Anthony & Jesse
Background
What is Retinotopy?
Early visual areas are organized by a principle known as retinotopy. The basic idea behind this principle is that stimulation of adjacent regions of the visual field activate adjacent locations on the cortical surface, and specific locations in these areas respond to stimulation only in particular parts of the visual field. In addition, the preference for particular locations in the visual field across the cortical surface is highly consistent across individuals and can be mapped with fMRI.
Discovery of Visual Field Maps
In the early 1900s, Inouye and Holmes are the first to discover that the location of lesions to primary visual cortex (V1) is related to visual field deficits. For instance, damage to the V1 in the left hemisphere results in impaired vision in the right visual field and damage to the anterior portion of V1 results in impaired vision at peripheral locations in the visual field.
Electrophysiological recordings in the 1940s identified additional field maps adjacent to V1 such as V2 and V3. Each map contains a representation of the entire visual field when combined across hemispheres. However, transitions between maps are smooth in that the areas near the boundaries of field maps both respond to nearby locations in the visual field, and locations in the visual field can be represented by two paramters: Polar angle and eccentricity.
Polar Angle and Eccentricity Bias
Each visual field map in each hemisphere has either an entire hemifield representation of visual space (or a quarter-field representation if separating maps such as V2 and V3 into ventral and dorsal subdivisions). In order to determine which part of the visual field an area is representing, we can use a stimulus that sweeps across the visual field at different polar angles (see figure F, to the right). BOLD activity that correlates with either the upper, horizontal, or lower visual field will be color-coded accordingly, allowing us to identify when there is a mirror-reversal of polar angle mapping. These reversals mark the dividing boundaries between different visual field maps in human cortex. For example, V1 has a hemifield representation, but V2v has a quarter-field representations in which the mapping of polar angle is mirror reversed relative to V1. Similarly, the representation of polar angle in V3v is mirror reversed relative to V2v.
While the cortex is divided according to reversals of polar angle representations, shared across all of the these field maps is an organization of eccentricity biases. As shown in figure E, foveal representations are more posterior, with increasingly peripheral biases radiating anteriorly. V1 through V4 have their foveal representations clustered in the posterior calcarine, known as the confluent fovea. There are other foveal representations, such as those on the ventral occipital surface (VO-1 & VO-2) or the parahippocampal gyrus (PHC-1 & PHC-2).
Beyond the Occipital Lobe
Interestingly, retinotopic representations of visual space aren't constrained to the occipital lobe, with recent studies demonstrating that they extend well into the parietal and temporal lobes. As visible within the figure to the right, many visual field maps are reliably identifiable across subjects dorsal and ventral to the occipital lobe.
Swisher et al. 2007 demonstrated that the posterior parietal cortex in humans is reliably activated by visual stimulation and is organized with repeating contralateral hemifield represenations running along the medial intraparietal sulcus. While the role of the PPC in cognition is under study, the existence of visual field maps restricts the potential processing in this region to visual in nature.
Furthermore, Arcaro et al. 2009 have shown that, anterior to VO maps, are visual field maps that extend across the colateral sulcus into parahippocampal cortex. As illustrated in the figure to the right, PHC-1 and PHC-2 both contain representations of an entire hemifield and share a fovea. Both PHC maps have a strong preference for peripheral stimuli, and considering that these maps overlap with traditionally defined PPA, this data suggest that high-level vision may be constrained by more low-level representations and contain more functional subunits than previously thought.
Methods for Mapping Visual Cortex
Traveling Wave Analysis
Engel et al. 1994 developed a method for defining visual field maps with fMRI by using stimuli that elicit a traveling wave of activation across the cortical surface. Since visual cortex is organized with according to polar angle and eccentricity, different stimuli must be used to generate traveling waves of activation that sweep from one end of a map through to the other in a single cycle. In typical retinotopic mapping scans, the stimulus cycle is repeated six times and this allows phase encoding to be performed.
