Neuronal Entropy Depends on the Level of Alertness in the Parkinsonian Globus Pallidus in vivo

Dorsal and median raphe neuronal firing dynamics characterized by nonlinear measures

The dorsal (DRN) and median (MRN) raphe are important nuclei involved in similar functions, including mood and sleep, but playing distinct roles. These nuclei have a different composition of neuronal types and set of neuronal connections, which among other factors, determine their neuronal dynamics. Most works characterize the neuronal dynamics using classic measures, such as using the average spiking frequency (FR), the coefficient of variation (CV), and action potential duration (APD). In the current study, to refine the characterization of neuronal firing profiles, we examined the neurons within the raphe nuclei. Through the utilization of nonlinear measures, our objective was to discern the redundancy and complementarity of these measures, particularly in comparison with classic methods. To do this, we analyzed the neuronal basal firing profile in both nuclei of urethane-anesthetized rats using the Shannon entropy (Bins Entropy) of the inter-spike intervals, permutation entropy of ordinal patterns (OP Entropy), and Permutation Lempel-Ziv Complexity (PLZC). Firstly, we found that classic (i.e., FR, CV, and APD) and nonlinear measures fail to distinguish between the dynamics of DRN and MRN neurons, except for the OP Entropy. We also found strong relationships between measures, including the CV with FR, CV with Bins entropy, and FR with PLZC, which imply redundant information. However, APD and OP Entropy have either a weak or no relationship with the rest of the measures tested, suggesting that they provide complementary information to the characterization of the neuronal firing profiles. Secondly, we studied how these measures are affected by the oscillatory properties of the firing patterns, including rhythmicity, bursting patterns, and clock-like behavior. We found that all measures are sensitive to rhythmicity, except for the OP Entropy. Overall, our work highlights OP Entropy as a powerful and useful quantity for the characterization of neuronal discharge patterns.

From signals to music: a bottom-up approach to the structure of neuronal activity

Introduction

The search for the "neural code" has been a fundamental quest in neuroscience, concerned with the way neurons and neuronal systems process and transmit information. However, the term "code" has been mostly used as a metaphor, seldom acknowledging the formal definitions introduced by information theory, and the contributions of linguistics and semiotics not at all. The heuristic potential of the latter was suggested by structuralism, which turned the methods and findings of linguistics to other fields of knowledge. For the study of complex communication systems, such as human language and music, the necessity of an approach that considers multilayered, nested, structured organization of symbols becomes evident. We work under the hypothesis that the neural code might be as complex as these human-made codes. To test this, we propose a bottom-up approach, constructing a symbolic logic in order to translate neuronal signals into music scores.

Methods

We recorded single cells' activity from the rat's globus pallidus pars interna under conditions of full alertness, blindfoldedness and environmental silence. We analyzed the signals with statistical, spectral, and complex methods, including Fast Fourier Transform, Hurst exponent and recurrence plot analysis.

Results

The results indicated complex behavior and recurrence graphs consistent with fractality, and a Hurst exponent >0.5, evidencing temporal persistence. On the whole, these features point toward a complex behavior of the time series analyzed, also present in classical music, which upholds the hypothesis of structural similarities between music and neuronal activity. Furthermore, through our experiment we performed a comparison between music and raw neuronal activity. Our results point to the same conclusion, showing the structures of music and neuronal activity to be homologous. The scores were not only spontaneously tonal, but they exhibited structure and features normally present in human-made musical creations.

Discussion

The hypothesis of a structural homology between the neural code and the code of music holds, suggesting that some of the insights introduced by linguistic and semiotic theory might be a useful methodological resource to go beyond the limits set by metaphoric notions of "code."

Entropy Could Quantify Brain Activation Induced by Mechanical Impedance-Restrained Active Arm Motion: A Functional NIRS Study

Brain activation has been used to understand brain-level events associated with cognitive tasks or physical tasks. As a quantitative measure for brain activation, we propose entropy in place of signal amplitude and beta value, which are widely used, but sometimes criticized for their limitations and shortcomings as such measures. To investigate the relevance of our proposition, we provided 22 subjects with physical stimuli through elbow extension-flexion motions by using our exoskeleton robot, measured brain activation in terms of entropy, signal amplitude, and beta value; and compared entropy with the other two. The results show that entropy is superior, in that its change appeared in limited, well established, motor areas, while signal amplitude and beta value changes appeared in a widespread fashion, contradicting the modularity theory. Entropy can predict increase in brain activation with task duration, while the other two cannot. When stimuli shifted from the rest state to the task state, entropy exhibited a similar increase as the other two did. Although entropy showed only a part of the phenomenon induced by task strength, it showed superiority by showing a decrease in brain activation that the other two did not show. Moreover, entropy was capable of identifying the physiologically important location.

