithm for solving regularized Optimal Transport problems on the GPU, with a linear memory footprint. Relying on Sinkhorn divergences which are convex, smooth and positive definite loss functions, this method enables the computation of transport plans between millions of points in a matter of minutes. We show the effectiveness of this approach on brain tractograms modeled either as bundles of fibers or as track density maps. We use the resulting smooth assignments to perform label transfer for atlas-based segmentation of fiber tractograms. The parameters – blur and reach – of our method are meaningful, defining the minimum and maximum distance at which two fibers are compared with each other. They can be set according to anatomical knowledge. Furthermore, we also propose to estimate a probabilistic atlas of a population of track density maps as a Wasserstein barycenter. Our CUDA implementation is endowed with a user-friendly PyTorch interface, freely available on the PyPi repository (pip install geomloss) and at www.kernel-operations.io/geomloss.

2018

Eurographics-W

Progressive and Efficient Multi-Resolution Representations for Brain Tractograms

Corentin Mercier, Pietro Gori, Damien Rohmer, Marie-Paule Cani, Tamy Boubekeur, Jean-Marc Thiery, and Isabelle Bloch

In Eurographics Workshop VCBM, 2018

Abstract DOI Paper Code

Current tractography methods generate tractograms composed of millions of 3D polylines, called fibers, making visualization and interpretation extremely challenging, thus complexifying the use of this technique in a clinical environment. We propose to progressively simplify tractograms by grouping similar fibers into generalized cylinders. This produces a fine-grained multiresolution model that provides a progressive and real-time navigation through different levels of detail. This model preserves the overall structure of the tractogram and can be adapted to different measures of similarity. We also provide an efficient implementation of the method based on a Delaunay tetrahedralization. We illustrate our method using the Human Connectome Project dataset.

2017

MedIA

A Bayesian framework for joint morphometry of surface and curve meshes in multi-object complexes

Pietro Gori, Olivier Colliot, Linda Marrakchi-Kacem, Yulia Worbe, Cyril Poupon, Andreas Hartmann, Nicholas Ayache, and Stanley Durrleman

Medical Image Analysis, 2017

Abstract DOI Paper

We present a Bayesian framework for atlas construction of multi-object shape complexes comprised of both surface and curve meshes. It is general and can be applied to any parametric deformation framework and to all shape models with which it is possible to define probability density functions (PDF). Here, both curve and surface meshes are modelled as Gaussian random varifolds, using a finite-dimensional approximation space on which PDFs can be defined. Using this framework, we can automatically estimate the parameters balancing data-terms and deformation regularity, which previously required user tuning. Moreover, it is also possible to estimate a well-conditioned covariance matrix of the deformation parameters. We also extend the proposed framework to data-sets with multiple group labels. Groups share the same template and their deformation parameters are modelled with different distributions. We can statistically compare the groups’distributions since they are defined on the same space. We test our algorithm on 20 Gilles de la Tourette patients and 20 control subjects, using three sub-cortical regions and their incident white matter fiber bundles. We compare their morphological characteristics and variations using a single diffeomorphism in the ambient space. The proposed method will be integrated with the Deformetrica software package, publicly available at www.deformetrica.org.

2016

IEEE TMI

Parsimonious Approximation of Streamline Trajectories in White Matter Fiber Bundles

Pietro Gori, Olivier Colliot, Linda Marrakchi-Kacem, Yulia Worbe, Fabrizio De Vico Fallani, Mario Chavez, Cyril Poupon, Andreas Hartmann, Nicholas Ayache, and Stanley Durrleman

IEEE Transactions on Medical Imaging, 2016

Abstract DOI

Fiber bundles stemming from tractography algorithms contain many streamlines. They require therefore a great amount of computer memory and computational resources to be stored, visualised and processed. We propose an approximation scheme for fiber bundles which results in a parsimonious representation of weighted prototypes. Prototypes are chosen among the streamlines and they represent groups of similar streamlines. Their weight is related to the number of approximated streamlines. Both streamlines and prototypes are modelled as weighted currents. This computational model does not need point-to-point correspondences and two streamlines are considered similar if their endpoints are close to each other and if their pathways follow similar trajectories. Moreover, the space of weighted currents is a vector space with a closed-form metric. This permits easy computation of the approximation error and the selection of the prototypes is based on the minimisation of this error. We propose an iterative algorithm which approximates independently and simultaneously all the fascicles of the bundle in a fast and accurate way. We show that the resulting representation preserves the shape of the bundle and it can be used to accurately reconstruct the original structural connectivity. We evaluate our algorithm on bundles obtained from both deterministic and probabilistic tractography algorithms. The resulting approximations use on average only 2% of the original streamlines as prototypes. This drastically reduces the computational burden of the processes where the geometry of the streamlines is considered. We demonstrate its effectiveness using as example the registration between two fiber bundles.

2015

IPMI

Joint Morphometry of Fiber Tracts and Gray Matter Structures Using Double Diffeomorphisms

Pietro Gori, Olivier Colliot, Linda Marrakchi-Kacem, Yulia Worbe, Alexandre Routier, Cyril Poupon, Andreas Hartmann, Nicholas Ayache, and Stanley Durrleman

In Information Processing in Medical Imaging (IPMI), 2015

Abstract Paper

This work proposes an atlas construction method to jointly analyse the relative position and shape of fiber tracts and gray matter structures. It is based on a double diffeomorphism which is a composition of two diffeomorphisms. The first diffeomorphism acts only on the white matter keeping fixed the gray matter of the atlas. The resulting white matter, together with the gray matter, are then deformed by the second diffeomorphism. The two diffeomorphisms are related and jointly optimised. In this way, the first diffeomorphisms explain the variability in structural connectivity within the population, namely both changes in the connected areas of the gray matter and in the geometry of the pathway of the tracts. The second diffeomorphisms put into correspondence the homologous anatomical structures across subjects. Fiber bundles are approximated with weighted prototypes using the metric of weighted currents. The atlas, the covariance matrix of deformation parameters and the noise variance of each structure are automatically estimated using a Bayesian approach. This method is applied to patients with Tourette syndrome and controls showing a variability in the structural connectivity of the left cortico-putamen circuit.