Stimuli
Eccentricity is mapped using stimuli consisting of a series of expanding concentric rings filled with a high contrast checkerboard pattern. One cycle of the stimulus entails the rings expanding from the most foveal eccentricity to the most peripheral eccentricity. The logic of this approach is that voxels in posterior V1 that respond to foveal stimulation will activate most strongly in the beginning of a cycle when the rings are in the center of the visual field, and voxels in anterior V1 that respond preferentially to peripheral stimulation and will show the greatest response towards the end of a cycle when the ring occupies outer parts in the visual field. Intermediate eccentricities activate intermediate locations in the eccentricity map.
Polar angle is mapped using a wedge checkerboard stimulus that rotates around the visual field like the hand of a clock with the point of the wedge fixed in the center of the screen. One cycle of this stimulus consists of the wedge rotating 360 degrees, which covers the whole visual field one time. In a typical polar angle scan, the wedge starts in the upper visual field and moves clockwise for six cycles. Each V1 has a representation of the contralateral hemifield that is flipped over the horizontal meridian. That is, regions in the upper portion of V1 represent the lower visual fiend and regions in lower V1 represent the upper visual field.
Phase Encoding
The traveling wave of response generated by the ring and wedge stimuli allow you to determine the the most effective eccentricity (or polar angle) for driving a given voxel using a technique known as phase encoding. This use of this technique depends on the ring (or wedge) stimulus sweeping across each location in the visual field once in each cycle of the stimulus. Therefore, voxels that are part of a visual field map should illustrate six peaks in their response over the course of a run containing six cycles. The fact that different eccentricities (or polar angles) are sampled at different times in the cycle allows you to determine the particular degree of eccentricity (or polar angle) that most strongly activates each voxel. For example, imagine this were the timecourse of a voxel in an eccentricity scan:
If the cycle begins with with rings that occupy space in the center of the visual field, the peaks in the response of voxels with a foveal preference should be earlier in time than peaks in the response of voxels with peripheral preference. Shown below is the phase-shifted timecourse of a voxel with a peripheral preference.
Finding the Phase
Decomposing each voxel's timecourse into discrete frequency bands using a Fourier transform allows you to estimate the proportion of variance explained by each signal modulation at each frequency. If a voxel is retinotopic, the frequency with the most energy should be equal to the number of cycles in the experiment. Shown below is the energy at each frequency extracted with the Fourier transform:
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As expected, the peak in this voxel's power spectrum is at 6 cycles, which is equal to the number of cycles in the experiment. This suggests that the voxel is retinotopic but is not informative about the particular eccentritiy (or polar angle) that optimally activates it. To determine the time lag that best explains the data, the 6-cycle sine wave is shifted and the phase shift that generates the best fit to the data is used to estimate the eccentricity (or polar angle) preferred by the voxel. If a voxel prefers foveal stimuli, for example, a small time shift should produce the best fit because foveal rings are presented at the beginning of the cycles in the eccentricity mapping experiment. Then, the same procedure is performed at every voxel, and a similar analysis can be applied to polar angle mapping experiments. To generate a map of polar angle and eccentricity biases, the range of phase shifts is color coded and mapped onto each voxel.
Population Receptive Field (pRF) Analysis
An alternative method for modeling the organization of retinotopic visual regions within human cortex, population receptive field (pRF) modeling, uses the nature of neuronal receptive fields, rather than traveling waves, as a method for correlating BOLD responses with spatially localized visual stimulation. One benefit of this model is that it also allows the user to model the size of neuronal population's receptive field.
