View source for Shape Analysis on Neuroimaging Data

'''Tanya Glozman
'''
== Introduction ==

Understanding the relationships between structure and function in the brain is a key interest in neuroscience. Many studies indicate a correlation between structural/shape abnormalities and functional differences between subjects ranging from behavioral changes through functional differences to neurological disorders - an overview can be found in [http://www.ncbi.nlm.nih.gov/pubmed/23623973] However, these studies focus mostly on cortical structures. In this project we explored the efficacy of projections in describing the shape of two types of neuroimaging data: cortical segments acquired from Structural MRI data and white matter fascicles (neuronal tracts) acquired from Diffusion Weighted MRI tractography data. We developed a new descriptor based on projections, and proved it's efficacy on these types of data by performing SVM-based classification of the different structures. We show that our simple descriptor greatly reduces the dimentionality of the problem while preserving fine shape information required to discriminate between different structures.

== Data ==

Two types of neuroimaging data were explored:

'''1.Structural MRI data'''

Structural MRI data comes in the form of 2D images of axial cross-sections of the brain. MR RF-sequences are designed to generate contrast between different tissues in the brain. Most commonly, T1-weighted images are acquired, showing good contrast between the white matter and the gray matter. 
Through collaboration with the Psychology department, we were given access to MRI scans of 10 different healthy subjects.
This data was first pre-processed using FreeSurfer [http://freesurfer.net/]- a freely available software offering a set of tools for analysis and visualization of brain imaging data. Among the available tools, FreeSurfer provides segmentation of white matter from the rest of the brain, skull stripping, registration of the cortical surface of an individual with an atlas, labeling and segmenting the various regions of the cortical surface. The output of this pre-processing step was a set of 35 cortical segments per subject.

'''2.Diffusion MRI + Tractography data
'''

Diffusion MRI is an inherently different MR imaging technique which allows mapping the diffusion process of molecules, mainly water, in biological tissues. Molecular diffusion patterns in tissues reflects interactions with macromolecules, fibers, membranes, etc. Water molecule diffusion patterns can therefore reveal microscopic details about tissue architecture, either normal or in a diseased state [http://en.wikipedia.org/wiki/Diffusion_MRI]. The structure of the neuronal axons of white matter in the brain causes anisotropy in water diffusion in these structures: water will diffuse more rapidly in the direction aligned with the internal structure, and more slowly as it moves perpendicular to the preferred direction. For more details regarding this technique the reader is referred to [http://en.wikipedia.org/wiki/Diffusion_MRI]. The complete collection of white matter fascicles in a large volume is called a connectome.
Through Collaboration with Dr. Franco Pestilli, from the Psychology department, we were given access to connectome data of 6 healthy subjects, pre-processed with LiFE technology developed by Pestilli et al. <ref name = LiFE>Pestilli, F. Yeatman, JD, Rokem, A., Kay, KN, and Wandell, BA. Modelbased neuroanatomy: Validation and statistical inference in living connectomes. Under review, Nature Methods.</ref>. Each connectome is composed of 20 different fascicles (major neuronal tracts in the brain).

== Methods ==
'''Calculate Features'''

We developed a shape descriptor based on projections. To compute the descriptor, we propose the following algorithm:

For every structure:

1.Find principal axes (using Principal Component Analysis, see [http://en.wikipedia.org/wiki/Principal_component_analysis] for details)

2.Calculate projections onto several angles around the principal axes by calculating the distribution matrix as follows:

* discretize the projection image evenly into a 20x20 bin
* count the number of point in each bin <math>D_{ij} = number points in bin (i,j)</math>
* normalize s.t. <math>\sum_{ij} D_{ij} = 1</math>

This calculating takes into account the thickness of the structure along the projection direction. 

In this canonical representation, we reduced the dimensionality of the problem (from a 3D point cloud to a set of 20x20 2D images. Data manipulation and processing become simpler, and capturing the shape information reduces to calculating 2D shape descriptors such as shape moments and Shannon entropy. These features carry information about the shapes’ center of mass, it’s orientation and amount of uncertainty each pixel contributes to the overall shape. 

2D Shape Moments are calculated as follows:
<math>\ M_{pq}=\int\limits_{-\infty}^{\infty} \int\limits_{-\infty}^{\infty} x^py^qf(x,y) \,dx\, dy</math>

Shannon entropy for each projection is calculated as follows:
<math>\ H(X)=-\sum_{i} {P(x_i) \log_b P(x_i)}</math>

We concatenate the calculated values into a feature vector used to describe the fascicle. 

'''Classification'''

To test the effectiveness of our method we use these descriptors to discriminate between different structures using SVM-based classification. For more details regarding SVM. the reader is referred to [].
We trained One-vs-All SVM classifiers using 80% of all examples for training, and the remaining 20% for testing.
Cross-validation was performed using Leave-One-Out method.

== Results ==
Figure 1[[File:TwoSubjectsBlackBackground.png|thumb]] shows the canonical representation we achieve using projections: upper panel displays the Left Anterior Thalamic Radiation fascicle in two subjects; lower panel displays the same fascicles projected onto their principal planes. It is evident that using projections reduces the dimensionality of the problem while still retaining much of the structural information. Using this canonical view it is possible to compare between the fascicles of different subjects.

Figure 2 [[File:20Fascicles.png|thumb]]shows the projections of the 20 different fascicles in one subject. The differences between the various structures are clearly seen in this representation. It is interesting to note, however, that there is a similarity between the images in the 1st and 2nd column and the images in the 3rd and 4th column. This is due to the fact that the fascicles are ordered such that the same fascicle on the left and right side are displayed one after the other.

Figure 3 [[File:20Fascicles.png|thumb]] shows the projections of the same fascicle (Right Thalamic Radiation) in 6 different subjects. The 'tree-like'structure is clearly seen in all images, but the fine details can also be spotted and used to identify differences.

Figure 4 [[File:confmat.png|thumb]] shows the confusion matrix for the classification of different fascicles. The nearly-diagonal structure of the confusion matrix for this experiment clearly shows that our simple descriptor is able to distinguish between different structures. Note the 2x2 block structure which hints on the symmetrical structure of the brain: the fascicles on the left and right side of the brain have a similar geometry.

Figure 5 [[File:structuralConfmat.png|thumb]] shows the confusion matrix for the classification of different cortical structures. Here too, the nearly diagonal structure proves the merit of our technique for this type of data.

== Conclusions ==

In summary, we developed a shape descriptor based on projections and proved it's effectiveness on two types of neuroimaging data. Our descriptor greately reduces the dimensionality and complexity of the problem while retaining the fine shape information. We plan to further develop our method and adjust it to differentiating between healthy and diseased populations with regards to neurological disorders.

== Appendix I ==
This project is ongoing. The data was acquired through collaboration with Dr. Franco Pestilli (for the connectome data )and Prof. Tony Norcia's group (for the structural MRI data). I am not free to share the data. Since we are hoping to publish the results of this work, we prefer to not share the code at this time. Please email tanyagl@stanford.edu to learn more.