Where do numbers come from? Have humans constructed a useful abstraction or do numbers somehow exist as part of the fabric of our universe?
Figure 1. The number sense, more technically known as numerosity, is mapped across the back of the human brain’s top right hemisphere. At top are shown color coded sets from 1 (red; left) to 7 (pink; right). The map shown at bottom right uses the same color coding over the brain area associated with 1 (red) to 7 (pink).
Recent research has shown that non-human animals, infants, and tribal people with no numerical language have an innate ability to distinguish numbers of things or sets. For example, they may distinguish a set of 2 dots from a set of 5. This capability, known as numerosity, appears to be a hard wired sense like touch or vision.
Studies reported in the research article “Topographic Representation of Numerosity in the Human Parietal Cortex” published September 6, 2013 in Science uses brain imaging in human subjects to test if numerosity is mapped across the surface of the human cerebral cortex like the body is for touch and the visual field is for vision.
The research team found a map from small numerosity (set of 1) to larger numerosity (set of about 7) from medial to lateral superior parietal cortex (see Figure 1 above). More cortex was devoted to the smaller sets than the larger sets. This corresponds with the greater accuracy subjects show in perceiving smaller sets.
Remarkably, these data demonstrate that human and non-human brains include structures that respond to the size of different sets of things in the environment. The number sense, the sense of something we may consider abstract in comparison with other brain mapped senses like touch and sight, appears necessary for survival and propagation of humans and at least some non-human animals. Does this call into question what we think of as real as opposed to an abstraction?
The Mouse Connectome Project’s publicly available whole brain connectivity atlas of the C57BL/6J mouse is being created to help provide data for generating testable ideas (hypotheses) about local brain circuits, brain function, behavior, and disease. The project provides data through the following link: http://www.mouseconnectome.org/iConnectome (see Figure 2 below).
Figure 2. This webpage is the access point to the Mouse Connectome Project’s data repository. The page lists the data and data characteristics which are viewed through the iConnectome Viewer (see text below).
There is no direct access to the raw data that I can find. Instead a tool named the iConnectome Viewer is provided. The user selects the data set they want to work with by checking the check box in the left-most column titled “Show” and then clicking on the “VIEW” button above.
The paper includes several figures that display data which lead the authors to hypothesize connections to and from the medial olfactory bulb (MOB) shown above in Figure 1. The beauty of shared data access begins to become apparent on noticing the case numbers referencing the data included in each figure caption.
Case numbers are listed in the Mouse Connectome Project data repository webpage in the column next to Show (see Figure 2 above). Type a case number into the Search box (under the “REFRESH” button at the far right and at the same level as the “VIEW” button) and the case list shrinks. I typed in case SW110403-01A from the paper’s Figure 7E-H into the search box, checked the check box next to the case number, and then clicked the “VIEW” button. An impressive looking viewer appeared, as shown in Figure 3 below.
Figure 3. The iConnectome Viewer displays the data contained in the Mouse Connectome Project’s whole brain connectivity atlas.
There are five main areas of the iConnectome Viewer. The navigation controls are grouped in upper left hand area. This area provides controls for zooming, panning, and refreshing the selected viewport (the viewer opens with one viewport but it may show up to four viewports at a time). Most navigation functions may also be accomplished through double-clicking, dragging, and other interface gestures. There is also a thumbnail view of the section in the currently selected viewport shown here. There is one set of navigation controls for all open viewports.
The data set and layer controls appear in the upper right portion of each open viewport. The case number of the data displayed in the viewport is displayed above a list of data types that may be layered one upon the other. The base layer that displays a standard Nissl stained section is selected by default. Above the base layer is the atlas layer which shows the appropriate section and data from the Allen Reference Atlas (ARA). The Allen Reference Atlas has become the standard high-resolution anatomic reference atlas accompanied by a systematic, hierarchically organized taxonomy of mouse brain structures created by the Allen Institute for Brain Science. The other layers are for each type of label used in the case study. A lot of important information for each section is displayed when you mouse over the blue information button “i” to the left of the case study number including the section coordinates.
