Corresponding author D. Y. Ts'o: SUNY Upstate Medical University, Syracuse, NY, USA. Email: firstname.lastname@example.org
Among the crowning achievements of Hubel and Wiesel's highly influential studies on primary visual cortex is the description of the cortical hypercolumn, a set of cortical columns with functional properties spanning a particular parameter space. This fundamental concept laid the groundwork for the notion of a modular sensory cortex, canonical cortical circuits and an understanding of visual field coverage beyond simple retinotopy. Surprisingly, the search for and description of analogous hypercolumnar organizations in other cortical areas to date has been limited. In the present work, we have applied the hypercolumn concept to the functional organization of the second visual area, V2. We found it important to separate out the original definition of the hypercolumn from other associated observations and concepts, not all of which are applicable to V2. We present results indicating that, as in V1, the V2 hypercolumns for orientation and binocular interaction (disparity) run roughly orthogonal to each other. We quantified the ‘nearest neighbour’ periodicities for the hypercolumns for ocular dominance, orientation, colour and disparity, and found a marked similarity in the periodicities of all of these hypercolumns, both across hypercolumn type and across visual areas V1 and V2. The results support an underlying common mechanism that constrains the anatomical extent of hypercolumn systems, and highlight the original definition of the cortical hypercolumn.
On this occasion of the 50th anniversary recognition of Hubel and Wiesel's earliest published works together, it seems appropriate to re-examine perhaps one of the most beautiful and, at least for me personally, satisfying collection of concepts – those associated with the notion of a ‘hypercolumn’ in primary visual cortex. Coverage of the hypercolumn concept has been ubiquitous in neuroscience textbooks for the past few decades, as well as in undergraduate courses in neuroscience, psychology, neurocomputation and related fields. Yet the actual definition of the term has been often confused or lost in a cloud of related concepts, interpretations and sequelae, not all attributable nor even faithful to those originally proposed by Hubel and Wiesel. Perhaps then, this fuzziness surrounding the hypercolumn is not unlike that surrounding Einstein's Special Theory of Relativity.
For the record, then, Hubel & Wiesel (1974), in defining the hypercolumn, sought to ‘extend the concept of the (cortical) column and consider a complete array of columns as a small machine that looks after all values of a given variable’. They then went on to make a number of particularly insightful and significant observations, including:
• the two receptive field properties or parameters (in addition to retinotopy) that they knew exhibited a columnar organization, ocular dominance and orientation, could both be considered to also form hypercolumns, i.e. a set of contiguous (neighbouring) cortical columns exhibiting an orderly progression of their respective parameters that spanned all possible values (see Fig. 1);
• each of these two types of hypercolumns required approximately 1 mm of cortical territory to cycle back to the beginning, with any given cortical neuron exhibiting both properties (i.e. the mapping of these two properties are overlapped and co-existent);
• since primary visual cortex is also retinotopically organized, such traversals of cortical territory also meant a shift in retinotopic position. However given receptive field size and scatter at any given eccentricity, this shift in position was relatively slower such that the collection of receptive field positions within a given reckoning of a hypercolumn all overlapped each other. It required a jump of roughly two hypercolumns' worth of cortical territory (about 2 mm) to find receptive fields that were clearly non-overlapping with the original starting point.Our esteemed investigators further speculated that:
• the system of ocular dominance hypercolumns and that of the orientation hypercolumns might run orthogonal to each other, creating within a 1 mm2 patch of visual cortex the famous ‘ice cube model’, so often mistaken for the hypercolumn itself. They suggested that an orthogonal arrangement of these two hypercolumn systems would provide for an optimal opportunity for interactions between the two cortical maps. This orthogonality has been since confirmed as being generally correct by several optical imaging studies (Bartfeld & Grinvald, 1992; Obermayer & Blasdel, 1993; Hübener et al. 1997; see Fig. 2);
• given the proposed ice cube model of 1 mm2 of visual cortex, and the observation of the behaviour of visual field coverage, it may be considered that a given 1 mm2 of visual cortex contains all the cortical machinery required to process visual information in all possible ways for a given point in visual space (or rather that 2 mm2 contains ‘more than enough machinery … ’Hubel & Wiesel, 1977).