Parkinsonism Differently Affects the Single Neuronal Activity in the Primary and Supplementary Motor Areas in Monkeys: An Investigation in Linear and Nonlinear Domains

The changes in neuronal firing activity in the primary motor cortex (M1) and supplementary motor area (SMA) were compared in monkeys rendered parkinsonian by treatment with 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine. The neuronal dynamic was characterized using mathematical tools defined in different frameworks (rate, oscillations or complex patterns). Then, and for each cortical area, multivariate and discriminate analyses were further performed on these features to identify those important to differentiate between the normal and the pathological neuronal activity. Our results show a different order in the importance of the features to discriminate the pathological state in each cortical area which suggests that the M1 and the SMA exhibit dissimilarities in their neuronal alterations induced by parkinsonism. Our findings highlight the need for multiple mathematical frameworks to best characterize the pathological neuronal activity related to parkinsonism. Future translational studies are warranted to investigate the causal relationships between cortical region-specificities, dominant pathological hallmarks and symptoms.

On the Motion of Spikes: Turbulent-Like Neuronal Activity in the Human Basal Ganglia

Neuronal signals are usually characterized in terms of their discharge rate, a description inadequate to account for the complex temporal organization of spike trains. Complex temporal properties, which are characteristic of neuronal systems, can only be described with the appropriate, complex mathematical tools. Here, I apply high order structure functions to the analysis of neuronal signals recorded from parkinsonian patients during functional neurosurgery, recovering multifractal properties. To achieve an accurate model of such multifractality is critical for understanding the basal ganglia, since other non-linear properties, such as entropy, depend on the fractal properties of complex systems. I propose a new approach to the study of neuronal signals: to study spiking activity in terms of the velocity of spikes, defining it as the inverse function of the instantaneous frequency. I introduce a neural field model that includes a non-linear gradient field, representing neuronal excitability, and a diffusive term to consider the physical properties of the electric field. Multifractality is present in the model for a range of diffusion coefficients, and multifractal temporal properties are mirrored into space. The model reproduces the behavior of human basal ganglia neurons and shows that it is like that of turbulent fluids. The results obtained from the model predict that passive electric properties of neuronal activity, including ephaptic coupling, are far more relevant to the human brain than what is usually considered: passive electric properties determine the temporal and spatial organization of neuronal activity in the neural tissue.

Subthalamic neural entropy is a feature of freezing of gait in freely moving people with Parkinson's disease

The goal of this study was to investigate subthalamic (STN) neural features of Freezers and Non-Freezers with Parkinson's disease (PD), while freely walking without freezing of gait (FOG) and during periods of FOG, which were better elicited during a novel turning and barrier gait task than during forward walking.

METHODS

Synchronous STN local field potentials (LFPs), shank angular velocities, and ground reaction forces were measured in fourteen PD subjects (eight Freezers) off medication, OFF deep brain stimulation (DBS), using an investigative, implanted, sensing neurostimulator (Activa® PC+S, Medtronic, Inc.). Tasks included standing still, instrumented forward walking, stepping in place on dual forceplates, and instrumented walking through a turning and barrier course.

RESULTS

During locomotion without FOG, Freezers showed lower beta (13-30Hz) power (P=0.036) and greater beta Sample Entropy (P=0.032), than Non-Freezers, as well as greater gait asymmetry and arrhythmicity (P<0.05 for both). No differences in alpha/beta power and/or entropy were evident at rest. During periods of FOG, Freezers showed greater alpha (8-12Hz) Sample Entropy (P<0.001) than during walking without FOG.

CONCLUSIONS

A novel turning and barrier course was superior to FW in eliciting FOG. Greater unpredictability in subthalamic beta rhythms was evident during stepping without freezing episodes in Freezers compared to Non-Freezers, whereas greater unpredictability in alpha rhythms was evident in Freezers during FOG. Non-linear analysis of dynamic neural signals during gait in freely moving people with PD may yield greater insight into the pathophysiology of FOG; whether the increases in STN entropy are causative or compensatory remains to be determined. Some beta LFP power may be useful for rhythmic, symmetric gait and DBS parameters, which completely attenuate STN beta power may worsen rather than improve FOG.

