Elsevier

NeuroImage

Volume 31, Issue 1, 15 May 2006, Pages 125-138
NeuroImage

Estimating linear cortical magnification in human primary visual cortex via dynamic programming

https://doi.org/10.1016/j.neuroimage.2005.11.049Get rights and content

Abstract

Human primary visual cortex is organized retinotopically, with adjacent locations in cortex representing adjacent locations on the retina. The spatial sampling in cortex is highly nonuniform: the amount of cortex devoted to a unit area of retina decreases with increasing retinal eccentricity. This sampling property can be quantified by the linear cortical magnification factor, which is expressed in terms of millimeters of cortex per degree of visual angle. In this paper, we present a new method using dynamic programming and fMRI retinotopic eccentricity mapping to estimate the linear cortical magnification factor in human primary visual cortex (V1). We localized cortical activity while subjects viewed each of seven stationary contrast- reversing radial checkerboard rings of equal thickness that tiled the visual field from 1.62 to 12.96 degrees of eccentricity. Imaging data from all epochs of each ring were contrasted with data from fixation epochs on a subject-by-subject basis. The resulting t statistic maps were then superimposed on a local coordinate system constructed from the gray/white matter boundary surface of each individual subject's occipital lobe, separately for each ring. Smoothed maps of functional activity on the cortical surface were constructed using orthonormal bases of the Laplace–Beltrami operator that incorporate the geometry of the cortical surface. This allowed us to stably track the ridge of maximum activation due to each ring via dynamic programming optimization over all possible paths on the cortical surface. We estimated the linear cortical magnification factor by calculating geodesic distances between activation ridges on the cortical surface in a population of five normal subjects. The reliability of these estimates was assessed by comparing results based on data from one quadrant to those based on data from the full hemifield along with a split-half reliability analysis.

Introduction

Studies of visual field loss following cortical lesions have shown that human primary visual cortex is retinotopically organized: adjacent neurons in the visual cortex correspond to adjacent locations in the visual field (Inouye, 1909, Holmes, 1918, Horton and Hoyt, 1991). The center of the visual field occupies the occipital pole, while the periphery is mapped to more anterior parts of the occipital cortex, forming a retinotopic eccentricity map. Within primary visual cortex (area V1), as one moves from the V1/V2d (dorsal V2) border through the calcarine sulcus to the V1/V2v (ventral V2) border, the representation of the visual field sweeps from the lower vertical meridian through the horizontal meridian to the upper vertical meridian, forming a retinotopic polar angle map. Such mapping of retinal space to cortical space is referred to as retinotopy. The spatial sampling of the visual cortex is highly nonuniform: the cortical representation of the fovea is much larger than that of the periphery. Daniel and Whitteridge (1961) first used the term linear cortical magnification factor to refer to the quantitative relationship between visual cortex and visual field in terms of the number of millimeters of visual cortex representing one degree of visual field at any given eccentricity.

Anatomical magnetic resonance imaging and functional magnetic resonance imaging (MRI, fMRI) have made it possible to precisely delineate the retinotopic organization of human visual cortex and quantitatively investigate the linear cortical magnification factor, especially in area V1 (Schneider et al., 1993, Engel et al., 1994, Sereno et al., 1995, Engel et al., 1997, Tootell et al., 1997, DeYoe et al., 1996, Duncan and Boynton, 2003). These techniques open clinical possibilities to study visual pathology and develop new strategies for rehabilitation (Baseler et al., 1999, Morland et al., 2001, Sunness et al., 2004, Baker et al., 2005). The following broad steps are involved in fMRI retinotopic mapping using phase-encoding stimuli (expanding ring and rotating wedge, or stationary rings and wedges) (Schneider et al., 1993, Engel et al., 1994, Shipp et al., 1995, Tootell et al., 1995, Sereno et al., 1995): the reconstruction of the highly convoluted cortical surface, including classification of tissues (Dale and Sereno, 1993, Well et al., 1996, Kapur et al., 1996, Thompson et al., 1996, Teo et al., 1997, Dale et al., 1999, Miller et al., 2000, Joshi et al., 1999, Ratnanather et al., 2001, Xu et al., 1999, Harris et al., 1999, MacDonald et al., 2000, Fischl et al., 2001, Zhang et al., 2000, Zhang et al., 2001a, Zhang et al., 2001b, Fischl et al., 2002, Shattuck and Leahy, 2001), topological correction of the surface mesh (Shattuck et al., 2001, Han et al., 2001, Han et al., 2002), and unfolding the cortical surface into a 2D plane (Thompson et al., 1996, Van Essen et al., 1998, Toga, 1999, Angenent et al., 1999, Fischl et al., 1999a, Fischl et al., 1999b, Hurdal et al., 1999, Lewis and Van Essen, 2000, Collins and Stephenson, 2003b); analysis of the fMRI response (Engel et al., 1997, Andrade et al., 2001, Warnking et al., 2002); smoothing of functional data over the cortical surface (Andrade et al., 2001, Warnking et al., 2002); localization of functional response to phase-encoded stimuli; and, finally, measurement of the linear cortical magnification factor (Sereno et al., 1995, Engel et al., 1997, Duncan and Boynton, 2003).