The hypercolumn is a prime example of the powerful summarizing concepts that Hubel and Wiesel gave us, becoming either an inspiration or the bane, to generations of budding neuroscientists, struggling medical students and fledgling computational modellers. For me personally, learning of the hypercolumn helped bring order and rationality to the daunting prospect of arriving at a mechanistic understanding of the complexities of visual processing. It was a glimmer of light in terms of tackling how the cortex handles the multidimensionality of the problem of vision, and was an inspirational example of how the brain could be made understandable and beautiful.
The set of observations and speculations listed above, then, though not part of the definition of the hypercolumn, have been carried along as the greater conceptual framework with which the hypercolumn is generally associated. Nevertheless it seems important to clearly delineate these observations as separate notions, some of which may not be as readily applied when considering the notion of hypercolumns beyond Hubel and Wiesel's original context in V1. Some subsequent authors have presumed that these notions of the hypercolumns suggest a discretely crystalline view of cortical organization, although it seems obvious that such an idea cannot be correct, at least strictly so. Together with the earlier findings of Mountcastle (1957) describing the cortical column, however, these ideas supported a modular view of the organization of neocortex. The status of the cortical column itself has been the subject of much debate, and expertly reviewed by several authors, including Mountcastle (1997), Buxhoeveden & Casanova (2002), Lund et al. (2003) and Horton & Adams (2005). Here, we will focus on the hypercolumn, particularly as originally defined.
The advent of the optical imaging technique made it possible to visualize the actual arrangement of the V1 hypercolumns in great detail (Blasdel & Salama, 1986; Ts'o et al. 1990; Bartfeld & Grinvald, 1992; Obermayer & Blasdel, 1993; Hübener et al. 1997). The results from these functional imaging studies have largely confirmed many of the key points of the original ice cube model. Such results in conjunction with studies focused on the cytochrome oxidase (CO) blobs of V1 (e.g. Horton 1984; Livingstone & Hubel, 1984) have also provided important revisions and extensions to our understanding of the functional organization of V1. Chief among these revisions is the description of the ‘pinwheel’ arrangement of orientation (Bonhoeffer & Grinvald, 1991, 1993) and the inclusion of the CO blobs and the representation of colour processing within this framework. Indeed there still exists substantial controversy as to the nature and organization of colour processing within V1, a topic outside the scope of this article. It seems likely that yet another new imaging technique, two-photon functional microscopy, will provide the most definitive answers to these questions and other questions of functional representations at the single cell level (e.g. Chatterjee et al. 2008).
Hypercolumns beyond V1
Given the impact of the hypercolumn to the field, it is perhaps a bit surprising, then, that attempts to apply the notion of a hypercolumn outside of primary visual cortex haven't been quite as frequent as one might expect. Certainly one contributing factor may be the paucity of well-described orderly maps of cortical representations in different cortical areas. The methodology of cortical optical imaging has provided perhaps the most important current tool for revealing such maps when the cortical territory in question is available on the surface. The original, painstaking method of careful, systematic single-unit recording continues to be used, perhaps heroically, as well (e.g. Albright et al. 1984; DeAngelis & Newsome, 1999; Diogo et al. 2008). However, one wonders also if the bar has been set a bit too high, in considering the wonderfully interlocking concepts of the Hubel and Wiesel hypercolumn in V1 and the ice cube model. ‘Merely’ finding a new bona fide hypercolumn, which is a periodic orderly representation of a given parameter, would seem to be significant enough. In addition, the underlying cortical architecture and circuitry that might be responsible for the geometry of the V1 hypercolumn seem to be understudied as well. That is more than a mere coincidence; it is likely that a set of cortical properties or rules underlies the 1 mm extent of V1 hypercolumns, a notion that has been incorporated into computational models of V1.
