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Grosu GF, Hopp AV, Moca VV, Bârzan H, Ciuparu A, Ercsey-Ravasz M, Winkel M, Linde H, Mureșan RC. The fractal brain: scale-invariance in structure and dynamics. Cereb Cortex 2023; 33:4574-4605. [PMID: 36156074 PMCID: PMC10110456 DOI: 10.1093/cercor/bhac363] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Revised: 08/09/2022] [Accepted: 08/10/2022] [Indexed: 11/12/2022] Open
Abstract
The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.
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Affiliation(s)
- George F Grosu
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
- Faculty of Electronics, Telecommunications and Information Technology, Technical University of Cluj-Napoca, Str. Memorandumului 28, 400114 Cluj-Napoca, Romania
| | | | - Vasile V Moca
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
| | - Harald Bârzan
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
- Faculty of Electronics, Telecommunications and Information Technology, Technical University of Cluj-Napoca, Str. Memorandumului 28, 400114 Cluj-Napoca, Romania
| | - Andrei Ciuparu
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
- Faculty of Electronics, Telecommunications and Information Technology, Technical University of Cluj-Napoca, Str. Memorandumului 28, 400114 Cluj-Napoca, Romania
| | - Maria Ercsey-Ravasz
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
- Faculty of Physics, Babes-Bolyai University, Str. Mihail Kogalniceanu 1, 400084 Cluj-Napoca, Romania
| | - Mathias Winkel
- Merck KGaA, Frankfurter Straße 250, 64293 Darmstadt, Germany
| | - Helmut Linde
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
- Merck KGaA, Frankfurter Straße 250, 64293 Darmstadt, Germany
| | - Raul C Mureșan
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
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Killey C, Cleary S, Orr J, Frisbee JC, Jackson D, Twynstra J. The contribution of muscarinic-receptor-mediated responses to epineurial vascular diameter at the sciatic nerve. Can J Physiol Pharmacol 2018; 96:855-858. [PMID: 29883548 DOI: 10.1139/cjpp-2018-0166] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
This study used an anaesthetized rat model to directly observe changes in diameter of the vessels supplying the sciatic nerve in response to acetylcholine (10-4 M), a muscarinic receptor agonist, and atropine (10-5 M), a muscarinic receptor antagonist. Topical application of acetylcholine resulted in increases in vessel diameter (baseline: 22.0 ± 2.5 μm, acetylcholine: 28.8 ± 3.3 μm), while topical application of atropine resulted in a decrease in diameter (baseline: 26.6 ± 3.2 μm, atropine: 15.5 ± 3.6 μm) of the epineurial vessels. Mean arterial pressure was not affected by either acetylcholine (baseline: 103.8 ± 1.8 mm Hg, acetylcholine: 102.8 ± 3.2 mm Hg) or atropine (baseline: 104.0 ± 1.9 mm Hg, atropine: 105.2 ± 2.2 mm Hg). These data suggest that muscarinic-receptor-mediated responses can affect the diameter of the epineurial vessels at the sciatic nerve. In addition, muscarinic-receptor-mediated responses appear to contribute to baseline diameter of epineurial vessels at the sciatic nerve.
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Affiliation(s)
- Chelsa Killey
- a School of Food and Nutritional Sciences, Brescia University College, London, ON N6G 1H2, Canada
| | - Shane Cleary
- a School of Food and Nutritional Sciences, Brescia University College, London, ON N6G 1H2, Canada
| | - Julie Orr
- a School of Food and Nutritional Sciences, Brescia University College, London, ON N6G 1H2, Canada
| | - Jefferson C Frisbee
- b Department of Medical Biophysics, Schulich School of Medicine and Dentistry, University of Western Ontario, London, ON N6A 3K7, Canada
| | - Dwayne Jackson
- b Department of Medical Biophysics, Schulich School of Medicine and Dentistry, University of Western Ontario, London, ON N6A 3K7, Canada
| | - Jasna Twynstra
- a School of Food and Nutritional Sciences, Brescia University College, London, ON N6G 1H2, Canada.,b Department of Medical Biophysics, Schulich School of Medicine and Dentistry, University of Western Ontario, London, ON N6A 3K7, Canada
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Zorick T, Mandelkern MA. Discrete Scale Invariance of Human Large EEG Voltage Deflections is More Prominent in Waking than Sleep Stage 2. Front Hum Neurosci 2015; 9:638. [PMID: 26696860 PMCID: PMC4667071 DOI: 10.3389/fnhum.2015.00638] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2015] [Accepted: 11/09/2015] [Indexed: 11/24/2022] Open
Abstract
Electroencephalography (EEG) is typically viewed through the lens of spectral analysis. Recently, multiple lines of evidence have demonstrated that the underlying neuronal dynamics are characterized by scale-free avalanches. These results suggest that techniques from statistical physics may be used to analyze EEG signals. We utilized a publicly available database of fourteen subjects with waking and sleep stage 2 EEG tracings per subject, and observe that power-law dynamics of critical-state neuronal avalanches are not sufficient to fully describe essential features of EEG signals. We hypothesized that this could reflect the phenomenon of discrete scale invariance (DSI) in EEG large voltage deflections (LVDs) as being more prominent in waking consciousness. We isolated LVDs, and analyzed logarithmically transformed LVD size probability density functions (PDF) to assess for DSI. We find evidence of increased DSI in waking, as opposed to sleep stage 2 consciousness. We also show that the signatures of DSI are specific for EEG LVDs, and not a general feature of fractal simulations with similar statistical properties to EEG. Removing only LVDs from waking EEG produces a reduction in power in the alpha and beta frequency bands. These findings may represent a new insight into the understanding of the cortical dynamics underlying consciousness.