Illustrated in the figure above is the pipeline for analysis performed on a voxel-by-voxel basis in pRF analyses. The largest assumption of the pRF analysis is that neurons are clustered in populations that share similarly positioned and sized receptive fields. The first step of the pRF pipeline is to thus model this receptive field (RF) with a position (X,Y) in visual space and a certain size (sigma). In step 2, given a certain stimulus, which in this example figure is a rotating wedge, we predict that this wedge will stimulate this RF at only a certain time (when it is in the upper right quadrant) and at some intensity given how much of the RF the wedge falls in. Given this model, stimulus, and an HRF, we can create a prediction timecourse of this voxel's activity if it had this RF. We then see how good of a fit this prediction is with the voxel's actual timecourse is. When the model gets the correct RF, the error between predicted and measured timecourses will be minimal, and the model will have "solved" this voxel's RF. This process is iterative, and the model will go through several fits, each time changing the size of the 2D gaussian modeling the RF (sigma) and the RF's position in space. Each receptive field can be modeled mathematically as:
and the final receptive field per voxel is achieved in two steps. First, with spatial smoothing of the data to find a coarse solution of a smoothed brain region's RF, and then a fine calculation of RF solutions per voxel. This coarse-to-fine method minimizes the amount of calculation time while maximizing the probability of finding a global solution (Dumoulin & Wandell 2008). This explained in more detail in the methods below.
Methods
Given identical stimuli--rotation wedges and expanding rings(below)--which analysis, traveling wave vs. pRF, will prove to yield more reliable and interpretable eccentricity and polar angle maps of human visual cortex? Below are the methods used to answer this question.
Defining Occipital Field Maps
In order to interpret the results and make more accurate comparisons and contrasts between the traveling wave and pRF model results, we defined V1-V4 on each subject's brain using the pRF results from the analysis of the sliding bars stimuli. Boundaries were drawn beginning with V1, which is known to have a contralateral hemifield representation, and then radiating visual field maps were drawn at quarter-field mirror reversals. Area hV4 was drawn according to the anatomy of the posterior transverse colateral sulcus (PTCOS).
PRF & Traveling Wave Model Fits
Traveling Wave Model Fitting
See phase encoding section of the methods above.
pRF Model Fitting
Solving the pRF model involves a two-step process, which starts with a coarse analysis and then ends with a fine-coarse calculation that is spatially constrained by the solution from the coarse analysis. The first coarse step, called grid fitting, involves resampling the functional data to 1mm isotropic voxels. The data is then smoothed according to a 5mm FWHM gaussian kernel (to remove high-frequency noise) which respects the topology of the cortical sheet. In the second stage, fine fitting, no spatial smoothing occurs, and the final pRF is achieved by independently deriving the location of the RF (X and Y locations) and the size of the RF (sigma). X and Y coordinates, after a polar transformation, can yield traditional eccentricity maps, as well as the polar angle field maps.
Results
Eccentricity
Polar Angle Maps
Conclusions
References
Acaro, M.J., McMains, S.A., Singer, B.D., & Kastner, S. (2009) Retinotopic organization of human ventral visual cortex. J Neurosci, 29, 10638-10652.
Amano, K., Wandell, B.A., & Dumoulin, S. (2009). Visual field maps, population receptive field sizes, and visual field coverage in the human MT+ complex. J Neurophysiol, 102, 2704-2718.
Dumoulin, S., & Wandell, B.A. (2008). Population receptive field estimates in human visual cortex. NeuroImage, 39, 647-660.
Engel, S.A., Rumelhart, D.E., Wandell, B.A., Lee, A.T., Glover, G.H., Chichilniski, E.J., & Shadlen, M.N. (1994). Functional magnetic resonance imaging of human visual cortex. Nature, 369, 525.
Holmes, G. (1918). Disturbances of vision by cerebral lesions. Bre. J. Opthal., 2, 353–384.
Inouye, T. (1909). Die Sehstroungen bei Schussverietzungen der kortikalen Sehsphare (Leipzig, W.: Engelmann).
Swisher, J.D., Halko, M.A., Merabet, L.B., McMains, S.A., & Somers, D.C. (2007). Visual topography of human intraparietal sulcus. J Neurosci, 27(20), 5326–5337.
Wandell, B.A., Dumoulin, S., & Brewer, A.A. (2007). Visual field maps in human cortex. Neuron, 56, 366-383.
Wandell, B.A., & Winawer, J. (2011). Imaging retinotopic maps in the human brain. Vision Research, 51, 718-737.