RESULTSMETHODS

Quantitative Metrics for Describing Topographic Organization in IndividualsCody Allen1; Anthony I. Jack, PhD2

1Department of Physics; 2Department of Cognitive Science Case Western Reserve University

ABSTRACTVisual areas in the brain of both monkey and man contain organized maps of the visual field. These maps can be measured using fMRI while participants view visual stimuli presented at different locations relative to a fixation point. However, current methods for topographic mapping are purely qualitative in nature, and involve using visual inspection to search for consistent patterns in pseudo-colored figures. We seek to develop a method of quantitatively describing topographic organization on the cortical surface, allowing us to describe differences between individuals, and between distinct visual areas in occipital, parietal, and frontal cortex. In addition to developing quantitative metrics, more meaningful color-coded topographic maps will be created with the use of overlaid gradient fields. A goal of this research is to identify the neural basis for individual differences in visuo-spatial ability. The techniques developed in this research might one day be used to predict how well a person can perform word searches, play baseball, or even solve physics problems.

1. Delayed Saccade TaskBlood-oxygen-level dependent (BOLD) fMRI data is collected as a subject performs the delayed saccade task depicted in Fig 1 for angles, θ, of 30°, 90°, 150°, 210°, 270°, and 330°. Collectively, these angles represent the top, middle, and bottom of both the left and the right visual field.

2. Map ResponsesIn order to create a topographic map, the cortical surface is squished into a 2D representation, much as globes are represented by flat maps. The fMRI data points are tied to points on this 2D surface, and for each one, it is determined whether local neurons responded most strongly to stimulation in the top, middle, or bottom of the visual field. The color scheme depicted in Fig 2 (a), is used when creating the colored scatter plot shown in Fig 2 (b).

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Fig 1. Delayed saccade task: A visual stimulus is displayed at angle θ, and after it disappears, the subject performs a saccade, glancing at the previous location of the stimulus and then returning focus to the central fixation point.

Fig 3. Colored surface mapping: The scatter plot shown in Fig 2 (b) is transformed into this surface plot. Darker shading signifies areas that were not preferential to a particular region of the visual field.

Fig 4. Colored surface mapping with overlaid gradient field: A gradient field is superimposed on a magnified region of the surface plot shown in Fig 3. The arrows indicate the direction of greatest change in visual field representation and are colored as shown in Fig 2 (a). For example, cyan arrows show a trend from the top of the visual field to the bottom.

Fig 6. Strength of regression by region: The x-axis displays the coefficient of determination (R2) of the regression model for each region on the y-axis. The dorsal path of V2 shows the greatest topographic organization, while extra-occipital regions such as LIP, DLPFC, and FEF show little to no retinotopic organization.

Fig 5. Strength of regression as a function of cutoff: Plots such as this one are used to determine the optimal 3D (volume) and 2D (surface) cutoffs for the regression model. The lines represent different volume cutoffs (in mm). For this particular region (V3), the optimal volume cutoff is 3 mm and the optimal surface cutoff is near 5 mm, as this is where the coefficient of determination is greatest.

Transdisciplinary approaches to the mind

CWRUDepartment of Cognitive Science

Fig 2. Colored point mapping: (a) Colors assigned to the top, middle, and bottom of the visual field for plotting purposes. The arrows are described in the caption of Fig 4. (b) 2D topographic map of dorsal visual cortex that uses this color scheme. Each point shows whether that region of the cortex exhibited the greatest fMRI response to stimulation in the top, middle, or bottom of the visual field.

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3. Create Surface MapThe scatter plot shown in Fig 2 (b) is transformed into the surface plot shown in Fig 3, which better represents that the map is of a cortical surface and not a random scatter of points. In this surface plot, the color intensity is proportional to the consistency with which an area showed a preferential response to a particular region of the visual field. For example, a brightly green area responded most strongly to the bottom of the visual field across trials, while a dark, shaded region did not show preference.

4. Create Regression ModelFor each of the data points shown in Fig 2 (b), the goal is to look at nearby points to see if a trend can be identified. Such a trend would suggest topographic organization. “Nearby” points are defined as those located within a certain radius on the true 3D cortical surface and also within a separate 2D radius in the flat cortical representation. These 3D and 2D radii are referred to as the volume cutoff and surface cutoff, respectively.

Three multilinear regression models are built with the 2D x and y coordinates of nearby points as predictors. In the first, the difference in strength between the “top” and “middle” responses serves as the response associated with the predictors, and is referred to as Up-Mid. Similarly, the other two models correspond to Up-Down and Mid-Down. The coefficient of determination (R2) corresponds to how well location can be used to predict a preferential response, and therefore is correlates to topographic organization. The slopes in this regression model refer to how strongly visual field representation is changing with location and can be viewed graphically as the overlaid gradient field shown in Fig 4.

In order to determine appropriate volume and surface cutoffs for different regions of the cortex, many cutoffs were used and those which produced the highest coefficients of determination for the regression model were considered optimal. It was found that a constant volume cutoff near 2.75 mm was optimal across all regions and the optimal surface cutoff varied by region as shown in Table 1.

Table 1. Optimal surface cutoff by region. The surface cutoff on the right results in the highest coefficient of determination for the region on the left.

CONCLUSIONSThe results from the analytic method shown in Fig 6 show strong topographic organization in early occipital visual areas, as was previously known to exist. The results also show little or no retinotopic organization in extra-occipital regions such as FEF, DLPFC, and LIP, where topographic organization has been proposed, but not yet quantitatively shown to exist.

The analytic method is promising and could be generalized to investigate topographic organization beyond retinotopy. However, further studies should establish a false alarm rate to ensure that over-fitting in the regression model is not producing misleading results. An interesting use of this method would be to look for a correlation between topographic organization and performance on visuo-spatial tasks. Such a study might one day use fMRI data to predict how well a subject performs word searches, plays baseball, or perhaps even solves physics problems!

ACKNOWLEDGMENTSI would like to thank Tom Reid and Dr. Robert Brown of the CWRU Department of Physics for their contributions to this project. They laid the foundation that made this project possible.