In our 1995 paper (Roe & Ts'o, 1995) on the relationship between the segregation of receptive field properties in the thick, thin and pale cytochrome oxidase (CO) stripes of V2 and the mapping of retinotopy, we offered some further thoughts on the applicability of the hypercolumn concept to the architecture of primate V2. We observed that the description of the CO blobs as centres of colour processing in V1 invited the possibility of the notion of colour hypercolumns in V1 that might join the hypercolumns of ocular dominance and orientation. Whether colour hypercolumns in V1 can be said to fully meet a strict definition of a hypercolumn and also possess an approximate 1 mm periodicity remains to be shown (see Ts'o & Gilbert, 1988; Dow, 2002; Landisman & Ts'o, 2002; Xiao et al. 2007; Lu & Roe, 2008). However, studies describing an organization of differing directions in colour space in V1, despite some controversies and significant differences in methodologies, are all generally compatible with the prospects of a ‘complete’ representation of colour within the same 1 mm2 of the primate V1 ice cube, at least in the parafoveal representation, even as the representation of colour itself shifts from that observed in the lateral geniculate nucleus (LGN) to higher cortical elaborations of colour representations (e.g. double opponency, colour orientation, non-cardinal colour tuning, etc.; Ts'o et al. 1998). It may require the fine resolution of two-photon functional microscopy to unambiguously demonstrate the actual nature of any colour hypercolumn in V1 (see Chatterjee et al. 2008). It also remains to be shown whether such colour hypercolumns can be said to run orthogonally to the other hypercolumn systems in V1, and raises the question of just how many cortical maps can be orthogonal to each other in any given cortical area, a topic that has been addressed by modelling studies (e.g. Swindale, 1998, 2000).
Another obvious observation we made (Roe & Ts'o, 1995) was that, whereas the CO blobs in V1 seem to have been inserted as a segregated, foreign system into the ongoing fabric of the cortical representations of ocular dominance and orientation (as suggested by Livingstone & Hubel, 1984), the CO thin stripes that carry on colour processing in V2 are perhaps the peers of the V2 representations for orientation and binocular interaction (disparity, Fig. 1). This difference leads to a different consequence for the application of the hypercolumn concept in V2. The presumptive colour hypercolumns of V1 are likely to occupy the same 1 mm2 cortex as the other hypercolumn systems of the ice cube, even if the blobs may be viewed as ‘micro’-segregated. In contrast, the colour/thin stripes of V2 exist as completely separate 1.5 mm stripes of cortical territory, quite apart from the hypercolumns for orientation and binocular interaction – it could be said that they are ‘macro’-segregated. Since the colour hypercolumns of V2 do not occupy the same cortical territory as the other V2 hypercolumns, we felt it necessary to introduce a new term, the point set, to describe the set of hypercolumns that analyses all stimulus parameters for a given point in visual space. In V1, the point set corresponds to the ice cube, but in V2, one requires at least a set comprising a thick stripe, a thin stripe and the intervening pale stripes, some 6 mm of V2. In V1, the point image, the cortical region activated by a point stimulus, as described by Hubel & Wiesel (1974), is approximately 1.5–2 mm (1.5–2 hypercolumns and 1.5–2 point sets) square (see Fig. 3). In V2, the point image also appears to be 1.5–2 point sets (at least 8 mm), though much larger than a V2 hypercolumn (a typical stripe width is 1–1.5 mm, Fig. 3). Clearly the notion of a point set, like that of a point image, depends on a well delineated topographic map, though it is conceivable that there may be point representations in cortical maps of spaces other than visual space. What these observations about the organization of V2 suggest is that when considering the application of the hypercolumn concept to V2, we will need to separate out the original definition of the hypercolumn, which would seem to be applicable to V2, from other associated notions, some of which will not be applicable. One notion that may still be carried over into V2 is a possible relationship between the organization for orientation and binocular interaction (disparity), which have been shown to co-exist within the thick stripes of V2 (DeYoe & VanEssen, 1985; Hubel & Livingstone, 1987; Roe & Ts'o, 1995; Ts'o et al. 2001; Chen et al. 2008).
