We thank the VISTA software group (Brian Wandell and associates, at Stanford).
S. S. was supported by McNair 2280403105,NEI R01-EY109272, and NEI R01-EY024019 and as HHMI Early Carrer Award. A. P. and G. K. was supported by the Max-Planck Society, G. K. was supported by the PLASTICISE project of the 7th Framework Programme of the European Commission, Contract no. HEATH-F2-2009-223524.

1. Data Acquisition
<ol>
	<li>Prepare a stimulus protocol that is effective in eliciting a reliable retinotopic visual response as previously described in Dumoulin and Wandell1 and Lee et al.2. However, other well established paradigms are also applicable depending on the specific experimental question to be addressed.</li>
	<li>Present bar stimuli drifting across the screen sequentially along 8 directions of space, in steps of 45 degrees. Ensure that the motion is in synchrony with scann...

<ol>
	<li>Dumoulin, S. O., Wandell, B. A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Population+receptive+field+estimates+in+human+visual+cortex.">Population receptive field estimates in human visual cortex.</a> Neuroimage. 39, 647-660 (2008).</li><li>Lee, S., Papanikolaou, A., Logothetis, N. K., Smirnakis, S. M., Keliris, G. A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+new+method+for+estimating+population+receptive+field+topography+in+visual+cortex.">A new method for estimating population receptive field topography in visual cortex.</a> Neuroimage. 81, 144-157 (2013).</li><li>Hastie, T., Tibshirani, R., Friedman, J. H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> The elements of statistical learning : data mining, inference, and prediction. , (2009).</li><li>Sereno, M. I., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Borders+of+multiple+visual+areas+in+humans+revealed+by+functional+magnetic+resonance+imaging.">Borders of multiple visual areas in humans revealed by functional magnetic resonance imaging.</a> Science. 268, 889-893 (1995).</li><li>Engel, S. A., Glover, G. H., Wandell, B. A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Retinotopic+organization+in+human+visual+cortex+and+the+spatial+precision+of+functional+MRI.">Retinotopic organization in human visual cortex and the spatial precision of functional MRI.</a> Cereb Cortex. 7, 181-192 (1997).</li><li>Engel, S. A., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=fMRI+of+human+visual+cortex.">fMRI of human visual cortex.</a> Nature. 369, 525 (1994).</li><li>DeYoe, E. A., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mapping+striate+and+extrastriate+visual+areas+in+human+cerebral+cortex.">Mapping striate and extrastriate visual areas in human cerebral cortex.</a> Proc Natl Acad Sci U S A. 93, 2382-2386 (1996).</li><li>Greene, C. A., Dumoulin, S. O., Harvey, B. M., Ress, D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Measurement+of+population+receptive+fields+in+human+early+visual+cortex+using+back-projection+tomography.">Measurement of population receptive fields in human early visual cortex using back-projection tomography.</a> J Vis. , (2014).</li><li>Zuiderbaan, W., Harvey, B. M., Dumoulin, S. O. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Modeling+center-surround+configurations+in+population+receptive+fields+using+fMRI.">Modeling center-surround configurations in population receptive fields using fMRI.</a> J Vis. , (2012).</li><li>Harvey, B. M., Dumoulin, S. O. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+relationship+between+cortical+magnification+factor+and+population+receptive+field+size+in+human+visual+cortex:+constancies+in+cortical+architecture.">The relationship between cortical magnification factor and population receptive field size in human visual cortex: constancies in cortical architecture.</a> J Neurosci. 31, 13604-13612 (2011).</li><li>Haak, K. V., Cornelissen, F. W., Morland, A. B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Population+receptive+field+dynamics+in+human+visual+cortex.">Population receptive field dynamics in human visual cortex.</a> PLoS One. 7, e37686 (2012).</li></ol>

This article demonstrates how to estimate the topography of visual population receptive fields in human visual cortex and how to use it to select an appropriate parametric model for the receptive field. For a successful retinotopy, an appropriate stimulation protocol and an efficient analysis method should be selected, and the subject&#8217;s experimental parameters (motion and fixation) should be optimized. Bar stimuli moving sequentially across the visual field are an efficient stimulus paradigm for pRF estimation as i...

