Estimating Neuronal Information: Logarithmic Binning of Neuronal Inter-Spike Intervals

Frequency-dependent spike-pattern changes in motor cortex during thalamic deep brain stimulation

The cerebellar-receiving area of the motor thalamus is the primary anatomical target for treating essential tremor with deep brain stimulation (DBS). Although neuroimaging studies have shown that higher stimulation frequencies in this target correlate with increased cortical metabolic activity, less is known about the cellular-level functional changes that occur in the primary motor cortex (M1) with thalamic stimulation and how these changes depend on the frequency of DBS. In this study, we used a preclinical animal model of DBS to collect single-unit spike recordings in M1 before, during, and after DBS targeting the cerebellar-receiving area of the motor thalamus (VPLo, nucleus ventralis posterior lateralis pars oralis). The effects of VPLo-DBS on M1 spike rates, interspike interval entropy, and peristimulus phase-locking were compared across stimulus pulse train frequencies ranging from 10 to 130 Hz. Although VPLo-DBS modulated the spike rates of 20-50% of individual M1 cells in a frequency-dependent manner, the population-level average spike rate only weakly depended on stimulation frequency. In contrast, the population-level entropy measure showed a pronounced decrease with high-frequency stimulation, caused by a subpopulation of cells that exhibited strong phase-locking and general spike-pattern regularization. Contrarily, low-frequency stimulation induced an entropy increase (spike-pattern disordering) in a relatively large portion of the recorded population, which diminished with higher stimulation frequencies. These results also suggest that changes in phase-locking and spike-pattern entropy are not necessarily equivalent pattern phenomena, but rather that they should both be weighed when quantifying stimulation-induced spike-pattern changes.NEW & NOTEWORTHY The network mechanisms of thalamic deep brain stimulation (DBS) are not well understood at the cellular level. This study investigated the neuronal firing rate and pattern changes in the motor cortex resulting from stimulation of the cerebellar-receiving area of the motor thalamus. We showed that there is a nonintuitive relationship between general entropy-based spike-pattern measures and phase-locked regularization to DBS.

Limitations to Estimating Mutual Information in Large Neural Populations

Information theory provides a powerful framework to analyse the representation of sensory stimuli in neural population activity. However, estimating the quantities involved such as entropy and mutual information from finite samples is notoriously hard and any direct estimate is known to be heavily biased. This is especially true when considering large neural populations. We study a simple model of sensory processing and show through a combinatorial argument that, with high probability, for large neural populations any finite number of samples of neural activity in response to a set of stimuli is mutually distinct. As a consequence, the mutual information when estimated directly from empirical histograms will be equal to the stimulus entropy. Importantly, this is the case irrespective of the precise relation between stimulus and neural activity and corresponds to a maximal bias. This argument is general and applies to any application of information theory, where the state space is large and one relies on empirical histograms. Overall, this work highlights the need for alternative approaches for an information theoretic analysis when dealing with large neural populations.

Deep brain stimulation induces sparse distributions of locally modulated neuronal activity

Deep brain stimulation (DBS) therapy is a potent tool for treating a range of brain disorders. High frequency stimulation (HFS) patterns used in DBS therapy are known to modulate neuronal spike rates and patterns in the stimulated nucleus; however, the spatial distribution of these modulated responses are not well understood. Computational models suggest that HFS modulates a volume of tissue spatially concentrated around the active electrode. Here, we tested this theory by investigating modulation of spike rates and patterns in non-human primate motor thalamus while stimulating the cerebellar-receiving area of motor thalamus, the primary DBS target for treating Essential Tremor. HFS inhibited spike activity in the majority of recorded cells, but increasing stimulation amplitude also shifted the response to a greater degree of spike pattern modulation. Modulated responses in both categories exhibited a sparse and long-range spatial distribution within motor thalamus, suggesting that stimulation preferentially affects afferent and efferent axonal processes traversing near the active electrode and that the resulting modulated volume strongly depends on the local connectome of these axonal processes. Such findings have important implications for current clinical efforts building predictive computational models of DBS therapy, developing directional DBS lead technology, and formulating closed-loop DBS strategies.