V2 disparity organization
The mapping of the property of stimulus orientation in V1 and V2 using optical imaging methods has been demonstrated previously by several groups (e.g. Ts'o et al. 1990; Malach et al. 1994; Roe & Ts'o, 1995, see Fig. 4) and in V2 has been shown to overlie the pale and thick stripes. Optical imaging has also shown that regions of relatively poor orientation tuning overlie the CO blobs of V1 and the CO thin stripes of V2 (Ts'o et al. 1990; Roe & Ts'o, 1995; see also Fig. 4). More recent data from optical imaging studies of V2 permit further observations about the notion of hypercolumns in V2, and their comparison with those in V1. First hinted at by Hubel and Wiesel themselves (Hubel & Wiesel, 1970), then amplified by subsequent electrophysiological studies (e.g. DeYoe & VanEssen, 1985; Roe & Ts'o, 1995; Cumming & Parker, 1997), and finally by optical imaging studies (Burkitt et al. 1998; Ts'o & Burkitt, 1999; Ts'o et al. 2001; Chen et al. 2008), we now know that V2 possesses a highly organized representation for binocular disparity. In Fig. 5A, we show the ‘single condition’ optical imaging maps for a series of seven disparities, each at one of four tested orientations. The disparities tested were orthogonal to the given orientation. Summing across disparities yields the orientation sum maps seen in Fig. 5B (top row). A polar map (Ts'o et al. 1990, see Methods) of orientation can then be computed (Figs 6A and 7B). Applying a modified polar analysis to the disparity data for each orientation, wherein pseudocolour is used to code for disparity yielded ‘disparity partials’ for each orientation (Fig. 5B middle row, Fig. 6A right column). They show the organization of orientation as modulations in the neutral colours (white/grey/black), and disparity tuning as variations in colour (red/blue/green, see Fig. 6C for the pseudocolour mapping legend). In examining these disparity partials, we noted that there was little or no disparity tuning at the horizontal orientation (vertical disparities). We therefore adjusted for the horizontal disparity component taken at the oblique orientation angles and combined these data (Figs 5B and 6) to yield a pseudocolour map of disparity free of orientation specific information. These pseudocolour disparity maps reveal cortical regions exhibiting near (greenish), far (reddish), tuned excitatory (bluish) and tuned inhibitory (yellowish) disparity responses, as well as sites with no disparity tuning (shades of grey).
To confirm the validity of these V2 disparity maps, we conducted multiple single unit recordings, as seen in Fig. 6B. Individual electrode penetrations targeted specific sites within the disparity tuned regions of V2 and the disparity tuning curves from at least three separate units were obtained. Sample tuning curves are shown in Fig. 6B. Electrolytic lesions were placed in the recording field (marked L) to aid in reconstruction and alignment, although the primary registration used the pattern of the surface vasculature and the obtained images.
Given maps of disparity in the thick stripes and orientation maps from the same piece of cortex, we can ask what is the relationship or arrangement of the orientation and disparity maps in V2?Figure 7A and B shows the pattern of iso-contour lines in the orientation maps and disparity maps of V2. Figure 7C and E shows the overlay of these two maps. Another example is shown in Fig. 8, along with the computation of inter-map crossing angle. It can be seen that in general the maps of orientation and binocular disparity run roughly orthogonal in V2, in a manner analogous to the orthogonal arrangement of ocular dominance and orientation in V1. Thus the hypercolumns for orientation and binocular interaction in V2 run orthogonal to each other and occupy the same cortical territory, just as they do in V1.
It is attractive to speculate that cortical hypercolumns as a rule tend to run orthogonal to each other when the hypercolumns co-exist within the same cortical tissue, as is the case in the two clearest examples in the primate (orientation and ocular dominance or disparity, see also Hübener et al. 1997). The fact that the presumptive colour hypercolumns in V1 and V2 are largely segregated anatomically, whether in ‘micro’ or ‘macro’ fashion, from these two other hypercolumn systems, suggests that orthogonal mapping isn't entirely pervasive. Although colour oriented neurons have been described in V1 and V2 (e.g. Ts'o & Gilbert, 1988; Roe & Ts'o, 1995), no orderly representation has yet been reported. In the case of oriented cells within the thin/colour stripes of V2, we have found a lack of columnar organization (Ts'o et al. 2001). Perhaps an orthogonal arrangement of colour and orientation (and disparity?), and the full-scale interaction that it must represent, is deferred to a higher cortical area such as V4. There have been other reports of non-columnar organizations to receptive field properties such as orientation (e.g. Van Hooser et al. 2005), as well as the weak organization for ocular dominance found in the squirrel monkey – both prompting the question of necessity or purpose of the cortical column itself (Horton & Adams, 2005). Perhaps equally intriguing is the finding of orientation columns and maps in the auditory cortex of the re-wired ferret (Sharma et al. 2000).
