scholarly journals Lognormal firing rate distribution reveals prominent fluctuation–driven regime in spinal motor networks

eLife ◽  
2016 ◽  
Vol 5 ◽  
Author(s):  
Peter C Petersen ◽  
Rune W Berg
Keyword(s):  
Neuronal Population ◽  
Output Curve ◽  
Input Output ◽  
Rhythmic Movements ◽  
Trade Off ◽  
Firing Rates ◽  
Spinal Motor ◽  
Rich Diversity ◽  
The Mean ◽  
Lumbar Spinal

When spinal circuits generate rhythmic movements it is important that the neuronal activity remains within stable bounds to avoid saturation and to preserve responsiveness. Here, we simultaneously record from hundreds of neurons in lumbar spinal circuits of turtles and establish the neuronal fraction that operates within either a ‘mean-driven’ or a ‘fluctuation–driven’ regime. Fluctuation-driven neurons have a ‘supralinear’ input-output curve, which enhances sensitivity, whereas the mean-driven regime reduces sensitivity. We find a rich diversity of firing rates across the neuronal population as reflected in a lognormal distribution and demonstrate that half of the neurons spend at least 50 % of the time in the ‘fluctuation–driven’ regime regardless of behavior. Because of the disparity in input–output properties for these two regimes, this fraction may reflect a fine trade–off between stability and sensitivity in order to maintain flexibility across behaviors.

scholarly journals Lognormal firing rate distribution reveals prominent fluctuation-driven regime in spinal motor networks

2016 ◽  
Author(s):  
Peter C. Petersen ◽  
Rune W. Berg
Keyword(s):  
Neuronal Population ◽  
Output Curve ◽  
Dynamical Regime ◽  
Rhythmic Movements ◽  
Firing Rates ◽  
Motor Behaviors ◽  
Spinal Motor ◽  
Rich Diversity ◽  
The Mean ◽  
Lumbar Spinal

ABSTRACTWhen spinal circuits generate rhythmic movements it is important that the neuronal activity remains within stable bounds to avoid saturation and to preserve responsiveness. In what dynamical regime does the neuronal population operate in order to achieve this? Here, we simultaneously record from hundreds of neurons in lumbar spinal circuits and establish the neuronal fraction that operates within either a ‘mean-driven’ or a ‘fluctuation–driven’ regime during generation of multiple motor behaviors. We find a rich diversity of firing rates across the neuronal population as reflected in a lognormal distribution and demonstrate that half of the neurons spend at least 50% of the time in the ‘fluctuation–driven’ regime regardless of behavior. Since neurons in this regime have a ‘supralinear’ input–output curve, which enhances sensitivity, whereas the mean–driven regime reduces sensitivity, this fraction may reflect a fine trade–off between stability and sensitivity in order to maintain flexibility across motor behaviors.

scholarly journals A deep convolutional visual encoding model of neuronal responses in the LGN

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Eslam Mounier ◽  
Bassem Abdullah ◽  
Hani Mahdi ◽  
Seif Eldawlatly
Keyword(s):  
Firing Rate ◽  
Visual Information ◽  
Visual Stimulation ◽  
Neuronal Population ◽  
Neuronal Firing ◽  
Electrode Arrays ◽  
Deep Convolutional Neural Networks ◽  
Firing Rates ◽  
Spatiotemporal Representation

AbstractThe Lateral Geniculate Nucleus (LGN) represents one of the major processing sites along the visual pathway. Despite its crucial role in processing visual information and its utility as one target for recently developed visual prostheses, it is much less studied compared to the retina and the visual cortex. In this paper, we introduce a deep learning encoder to predict LGN neuronal firing in response to different visual stimulation patterns. The encoder comprises a deep Convolutional Neural Network (CNN) that incorporates visual stimulus spatiotemporal representation in addition to LGN neuronal firing history to predict the response of LGN neurons. Extracellular activity was recorded in vivo using multi-electrode arrays from single units in the LGN in 12 anesthetized rats with a total neuronal population of 150 units. Neural activity was recorded in response to single-pixel, checkerboard and geometrical shapes visual stimulation patterns. Extracted firing rates and the corresponding stimulation patterns were used to train the model. The performance of the model was assessed using different testing data sets and different firing rate windows. An overall mean correlation coefficient between the actual and the predicted firing rates of 0.57 and 0.7 was achieved for the 10 ms and the 50 ms firing rate windows, respectively. Results demonstrate that the model is robust to variability in the spatiotemporal properties of the recorded neurons outperforming other examined models including the state-of-the-art Generalized Linear Model (GLM). The results indicate the potential of deep convolutional neural networks as viable models of LGN firing.

Nitrogen use efficiency: does a trade-off exist between the N productivity and the mean residence time within species?