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Affiliation(s)
- Todd Zorick
- Greater Los Angeles Veterans Administration Healthcare System, Departments of Psychiatry, (TZ) and Imaging (MM), University of California Los Angeles, CA, USA ; Department of Psychiatry and Biobehavioral Sciences, University of California Los Angeles, CA, USA
| | - Mark A Mandelkern
- Greater Los Angeles Veterans Administration Healthcare System, Departments of Psychiatry, (TZ) and Imaging (MM), University of California Los Angeles, CA, USA ; Department of Physics, University of California Irvine, CA, USA
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Abstract
At rest, the brain is traversed by spontaneous functional connectivity patterns. Two hypotheses have been proposed for their origins: they may reflect a continuous stream of ongoing cognitive processes as well as random fluctuations shaped by a fixed anatomical connectivity matrix. Here we show that both sources contribute to the shaping of resting-state networks, yet with distinct contributions during consciousness and anesthesia. We measured dynamical functional connectivity with functional MRI during the resting state in awake and anesthetized monkeys. Under anesthesia, the more frequent functional connectivity patterns inherit the structure of anatomical connectivity, exhibit fewer small-world properties, and lack negative correlations. Conversely, wakefulness is characterized by the sequential exploration of a richer repertoire of functional configurations, often dissimilar to anatomical structure, and comprising positive and negative correlations among brain regions. These results reconcile theories of consciousness with observations of long-range correlation in the anesthetized brain and show that a rich functional dynamics might constitute a signature of consciousness, with potential clinical implications for the detection of awareness in anesthesia and brain-lesioned patients.
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Abstract
The kidneys play a central role in cardiovascular homeostasis by ensuring a balance between the fluid taken in and that lost and excreted during everyday activities. This ensures stability of extracellular fluid volume and maintenance of normal levels of blood pressure. Renal fluid handling is controlled via neural and humoral influences, with the former determining a rapid dynamic response to changing intake of sodium whereas the latter cause a slower longer-term modulation of sodium and water handling. Activity in the renal sympathetic nerves arises from an integration of information from the high and low pressure cardiovascular baroreceptors, the somatosensory and visceral systems as well as the higher cortical centers. Each sensory system provides varying input to the autonomic centers of the hypothalamic and medullary areas of the brain at a level appropriate to the activity being performed. In pathophysiological states, such as hypertension, heart failure and chronic renal disease, there may be an inappropriate sympathoexcitation causing sodium retention which exacerbates the disease process. The contribution of the renal sympathetic nerves to these cardiovascular diseases is beginning to be appreciated with the demonstration that renal denervation of resistant hypertensive patients results in a long-term normalization of blood pressure.
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Affiliation(s)
- Edward J Johns
- Department of Physiology, University College Cork, Cork, Republic of Ireland.
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Comparison of different methods of heart rate entropy analysis during acute anoxia superimposed on a chronic rat model of pulmonary hypertension. Med Eng Phys 2012; 35:559-68. [PMID: 22818405 DOI: 10.1016/j.medengphy.2012.06.020] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2011] [Revised: 06/19/2012] [Accepted: 06/27/2012] [Indexed: 11/22/2022]
Abstract
Acute life-threatening situations are particularly critical when superimposed on chronic diseases. The objective of this study was the assessment of heart rate (HR) dynamics during episodes of acute anoxia superimposed on a rat model of chronic pulmonary hypertension. In 10 adult Wistar rats, five weeks after pulmonary hypertension induction with Monocrotaline, we analysed eight 1-min HR segments, during episodes of baseline, mechanical ventilation and acute anoxia, using linear indices, approximate entropy (ApEn), sample entropy (SampEn) and multiscale entropy (MSE). The transition from baseline or mechanical ventilation to early anoxia was identified through almost all indices, but SampEn(2,0.6) was the index that better identified all the transitions. MSE presented limited performance, possibly due to the non-stationary nature and short duration of the acute anoxia episodes. A systematic evaluation of all computed HR indices may help to identify which indices or combination of indices more adequately discriminates and monitors critical acute events superimposed on chronic clinical conditions.
