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In still another experiment where we graph orientation against track distance, three reversals separated long, straight progressions.
few millimeters. The graph on the next page shows an example of a sequence with several such reversals.
We see in some experiments a final peculiarity called a fracture. Just as we are becoming mesmerized by the relentless regularity, observing shift after shift in the same direction, we see on rare occasions a sudden break in the sequence, with a shift of 45 to 90 degrees. The sequence then resumes with the same regularity, but often with a reversal from clockwise to counterclockwise. The graph on page 29 shows such a fracture, followed a few tenths of a millimeter later by another one.
The problem of learning what these groupings, or regions of constant orientation, look like if viewed from above the cortex has proved much more difficult than viewing ocular-dominance columns from the same perspective.
Until very recently we have had no direct way of seeing the orientation groupings and have had to try to deduce the form from microelectrode penetrations such as those I have shown here. The reversals and fractures both suggest that the geometry is not simple. On the other hand, the linear regularity that we see, often over millimeter after millimeter of cortex, must imply a regularity at least within small regions of cortex; the reversals and fractures would then suggest that the regularity is broken up every few millimeters.
Within these regions of regularity, we can predict the geometry to some extent. Suppose that the region is such that wherever we explore it with an electrode parallel to the surface, we see regularity—no reversals and no fractures—that is, everywhere we obtain graphs like the one on page 29. If we had enough of these graphs, we could ultimately construct a three-dimensional graph, as in the illustration shown on the facing page, with orientation represented on a vertical axis (z) plotted against cortical distance on horizontal axes (x and y). Orientations would then be represented on a surface such as the tilted plane in this illustration, in cases where the graphs were straight lines, and otherwise on some kind of curved surface. In this three-dimensional graph horizontal planes (the x-y plane or planes parallel to it) would intersect this surface in lines, contour lines of constant orientation (iso-orientation lines)
analogous to lines of constant height in a contour map in geography. Undulations—hills, valleys, ridges—in the 3-D graph would give reversals in some orientation-versus-distance plots; sudden breaks in the form of cliffs would lead to the fractures. The main message from this argument is that regions of regularity imply the possibility of plotting a contour map, which means that regions of constant orientation, seen looking down on the cortex from above, must be stripes. Because orientations plotted in vertical penetrations through the cortex are constant, the regions in three dimensions must be slabs. And because the iso-orientation lines may curve, the slabs need not be flat like slices of bread. Much of this has been demonstrated directly in experiments making two or three parallel penetrations less than a millimeter apart, and the threedimensional form has been reconstructed at least over those tiny volumes.
If our reasoning is right, occasional penetrations should occur in the same direction as contour lines, and orientation should be constant. This does happen, but not very often. That, too, is what we would predict, because trigonometry tells us that a small departure from a contour line, in a penetration's direction, gives a rather large change in slope, so that few graphs of orientation versus distance should be very close to horizontal.
The number of degrees of orientation represented in a square millimeter of cortex should be given by the steepest slopes that we find. This is about 400 degrees per millimeter, which means a full complement of 180 degrees of orientation in about o. 5 millimeter. This is a number to have in mind when we return to contemplate the topography of the cortex and its striking uniformity.
Here, I cannot resist pointing out that the thickness of a pair of ocular-dominance columns is 0.4 plus 0.4 millimeter, or roughly i millimeter, double, but about the same order of magnitude, as the set of orientation slabs.
Deoxyglucose mapping was soon seized on as a direct way of determining orientation-column geometry. We simply stimulated with parallel stripes, keeping orientation constant, say vertical, for the entire period of stimulation.
The pattern we obtained, as shown in the top autoradiograph on the facing page, was far more complex than that of ocular-dominance columns. Nevertheless the periodicity was clear, with i millimeter or less from one dense region to the next, as would be expected from the physiology—the distance an electrode has to move to go from a given orientation, such as vertical, through all intermediates and back to vertical. Some places showed stripelike regularity extending for several square millimeters. We had wondered whether the orientation slabs and the ocular-dominance stripes might in any way be related in their geometry—for example, be parallel or intersect at 90 degrees. In the same experiment, we were able to reveal the ocular-dominance columns by injecting the eye with a radioactive amino acid and to look at the same block of tissue by the two methods, as shown in the second autoradiograph on the facing page. We could see no obvious correlation. Given the complex pattern of the orientation domains, compared with the relatively much simpler pattern of the ocular-dominance columns, it was hard to see how the two patterns could be closely related.
For some types of questions the deoxyglucose method has a serious limitation. It is hard always to be sure that the pattern we obtain is really related to whatever stimulus variable we have used. For example, using black and white vertical stripes as a stimulus, how can we be sure the pattern is caused by verticality—that the dark areas contain cells responding to vertical, the light areas, cells responding to nonvertical? The features of the stimulus responsible for the pattern could be the use of black-white, as opposed to color, or the use of coarse stripes, as opposed to fine ones, or the placing of the screen at some

   
 

In the same animal as above, one eye had been injected a week earlier with radioactive amino acid (proline), and after washing the section in water to dissolve the 2-deoxyglucose, an autoradiograph was prepared from the same region as in the upper autoradiograph. Label shows ocular-dominance columns. These have no obvious relationship to the orientation columns.
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After the injection of deoxy glucose, the visual fields of the anesthetized monkey were stimulated with slowly moving vertical black and white stripes. The resulting autoradiograph shows dense periodic labeling, for example in layers 5 and 6 (large central elongated area). The dark gray narrow ring outside this, layer 4C(3, is uniformly labeled, as expected, because the cells are not orientation selective.

The surface of the cortex is plotted on the x-y plane in this three dimensional map;
the vertical (z) axis represents orientation.
If for all directions of electrode tracks straight line orientation-versus-distance plots are produced, the surface generated will be a plane, and intersections of the surface (whether planar or not) with the x-y plane, and planes parallel to it, will give contour lines. (This sounds more complicated than it is! The same reasoning applies if the x-y plane is the surface of Tierra del Fuego and the z axis represents altitude or average rainfall in January or temperature.)

 
 
 
 
 

This penetration showed two fractures, or sudden shifts in orientation, following and followed by regular sequences of shifts.


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