by Wojciech Czarnecki
1. Connectome
In 2003 The Human Genome Project was completed after twelve years of intense work of specialists from all over the world which started the era of genomics. While genes define our inborn characteristics, what is still a mystery is how exactly our knowledge, memories and skills are stored. One possible hypothesis says that this kind of information is encoded in the way neurons are connected in our brain [1]. If such information could be easily obtained for a particular human being, it would be possible for example to easily diagnose mental disorders and, what is equally (or even more) significant – investigate how our brain works.
As defined by Hagmann [2], the connectome is a set of all connections in a brain, considered as a single entity. So one can view it as a graph where vertices are particular neurons, and the edges are connections between them. So far only one structure of this kind is known – connectome (with 302 vertices and about 7000 edges) of the nematode C. Elegans [3] (see fig. 1).
Figure 1. C. Elegans connectome visualized with Mathematica.
The human brain consists of about one hundred billion neurons, accompanied by almost ten thousands more connections between each of them [4]. It is over one million times more than the length of the human genome. Such an enormous size of data leads to many problems:
- Data acquisition – to achieve the greatest possible accuracy of the process one needs an EM/MR images in nano- or micrometer scale of the whole brain.
- Storage – even if the edges are represented as pairs of integers, one would still need about 10 exabytes (10 x 1015 bytes) of space to store a single connectome (which is about 3% of the world’s total stored analog and digital content[5]).
- Need for fast reconstruction algorithms (of O(n) complexity).
- Need for methods of statistical analysis of massive graphs.
2. Current methods
One of the possible input data for the connectome problem is a stack of images from electron microscopy (see fig. 2), for which identification of particular neurons is required. In computer science such a problem is called image segmentation – for a given image (or set of images) one needs to decide for each image pixel (voxel) to which class (object) it belongs.
Figure 2. From left: sample EM image, its boundary labeling and resulting segmentation. For more details see Jain V, Turaga SC, Seung HS. Machines that learn to segment images: a crucial technology of connectomics. Current Opinion in Neurobiology, 2010.
The first approach to the problem (and currently the only fully successful one) was a manual annotation of the neurons in the microscopy image data. While it was possible to accomplish this for a few hundred neurons, the big brain size of more complex beings (like mammals) require much faster, fully automated methods.
Most of the current algorithms work in two phases – first, they detect boundaries (the edges of each object), and then simply search for connected components in the image graph, where the edge between two pixels exists if and only if they are adjacent and there is no boundary between them.
For such an approach, boundary detection can be achieved by using for example:
- Simple edge detectors (Sobel [6], Gaussian based [7], Canny [8]).
- Haar wavelet transform based method [9].
- Statistical methods [10].
- Machine learning algorithms [11].
Second phase can be easily done by BFS (or DFS) search through the image graph. After that, layer by layer, the segmented images can be connected to find out which neurons are connected.
In more advanced algorithms boundary detection is replaced with so-called affinity graph generation, where instead of labeling pixels “boundary” or “not boundary” the algorithm estimates for each of its neighborhood likelihood that two pixels are in the same region/object (see fig 3.).
Figure 3. A. Sample EM image, B. Segmentation made by human expert, C. and D. Segmentations based on affinity graphs. For more details see Turaga, S. C., Murray, J. F., Jain, V., Roth, F., Helmstaedter, M., Briggman, K., Denk, W., et al. (2010). Convolutional networks can learn to generate affinity graphs for image segmentation. Neural Computation, 22(2), 511-38. MIT Press.
3. Alternative approaches and current progress
There are also much simpler formulations of the brain mapping problem. Instead of an exact graph of all neuron connections, one can search for more statistical information about how groups of neurons or brain regions are connected to each other. Once this is solved, precise neuron-to-neuron mapping can be done independently on each of such structures, ensuring the distributed nature of the whole process.
As stated in the section 1. – only one full connectome is known, but because of the major advances in the imaging techniques (especially diffusion magnetic resonance and functional magnetic resonance), some major fiber bundles are reconstructed, and some anatomically and structurally distinct areas are identified.
4. Future
There are at least a few projects related to the connectome reconstruction – the Human Connectome Project, the Open Connectome Project, the Mouse Connectome Project, and The Seung Lab at MIT — each with a different approach to the problem, and different possible outcomes. As for now we, live in the age of genomics, but in just few years from now we might witnesses a the new era – the era of connectomics.
I encourage the reader to follow some of the links placed at the end of this article and watch the inspiring speech by Sebastian Seung, PhD.
5. Useful links
- C. Elegans Connectome http://www.wormatlas.org/neuronalwiring.html
- Human Connectome Project http://www.humanconnectomeproject.org/
- Open Connectome Project http://openconnectomeproject.org/
- Seung Lab http://hebb.mit.edu/seunglab/home
- Mouse Connectome Project http://www.mouseconnectome.org/
6. References
[1] Connectomics: Tracing the Wires of the Brain (Dana Foundation) http://www.dana.org/news/cerebrum/detail.aspx?id=13758
[2] Hagmann, P. (2005). From diffusion mri to brain connectomics. Science. Institut de traitement des signaux PROGRAMME DOCTORAL EN INFORMATIQUE ET COMMUNICATIONS POUR LʼOBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES PAR Docteur en médecine, Université de Lausanne.
[3] White, J. G., Southgate, E., Thomson, J. N., & Brenner, S. (1986). The Structure of the Nervous System of the Nematode Caenorhabditis elegans.Philosophical Transactions of the Royal Society B Biological Sciences,314(1165), 1-340. The Royal Society.
[4] Drachman, D. A. (2005). Do we have brain to spare? Neurology.
[5] Martin Hilbert and Priscila López. The World’s Technological Capacity to Store, Communicate, and Compute Information. Science, 10 February 2011.
[6] Kittler, J. (1983). On the accuracy of the Sobel edge detector. Image Vision Computing, 1(1), 37-42.
[7] Marr, D., & Hildreth, E. (1980). Theory of edge detection. Proceedings of the Royal Society of London Series B Containing papers of a Biological character Royal Society Great Britain, 207(1167), 187-217.
[8] Ding, L. (2001). Canny edge detector. Most, 34(3), 721-725. Computer Science and Engineering Department Wright State University.
[9] Heric, D., & Zazula, D. (2007). Combined edge detection using wavelet transform and signal registration. Image and Vision Computing, 25(5), 652-662. ELSEVIER SCIENCE BV.
[10] Cues, E., Konishi, S., Yuille, A. L., Coughlan, J. M., & Zhu, S. C. (2003). Statistical Edge Detection : Learning and Evaluating Statistical Edge Detection : Learning and Evaluating Edge Cues. Analysis, 25(1), 29-36.
[11] Lu, S., Wang, Z., & Shen, J. (2003). Neuro-fuzzy synergism to the intelligent system for edge detection and enhancement. Pattern Recognition, 36(10), 2395-2409.
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