Cited by 1,178Functional Brain Connectivity StudiesNeural dynamics and brain functionAdvanced Neuroimaging Techniques and Applications

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Cortex: Statistics and Geometry of Neuronal Connectivity

Braitenberg, Valentino, Schüz, Almut·1998·Springer eBooks

DOI 10.1007/978-3-662-03733-1

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“Overall, the vast majority of cortical excitatory synapses and almost all inhibitory synapses, originate from neurons within cortex (Braitenberg & Schüz, 1998).”
Influential
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“, 1979) have been generalized in rules stating that connections are untargeted, that the fraction of axo-dendritic appositions forming synapses is constant, and that most connections are formed of only one synapse (Braitenberg and Schüz, 1998; Braitenberg, 2001).”
BackgroundMethodInfluential
Beyond the cortical column: abundance and physiology of horizontal connections imply a strong role for inputs from the surround
Boucsein, C. (2011) · Frontiers in Neuroscience · doi:10.3389/fnins.2011.00032 · Cited by 125
“…with radius d as N d f h P s sdsdcon E( ) ( )= ∫2 0πρ , with ρ = 60,000/mm3 (black trace) defining the cell density per cortex volume, fE = 0.85 representing the relative fraction of excitatory connections (Braitenberg and Schüz, 1998), and h = 1.3 mm defining the thickness of the gray matter.”
BackgroundInfluential
Gyrification and neural connectivity in schizophrenia
White, T. J. H., & Hilgetag, C. C. (2011) · Development and Psychopathology · doi:10.1017/s0954579410000842 · Cited by 121
Why Bilateral Damage Is Worse than Unilateral Damage to the Brain
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“This method assumes that connectional specificity at the level of classes of cells suffices to account for the properties of circuits [7–9].”
Method
Distinct GABAergic targets of feedforward and feedback connections between lower and higher areas of rat visual cortex
Gonchar, Y., & Burkhalter, A. (2003) · The Journal of Neuroscience · doi:10.1523/jneurosci.23-34-10904.2003 · Cited by 114
“The preference for PV neurons over other types of interneurons argues against an interareal connectivity that is strictly determined by axonal density (Braitenberg and Schüz, 1998; Traczy-Hornoch et al., 1999).”
Background
Fledgling pathoconnectomics of psychiatric disorders
Rubinov, M., & Bullmore, E. T. (2013) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2013.10.007 · Cited by 118
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Basselin, M., Chang, L., Bell, J. M., & Rapoport, S. I. (2005) · Neuropsychopharmacology · doi:10.1038/sj.npp.1300920 · Cited by 114
“This interpretation is consistent with evidence that glutamatergic receptors constitute about 75% of the synapses in the mammalian cortex, and that many of these synapses include NMDARs (Braitenberg and Schüz, 1998; Fonnum, 1984; Raichle and Gusnard, 2002).”
Result
Pattern formation in intracortical neuronal fields
Hutt, A., Bestehorn, M., & Wennekers, T. (2003) · Network Computation in Neural Systems · doi:10.1088/0954-898x_14_2_310 · Cited by 114
“The existence of a fixed point in the active part of the sigmoid function yields the restriction ae > ai (figure 1). There are indications that inhibitory gain factors can exceed excitatory gain factors [ 31 ], which might lead to ae ai for the rest of the paper.”
Background
How do general anaesthetics work?
Antkowiak, B. (2001) · Die Naturwissenschaften · doi:10.1007/s001140100230 · Cited by 111
“Neocortical cells are covered by as many as 2,000–10,000 synapses that originate from more than 500–5,000 presynaptic cells (Braitenberg 1978; Braitenberg and Schüz 1998).”