2008 ◽  
Vol 56 (3) ◽  
pp. 272 ◽  
Author(s):  
Zhi Y. Yuan ◽  
Han Y. H. Chen ◽  
Ling H. Li
Keyword(s):  
Residence Time ◽  
Nitrogen Use Efficiency ◽  
Mean Residence Time ◽  
Negative Relationship ◽  
Controlled Experiments ◽  
Nitrogen Use ◽  
Trade Off ◽  
N Supply ◽  
Use Efficiency ◽  
The Mean

Nitrogen use efficiency (NUE) can be divided into two components, i.e. N productivity (A) and the mean residence time (MRT). Controlled experiments indicate that there is not a trade-off between A and MRT within species, but this theory has not been well tested in field conditions. Here, we studied the A, MRT and NUE of Stipa krylovii Roshev. in a grassland over 4 years of N fertilisation experimentation. The three parameters (A, MRT and NUE) were significantly related to soil N supply and there was a negative relationship between A and MRT within this species (r = –0.775, P < 0.05), i.e. plants with higher A had lower MRT. Our results showed a trade-off between A and MRT within this Stipa species and this observed trade-off was attributed to different responses of A and MRT to soil fertility.

Stability Criteria for Distributed Nonlinear Sampled-Data Systems Defined by Green’s Functions

1974 ◽  
Vol 96 (3) ◽  
pp. 315-321 ◽  
Author(s):  
G. Jumarie
Keyword(s):  
Stability Criterion ◽  
Feedback Gain ◽  
Continuous Systems ◽  
Mean Square ◽  
Data Systems ◽  
Sampled Data ◽  
Input Output ◽  
Output Stability ◽  
Lumped Parameter ◽  
The Mean

Sampled-data, nonlinear, distributed systems, which exhibit a structure similar to that of the standard closed loop with lumped parameter, are investigated from the viewpoint of their input-output stability. These systems are governed by operational equations involving discrete Laplace-Green kernels. Their feedback gains are bounded by upper and lower values which depend explicitly on the time and the distributed parameter. The main result is: an input-output stability theorem is given which applies both in L∞ (O, ∞) and L2 (O, ∞). This criterion, which may be considered as being an extension of the ≪circle criterion≫, involves the mean square value on the bounds of the feedback gain. Stability conditions for continuous systems are derived from this result. In the special case of systems with distributed periodical time-varying feedback gains, a stability criterion is given which applies in Marcinkiewicz space M2 (O, ∞). This result which involves the mean square value of the feedback gain is generally less restrictive than the L2 (O, ∞) stability criterion mentioned above.

OBESITY AND SELF-REPORTED OUTCOME AFTER MINIMALLY INVASIVE LUMBAR SPINAL FUSION SURGERY

Neurosurgery ◽  
2008 ◽  
Vol 63 (5) ◽  
pp. 956-960 ◽  
Author(s):  
David S. Rosen ◽  
Sherise D. Ferguson ◽  
Alfred T. Ogden ◽  
Dezheng Huo ◽  
Richard G. Fessler
Keyword(s):  
Minimally Invasive ◽  
Linear Models ◽  
Short Form ◽  
Length Of Hospital Stay ◽  
Fusion Surgery ◽  
Body Habitus ◽  
Short Form 36 ◽  
Spinal Fusion Surgery ◽  
The Mean ◽  
Lumbar Spinal

Abstract OBJECTIVE Many patients undergoing lumbar spine fusion are overweight or obese. The relationship between body habitus and outcome after lumbar spine fusion surgery is not well defined. METHODS We analyzed a prospectively maintained database of self-reported pain and quality of life measures, including Visual Analog Scale pain score, Short Form 36, and Oswestry Disability Index. We selected patients undergoing minimally invasive transforaminal lumbar interbody fusion between September 2002 and June 2006 at a single institution. We used linear regression models and mixed-effects linear models to examine the relationships between body habitus and self-reported outcomes. RESULTS The analysis identified 110 patients meeting the study criteria, with a median follow-up period of 14.8 months. The mean age was 56 years, mean height was 169 cm, and mean weight was 82.2 kg. The mean body mass index (BMI) was 28.7 kg/m2; 31% of patients were overweight (BMI, 25–29.9), and 32% of patients were obese (BMI, &gt;30). Linear regression analysis did not identify a correlation between weight or BMI and pre- and postsurgery changes in any of the outcome measures. The significant findings observed in the mixed-effects linear models were that the changing patterns of Short Form 36 Body Pain subscale and Short Form 36 Vitality subscale varied significantly by category of BMI (P = 0.01 and P = 0.002, respectively), but not significantly if continuous BMI was used (P = 0.53 and P = 0.46, respectively). BMI correlated marginally with estimated blood loss (P = 0.08), but not operative time, length of hospital stay, or complications. CONCLUSION Among this cohort of minimally invasive lumbar fusion patients, body habitus measured by BMI, weight, or height did not have a significant relationship with most self-reported outcome measures, operative time, length of hospital stay, or complications. Obesity should not be considered a contraindication to minimally invasive lumbar spinal fusion surgery.

