Primal-size neural circuits in meta-periodic interaction.

Experimental observations of simultaneous activity in large cortical areas have seemed to justify a large network approach in early studies of neural information codes and memory capacity. This approach has overlooked, however, the segregated nature of cortical structure and functionality. Employing graph-theoretic results, we show that, given the estimated number of neurons in the human brain, there are only a few primal sizes that can be attributed to neural circuits under probabilistically sparse connectivity. The significance of this finding is that neural circuits of relatively small primal sizes in cyclic interaction, implied by inhibitory interneuron potentiation and excitatory inter-circuit potentiation, generate relatively long non-repetitious sequences of asynchronous primal-length periods. The meta-periodic nature of such circuit interaction translates into meta-periodic firing-rate dynamics, representing cortical information. It is finally shown that interacting neural circuits of primal sizes 7 or less exhaust most of the capacity of the human brain, with relatively little room to spare for circuits of larger primal sizes. This also appears to ratify experimental findings on the human working memory capacity.

Probabilistically segregated neural circuits and subcritical linguistics.

Early studies of cortical information codes and memory capacity have assumed large neural networks, which, subject to evenly probable binary (on/off) activity, were found to be endowed with large storage and retrieval capacities under the Hebbian paradigm. Here, we show that such networks are plagued with exceedingly high cross-network connectivity, yielding long code words, which are linguistically non-realistic and difficult to memorize and comprehend. Noting that the neural circuit activity code is jointly governed by somatic and synaptic activity states, termed neural circuit polarities, we show that, subject to subcritical polarity probability, random-graph-theoretic considerations imply small neural circuit segregation. Such circuits are shown to represent linguistically plausible cortical code words which, in turn, facilitate storage and retrieval of both circuit connectivity and firing-rate dynamics.

Primal categories of neural polarity codes.

Neuronal membrane and synapse polarities have been attracting considerable interest in recent years. Certain functional roles for such polarities have been suggested, yet, they have largely remained a subject for speculation and debate. Here, we note that neural circuit polarity codes, defined as sets of polarity permutations, divide into primal-size circuit polarity subcodes, which, sharing certain connectivity attributes, are called categories. Two long-debated, seemingly competing paradigms of neuronal self-feedback, namely, axonal discharge and synaptic mediation, are shown to jointly define the distinction between these categories. However, as the second paradigm contains the first, it is mathematically sufficient for complete specification of all categories. The analysis of primal-size circuit polarity categories is found to reveal, explain and extend experimentally observed cortical information capacity values termed "magical numbers", associated with "working memory". While these have been previously argued on grounds of psychological experiments, here they are further supported on analytic grounds by the so-called Hebbian memory paradigm. The information dimensionality associated with these capacities is found to be a consequence of prime factorization of composite circuit polarity code sizes. Different categories of circuit polarity, identical in size and neuronal parameters, are shown to generate different firing rate dynamics.

Circuit Polarity Effect of Cortical Connectivity, Activity, and Memory.

Experimental constraints have traditionally implied separate studies of different cortical functions, such as memory and sensory-motor control. Yet certain cortical modalities, while repeatedly observed and reported, have not been clearly identified with one cortical function or another. Specifically, while neuronal membrane and synapse polarities with respect to a certain potential value have been attracting considerable interest in recent years, the purposes of such polarities have largely remained a subject for speculation and debate. Formally identifying these polarities as on-off neuronal polarity gates, we analytically show that cortical circuit structure, behavior, and memory are all governed by the combined potent effect of these gates, which we collectively term circuit polarity. Employing widely accepted and biologically validated firing rate and plasticity paradigms, we show that circuit polarity is mathematically embedded in the corresponding models. Moreover, we show that the firing rate dynamics implied by these models are driven by ongoing circuit polarity gating dynamics. Furthermore, circuit polarity is shown to segregate cortical circuits into internally synchronous, externally asynchronous subcircuits, defining their firing rate modes in accordance with different cortical tasks. In contrast to the Hebbian paradigm, which is shown to be susceptible to mutual neuronal interference in the face of asynchrony, circuit polarity is shown to block such interference. Noting convergence of synaptic weights, we show that circuit polarity holds the key to cortical memory, having a segregated capacity linear in the number of neurons. While memory concealment is implied by complete neuronal silencing, memory is restored by reactivating the original circuit polarity. Finally, we show that incomplete deterioration or restoration of circuit polarity results in memory modification, which may be associated with partial or false recall, or novel innovation.