Background
Spatiotemporal dynamics of neural language processing: an MEG study using minimum-norm current estimates
Friedemann Pulvermüller, A., Юрьевич, Ш. Ю., & Ilmoniemi, R. J. (2003) · NeuroImage · doi:10.1016/s1053-8119(03)00356-2 · Cited by 109
“The newly available information about the temporal structure of the activation of cortical areas may be relevant for future theorizing about the brain basis of language and cognition ( Braitenberg, 1997; Pulvermu ¨ller, 2003).”
Background
A Guide to Emerging Technologies for Large-Scale and Whole-Brain Optical Imaging of Neuronal Activity
Weisenburger, S., & Vaziri, A. (2018) · Annual Review of Neuroscience · doi:10.1146/annurev-neuro-072116-031458 · Cited by 110
Spatial embedding of structural similarity in the cerebral cortex
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“These results shed light on how the brain may be wired consistently through a combination of specific patterning and general connection rules (31).”
Background
Motor cognition–motor semantics: Action perception theory of cognition and communication
Friedemann Pulvermüller, A., Moseley, R. L., Egorova, N., Shebani, Z., & Véronique Boulenger, A. (2013) · Neuropsychologia · doi:10.1016/j.neuropsychologia.2013.12.002 · Cited by 117
“As such they provide a mechanism for what Braitenberg and Schüz consider the primary function of the neocortex, namely " information mixing " , that is the joining together of specific information across modalities (Braitenberg & Schüz, 1998).”
BackgroundInfluential
Micromechanics of diffuse axonal injury: influence of axonal orientation and anisotropy
Cloots, R. R., van Dommelen, J. V., Nyberg, T., Kleiven, S., & Geers, M. (2011) · Biomechanics and Modeling in Mechanobiology · doi:10.1007/s10237-010-0243-5 · Cited by 112
“…about 5–10% consists of glial processes, 60–70% of neuronal processes (including their boutons and spines), 10–20% of somata and blood vessels, and the remaining part is the extracellular space (Fenstermacher et al. 1970; Braitenberg and Schüz 1998; Ventura and Harris 1999; Chklovskii et al. 2002).”
Background
Cell-type specific innervation of cortical pyramidal cells at their apical dendrites
Karimi, A., Odenthal, J., Drawitsch, F., Boergens, K. M., & Helmstaedter, M. (2020) · eLife · doi:10.7554/elife.46876 · Cited by 103
“For this analysis, we identified putative inhibitory versus excitatory synapses by their location on den- dritic shafts versus spines (See Materials and methods, [Braitenberg and Schüz, 1998; Kubota et al., 2016]).”
Method
Conservation of Regional Gene Expression in Mouse and Human Brain
Strand, A. D., Aragaki, A. K., Baquet, Z. C., Hodges, A., Cunningham, P., Holmans, P., Jones, K. R., Jones, L., Kooperberg, C. L., & Olson, J. M. (2007) · PLoS Genetics · doi:10.1371/journal.pgen.0030059 · Cited by 106
“brain structure and conservation of cell types within comparable regions [18,19].”
Background
Cortical Oscillations in Health and Disease
Traub, R. D., & Whittington, M. A. (2010) · doi:10.1093/acprof:oso/9780195342796.001.0001 · Cited by 108
A Balanced Memory Network
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“Second, connectivity is all to all, which is inconsistent with the sparse connectivity seen in cortex [47].”
Background
A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data
Mishchenko, Y., Vogelstein, J. T., & Paninski, L. (2011) · The Annals of Applied Statistics · doi:10.1214/09-aoas303 · Cited by 104
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A simple rule for axon outgrowth and synaptic competition generates realistic connection lengths and filling fractions.
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“The distance between spines on the dendritic tree, however, is significantly smaller than this search space, with typically two spines/µm for dendritic segments of cortical pyramidal cells (Braitenberg and Schuez, 1998).”
BackgroundMethod
In vivo two-photon voltage-sensitive dye imaging reveals top-down control of cortical layers 1 and 2 during wakefulness
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“As the average axon length per neuron in mouse neocortex is about 40 mm (Braitenberg and Schüz 1998), the above error-rate is sufficiently low, making reconstructions suitable for circuit level analyses of connectivity.”
