scholarly journals A principle of economy predicts the functional architecture of grid cells

eLife ◽  
2015 ◽  
Vol 4 ◽  
Author(s):  
Xue-Xin Wei ◽  
Jason Prentice ◽  
Vijay Balasubramanian
Keyword(s):  
Three Dimensions ◽  
Periodic Lattice ◽  
Grid System ◽  
Grid Cells ◽  
Grid Structure ◽  
Functional Architecture ◽  
Optimal Organization ◽  
Scale Ratio ◽  
Hierarchical Code ◽  
The Brain

Grid cells in the brain respond when an animal occupies a periodic lattice of ‘grid fields’ during navigation. Grids are organized in modules with different periodicity. We propose that the grid system implements a hierarchical code for space that economizes the number of neurons required to encode location with a given resolution across a range equal to the largest period. This theory predicts that (i) grid fields should lie on a triangular lattice, (ii) grid scales should follow a geometric progression, (iii) the ratio between adjacent grid scales should be √e for idealized neurons, and lie between 1.4 and 1.7 for realistic neurons, (iv) the scale ratio should vary modestly within and between animals. These results explain the measured grid structure in rodents. We also predict optimal organization in one and three dimensions, the number of modules, and, with added assumptions, the ratio between grid periods and field widths.

scholarly journals Complete coverage of space favors modularity of the grid system in the brain

2016 ◽  
Author(s):  
A. Sanzeni ◽  
V. Balasubramanian ◽  
G. Tiana ◽  
M. Vergassola
Keyword(s):  
Statistical Physics ◽  
Physical Space ◽  
Grid Cell ◽  
Triangular Grid ◽  
Grid System ◽  
Grid Cells ◽  
Scaling Relation ◽  
Complete Coverage ◽  
Space Experiments ◽  
The Brain

Grid cells in the entorhinal cortex fire when animals that are exploring a certain region of space occupy the vertices of a triangular grid that spans the environment. Different neurons feature triangular grids that differ in their properties of periodicity, orientation and ellipticity. Taken together, these grids allow the animal to maintain an internal, mental representation of physical space. Experiments show that grid cells are modular, i.e. there are groups of neurons which have grids with similar periodicity, orientation and ellipticity. We use statistical physics methods to derive a relation between variability of the properties of the grids within a module and the range of space that can be covered completely (i.e. without gaps) by the grid system with high probability. Larger variability shrinks the range of representation, providing a functional rationale for the experimentally observed co-modularity of grid cell periodicity, orientation and ellipticity. We obtain a scaling relation between the number of neurons and the period of a module, given the variability and coverage range. Specifically, we predict how many more neurons are required at smaller grid scales than at larger ones.

Advantages of Complementary Stereo Images as Viewed with the Low-Temperature Field-Emission SEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1314-1315
Author(s):  
William P. Wergin ◽  
Eric F. Erbe
Keyword(s):  
Fold Increase ◽  
Horizontal Displacement ◽  
Three Dimensions ◽  
Stereo Image ◽  
Stereo Pair ◽  
Sem Micrograph ◽  
Left And Right ◽  
The Common ◽  
The Brain ◽  
Pair Analysis

The eye-brain complex allows those of us with normal vision to perceive and evaluate our surroundings in three-dimensions (3-D). The principle factor that makes this possible is parallax - the horizontal displacement of objects that results from the independent views that the left and right eyes detect and simultaneously transmit to the brain for superimposition. The common SEM micrograph is a 2-D representation of a 3-D specimen. Depriving the brain of the 3-D view can lead to erroneous conclusions about the relative sizes, positions and convergence of structures within a specimen. In addition, Walter has suggested that the stereo image contains information equivalent to a two-fold increase in magnification over that found in a 2-D image. Because of these factors, stereo pair analysis should be routinely employed when studying specimens.Imaging complementary faces of a fractured specimen is a second method by which the topography of a specimen can be more accurately evaluated.

Differences in the brain stem terminations of large- and small-diameter vestibular primary afferents

1995 ◽  
Vol 74 (3) ◽  
pp. 1362-1366 ◽  
Author(s):  
J. A. Huwe ◽  
E. H. Peterson
Keyword(s):  
Brain Stem ◽  
Large Diameter ◽  
Small Diameter ◽  
Movement Control ◽  
Three Dimensions ◽  
Significant Shift ◽  
Axon Diameter ◽  
Vestibular Complex ◽  
The Brain ◽  
Adjacent Brain