Another seminal feature of the original Hubel and Wiesel hypercolumn was the seemingly conserved ∼1 mm extent, at least in V1. Yet, we and others have previously described the geometry of iso-orientation modules in V2 (e.g Malach et al. 1994; Roe & Ts'o, 1995; Ts'o et al. 2001), and noted that they are significantly larger than those in V1, occupying from 6 to 10 times the cortical territory compared with V1. However, when examining the ‘nearest neighbour’ periodicity of the orientation columns of V2, a different impression emerges. Due to the substantial anisotropy of the V2 orientation modules, the distance between a given orientation representation and the closest like-oriented neighbour is considerably shorter than even a single stripe width (1.2–1.5 mm, see Fig. 9). To quantify this notion, we assessed the periodicity of functional maps obtained with intrinsic signal optical imaging using the two-dimensional power spectral density (PSD) of the image. We calculated the PSD by performing an FFT (fast Fourier transform) on the windowed autocorrelation function of a region of interest within the image. The location of the peak at the highest spatial frequency was then found and the periodicity was calculated as its inverse.
A representative example of the PSD estimate of the outlined region of an ocular dominance map is shown in Fig. 10. The highest amplitude pixel in the PSD is designated as the periodicity of ocular dominance for this cortical sample (the anti-symmetric nature of the FFT actually yields two peaks, but with the same radial distance from the centre). The measured periodicity of 0.83 mm corresponds well with the rest of the population (Fig. 11).
We performed the same analysis on functional maps of orientation, colour, and disparity. The maps of colour organization were based on difference maps between cortical activation due to low spatial frequency chromatic iso-luminant gratings of four different orientations, modulated in the red-green direction in DKL colour space (Derrington et al. 1984), versus activation maps obtained when presenting luminance gratings. A typical orientation map and disparity map from the same cortical region is depicted in Fig. 10. V1 and V2 regions of interest were selected (guided by its corresponding ocular dominance map), and the corresponding periodicity measurements for the two regions in the orientation map were found to be 0.75 mm and 0.83 mm, respectively, while the periodicity for the disparity map was 0.85 mm. The periodicity of the ocular dominance map generated in the same cortical sample was similar (0.83 mm). This example serves as a demonstration that the periodicity values of functional maps remain similar across V1 and V2, as well as between three distinct hypercolumns: ocular dominance, disparity and orientation.
The periodicity values across our entire sample of imaging data from 94 cortical samples taken from 94 separate hemispheres in macaque monkeys showed a striking similarity between V1 and V2, and in all submodalities for which maps were obtained (Fig. 11). A substantial amount of the variance observed in Fig. 11 is likely to be due to individual variation between animals. Maps obtained in the same cortical sample/region in the same animal yielded very similar periodicity measurements to one another across multiple imaging sessions and across different experiment dates. Furthermore, periodicity values obtained from maps in different visual areas or from different submodalities, but in the same animal, may have a weak tendency to co-vary. Figure 12 shows the correspondence between periodicity values obtained in the orientation domain but across visual areas (Fig. 12B), and the correspondence between periodicity values obtained in V1 but across different hypercolumns (Fig. 12A). Even though there are a greater number of samples in which V2 orientation hypercolumns exhibited larger periodicity values than in V1, the differences in measured values are still small in comparison to the reported differences in geometric area between patches in the two visual areas (e.g. Ts'o et al. 1990; Malach et al. 1994; Roe & Ts'o, 1995).
In order to reconcile other reports examining the periodicity of functional maps (e.g. McLoughlin & Schiessl, 2006) with the results presented here, it is important to note that the shapes of the modules in V2 differ markedly from those in V1. As evident in the orientation map shown in Figs 9 and 10, the V2 patches appear oblong in shape, with a major axis angle fairly consistent from patch to patch. V1 patches, on the other hand, tend to appear more circular. This anisotropy made it necessary to perform the periodicity analysis along a single direction in the autocorrelogram in order to arrive at ‘nearest-neighbour’ distances. The direction was selected that contained a local maximum at the highest periodicity value. In contrast, the algorithm employed by McLoughlin & Schiessl (2006), used averaging along all directions in the autocorrelogram. These authors derived two measures: the mean and standard deviation of the distribution of radial distances to each local maximum in the autocorrelogram, and a second measure which collapsed the two-dimensional autocorrelogram into a single dimension by averaging the autocorrelation value for each radial distance. Their methods reduce the overall variability of the periodicity measurements, but in the process discards information about the anisotropies present. Indeed their approach explicitly ‘assumes that the pattern depicted by the autocorrelograms is circularly symmetric.’ Visual inspection of the V2 imaging data in their published report reveals the same anisotropies present in their data that we have observed in our V2 data, and further, if one applies the ‘nearest neighbour’ approach instead, to their imaging data, it appears to conform to our results (that is, performing the procedure depicted in Fig. 9 on the V2 imaging data of McLoughlin & Schiessl (2006) suggests nearest neighbour periodicity values similar to our results).