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Tian Y, Lei T, Yang Z, Zhang T. Urethane suppresses hippocampal CA1 neuron excitability via changes in presynaptic glutamate release and in potassium channel activity. Brain Res Bull 2012; 87:420-6. [PMID: 22314371 DOI: 10.1016/j.brainresbull.2012.01.006] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2011] [Revised: 11/30/2011] [Accepted: 01/10/2012] [Indexed: 12/22/2022]
Abstract
Urethane is a widely used anesthetic for animal experiments. Although urethane is thought to minimally interfere with neurophysiological processes and appears to preserve synaptic signal transmission, it has also been reported to produce depressive effects on neuronal excitability. In the present study, we used electrophysiological recordings to investigate the effects of urethane on rat hippocampal CA1 neurons. Whole-cell recordings were employed in a brain slice preparation to record discharges in current-clamp mode and sEPSCs or mEPSCs in voltage-clamp mode. Urethane was found to significantly increase both the interspike interval and the coefficient of variation of the firing. Moreover, it was found that the inter-event intervals of sEPSC/mEPSCs were increased, but the amplitude and the kinetic properties (rise time and decay time) of the sEPSC/mEPSC were not altered by urethane, which implies that potassium leak currents were involved in such effects. The results suggest that urethane significantly suppresses activity of hippocampal CA1 neurons and alters spontaneous pre-synaptic glutamatergic release possibly by activating potassium leak currents.
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Affiliation(s)
- Yutao Tian
- College of Life Sciences, Nankai University, Tianjin 300071, PR China
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Jackson DN, Ellis CG, Shoemaker JK. Estrogen modulates the contribution of neuropeptide Y to baseline hindlimb blood flow control in female Sprague-Dawley rats. Am J Physiol Regul Integr Comp Physiol 2010; 298:R1351-7. [PMID: 20219870 DOI: 10.1152/ajpregu.00420.2009] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
The purpose of this study was to determine the role of estrogen in neuropeptide Y (NPY) and Y(1) receptor (Y(1)R)-mediated vascular responses in female rats. Based on earlier work from our laboratory that female rats lacked an NPY contribution to hindlimb vascular conductance relative to males, we tested the hypothesis that estrogen modulates Y(1)R-mediated hindlimb blood flow control. Thus it was expected that ovariectomy would: 1) increase skeletal muscle Y(1)R expression, 2) decrease skeletal muscle Y(2) receptor (Y(2)R) expression, 3) decrease peptidase activity, and/or 4) increase overall skeletal muscle NPY concentration. Separate groups of control (CTL), ovariectomized (OVX), and OVX + 17beta-estradiol replacement (OVX + E(2); 21-day pellet) rats were studied. Animals were anesthetized and given localized hindlimb delivery of BIBP-3226 (Y(1)R antagonist), while femoral artery blood flow and blood pressure were recorded. Tissue samples from the white and red vastus lateralis muscle were extracted to examine Y(1)R and Y(2)R expression, peptidase activity, and NPY concentration. We found that Y(1)R blockade resulted in increased baseline hindlimb blood flow and vascular conductance in OVX rats, whereas no change was noted in CTL or OVX + E(2) groups (P < 0.05). This enhanced functional effect in the OVX group aligned with greater skeletal muscle Y(1)R expression in white vastus muscle and a substantial increase in NPY concentration in both white and red vastus muscle compared with CTL and OVX + E(2) groups. There was no change in Y(2)R expression or peptidase activity among the groups. These data support the hypothesis that estrogen blunts Y(1)R activation in the rat hindlimb through an effect on Y(1)R expression and NPY concentration.
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Affiliation(s)
- Dwayne N Jackson
- Department of Medical Biophysics, Schulich School of Medicine & Dentistry, University of Western Ontario, London, Ontario, Canada.
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Valencia JF, Porta A, Vallverdú M, Clarià F, Baranowski R, Orłowska-Baranowska E, Caminal P. Refined Multiscale Entropy: Application to 24-h Holter Recordings of Heart Period Variability in Healthy and Aortic Stenosis Subjects. IEEE Trans Biomed Eng 2009; 56:2202-13. [PMID: 19457745 DOI: 10.1109/tbme.2009.2021986] [Citation(s) in RCA: 159] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- José Fernando Valencia
- Department of Automatic Control (ESAII), Centre for Biomedical Engineering Research, El Centro de Investigación Biomédica en Red of Bioengineering, Biomaterials and Nanomedicine, Technical University of Catalonia, Barcelona, Spain.
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Robin K, Maurice N, Degos B, Deniau JM, Martinerie J, Pezard L. Assessment of bursting activity and interspike intervals variability: a case study for methodological comparison. J Neurosci Methods 2009; 179:142-9. [PMID: 19428520 DOI: 10.1016/j.jneumeth.2009.01.020] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2008] [Revised: 01/19/2009] [Accepted: 01/19/2009] [Indexed: 11/27/2022]
Abstract
The detection and characterization of bursting activity remains a topic where no consensual definition has been reached so far. We compare here three different approaches of spike trains variability: statistical characterization (average frequency, coefficient of variation), burst detection (Poisson and rank surprise) and multi-scale analysis (detrended fluctuations analysis). Using both real and simulated data, we show that Poisson surprise provides information closely related to the coefficient of variation and that rank surprise detects significant bursts which are associated with long-range correlations. Since these long-range correlations are only adequately characterized with multi-scale analysis, this study emphasizes the complementarity of these approaches for the complete characterization of spike trains.
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Affiliation(s)
- Kristelle Robin
- Ecole Supérieure de Physique et de Chimie Industrielles de la ville de Paris, France
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