Information in pallidal neurons increases with parkinsonian severity

INTRODUCTION

The motor symptoms of Parkinson's disease (PD) present with pathological neuronal activity in the basal ganglia. Although neuronal firing rate changes in the globus pallidus internus (GPi) and externus (GPe) are reported to underlie the development of PD motor signs, firing rates change inconsistently, vary confoundingly with some therapies, and are poor indicators of symptom severity.

METHODS

We explored the relationship between parkinsonian symptom severity and the effectiveness with which pallidal neurons transmit information. We quantify neuronal entropy and information - alternatives to firing rate and correlations respectively - in and between GPe and GPi neurons using a progressive, 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine, non-human primate model of PD.

RESULTS

Neuronal entropy and symptom severity were not linearly correlated: in both pallidal segments, entropy increased from naive to moderate parkinsonism, but decreased with further progression to the severely parkinsonian condition. In contrast, information transmitted from GPe to GPi increased consistently with symptom severity. Furthermore, antidromic information from GPi to GPe increased substantially with symptom severity. Together, these findings suggest that as parkinsonian severity increases, more and more information enters GPe and GPi from common sources, diminishing the relative importance of the orthodromic GPe to GPi connection.

CONCLUSIONS

With parkinsonian progression, the direct and indirect pathways lose their independence and start to convey redundant information. We hypothesize that a loss of parallel processing impairs the ability of the network to select and implement motor commands, thus promoting the hypokinetic symptoms of PD.

Subthalamic deep brain stimulation reduces pathological information transmission to the thalamus in a rat model of parkinsonism

The degeneration of dopaminergic neurons in the substantia nigra pars compacta leads to parkinsonian motor symptoms via changes in electrophysiological activity throughout the basal ganglia. High-frequency deep brain stimulation (DBS) partially treats these symptoms, but the mechanisms are unclear. We hypothesize that motor symptoms of Parkinson’s disease (PD) are associated with increased information transmission from basal ganglia output neurons to motor thalamus input neurons and that therapeutic DBS of the subthalamic nucleus (STN) treats these symptoms by reducing this extraneous information transmission. We tested these hypotheses in a unilateral, 6-hydroxydopamine-lesioned rodent model of hemiparkinsonism. Information transfer between basal ganglia output neurons and motor thalamus input neurons increased in both the orthodromic and antidromic directions with hemiparkinsonian (hPD) onset, and these changes were reversed by behaviorally therapeutic STN-DBS. Omnidirectional information increases in the parkinsonian state underscore the detrimental nature of that pathological information and suggest a loss of information channel independence. Therapeutic STN-DBS reduced that pathological information, suggesting an effective increase in the number of independent information channels. We interpret these data with a model in which pathological information and fewer information channels diminishes the scope of possible motor activities, driving parkinsonian symptoms. In this model, STN-DBS restores information-channel independence by eliminating or masking the parkinsonism-associated information, and thus enlarges the scope of possible motor activities, alleviating parkinsonian symptoms.

Movement-related discharge in the macaque globus pallidus during high-frequency stimulation of the subthalamic nucleus

Deep brain stimulation (DBS) of the subthalamic nucleus (STN-DBS) has largely replaced ablative therapies for Parkinson's disease. Because of the similar efficacies of the two treatments, it has been proposed that DBS acts by creating an "informational lesion," whereby pathologic neuronal firing patterns are replaced by low-entropy, stimulus-entrained firing patterns. The informational lesion hypothesis, in its current form, states that DBS blocks the transmission of all information from the basal ganglia, including both pathologic firing patterns and normal, task-related modulations in activity. We tested this prediction in two healthy rhesus macaques by recording single-unit spiking activity from the globus pallidus (232 neurons) while the animals completed choice reaction time reaching movements with and without STN-DBS. Despite strong effects of DBS on the activity of most pallidal cells, reach-related modulations in firing rate were equally prevalent in the DBS-on and DBS-off states. This remained true even when the analysis was restricted to cells affected significantly by DBS. In addition, the overall form and timing of perimovement modulations in firing rate were preserved between DBS-on and DBS-off states in the majority of neurons (66%). Active movement and DBS had largely additive effects on the firing rate of most neurons, indicating an orthogonal relationship in which both inputs contribute independently to the overall firing rate of pallidal neurons. These findings suggest that STN-DBS does not act as an indiscriminate informational lesion but rather as a filter that permits task-related modulations in activity while, presumably, eliminating the pathological firing associated with parkinsonism.