Structure Function Revisited: A Simple Tool for Complex Analysis of Neuronal Activity

Neural systems are characterized by their complex dynamics, reflected on signals produced by neurons and neuronal ensembles. This complexity exhibits specific features in health, disease and in different states of consciousness, and can be considered a hallmark of certain neurologic and neuropsychiatric conditions. To measure complexity from neurophysiologic signals, a number of different nonlinear tools of analysis are available. However, not all of these tools are easy to implement, or able to handle clinical data, often obtained in less than ideal conditions in comparison to laboratory or simulated data. Recently, the temporal structure function emerged as a powerful tool for the analysis of complex properties of neuronal activity. The temporal structure function is efficient computationally and it can be robustly estimated from short signals. However, the application of this tool to neuronal data is relatively new, making the interpretation of results difficult. In this methods paper we describe a step by step algorithm for the calculation and characterization of the structure function. We apply this algorithm to oscillatory, random and complex toy signals, and test the effect of added noise. We show that: (1) the mean slope of the structure function is zero in the case of random signals; (2) oscillations are reflected on the shape of the structure function, but they don't modify the mean slope if complex correlations are absent; (3) nonlinear systems produce structure functions with nonzero slope up to a critical point, where the function turns into a plateau. Two characteristic numbers can be extracted to quantify the behavior of the structure function in the case of nonlinear systems: (1). the point where the plateau starts (the inflection point, where the slope change occurs), and (2). the height of the plateau. While the inflection point is related to the scale where correlations weaken, the height of the plateau is related to the noise present in the signal. To exemplify our method we calculate structure functions of neuronal recordings from the basal ganglia of parkinsonian and healthy rats, and draw guidelines for their interpretation in light of the results obtained from our toy signals.

Neuronal Entropy-Rate Feature of Entopeduncular Nucleus in Rat Model of Parkinson's Disease

The function of the nigro-striatal pathway on neuronal entropy in the basal ganglia (BG) output nucleus, i.e. the entopeduncular nucleus (EPN) was investigated in the unilaterally 6-hyroxydopamine (6-OHDA)-lesioned rat model of Parkinson's disease (PD). In both control subjects and subjects with 6-OHDA lesion of dopamine (DA) the nigro-striatal pathway, a histological hallmark for parkinsonism, neuronal entropy in EPN was maximal in neurons with firing rates ranging between 15 and 25 Hz. In 6-OHDA lesioned rats, neuronal entropy in the EPN was specifically higher in neurons with firing rates above 25 Hz. Our data establishes that the nigro-striatal pathway controls neuronal entropy in motor circuitry and that the parkinsonian condition is associated with abnormal relationship between firing rate and neuronal entropy in BG output nuclei. The neuronal firing rates and entropy relationship provide putative relevant electrophysiological information to investigate the sensory-motor processing in normal condition and conditions such as movement disorders.

Neural code alterations and abnormal time patterns in Parkinson's disease

OBJECTIVE

The neural code used by the basal ganglia is a current question in neuroscience, relevant for the understanding of the pathophysiology of Parkinson's disease. While a rate code is known to participate in the communication between the basal ganglia and the motor thalamus/cortex, different lines of evidence have also favored the presence of complex time patterns in the discharge of the basal ganglia. To gain insight into the way the basal ganglia code information, we studied the activity of the globus pallidus pars interna (GPi), an output node of the circuit.

APPROACH

We implemented the 6-hydroxydopamine model of Parkinsonism in Sprague-Dawley rats, and recorded the spontaneous discharge of single GPi neurons, in head-restrained conditions at full alertness. Analyzing the temporal structure function, we looked for characteristic scales in the neuronal discharge of the GPi.

MAIN RESULTS

At a low-scale, we observed the presence of dynamic processes, which allow the transmission of time patterns. Conversely, at a middle-scale, stochastic processes force the use of a rate code. Regarding the time patterns transmitted, we measured the word length and found that it is increased in Parkinson's disease. Furthermore, it showed a positive correlation with the frequency of discharge, indicating that an exacerbation of this abnormal time pattern length can be expected, as the dopamine depletion progresses.

SIGNIFICANCE

We conclude that a rate code and a time pattern code can co-exist in the basal ganglia at different temporal scales. However, their normal balance is progressively altered and replaced by pathological time patterns in Parkinson's disease.

Multiple-time-scale framework for understanding the progression of Parkinson's disease

Parkinson's disease is marked by neurodegenerative processes that affect the pattern of discharge of basal ganglia neurons. The main features observed in the parkinsonian globus pallidus pars interna (GPi), a subdomain of the basal ganglia that is involved in the regulation of voluntary movement, are pathologically increased and synchronized neuronal activity. How these changes affect the implemented neuronal code is not well understood. Our experimental temporal structure-function analysis shows that in parkinsonian animals the rate-coding window of GPi neurons needed for the proper performance of voluntary actions is reduced. The model of the GPi network that we develop and discuss here reveals indeed that the size of the rate-coding window shrinks as the network activity increases and is expanded if the coupling strength among the neurons is increased. This leads to the novel interpretation that the pathological neuronal synchronization in Parkinson's disease in the GPi is the result of a collective attempt to counterbalance the shrinking of the rate-coding window due to increased activity in GPi neurons.