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“Roughly, 80% of the cortical neurons are excitatory [3].”
BackgroundMethodInfluential
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EM connectomics reveals axonal target variation in a sequence-generating network
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“Instead, the architecture we observed may arise naturally from a pattern that initially follows Peters’ rule (Braitenberg and Schüz, 1998), which predicts synaptic connections between cell types with intermingled axonal and dendritic arbors (Rees et al., 2017), but is then refined as the Video 4.”
Background
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“Synapses can be scattered, seemingly randomly in dendrites, with the location of synapses being determined by anatomy (Braitenberg and Schüz, 2013).”
Background
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“Individual or assemblies of physically close neurons have a higher probability of being connected than spatially remote neurons or regions (Braitenberg and Schüz, 1998; Hellwig, 2000; Cherniak, 1994).”
Rewiring neural interactions by micro-stimulation
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“achieve a realistic number of incoming connections per neuron of ≈ 10000 (Braitenberg and Schüz, 2013) 323 with a biologically plausible connection probability of ≈ 0.”
Background
Functional connectomics reveals general wiring rule in mouse visual cortex
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“The majority of synaptic inputs onto neurons in the neocortex originate from nearby neurons within the same cortical area, producing local microcircuits that are ubiquitous in neocortex (Braitenberg and Schüz, 1998; Douglas and Martin, 2004; White, 2007).”
Automation of 3D reconstruction of neural tissue from large volume of conventional serial section transmission electron micrographs
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“(Compare this with 5-10mm of axonal wire present in a typical cube of mammalian neuropil of 1000μm(3) and 20-40mm of axonal wire in a typical axonal arbor of single pyramidal neuron (Braitenberg and Schuz, 1998).”
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Berger, T. K., Perin, R., Silberberg, G., & Markram, H. (2009) · The Journal of Physiology · doi:10.1113/jphysiol.2009.176552 · Cited by 96
“(Braitenberg & Schüz, 1998), and the distribution of many though not all visualizable molecular markers is relatively homogeneous (Dong, 2007).”
Background
Selective Activation of Resting-State Networks following Focal Stimulation in a Connectome-Based Network Model of the Human Brain
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“5), which is in keeping with known statistics of synapses within a population, namely 50% of intracortical and 50% of corticocortical fibers (Braitenberg and Schüz, 1998).”
Background
Early MEG Activation Dynamics in the Left Temporal and Inferior Frontal Cortex Reflect Semantic Context Integration
Юрьевич, Ш. Ю., & Friedemann Pulvermüller, A. (2007) · Journal of Cognitive Neuroscience · doi:10.1162/jocn.2007.19.10.1633 · Cited by 96
“…of 20 msec between superior temporal and inferior frontal cortices may be caused by the conduction of action potentials through the most common myelinated cortico-cortical fibers (Braitenberg & Schüz, 1998; Aboitiz, Scheibel, Fisher, & Zaidel, 1992), possibly in the arcuate and uncinate fasciculi.”
Background
Resolving Structural Variability in Network Models and the Brain
Klimm, F., Bassett, D. S., Carlson, J. M., & Mucha, P. J. (2014) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003491 · Cited by 89
“Although a homogeneous random distribution of links has been suggested to characterize the small-scale structure of neuron-to-neuron connections [89,90], the large-scale structure of human and animal brains instead displays heterogeneous connectivity [67].”
Background
A Unified Dynamic Model for Learning, Replay, and Sharp-Wave/Ripples
Jahnke, S., Timme, M., & Memmesheimer, R.-M. (2015) · Journal of Neuroscience · doi:10.1523/jneurosci.3977-14.2015 · Cited by 90
“However, since cortical neural networks are overall sparse (Braitenberg and Schüz, 1998; Holmgren et al., 2003), we may also expect some level of dilution for embedded feedforward chains.”