1. We visualized the central axons of 32 vestibular afferents from the posterior canal by extracellular application of horseradish peroxidase, reconstructed them in three dimensions, and quantified their morphology. Here we compare the descending limbs of central axons that differ in parent axon diameter. 2. The brain stem distribution of descending limb terminals (collaterals and associated varicosities) varies systematically with parent axon diameter. Large-diameter afferents concentrate their terminals in rostral regions of the medial/descending nuclei. As axon diameter decreases, there is a significant shift of terminal concentration toward the caudal vestibular complex and adjacent brain stem. 3. Rostral and caudal regions of the medial/descending nuclei have different labyrinthine, cerebellar, intrinsic, commissural, and spinal connections; they are believed to play different roles in head movement control. Our data help clarify the functions of large- and small-diameter afferents by showing that they contribute differentially to rostral and caudal vestibular complex.

scholarly journals Comparing Glioblastoma Surgery Decisions Between Teams Using Brain Maps of Tumor Locations, Biopsies, and Resections

2019 ◽  
pp. 1-12 ◽  
Author(s):  
Domenique M.J. Müller ◽  
Pierre A.J.T. Robe ◽  
Roelant S. Eijgelaar ◽  
Marnix G. Witte ◽  
Martin Visser ◽  
...  
Keyword(s):  
Tumor Location ◽  
Three Dimensions ◽  
Multidisciplinary Teams ◽  
Surgical Removal ◽  
Treatment Variation ◽  
Probability Maps ◽  
Resected Patient ◽  
The Right ◽  
Referral Bias ◽  
The Brain

Purpose The aim of glioblastoma surgery is to maximize the extent of resection while preserving functional integrity, which depends on the location within the brain. A standard to compare these decisions is lacking. We present a volumetric voxel-wise method for direct comparison between two multidisciplinary teams of glioblastoma surgery decisions throughout the brain. Methods Adults undergoing first-time glioblastoma surgery from 2012 to 2013 performed by two neuro-oncologic teams were included. Patients had had a diagnostic biopsy or resection. Preoperative tumors and postoperative residues were segmented on magnetic resonance imaging in three dimensions and registered to standard brain space. Voxel-wise probability maps of tumor location, biopsy, and resection were constructed for each team to compare patient referral bias, indication variation, and treatment variation. To evaluate the quality of care, subgroups of differentially resected brain regions were analyzed for survival and functional outcome. Results One team included 101 patients, and the other included 174; 91 tumors were biopsied, and 181 were resected. Patient characteristics were largely comparable between teams. Distributions of tumor locations were dissimilar, suggesting referral bias. Distributions of biopsies were similar, suggesting absence of indication variation. Differentially resected regions were identified in the anterior limb of the right internal capsule and the right caudate nucleus, indicating treatment variation. Patients with (n = 12) and without (n = 6) surgical removal in these regions had similar overall survival and similar permanent neurologic deficits. Conclusion Probability maps of tumor location, biopsy, and resection provide additional information that can inform surgical decision making across multidisciplinary teams for patients with glioblastoma.

scholarly journals Nervous Activity of the Brain in Five Dimensions

Biophysica ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 38-47
Author(s):  
Arturo Tozzi ◽  
James F. Peters ◽  
Norbert Jausovec ◽  
Arjuna P. H. Don ◽  
Sheela Ramanna ◽  
...  
Keyword(s):  
Fourier Analysis ◽  
Nervous Activity ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Data Sets ◽  
Spatial And Temporal Patterns ◽  
Five Dimensions ◽  
Four Dimensions ◽  
Scale Free ◽  
The Brain

The nervous activity of the brain takes place in higher-dimensional functional spaces. It has been proposed that the brain might be equipped with phase spaces characterized by four spatial dimensions plus time, instead of the classical three plus time. This suggests that global visualization methods for exploiting four-dimensional maps of three-dimensional experimental data sets might be used in neuroscience. We asked whether it is feasible to describe the four-dimensional trajectories (plus time) of two-dimensional (plus time) electroencephalographic traces (EEG). We made use of quaternion orthographic projections to map to the surface of four-dimensional hyperspheres EEG signal patches treated with Fourier analysis. Once achieved the proper quaternion maps, we show that this multi-dimensional procedure brings undoubted benefits. The treatment of EEG traces with Fourier analysis allows the investigation the scale-free activity of the brain in terms of trajectories on hyperspheres and quaternionic networks. Repetitive spatial and temporal patterns undetectable in three dimensions (plus time) are easily enlightened in four dimensions (plus time). Further, a quaternionic approach makes it feasible to identify spatially far apart and temporally distant periodic trajectories with the same features, such as, e.g., the same oscillatory frequency or amplitude. This leads to an incisive operational assessment of global or broken symmetries, domains of attraction inside three-dimensional projections and matching descriptions between the apparently random paths hidden in the very structure of nervous fractal signals.