Developmental metaplasticity in neural circuit codes of firing and structure.

Firing-rate dynamics have been hypothesized to mediate inter-neural information transfer in the brain. While the Hebbian paradigm, relating learning and memory to firing activity, has put synaptic efficacy variation at the center of cortical plasticity, we suggest that the external expression of plasticity by changes in the firing-rate dynamics represents a more general notion of plasticity. Hypothesizing that time constants of plasticity and firing dynamics increase with age, and employing the filtering property of the neuron, we obtain the elementary code of global attractors associated with the firing-rate dynamics in each developmental stage. We define a neural circuit connectivity code as an indivisible set of circuit structures generated by membrane and synapse activation and silencing. Synchronous firing patterns under parameter uniformity, and asynchronous circuit firing are shown to be driven, respectively, by membrane and synapse silencing and reactivation, and maintained by the neuronal filtering property. Analytic, graphical and simulation representation of the discrete iteration maps and of the global attractor codes of neural firing rate are found to be consistent with previous empirical neurobiological findings, which have lacked, however, a specific correspondence between firing modes, time constants, circuit connectivity and cortical developmental stages.

Closed-loop auditory feedback for the improvement of gait in patients with Parkinson's disease.

OBJECTIVE: To study the effects of closed-loop auditory feedback cues, corresponding to patient self-motion, on the walking abilities of patients with Parkinson's disease, in comparison to the effects of open-loop (metronome-like) auditory cues. METHODS: Sixteen patients on their regular medication schedule participated. A device which translates patient steps into a clicking cue sounded by earphones provides auditory feedback for gait pattern correction. Walking speed and stride length are measured. Device-on performance is compared to device-off performance and to baseline performance, and short-term residual performance following 15 min rest is compared to baseline performance. RESULTS: Device-on performance was found to represent, on average, 10.72%±19.53% improvement in walking speed and 6.77%±6.57% improvement in stride length with respect to device-off performance, and an average improvement of 12.37%±18.37% in walking speed and 4.30%±3.64% in stride length with respect to baseline performance, with 87.5% and 81.25% of the patients improving their walking speed and stride length, respectively. Average short-term residual performance showed 9.09%±6.34% improvement in walking speed and 6.52%±4.36% improvement in stride length, compared to baseline performance, with 85.71% of the patients improving in both walking speed and stride length. CONCLUSIONS: Closed-loop auditory feedback improves walking speed and stride length in patients with Parkinson's disease. Improvement in walking speed is more pronounced than improvement in stride length. Yet, in contrast to previously studied open-loop auditory cues, training with closed-loop auditory feedback results in non-negligible on-line improvement in stride length. Moreover, in contrast to previously reported results of open-loop auditory cuing, training with closed-loop auditory feedback has residual effects, which suggest the examination of this approach in a comprehensive therapy program.

Virtual reality feedback cues for improvement of gait in patients with Parkinson's disease.

BACKGROUND: Our aim was to study the effects of visual feedback cues, responding dynamically to patient's self-motion and provided through a portable see-through virtual reality apparatus, on the walking abilities of patients with Parkinson's disease. METHODS: Twenty patients participated. On-line and residual effects on walking speed and stride length were measured. RESULTS: Attaching the visual feedback device to the patient with the display turned off showed a negligible effect of about 2%. With the display turned on, 56% of the patients improved either their walking speed, or their stride length, or both, by over 20%. After device removal, and waiting for 15 minutes, the patients were instructed to walk again: 68% of the patients showed over 20% improvement in either walking speed or stride length or both. One week after participating in the first test, 36% of the patients showed over 20% improvement in baseline performance with respect to the previous test. Some of the patients reported that they still walked on the tiles in their minds. DISCUSSION: Improvements in walking abilities were measured in patients with Parkinson's disease using virtual reality visual feedback cues. Residual effects suggest the examination of this approach in a comprehensive therapy program.

