Analyzing Brain Plasticity in Math Learning Using Automated Dissection and Analysis of White Matter Tracts Through dMRI

Participants : Dietsje Jolles [Stanford Medical School] , Demian Wassermann, Ritika Chokhani [Stanford Medical School] , Jennifer Richardson [Stanford Medical School] , Caitlin Tenison [Stanford Medical School] , Roland Bammer [Stanford Medical School] , Lynn Fuchs [Vanderbit University] , Kaustubh Supekar [Stanford Medical School] , Vinod Menon [Stanford Medical School] .

In a collaboration with Stanford Medical School, we explored longitudinal changes in white matter connectivity triggered by intensive math learning. Plasticity of white matter tracts is thought to be essential for cognitive development and academic skill acquisition in children. However, a dearth of high-quality diffusion tensor imaging (DTI) data measuring longitudinal changes with learning, as well as methodological difficulties in multi-time point tract identification have limited our ability to investigate plasticity of specific white matter tracts. With this contribution, we examined learning-related changes of white matter tracts innervating inferior parietal, prefrontal and temporal regions following an intense two-month math tutoring program. DTI data were acquired from 18 third grade children, both before and after tutoring. A novel fiber tracking algorithm based on a White Matter Query Language (WMQL) was used to identify three sections of the superior longitudinal fasciculus (SLF) linking frontal and parietal (SLF-FP), parietal and temporal (SLF-PT) and frontal and temporal (SLF-FT) cortices, from which we created child-specific probabilistic maps. The SLF-FP, SLF-FT, and SLF-PT tracts identified with the WMQL method were highly reliable across the two time points and showed close correspondence to tracts previously described in adults. Notably, individual differences in behavioral gains after two months of tutoring were specifically correlated with plasticity in the left SLF-FT tract. Our results extend previous findings of individual differences in white matter integrity, and provide important new insights into white matter plasticity related to math learning in childhood. More generally, our quantitative approach will be useful for future studies examining longitudinal changes in white matter integrity associated with cognitive skill development.

Quantifying Uncertainty in Diffeomorphic Medical Landmark Registration

Participants : Demian Wassermann, Matt Toew [Harvard Medical School - Brigham and Women's Hospital] , Marc Niethammer [University of North Carolina at Chapel Hill] , William Wells Iii [Harvard Medical School - Brigham and Women's Hospital, MIT] .

In a collaboration with Harvard Medical School, the Brigham and Women's Hospital, MIT and the University of North Carolina at Chapel Hill, we proposed a novel mathematical framework to represent uncertainty in diffeomorphic registration techniques. Particularly, we introduced a novel mathematical framework for representing uncertainty in large deformation diffeomorphic image registration. The Bayesian posterior distribution over the deformations aligning a moving and a fixed image is approximated via a variational formulation. A stochastic differential equation (SDE) modeling the deformations as the evolution of a time-varying velocity field leads to a prior density over deformations in the form of a Gaussian process. This permits estimating the full posterior distribution in order to represent uncertainty, in contrast to methods in which the posterior is approximated via Monte Carlo sampling or maximized in maximum a-posteriori (MAP) estimation. The framework was demonstrated in the case of landmark-based image registration, including simulated data and annotated pre and intra-operative 3D images. This type of registration can be extended to several anatomical objects such as white matter tracts represented as streamlines.

Group Comparisons on White Matter Tracts in Native Space

Participants : Eleftherios Garyfallidis [University of Sherbrooke] , Demian Wassermann, Maxime Descoteaux [University of Sherbrooke] .

Let us suppose that we want to study specific fiber bundles in different subjects. The common approach would be to use a voxel-wise analyses which will warp scalar volumes in a common space, e.g. MNI space, and show how every subject differentiates from an average template. However, we know that with averaging and warping much of the specific information about the individual subjects' differences is lost. In this work, we provide a solution to this problem by using local streamline registration of specific bundles from different subjects. We show that with this new method we can keep track of the differences from every subject to every other subject in our group study.

Perfusion Deconvolution via SHORE and Laplacian Regularization

Participants : Marco Pizzolato, Auro Ghosh, Timothé Boutelier [Olea Medical, La Ciotat] , Rachid Deriche.

Perfusion imaging comprehensively refers to the recovery of parameters of interest which are related to the passage of blood in the parenchyma (i.e. the functional part) of a tissue. The amount of perfusion is related to both the functionality of the parenchyma and its level of activity. By means of imaging techniques such as Dynamic Susceptibility Contrast MRI it is possible, in each voxel, to measure the tissue concentration $Ct\left(t\right)$ of a tracer injected before the scanning in the vascular system. According to the indicator dilution theory1 this is related to the concentration measured in an arterial region $Ca\left(t\right)$ described by a convolution with $R\left(t\right)$ that is the unknown residue function expressing the remaining time-dependent tracer quantity in the voxel. Historically $R\left(t\right)$ is obtained exploiting the convolution theorem $R\left(t\right)=FT-1FT\left[Ct\right(t\left)\right]/FT\left[Ca\right(t\left)\right]$ . However deconvolution is an ill-posed problem making this method very sensitive to noise. Many regularization techniques have been proposed but among all the most adopted technique is truncated Singular Value Decomposition, tSVD. However tSVD is known to underestimate an important perfusion parameter that is the blood flow BF, which can be computed as the maximum peak of the recovered $R\left(t\right)$. In this work we propose to use the Simple Harmonic Reconstruction and Estimation framework (SHORE) to estimate $R\left(t\right)$ in order to obtain a better parameter estimation. We regularize SHORE using Laplacian regularization. We compare the results with tSVD.

This work has been submitted to ISMRM 2015.

Perfusion MRI Deconvolution with Delay Estimation and Non-negativity Constraints

Participants : Marco Pizzolato, Auro Ghosh, Timothé Boutelier [Olea Medical, La Ciotat] , Rachid Deriche.

Perfusion MRI deconvolution aims to recover the time-dependent residual amount of indicator (residue function) from the measured arterial and tissue concentration time-curves. The deconvolution is complicated by the presence of a time lag between the measured concentrations. Moreover the residue function must be non-negative and its shape may become non-monotonic due to dispersion phenomena. We introduce Modified Exponential Bases (MEB) to perform deconvolution. The MEB generalizes the previously proposed exponential approximation (EA) by taking into account the time lag and introducing non-negativity constraints for the recovered residue function also in the case of non-monotonic dispersed shapes, thus overcoming the limitation due to the non-increasing assumtion of the EA. The deconvolution problem is solved linearly. Quantitative comparisons with the widespread block-circulant Singular Value Decomposition show favorable results in recovering the residue function.

This work has been submitted to ISBI 2015.