The section controls are grouped along the bottom of the iConnectome Viewer. The sagittal view of the brain at bottom left has a yellow vertical bar you may drag right and left to show sections from different coronal planes. The data layer buttons above the brain are the same as the data layers provided in each viewport. To the right is an array of coronal sections with the particular section you selected using the vertical bar shown with a yellow outline. You may click on a different coronal section and it will be outlined in yellow and the yellow vertical bar in the sagittal section at left will reposition appropriately.
The viewport and menu tool bar display along the top of the iConnectome Viewer. At left, above the navigation controls, are the buttons that control the layout of the viewports. From left to right they are the single, double, 2×2, and tab viewport layout. The button to the right of the four viewport buttons is very important. It’s the synchronize viewports button. When synchronize is activated, any navigation action performed in one viewport is mirrored in the others.
Figure 4. The Mouse Connectome Project’s data repository paired with the iConnectome Viewer provide a powerful mouse brain atlas for the 21st century.
It’s time for you to take a test drive.
Click on the Dual View button in the viewport tool bar at top left.
Now click on the Link Viewports button.
Move the vertical yellow line to the right in the sagittal brain section at bottom left. The sections in the left and right viewports synchronize. In fact, they’re exactly the same because the data layers are both set to base.
To make this more interesting, in the right viewport click on the base button in the data set and layer controls area. The section should disappear.
Click on the atlas button. Now the right viewport should display the exact same part of the brain displayed in the left viewport except the section at right is from the Allen Reference Atlas and it includes a diagram with structure names.
Zoom in to take a closer look by double clicking in the viewport or by using the slider in the navigation area.
Make this even more interesting by selecting the fg (Fluorogold) data set in the left viewport.
Your iConnectome Viewer should look similar to the one pictured in Figure 4 above. The Mouse Connectome Project’s whole brain connectivity atlas and iConnectome Viewer combine to provide a powerful mouse brain atlas for the 21st century. The main shortfall that I see is the apparent inability for public access of the raw data in the repository. Access to the raw data is essential for investigators to be able to go beyond the atlas and to using machine processing to quantitatively analyze mouse brain connectivity.
Figure 1. The graphs show the balance between path length economy (y-axis) and wire length economy (x-axis) in cerebral cortical spiny cells (left) and basket cells (right). Full path length optimization results in the star tree morphology (bright green). Full wire length optimization results in the minimal spanning tree morphology (blue). Reconstructed axons were found to have a bias towards wire length optimization (red). From Figure 4 in “Communication and wiring in the cortical connectome” (published October 16, 2012 in Frontiers in Neuroanatomy).
Understanding how the brain is wired is fundamental to understanding how the brain works. Graph Theory, used extensively in analyses of computer network related data, is one of the more recent mathematical tools applied to trying to understand how the brain is wired.
A paper published last month asks if brain wiring is optimized to balance the amount of material used to create a biological “wire” and the time it takes for a signal to go from one place to another. The authors of “Communication and wiring in the cortical connectome” (published October 16, 2012 in Frontiers in Neuroanatomy) apply graph theory to answer the question.
The authors address three different levels of structural brain organization:
the single cell
the local neural circuit
fiber tracts connecting cortical regions
The authors found that sufficient quantitative neuron morphology data and inter-regional cerebral cortical connectivity data exist to provide insight at these levels. However, they found that quantitative data were severely lacking for local cortical neuron circuits and they were unable to provide insight using their graph theory techniques at this level.
The investigation pointed to an optimization between the path length from one node to another and the length of the wire between the two nodes. There seems to be a bias towards wire length optimization (see Figure 1 above). These data suggest that recently developed tracing techniques (see Other related blog posts below) may provide the morphologically detailed data that will enable the discovery of general principles behind how the brain is wired.