Although many fMRI retinotopic mapping studies in human primary visual cortex have been carried out in the last decade, there is no generally-accepted consensus about how to smooth functional data over the cortical surface while taking the cortical geometry into account. Furthermore, no methods for automatically delimiting the boundaries of V1 using fMRI have been generally accepted by the scientific community.

In this paper, we present all steps necessary for fMRI retinotopic mapping analysis and linear cortical magnification factor estimation in human primary visual cortex, from fMRI experimental design and anatomical MRI analysis to quantitative measurement of the linear cortical magnification. We use methods proposed by our own group and others for stimulus design, functional volume-based analysis, anatomical MRI segmentation, and unfolding the cortical surface. We present new methods for associating functional volume data with the cortical surface, smoothing functional data on the cortical surface using the geometric characteristics of the cortical surface expressed via orthonormal bases of the Laplace–Beltrami operator, automatically defining the V1 boundaries and tracking ridges of maximum activation evoked by stationary contrast-reversing rings via dynamic programming optimization, and measuring the linear cortical magnification factor in human primary visual cortex. We report results of the linear cortical magnification factor estimation in the left and right primary visual cortices in a population of five normal subjects. Finally, we test the multirun reliability of the estimates by comparing them based on the set of all odd- or even-numbered fMRI runs with estimates based on all fMRI runs and the spatial reliability of the estimates by comparing estimates based on data limited to the upper or lower quadrant in each visual hemifield with estimates based on the entire hemifield.

Section snippets

Acquisition

Functional MRI was performed using a Philips Intera 3.0 T scanner located at the F. M. Kirby Research Center for Functional Brain Imaging at the Kennedy Krieger Institute, Baltimore, MD. All images were acquired using a SENSE parallel imaging head coil.

We used single-shot echo-planar imaging (EPI) of 23 ascending 2 mm (no gap) axial-oblique slices with a field of view of 128 mm2 and a 64 × 64 matrix allowing partial-brain coverage at high resolution (2 mm3). Slices were positioned so as to

Results

We studied the retinotopic map in a population of five young adults (four males and one female) with normal vision and no known neurological impairments.

Conclusion and discussion

This paper presents methods for retinotopic eccentricity mapping and linear cortical magnification estimation in human primary visual cortex using fMRI and dynamic programming methods. We studied retinotopic eccentricity maps of left and right visual cortices in five normal subjects. Primary visual cortex boundaries are defined by the vertical meridia; the horizontal meridian separates each visual hemifield into upper and lower quadrants. The ridge of maximum activation evoked by each ring was

Acknowledgments

The work reported here was supported by NIH grants: 1 P41 RR15241, 1 R01 EB00975, 1 P20 MH621130, and 1 R01 DA13165. The authors thank Dr. Xiao Han of Massachusetts General Hospital for the topology-correction method and the connectivity-consistent isosurface algorithm. The authors also thank Dr. Ken Stephenson of University of Tennessee for providing CirclePack software (http://www.math.utk.edu/kens) to create the hyperbolic maps.

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