The Brain Stem Saccadic Burst Generator Encodes Gaze in Three-Dimensional Space

2008 ◽  
Vol 99 (5) ◽  
pp. 2602-2616 ◽  
Author(s):  
Marion R. Van Horn ◽  
Pierre A. Sylvestre ◽  
Kathleen E. Cullen
Keyword(s):  
Eye Movements ◽  
Brain Stem ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Saccadic Eye Movements ◽  
Three Dimensions ◽  
Related Information ◽  
Computer Based ◽  
Different Depths ◽  
The Brain

When we look between objects located at different depths the horizontal movement of each eye is different from that of the other, yet temporally synchronized. Traditionally, a vergence-specific neuronal subsystem, independent from other oculomotor subsystems, has been thought to generate all eye movements in depth. However, recent studies have challenged this view by unmasking interactions between vergence and saccadic eye movements during disconjugate saccades. Here, we combined experimental and modeling approaches to address whether the premotor command to generate disconjugate saccades originates exclusively in “vergence centers.” We found that the brain stem burst generator, which is commonly assumed to drive only the conjugate component of eye movements, carries substantial vergence-related information during disconjugate saccades. Notably, facilitated vergence velocities during disconjugate saccades were synchronized with the burst onset of excitatory and inhibitory brain stem saccadic burst neurons (SBNs). Furthermore, the time-varying discharge properties of the majority of SBNs (>70%) preferentially encoded the dynamics of an individual eye during disconjugate saccades. When these experimental results were implemented into a computer-based simulation, to further evaluate the contribution of the saccadic burst generator in generating disconjugate saccades, we found that it carries all the vergence drive that is necessary to shape the activity of the abducens motoneurons to which it projects. Taken together, our results provide evidence that the premotor commands from the brain stem saccadic circuitry, to the target motoneurons, are sufficient to ensure the accurate control shifts of gaze in three dimensions.

scholarly journals A geometric attractor mechanism for self-organization of entorhinal grid modules

eLife ◽  
2019 ◽  
Vol 8 ◽  
Author(s):  
Louis Kang ◽  
Vijay Balasubramanian
Keyword(s):  
Entorhinal Cortex ◽  
Network Models ◽  
Recurrent Inhibition ◽  
Modular Structure ◽  
Self Organization ◽  
Periodic Lattice ◽  
Grid Cells ◽  
Medial Entorhinal Cortex ◽  
Attractor Network ◽  
Discrete Values

Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of ‘grid fields’ in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated on average by ratios in the range 1.4–1.7. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

scholarly journals Manipulating the structure of natural scenes using wavelets to study the functional architecture of perceptual hierarchies in the brain

NeuroImage ◽  
2020 ◽  
Vol 221 ◽  
pp. 117173
Author(s):  
Alexander M. Puckett ◽  
Mark M. Schira ◽  
Zoey J. Isherwood ◽  
Jonathan D. Victor ◽  
James A. Roberts ◽  
...  
Keyword(s):  
Natural Scenes ◽  
Functional Architecture ◽  
The Brain

NEUROBIOLOGY:How the Brain Sees in Three Dimensions

1998 ◽  
Vol 281 (5376) ◽  
pp. 500-501 ◽  
Author(s):  
M. Barinaga
Keyword(s):  
Three Dimensions ◽  
The Brain

The Eisenstein-Vygotsky-Luria Collaboration

Projections ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 23-44 ◽  
Author(s):  
Julia Vassilieva
Keyword(s):  
Crucial Role ◽  
Cultural Psychology ◽  
Film Theory ◽  
Theory And Practice ◽  
Functional Architecture ◽  
Cultural Mediation ◽  
Sergei Eisenstein ◽  
Lev Vygotsky ◽  
Russian Film ◽  
The Brain

This article analyzes the unique historical collaboration between the revolutionary Russian film director Sergei Eisenstein (1898–1948), the cultural psychologist Lev Vygotsky (1896–1934), and the founder of contemporary neuropsychology, Alexander Luria (1902–1977). Vygotsky’s legacy is associated primarily with the idea that cultural mediation plays a crucial role in the emergence and development of personality and cognition. His collaborator, Luria, laid the foundations of contemporary neuropsychology and demonstrated that cultural mediation also changes the functional architecture of the brain. In my analysis, I demonstrate how the Eisenstein-Vygotsky-Luria collaboration exemplifies a strategy of productive triangulation that harnesses three disciplinary perspectives: those of cultural psychology, neuropsychology, and film theory and practice.

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