Minimally invasive anteroposterior combined surgery using lateral lumbar interbody fusion without corpectomy for treatment of lumbar spinal canal stenosis associated with osteoporotic vertebral collapse

2021 ◽  
pp. 1-9
Author(s):  
Kentaro Fukuda ◽  
Hiroyuki Katoh ◽  
Yuichiro Takahashi ◽  
Kazuya Kitamura ◽  
Daiki Ikeda
Keyword(s):  
Interbody Fusion ◽  
Combined Surgery ◽  
Vertebral Collapse ◽  
Short Segment ◽  
Canal Stenosis ◽  
The Mean ◽  
Osteoporotic Vertebral Collapse ◽  
Anterior Support ◽  
Lumbar Spinal

OBJECTIVE Various reconstructive surgical procedures have been described for lumbar spinal canal stenosis (LSCS) with osteoporotic vertebral collapse (OVC); however, the optimal surgery remains controversial. In this study, the authors aimed to report the clinical and radiographic outcomes of their novel, less invasive, short-segment anteroposterior combined surgery (APCS) that utilized oblique lateral interbody fusion (OLIF) and posterior fusion without corpectomy to achieve decompression and reconstruction of anterior support in patients with LSCS-OVC. METHODS In this retrospective study, 20 patients with LSCS-OVC (mean age 79.6 years) underwent APCS and received follow-up for a mean of 38.6 months. All patients were unable to walk without support owing to severe low-back and leg pain. Cleft formations in the fractured vertebrae were identified on CT. APCS was performed on the basis of a novel classification of OVC into three types. In type A fractures with a collapsed rostral endplate, combined monosegment OLIF and posterior spinal fusion (PSF) were performed between the collapsed and rostral adjacent vertebrae. In type B fractures with a collapsed caudal endplate, combined monosegment OLIF and PSF were performed between the collapsed and caudal adjacent vertebrae. In type C fractures with severe collapse of both the rostral and caudal endplates, bisegment OLIF and PSF were performed between the rostral and caudal adjacent vertebrae, and pedicle screws were also inserted into the collapsed vertebra. Preoperative and postoperative clinical and radiographical status were reviewed. RESULTS The mean number of fusion segments was 1.6. Walking ability improved in all patients, and the mean Japanese Orthopaedic Association score for recovery rate was 65.7%. At 1 year postoperatively, the mean preoperative Oswestry Disability Index of 65.6% had significantly improved to 21.1%. The mean local lordotic angle, which was −5.9° preoperatively, was corrected to 10.5° with surgery and was maintained at 7.7° at the final follow-up. The mean corrective angle was 16.4°, and the mean correction loss was 2.8°. CONCLUSIONS The authors have proposed using minimally invasive, short-segment APCS with OLIF, tailored to the morphology of the collapsed vertebra, to treat LSCS-OVC. APCS achieves neural decompression, reconstruction of anterior support, and correction of local alignment.

scholarly journals Efficient generation of reciprocal signals by inhibition

2012 ◽  
Vol 107 (9) ◽  
pp. 2453-2462 ◽  
Author(s):  
Sung-min Park ◽  
Esra Tara ◽  
Kamran Khodakhah
Keyword(s):  
Purkinje Cells ◽  
Granule Cell ◽  
Granule Cells ◽  
Mossy Fiber ◽  
Cell Activity ◽  
Common Mechanism ◽  
Input Output ◽  
Firing Rates ◽  
Neuronal Computation ◽  
The Brain

Reciprocal activity between populations of neurons has been widely observed in the brain and is essential for neuronal computation. The different mechanisms by which reciprocal neuronal activity is generated remain to be established. A common motif in neuronal circuits is the presence of afferents that provide excitation to one set of principal neurons and, via interneurons, inhibition to a second set of principal neurons. This circuitry can be the substrate for generation of reciprocal signals. Here we demonstrate that this equivalent circuit in the cerebellar cortex enables the reciprocal firing rates of Purkinje cells to be efficiently generated from a common set of mossy fiber inputs. The activity of a mossy fiber is relayed to Purkinje cells positioned immediately above it by excitatory granule cells. The firing rates of these Purkinje cells increase as a linear function of mossy fiber, and thus granule cell, activity. In addition to exciting Purkinje cells positioned immediately above it, the activity of a mossy fiber is relayed to laterally positioned Purkinje cells by a disynaptic granule cell → molecular layer interneuron pathway. Here we show in acutely prepared cerebellar slices that the input-output relationship of these laterally positioned Purkinje cells is linear and reciprocal to the first set. A similar linear input-output relationship between decreases in Purkinje cell firing and strength of stimulation of laterally positioned granule cells was also observed in vivo. Use of interneurons to generate reciprocal firing rates may be a common mechanism by which the brain generates reciprocal signals.

