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Kaufmann D, Theriot JJ, Zyuzin J, Service CA, Chang JC, Tang YT, Bogdanov VB, Multon S, Schoenen J, Ju YS, Brennan KC. Heterogeneous incidence and propagation of spreading depolarizations. J Cereb Blood Flow Metab 2017; 37:1748-1762. [PMID: 27562866 PMCID: PMC5435294 DOI: 10.1177/0271678x16659496] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/16/2016] [Revised: 05/27/2016] [Accepted: 06/06/2016] [Indexed: 12/17/2022]
Abstract
Spreading depolarizations are implicated in a diverse set of neurologic diseases. They are unusual forms of nervous system activity in that they propagate very slowly and approximately concentrically, apparently not respecting the anatomic, synaptic, functional, or vascular architecture of the brain. However, there is evidence that spreading depolarizations are not truly concentric, isotropic, or homogeneous, either in space or in time. Here we present evidence from KCl-induced spreading depolarizations, in mouse and rat, in vivo and in vitro, showing the great variability that these depolarizations can exhibit. This variability can help inform the mechanistic understanding of spreading depolarizations, and it has implications for their phenomenology in neurologic disease.
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Affiliation(s)
- Dan Kaufmann
- Department of Neurology, University of Utah, Salt Lake City, UT, USA
| | - Jeremy J Theriot
- Department of Neurology, University of Utah, Salt Lake City, UT, USA
- Department of Neurology, University of California Los Angeles, Los Angeles, CA, USA
| | - Jekaterina Zyuzin
- Department of Neurology, University of California Los Angeles, Los Angeles, CA, USA
| | - C Austin Service
- Department of Neurology, University of Utah, Salt Lake City, UT, USA
| | - Joshua C Chang
- Rehabilitation Medicine Department, Mark O. Hatfield Clinical Research Center, National Institutes of Health, Bethesda, MD, USA
- Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, USA
| | - Y Tanye Tang
- Department of Mechanical and Aerospace Engineering, University of California Los Angeles, Los Angeles, CA, USA
| | - Vladimir B Bogdanov
- Department of Neurology, University of Utah, Salt Lake City, UT, USA
- Department of Neurology, University of Liège, Liège, Belgium
| | - Sylvie Multon
- Department of Neurology, University of Liège, Liège, Belgium
| | - Jean Schoenen
- Department of Neurology, University of Liège, Liège, Belgium
| | - Y Sungtaek Ju
- Department of Mechanical and Aerospace Engineering, University of California Los Angeles, Los Angeles, CA, USA
| | - KC Brennan
- Department of Neurology, University of Utah, Salt Lake City, UT, USA
- Department of Neurology, University of California Los Angeles, Los Angeles, CA, USA
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Chang JC, Chou T. Iterative graph cuts for image segmentation with a nonlinear statistical shape prior. JOURNAL OF MATHEMATICAL IMAGING AND VISION 2014; 49:87-97. [PMID: 24678141 PMCID: PMC3963360 DOI: 10.1007/s10851-013-0440-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Shape-based regularization has proven to be a useful method for delineating objects within noisy images where one has prior knowledge of the shape of the targeted object. When a collection of possible shapes is available, the specification of a shape prior using kernel density estimation is a natural technique. Unfortunately, energy functionals arising from kernel density estimation are of a form that makes them impossible to directly minimize using efficient optimization algorithms such as graph cuts. Our main contribution is to show how one may recast the energy functional into a form that is minimizable iteratively and efficiently using graph cuts.
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Affiliation(s)
- Joshua C. Chang
- Mathematical Biosciences Institute, The Ohio State University, Jennings Hall, 3rd Floor, 1735 Neil Avenue, Columbus, Ohio 43210
| | - Tom Chou
- UCLA Biomathematics and Mathematics, BOX 951766, Room 5303 Life Sciences, Los Angeles, CA 90095-1766
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