Background
Balanced Excitatory and Inhibitory Synaptic Currents Promote Efficient Coding and Metabolic Efficiency
Sengupta, B., Laughlin, S. B., & Niven, J. E. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003263 · Cited by 96
“A single cortical neuron makes recurrent excitatory synaptic connections with many other cortical neurons, of which about 85% of the synapses are with other excitatory neurons [2,3,55,56].”
Background
Communication through Resonance in Spiking Neuronal Networks
Hahn, G., Bujan, A. F., Frégnac, Y., Aertsen, A., & Kumar, A. (2014) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003811 · Cited by 97
“However, biological neuronal networks are typically neither densely connected nor have strong synapses [11] and therefore the mechanisms that govern the propagation of neuronal activity in dense/strong FFNs are not always applicable.”
Background
Geometric Effects on Complex Network Structure in the Cortex
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Dissociation Between Local Field Potentials and Spiking Activity in Macaque Inferior Temporal Cortex Reveals Diagnosticity-Based Encoding of Complex Objects
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“It is estimated that between 60 and 70% of excitatory connections of a given pyramidal cell remain local and only between 30 and 40% project to other cortical area (Braitenberg and Schüz, 1998; Binzegger et al., 2004).”
Background
Cellular pathways of energy metabolism in the brain: Is glucose used by neurons or astrocytes?
Nehlig, A., & Coles, J. A. (2007) · Glia · doi:10.1002/glia.20376 · Cited by 91
Intrinsic Electrophysiology of Mouse Corticospinal Neurons: a Class-Specific Triad of Spike-Related Properties
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“…dendrites and dendritic spines, and vascular elements such as blood vessels and related cellular components, including endothelial cells and various blood cells (Braitenberg & Schuz, 1998), and the abundance of many transcripts can vary in a compartment-speciﬁ c manner (Cajigas et al., 2012).”
Optimal Information Storage in Noisy Synapses under Resource Constraints
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Glial Glutamine Homeostasis in Health and Disease
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Towards unconstrained compartment modeling in white matter using diffusion-relaxation MRI with tensor-valued diffusion encoding
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Efficient Parallel Simulation of Large-Scale Neuronal Networks on Clusters of Multiprocessor Computers
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“Just 1 mm(3) cortex contains some 10(5) neurons with 10(9) connections [1].”
Background
Neurobiological Mechanisms for Semantic Feature Extraction and Conceptual Flexibility
Friedemann Pulvermüller, A. (2018) · Topics in Cognitive Science · doi:10.1111/tops.12367 · Cited by 85
Coupling between neuronal activity and microcirculation: Implications for functional brain imaging
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“…vessel “senses” not one neuron, but many [capillary length 150–500 µm (Hudetz, 1997); median capillary length and distance 110 and 25 µm, respectively (Pawlik et al., 1981), whereas interneuronal distance is 30 µm and neuronal density is 40,000/mm3 (Abeles, 1991; Braitenberg and Schüz, 1998)].”
Background
Scaling of Brain Metabolism and Blood Flow in Relation to Capillary and Neural Scaling
Karbowski, J. (2011) · PLoS ONE · doi:10.1371/journal.pone.0026709 · Cited by 88
“Cortical volume data (for 2 hemispheres) are taken from [52,41,81].”
BackgroundMethodInfluential
All brains are made of this: a fundamental building block of brain matter with matching neuronal and glial masses
Mota, B., & Herculano‐Houzel, S. (2014) · Frontiers in Neuroanatomy · doi:10.3389/fnana.2014.00127 · Cited by 89
A Simple Rule for Dendritic Spine and Axonal Bouton Formation Can Account for Cortical Reorganization after Focal Retinal Lesions
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“The mircocircuit is represented by a two dimensional recurrent network of 400 neurons, of which 80% are excitatory and 20% inhibitory [53].”