Our results support the idea that the nearest-neighbour distance and therefore the periodicity of hypercolumns is conserved across differing feature maps and visual areas, at least in primate V1 and V2. Preliminary data in primate V4 also indicates a similar periodicity for orientation (Ghose & Ts'o, 1995, 1997). Perhaps this finding reflects some underlying constraint of cortical circuitry and/or development, such as the maximal extent of single inhibitory neurons, or single thalamic afferents.
Other possible hypercolumns
Several studies of the organization of colour processing in V2 using optical imaging have demonstrated an orderly arrangement of stimulus hue (Xiao et al. 2003; Lu & Roe, 2008), which may be considered to qualify as colour hypercolumns of V2. However, just as in V1, the representation and range of receptive field types that are sensitive to chromatic stimuli undergoes considerable elaboration (double opponent, colour spot cells, dark colour cells, etc), starting from cone-opponency. Therefore it is unclear how these disparate populations and representations are organized relative to the demonstrated arrangements of hue. In addition, there is some expectation that the representation of colour will be dependent on eccentricity. Since the processing of colour may be a subset of a system to represent surface properties, any colour hypercolumn may actually be embedded in a representation for additional surface properties, e.g. brightness. Indeed such other surface property representations have been reported in V2 (Hegde & Van Essen 2004; Wang et al. 2007).
The advent of optical imaging and its ability to map cortical patterns of response to multiple sets of stimuli has raised a more general problem. We now know that the apparent cortical representation of even a property as basic as orientation may alter appreciably, depending on the precise details of the stimulus set, the spatio-temporal parameters and how the oriented contour is presented (e.g. Basole et al. 2003). Despite such findings, the periodicity of the underlying hypercolumn appears to be maintained. Defining a hypercolumn then will require a careful choice as to what particular dimension is being tested. A distinction needs to be made between cortical maps that are an epiphenomenon or just a consequence of an underlying linear system versus maps in the traditional sense, that is representations of information that are designed to be read by a higher process.
As we alluded to earlier, it seems appropriate to make the distinction between computed receptive parameters and computed cortical maps versus maps that are direct anatomical derivatives of the sensory epithelium (e.g. retinotopy, tonotopy, somatotopy). Indeed the suggestion is that the computed maps may obey either rules of cortical circuitry, or development or both that constrain the geometry of the hypercolumn. On the other hand it may be that spatial or topographic mapping holds a special status regardless of whether it is inherent in the sensory epithelium or computed downstream (e.g. auditory space mapping, hippocampal place mapping)
So it may turn out that the concept associated with the V1 hypercolumn that proves to be more applicable to other cortical areas will actually be the original definition of the hypercolumn itself, the set of cortical columns that span a given parameter. Other related notions such as the coincidence of multiple hypercolumns within a 1 mm2 of cortex may be less universal. Certainly the point image of 1.5 hypercolumns in V1 will not apply to higher visual areas as retinotopy progressively degrades.
The rise of multi-photon functional microscopy as a means to assess the tuning properties of a patch of cortex at the single cell level promises to further refine and challenge the hypercolumn concept. For example, Kara & Boyd (2009) have reported a ‘micro-architecture’ for binocular phase disparity, at a scale several times smaller than classical hypercolumn. Undoubtedly additional cortical microarchitectures will be revealed in future multi-photon studies and may indicate a tier of cortical functional organization below that of the classical hypercolumn.