Incoordination between spikes and LFPs in Aβ1-42-mediated memory deficits in rats

Alzheimer's disease (AD) is a neurodegenerative disease that gradually induces cognitive deficits. Impairments of working memory have been typically observed in AD. It is well known that spikes and local field potentials (LFPs) as well as the coordination between them encode information in normal brain function. However, the abnormal coordination between spikes and LFPs in the cognitive deficits of AD has remained largely unexplored. As amyloid-β peptide (Aβ) is a causative factor for the cognitive impairments of AD, developing a mechanistic understanding of the contribution of Aβ to cognitive impairments may yield important insights into the pathophysiology of AD. In the present study, we simultaneously recorded spikes and LFPs from multiple electrodes implanted in the prefrontal cortex of rats (control and intra-hippocampal Aβ injection group) that performed a Y-maze working memory task. The information changes in spikes and LFPs during the task were assessed by calculation of entropy. Then the coordination between spikes and LFPs was estimated by the correlation of LFP entropy and spike entropy. Compared with the control group, the Aβ group showed significantly weaker coordination between spikes and LFPs. Our results indicate that the incoordination between spikes and LFPs may provide a potential mechanism for the cognitive deficits in working memory of AD.

Deep brain stimulation of the subthalamic nucleus reestablishes neuronal information transmission in the 6-OHDA rat model of parkinsonism

Pathophysiological activity of basal ganglia neurons accompanies the motor symptoms of Parkinson's disease. High-frequency (>90 Hz) deep brain stimulation (DBS) reduces parkinsonian symptoms, but the mechanisms remain unclear. We hypothesize that parkinsonism-associated electrophysiological changes constitute an increase in neuronal firing pattern disorder and a concomitant decrease in information transmission through the ventral basal ganglia, and that effective DBS alleviates symptoms by decreasing neuronal disorder while simultaneously increasing information transfer through the same regions. We tested these hypotheses in the freely behaving, 6-hydroxydopamine-lesioned rat model of hemiparkinsonism. Following the onset of parkinsonism, mean neuronal firing rates were unchanged, despite a significant increase in firing pattern disorder (i.e., neuronal entropy), in both the globus pallidus and substantia nigra pars reticulata. This increase in neuronal entropy was reversed by symptom-alleviating DBS. Whereas increases in signal entropy are most commonly indicative of similar increases in information transmission, directed information through both regions was substantially reduced (>70%) following the onset of parkinsonism. Again, this decrease in information transmission was partially reversed by DBS. Together, these results suggest that the parkinsonian basal ganglia are rife with entropic activity and incapable of functional information transmission. Furthermore, they indicate that symptom-alleviating DBS works by lowering the entropic noise floor, enabling more information-rich signal propagation. In this view, the symptoms of parkinsonism may be more a default mode, normally overridden by healthy basal ganglia information. When that information is abolished by parkinsonian pathophysiology, hypokinetic symptoms emerge.

Random bin for analyzing neuron spike trains

When analyzing neuron spike trains, it is always the problem of how to set the time bin. Bin width affects much to analyzed results of such as periodicity of the spike trains. Many approaches have been proposed to determine the bin setting. However, these bins are fixed through the analysis. In this paper, we propose a randomizing method of bin width and location instead of conventional fixed bin setting. This technique is applied to analyzing periodicity of interspike interval train. Also the sensitivity of the method is presented.