Physiology and Morphology of Shared and Specialized Spinal Interneurons for Locomotion and Scratching

2008 ◽  
Vol 99 (6) ◽  
pp. 2887-2901 ◽  
Author(s):  
Ari Berkowitz
Keyword(s):  
Direct Evidence ◽  
Ventral Horn ◽  
Morphological Properties ◽  
Rhythmic Movements ◽  
Potential Oscillations ◽  
Spinal Interneurons ◽  
Firing Rates ◽  
Motor Outputs ◽  
Membrane Potential Oscillations

Distinct types of rhythmic movements that use the same muscles are typically generated largely by shared multifunctional neurons in invertebrates, but less is known for vertebrates. Evidence suggests that locomotion and scratching are produced partly by shared spinal cord interneuronal circuity, although direct evidence with intracellular recording has been lacking. Here, spinal interneurons were recorded intracellularly during fictive swimming and fictive scratching in vivo and filled with Neurobiotin. Some interneurons that were rhythmically activated during both swimming and scratching had axon terminal arborizations in the ventral horn of the hindlimb enlargement, indicating their likely contribution to hindlimb motor outputs during both behaviors. We previously described a morphological group of spinal interneurons (“transverse interneurons” or T neurons) that were rhythmically activated during all forms of fictive scratching at higher peak firing rates and with larger membrane potential oscillations than scratch-activated spinal interneurons with different dendritic orientations. The current study demonstrates that T neurons are activated during both swimming and scratching and thus are components of the shared circuitry. Many spinal interneurons activated during fictive scratching are also activated during fictive swimming (scratch/swim neurons), but others are suppressed during swimming (scratch-specialized neurons). The current study demonstrates that some scratch-specialized neurons receive strong and long-lasting hyperpolarizing inhibition during fictive swimming and are also morphologically distinct from T neurons. Thus this study indicates that locomotion and scratching are produced by a combination of shared and dedicated interneurons whose physiological and morphological properties are beginning to be revealed.

Bursts and recurrences of bursts in the spike trains of spontaneously active striate cortex neurons

1985 ◽  
Vol 53 (4) ◽  
pp. 926-939 ◽  
Author(s):  
C. R. Legendy ◽  
M. Salcman
Keyword(s):  
Standard Deviation ◽  
Spike Train ◽  
Striate Cortex ◽  
Quantitative Measure ◽  
Spike Trains ◽  
Spike Rate ◽  
Occurrence Rate ◽  
Implanted Electrodes ◽  
Firing Rates ◽  
The Mean

Simultaneous recordings were made from small collections (2-7) of spontaneously active single units in the striate cortex of unanesthetized cats, by means of chronically implanted electrodes. The recorded spike trains were computer scanned for bursts of spikes, and the bursts were catalogued and studied. The firing rates of the neurons ranged from 0.16 to 32 spikes/s; the mean was 8.9 spikes/s, the standard deviation 7.0 spikes/s. Bursts of spikes were assigned a quantitative measure, termed Poisson surprise (S), defined as the negative logarithm of their probability in a random (Poisson) spike train. Only bursts having S greater than 10, corresponding to an occurrence rate of about 0.01 bursts/1,000 spikes in a random spike train, were considered to be of interest. Bursts having S greater than 10 occurred at a rate of about 5-15 bursts/1,000 spikes, or about 1-5 bursts/min. The rate slightly increased with spike rate; averaging about 2 bursts/min for neurons having 3 spikes/s and about 4.5 bursts/min for neurons having 30 spikes/s. About 21% of the recorded units emitted significantly fewer bursts than the rest (below 1 burst/1,000 spikes). The percentage of these neurons was independent of spike rate. The spike rate during bursts was found to be about 3-6 times the average spike rate; about the same for longer as for shorter bursts. Bursts typically contained 10-50 spikes and lasted 0.5-2.0 s. When the number of spikes in the successively emitted bursts was listed, it was found that in some neurons these numbers were not distributed at random but were clustered around one or more preferred values. In this sense, bursts occasionally "recurred" a few times in a few minutes. The finding suggests that neurons are highly reliable. When bursts of two or more simultaneously recorded neurons were compared, the bursts often appeared to be temporally close, especially between pairs of neurons recorded by the same electrode; but bursts seldom started and ended simultaneously on two channels. Recurring bursts emitted by one neuron were occasionally accompanied by time-locked recurring bursts by other neurons.

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