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Master's Thesis

Title and Overview

• Title: "Novel Methods for the Visualization and Analysis of Functional Maps in Cortex"
• Diploma (master's) thesis, Stanford University, CA, U.S.A., 11/2000 - 06/2001
• Sponsored by the Department of Psychology and the Department of Electrical Engineering
• Stanford's Vision, Imaging Science, and Technology Activities (VISTA) Homepage
• Supervisor at Stanford University: Professor Brian A. Wandell
• Supervisor at the University of Karlsruhe: Prof. Dr. rer. nat. Olaf Dössel

This page is intended to give an overview. For more information, please refer to my master's thesis (PDF). Screenshots of my software tool can be found here.

Abstract 

Semi-Automatic Identification of Retinotopic Visual Areas

PURPOSE: We present a tool to identify retinotopic visual areas in a simple, automatic, and objective way from fMRI data.

BACKGROUND: Viewing a flickering, rotating wedge visual stimulus creates a traveling wave in the visual cortex that can be measured with fMRI. The fMRI signals can be used to identify the retinotopic visual areas. The traveling wave is easier to visualize on a flattened representation than a 3-dimensional representation. Therefore, 2D images representing computationally flattened cortex are typically used to segregate the retinotopic visual areas. 

METHODS: We have developed a general approach for fitting a two-dimensional parameterized model (atlas) to a measured fMRI signal. The atlas represents an expected pattern of activity that can be found in most subjects; in this case, the organization of retinotopic visual areas. To identify the visual areas, the atlas is coarsely aligned with the measured signal. Then, the atlas is elastically deformed to fit the measured data by minimizing an energy function using a custom hierarchical optimization technique. The elastic deformation is based on a spline representation of the displacement field. 

RESULTS: We can overlay the visual areas from the deformed atlas onto the measurements. Thus, the retinotopic visual areas can be objectively and automatically identified based on standard traveling wave data. The visual areas found by the program are similar to those generated by an experienced human operator.

Introduction

Medical imaging techniques such as magnetic resonance imaging (MRI) can be used to visualize the brain. Not only the anatomy is of interest, but also functional measurements that help to understand how the brain works.

When looking at the human brain, the cortical surface with its many folds can be seen. The folds make it difficult to evaluate spatial relationships between different points on the cortical surface. Methods have been developed that allow flattening the cortex. It can then be displayed and viewed as a two-dimensional image. In addition to visualizing just the anatomy, functional magnetic resonance imaging (fMRI) can be used to overlay functional data onto the flattened anatomical image.

The flat view is particularly useful for dividing the visual cortex into different visual areas. fMRI images, recorded with different stimuli, can be used to separate the visual areas. Identifying the visual areas, i.e., finding the boundaries between visual areas, is important. The results can be used to compare normal individuals with observers who have various kinds of deficits.

The aim of this project is to separate different visual areas with the help of flattened representations of the visual cortex. 

The primary visual cortex (V1) and nearby areas show retinotopic organization. Therefore, it is possible to create a traveling wave response in these areas by stimulating the sensors in the retina with an appropriate stimulus. A stimulus that moves with a constant velocity will cause the responsive neurons within the visual field to respond with the same frequency. However, the temporal phase will be different for different neurons depending on their locations. fMRI images, recorded with rotating wedge stimuli, can be used to generate phase maps. These images show pattern of activity that are expected to separate the visual areas because the traveling wave reverses its direction at the boundaries.

To find the boundaries, a model (atlas) of the phase map is created. Phase maps from different brains are expected to vary by a deformable stretching of this atlas. The atlas is morphed to fit a measured phase map by minimizing an error metric (difference measure between atlas and data).  Since the locations of the boundaries in the atlas are known, the locations of the boundaries in the phase map can be obtained by overlaying the morphed atlas onto the phase map.

Aim

The borders can be found and marked manually (Figure 1 and Figure 2 ). The result obtained vary if different users have to find the boundaries and also if the same user has to mark boundaries in the same flat map at different times.

It is therefore desirable to make the separation effort more systematic and less user dependent. Our first aim is to automatically find the boundary between V1 and the area that surrounds it, V2.

Figure 1 Phase Map

Figure 2 Phase Map with Manually Marked Boundaries of V1

Methods

An atlas is created. This is a template of the pattern of activity that is expected to separate the visual areas. Phase maps from different brains vary by a deformable stretching of this atlas. The atlas is then morphed according to a measured phase map by minimizing some error. The parameters of the transformation may be used to characterize differences between people.

The procedure for finding boundaries is as follows. First, the user specifies points, e.g. on the boundaries. Second, the atlas (or the measured phase map) is rotated. The angle of rotation is determined automatically. Third, the phase map is cropped to the size of the atlas. Fourth, the atlas is adjusted to fit the data using hierarchical spline-based image registration (Szeliski). This image registration approach uses spline representations of the displacement field. The registration is done on low-resolution images first and the result of this first step is used to initialize higher-resolution estimates. Fifth, the phase map is displayed together with an overlay that shows the separated visual area(s) and/or boundaries.

A spline-based image registration algorithm was chosen because the flow field for every single pixel is very sensitive to noise. Also, the spline-based approach has advantages over correlation-based approaches in terms of computational efficiency.

Tools

• Windows 2000 Workstation

• MATLAB V.6 R.12

Background

• Computational Neuroimaging of Human Visual Cortex.
  B. Wandell (1999). Annual Review of Neuroscience v. 10 no. 22 Computational Neuroimaging of Human Visual Cortex

• Visualization and Measurement of the Cortical Surface. 
  B. Wandell, S. Chial and B. Backus (2000). Journal of Cognitive Neuroscience.  vol 12, no. 5. pp. 739-52.
  This paper describes the methods used in the unfolding software.  It also provides an overview of the principles, problems, and related methods that can be found at other sites.  

08/2009