In summary, the profoundly influential concepts surrounding the description of the hypercolumn in primary visual cortex by Hubel and Wiesel have not been applied extensively to other cortical areas. In the second primate visual area, V2, when these ideas are applied, some aspects fit well while others require adjustment. The original definition of the hypercolumn is quite reasonably applied to describe the organization of receptive field properties such as orientation, disparity and colour in V2. In addition, the orthogonal arrangement of orientation and binocular interaction (disparity) mirrors that found in V1, where both also occupy the same cortical territory. However, the point set, the description of the cortical region needed to analyse a given point in visual space for all stimulus parameters and its relation to the hypercolumn is quite different in V2 than in V1. Also not unexpectedly, given the increase in retinotopic distortion in V2, the relationship between the point image and the hypercolumn is not maintained in V2 as well. Future studies as to the functional organization of other cortical areas are required to determine whether the hypercolumn concept finds further application. To the extent that the geometry of V1 hypercolumns arises from intrinsic constraints of neocortical circuitry and/or development, it will be particularly interesting to anticipate whether a 1 mm periodicity can be found in other areas.
Lastly, I wish again to personally thank David and Torsten, and their many talented former students for the role models they became to generations of young neuroscientists, and for creating an era and a standard of excellence for how neuroscience should be conducted.
Monkeys, Macaca fascicularis, were initially anaesthetized with ketamine HCL (10 mg kg−1, i.m.) followed by sodium thiopental (20 mg kg−1, i.v. supplemented by a constant infusion of 1–2 mg kg−1 h−1). The animal was then intubated, neuromuscularly paralysed with vecuronium bromide (0.1 mg kg−1 h−1) and artificially respirated. The ECG, EEG, temperature and expired CO2 were monitored throughout the entire experiment. A retinoscope was used to determine the appropriate contact lenses to focus the eyes on a colour video monitor (CRT, Barco, Kortrijk, Belgium) or tangent screen 114 cm from the animal. The positions of the fovea of each eye were plotted on the screen with the aid of a fundus camera (Topcon, Paramus, NJ, USA). A craniotomy was made above the visual cortex and a stainless steel chamber was cemented over and around the craniotomy. After the dura was opened, the chamber was sealed with a glass cover plate and filled with Silicone oil. This sealed chamber minimized the movement of the cortex due to heartbeat and respiration. The actual position of the visual field representation of the region of visual cortex under study was determined electrophysiologically. The receptive field position and properties of single units were initially studied with slits of light from a hand-held projector. This recording arrangement was also used to perform electrophysiological confirmations of the functional maps obtained with optical imaging. Spike data were collected using the HIST (Kaare Christian, The Rockefeller University) program after the recorded signals passed through a window discriminator. The intrinsic signal imaging methods used for imaging orientation and colour organization in V1 and V2 have been previously described (Roe & Ts'o, 1995, Landisman & Ts'o, 2002), and employed a slow scan 12-bit CCD camera (Photometrics, Ltd, Tucson, AZ, USA) acquiring frames under 630 nm illumination. The isoluminant chromatic gratings were calibrated with the aid of a spectrophotometer (Photo Research, Chatsworth, CA, USA) and based on the cone spectral data of Smith and Pokorny. Post mortem CO histology was used to reconstruct and confirm the optical imaging and single-unit recording maps.
Binocular disparity experiments
Disparity stimuli were presented dicoptically on the stimulus CRT, with matching eye positions based on recordings of a binocular cell via a reference electrode placed in the foveal representation of V1. Eye position drift was constantly monitored via dual lasers reflected off small mirrors attached to each contact lens, and confirmed with frequent referral to the reference electrode recordings. Disparity stimuli generally consisted of a single 0.2 deg × 1.5 deg luminance bar presented at four different orientations (0 deg, 45 deg, 90 deg, 135 deg) and seven different disparities (near −1.0 deg, −0.5 deg, −0.25 deg, 0.0 deg, 0.25 deg, 0.5 deg, 1.0 deg far), with the disparities orthogonal to the orientation of the bar. Subsequent analyses for disparity tuning considered only the horizontal disparity component of each stimulus once it was determined that vertical disparity tuning was observed to be negligible.