Background
Complex Receptive Fields in Primary Visual Cortex
Martı́nez, L. M., & Alonso, J. (2003) · The Neuroscientist · doi:10.1177/1073858403252732 · Cited by 82
“Cortical neurons (simple or complex) receive abundant input from other cortical neurons both inhibitory and excitatory (e.g., Ahmed and others 1994; Callaway 1998; Fitzpatrick 1996; Braitenberg and Schuz 1998).”
Background
Physiologically based arousal state estimation and dynamics
Abeysuriya, R., RENNIE, C. J., & Robinson, P. A. (2015) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2015.06.002 · Cited by 82
The impact of neuron morphology on cortical network architecture
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Relationship between the diffusion time and the diffusion MRI signal observed at 17.2 tesla in the healthy rat brain cortex
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A modeler's view on the spatial structure of intrinsic horizontal connectivity in the neocortex
Voges, N., Schüz, A., Aertsen, A., & Rotter, S. (2010) · Progress in Neurobiology · doi:10.1016/j.pneurobio.2010.05.001 · Cited by 77
“The study by Kisvárday and Eysel (1992, cat area 17) was based on extracellular injections, but they were able to reconstruct the axonal and dendritic arborization of 10 individual PCs.”
InfluentialSelf-citation
Effects of Bicuculline Methiodide on Fast (>200 Hz) Electrical Oscillations in Rat Somatosensory Cortex
Jones, M. S., & Barth, D. S. (2002) · Journal of Neurophysiology · doi:10.1152/jn.2002.88.2.1016 · Cited by 81
Visual physiology of the layer 4 cortical circuit in silico
Arkhipov, A. S., Gouwens, N. W., Billeh, Y. N., Gratiy, S. L., Iyer, R., Wei, Z., Xu, Z., Abbasi-Asl, R., Berg, J., Buice, M. A., et al. (2018) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1006535 · Cited by 80
Brain-inspired spiking neural networks for decoding and understanding muscle activity and kinematics from electroencephalography signals during hand movements
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The Circuit Architecture of Whole Brains at the Mesoscopic Scale
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How the Cortex Gets Its Folds: An Inside-Out, Connectivity-Driven Model for the Scaling of Mammalian Cortical Folding
Mota, B., & Herculano‐Houzel, S. (2012) · Frontiers in Neuroanatomy · doi:10.3389/fnana.2012.00003 · Cited by 80
“The factor of 2 is due to the fact that we expect the vast majority of fibers in the WM to be cortico-cortical (Braitenberg and Schüz, 1998) and thus cross the WM–GM interface twice, coming in and out of the WM as they connect different areas of the cortical GM. Notice that because any deviation of…”
Background
Parcellation and Area-Area Connectivity as a Function of Neocortex Size
Changizi, M. A., & Shinsuke Shimojo, A. (2005) · Brain Behavior and Evolution · doi:10.1159/000085942 · Cited by 80
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Authors: Braitenberg, V., & Schüz, A.
Affiliations: Max Planck Society (DE)
Venue: Springer eBooks
Publisher: Springer Berlin Heidelberg
Published: 1998
DOI: 10.1007/978-3-662-03733-1
OpenAlex: W1603661052
Cited by: 1,178
References: 0
Citations by year: 2026: 14 · 2025: 30 · 2024: 38 · 2023: 62 · 2022: 38 · 2021: 54 · 2020: 34 · 2019: 57 · 2018: 49 · 2017: 44 · 2016: 42 · 2015: 57 · 2014: 53 · 2013: 51 · 2012: 64
FWCI: 4.64
Type: book
Language: en
Open access: closed
Licence: www.springer.com/tdm (tdm)
Locations: Springer eBooks (publishedVersion)
MPG.PuRe (Max Planck Society) (submittedVersion)
Topics: Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
Keywords: cerebral cortex, neuronal connectivity, cortical networks, mouse cortex, cortical geometry, corticocortical connections

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