Functional magnetic resonance imaging (fMRI) measures non-invasively the functional organization of visual cortex at a macroscopic scale (typically on the order of millimeters). Early fMRI retinotopy studies used a coherence measure between stimulus location and elicited BOLD responses4-7. These studies typically did not estimate population receptive field size. Later, Dumoulin and Wandell1 proposed a method to overcome such a limitation by explicitly modeling the pRF location and size, using a linear function of this model to predict the BOLD response. However, one limitation of this pioneering method is that the parametric pRF model has to be chosen a-priori, and may lead to erroneous pRF estimates if it turns out not to be appropriate. 
To overcome limitations of the parametric pRF-model method, new methods have been developed recently. These methods directly predict the BOLD response to the stimulus by reconstructing the pRF topography. A method8 proposed by Greene and colleagues reconstructs the pRF topography by back-projecting the BOLD responses to the individual 1D stimulus spaces and building the pRF topography in the 2D stimulus space like a typical computer tomography technique. On the other hand, the method2 proposed by us directly estimates the 2D pRF topography by using linear regression and applying a regularization technique. In this method, the pRF topography is represented as a set of weights which is multiplied by the stimulus to estimate the neuronal population response of a given voxel. Then, the final Blood Oxygen Level-Dependent (BOLD) response evoked by the stimulus is estimated by convolving the neuronal population response and the canonical hemodynamic response function. In order to solve the under-constrained linear system, additionally, ridge regression regularization is used to enforce sparseness (see Figure 1 below). The regularization technique suppresses noise and artifacts and thus allows our method to estimate the pRF topography more robustly.
The topographical methods do not force the pRF shape to have a certain parametric shape, and therefore can uncover the actual pRF structure. An appropriate parametric model can then be chosen based on the pRF topography. For example, the pRF topography can be used to separate the pRF center and surround, and then the subsequent pRF center modeling can be more accurate by minimizing the influence of surround suppression as well as the influence of other potential artifacts arising in areas distant to the pRF center. We have recently performed a quantitative comparison between our method and several other methods that directly (i.e. before estimating the topography) fit isotropic Gaussian1, anisotropic Gaussian, and difference of isotropic Gaussians to the pRF9. It was found that the topography-based method outperformed these methods with respect to pRF center modeling by achieving higher explained variance of the BOLD signal time series.
Accurate estimation of pRF properties in various areas reveals how they cover the visual field and is important for investigating the functional organization of the visual cortex particularly as it relates to visual perception. Properties such as how pRF size changes with eccentricity1,10 and pRF center surround organization9 are well studied in the human literature. The proposed method for estimating the pRF topography results in more accurate pRF parameter modeling and is more likely to reveal unknown regularities, not easily modeled a-priori in the direct parametric models. This approach will be especially suitable for studying pRF organization in patients with visual pathway lesions, for whom pRF structure is not necessarily predictable a-priori. Below is described how to estimate the pRF topography and how to use the topography to model the pRF center.

<table border="0" cellpadding="0" cellspacing="0" width="1009">
	<tbody>
		<tr height="21">
			<td height="21" style="height:21px;width:225px;">Name of Equipment/Software</td>
			<td style="width:219px;">Company/Provider</td>
			<td style="width:219px;"></td>
			<td style="width:347px;">Web address</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">MRI scanner</td>
			<td>Siemens/Philips/GE</td>
			<td></td>
			<td></td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">MATLAB</td>
			<td>The Mathworks, Inc.</td>
			<td></td>
			<td>http://www.mathworks.com&#160;</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">VISTA software</td>
			<td>VISTA software group</td>
			<td></td>
			<td>http://white.stanford.edu/newlm/index.php/Software</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">PsychoToolbox</td>
			<td>PsychoToolbox&#160;</td>
			<td></td>
			<td>http://psychtoolbox.org&#160;</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Eye Tracker(VisuaStimDigital)</td>
			<td>Resonance Technology Inc</td>
			<td></td>
			<td>http://mrivideo.com/</td>
		</tr>
	</tbody>
</table>

topographical estimation of visual population receptive fields by fmri

Visual cortex is retinotopically organized so that neighboring populations of cells map to neighboring parts of the visual field. Functional magnetic resonance imaging allows us to estimate voxel-based population receptive fields (pRF), i.e., the part of the visual field that activates the cells within each voxel. Prior, direct, pRF estimation methods1 suffer from certain limitations: 1) the pRF model is chosen a-priori and may not fully capture the actual pRF shape, and 2) pRF centers are prone to mislocalization near the border of the stimulus space. Here a new topographical pRF estimation method2 is proposed that largely circumvents these limitations. A linear model is used to predict the Blood Oxygen Level-Dependent (BOLD) signal by convolving the linear response of the pRF to the visual stimulus with the canonical hemodynamic response function. PRF topography is represented as a weight vector whose components represent the strength of the aggregate response of voxel neurons to stimuli presented at different visual field locations. The resulting linear equations can be solved for the pRF weight vector using ridge regression3, yielding the pRF topography. A pRF model that is matched to the estimated topography can then be chosen post-hoc, thereby improving the estimates of pRF parameters such as pRF-center location, pRF orientation, size, etc. Having the pRF topography available also allows the visual verification of pRF parameter estimates allowing the extraction of various pRF properties without having to make a-priori assumptions about the pRF structure. This approach promises to be particularly useful for investigating the pRF organization of patients with disorders of the visual system.

Accurate pRF modeling requires capturing pRF shapes correctly. Without knowing the pRF topography, the selection of circularly symmetric models used in prior studies1,9-11 is a reasonable choice. This is because, if the local retinotopic organization is homogeneous in all directions of visual field, a local population response could be represented as a circularly symmetric cumulative aggregate of neuronal responses. However, our observations demonstrate that this is not necessarily the case (Figure 2</...

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Topographical Estimation of Visual Population Receptive Fields by fMRI

It is important to obtain unbiased estimates of visual population receptive fields (pRFs) by functional magnetic resonance imaging. We use mild regularization constraints to estimate pRF topography without a-priori assumptions about pRF shape, allowing us to choose specific pRF models post-hoc. This is particularly advantageous in subjects with visual-pathway lesions.

Visual cortex is retinotopically organized so that neighboring populations of cells map to neighboring parts of the visual field. Functional magnetic ...

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9.1K visualizações.  Baylor College of Medicine. It is important to obtain unbiased estimates of visual population receptive fields (pRFs) by functional magnetic resonance imaging. We use mild regularization constraints to estimate pRF topography without a-priori assumptions about pRF shape, allowing us to choose specific pRF models post-hoc. This is particularly advantageous in subjects with visual-pathway lesions.