The algorithm for creating ‘polar maps’ of orientation and disparity tuning from optical imaging data is the same as originally used in Ts'o et al. 1990. It is not identical to that referred to in Bonhoeffer & Grinvald, 1993, although they also used the term ‘polar map’. The method is also distinct from the ‘angle maps’ and ‘angle-magnitude, HLS’ maps (Blasdel & Salama, 1986; Bonhoeffer & Grinvald, 1993) in that all acquired image data are used by mapping the data into an RGB pseudocolour space representation without any non-linear thresholding or the choosing of a direction of the maximal vector. Instead each pixel yields a vector magnitude and direction in pseudocolour space for each stimulus condition tested. For orientation maps, typically there would be either four or eight such vectors for each pixel, and for disparity, we typically tested seven separate disparities (and therefore computed seven separate vectors for each pixel). The magnitude of each vector is determined by the response magnitude to the given stimulus condition. The direction of each vector is a unique direction in RGB colour space that is equally spaced from the other vector directions. This arrangement leads to the following consequences: (1) if there is no response to any stimulus condition of the set, then all vectors are of zero length and the result is the pseudocolour code black, (2) if the particular cortical site is not tuned to any stimulus condition of the set and responds equally well (or poorly) to all the stimuli, then all the vector lengths are equal and will yield a neutral colour, from grey to white, (3) if there is some tuning or bias to one (or more) stimulus conditions, the resulting colour in the pseudocolour representation will possess a particular hue, saturation and intensity – admittedly the algorithm would not distinguish between no tuning and multi-modal tuning that is symmetric and balanced. Even though disparity is not a circular variable, the algorithm remains the same, except that the mapping between specific disparities and directions in RGB colour space is fractured between the extremes of near and far (green and red, no response condition is assigned a yellow vector). Another consequence of this method is that the resultant maps often show regions with poor tuning (the lack of saturated colours), which has proven to be useful in displaying sites of poor net orientation tuning (the CO blobs and thin stripes, Fig. 4, and lack of disparity organization in V1 and the pale and thin stripes of V2, Figs 6 and 7).
Functional imaging data from previous studies covering 94 separate recording sessions in macaque monkeys were analysed. Nearest-neighbour distances were evaluated by measuring the periodicity of these maps, defined by the peak of the filtered power spectral density (PSD). In order to obtain the PSD of a functional map, a region of interest (ROI) was first selected to capture the portion of the map with minimal artifacts from surface vasculature and other sources of noise. Since V1 and V2 were to be analysed separately, ROIs were selected for each area individually. The V1/V2 border was identified from the pattern of ocular dominance obtained in the same session. If a clear ocular dominance signal was absent, the results from the session were not included in the analysis.
For a given map, the PSD was calculated by performing an FFT on the windowed unbiased autocorrelation matrix of the ROI. Due to the antisymmetric nature of the two-dimensional autocorrelation matrix, half of the matrix is redundant and was therefore discarded. The remainder was cropped by a rectangular window approximately 1/4 the size in area of the autocorrelation matrix. The windowing procedure offers a decrease in variance of the PSD estimate by reducing the influence of the high-variance outer regions of the autocorrelation matrix. The PSD was then calculated from the FFT of the result and filtered with an iso-frequency rectangular (‘brickwall’) mask in frequency space, primarily to aid in the elimination of the low spatial frequency content prevalent in many of the functional maps. Typical filter cutoff points were on the order of 0.25–0.5 cycles per millimeter.
Due to the anisotropic periodicity generally found in V2, peaks with different values corresponding to different axes were often encountered. In contrast, V1 PSDs typically exhibited a ring-like band with a radius equivalent to the periodicity of the map. When trying to determine the nearest-neighbour value, the peak with the highest spatial frequency was chosen. Consequently, periodicity values measured in this manner for anisotropic maps would typically be smaller than those acquired under the assumption that maps are isotropic. To verify that the selected peak was indeed responsible for the observed pattern in the autocorrelogram (and not just a harmonic), the autocorrelation matrix was reconstructed from the filtered PSD using an inverse FFT and then compared to the original autocorrelation matrix. The spatial frequency corresponding to the location of the peak was determined by calculating the radial distance from the centre to the peak, after normalizing the axes to account for the different frequency resolutions in each direction of the PSD. The periodicity value was taken as its reciprocal.
We would also like to acknowledge the important contributions of Jun Lee, Hongbin Li, Jesse Schallek, Dorothy Joiner and Sandy McGillis, and the helpful comments on the manuscript from Brad Motter and Anna Roe. The work was generously supported by NIH EY08240.