Effect of visual feedback on the occipital-parietal-motor network in Parkinson's disease with freezing of gait.

Freezing of gait (FOG) is an elusive phenomenon that debilitates a large number of Parkinson's disease (PD) patients regardless of stage of disease, medication status, or deep brain stimulation implantation. Sensory feedback cues, especially visual feedback cues, have been shown to alleviate FOG episodes or even prevent episodes from occurring. Here, we examine cortical information flow between occipital, parietal, and motor areas during the pre-movement stage of gait in a PD-with-FOG patient that had a strong positive behavioral response to visual cues, one PD-with-FOG patient without any behavioral response to visual cues, and age-matched healthy controls, before and after training with visual feedback. Results for this case study show differences in cortical information flow between the responding PD-with-FOG patient and the other two subject types, notably, an increased information flow in the beta range. Tentatively suggesting the formation of an alternative cortical sensory-motor pathway during training with visual feedback, these results are proposed as subject for further verification employing larger cohorts of patients.

Virtual sensory feedback for gait improvement in neurological patients.

We review a treatment modality for movement disorders by sensory feedback. The natural closed-loop sensory-motor feedback system is imitated by a wearable virtual reality apparatus, employing body-mounted inertial sensors and responding dynamically to the patient's own motion. Clinical trials have shown a significant gait improvement in patients with Parkinson's disease using the apparatus. In contrast to open-loop devices, which impose constant-velocity visual cues in a "treadmill" fashion, or rhythmic auditory cues in a "metronome" fashion, requiring constant vigilance and attention strategies, and, in some cases, instigating freezing in Parkinson's patients, the closed-loop device improved gait parameters and eliminated freezing in most patients, without side effects. Patients with multiple sclerosis, previous stroke, senile gait, and cerebral palsy using the device also improved their balance and gait substantially. Training with the device has produced a residual improvement, suggesting virtual sensory feedback for the treatment of neurological movement disorders.

Global attractor alphabet of neural firing modes.

The elementary set, or alphabet, of neural firing modes is derived from the widely accepted conductance-based rectified firing-rate model. The firing dynamics of interacting neurons are shown to be governed by a multidimensional bilinear threshold discrete iteration map. The parameter-dependent global attractors of the map morph into 12 attractor types. Consistent with the dynamic modes observed in biological neuronal firing, the global attractor alphabet is highly visual and intuitive in the scalar, single-neuron case. As synapse permeability varies from high depression to high potentiation, the global attractor type varies from chaotic to multiplexed, oscillatory, fixed, and saturated. As membrane permeability decreases, the global attractor transforms from active to passive state. Under the same activation, learning and retrieval end at the same global attractor. The bilinear threshold structure of the multidimensional map associated with interacting neurons generalizes the global attractor alphabet of neuronal firing modes to multineuron systems. Selective positive or negative activation and neural interaction yield combinatorial revelation and concealment of stored neuronal global attractors.

Gait improvement in patients with cerebral palsy by visual and auditory feedback.

OBJECTIVES: To study the effects of gait training with visual and auditory feedback cues on the walking abilities of patients with gait disorders due to cerebral palsy. MATERIALS AND METHODS: Visual and auditory feedback cues were generated by a wearable device, driven by inertial sensors. Ten randomly selected patients with gait disorders due to cerebral palsy and seven age-matched healthy individuals trained with visual feedback cues, while ten patients and eight age-matched healthy individuals trained with auditory feedback cues. Baseline performance (walking speed and stride length along a 10-m straight track) was measured before device use. Following 20-min training with the device and a 20-min break, performance without the device was measured again and compared with the baseline performance. RESULTS: For the patients who trained with visual feedback, the average improvement was 21.70% ± 36.06% in the walking speed and 8.72% ± 9.47% in the stride length. For the patients who trained with auditory feedback, the average improvement was 25.43% ± 28.65% in the walking speed and 13.58% ± 13.10% in the stride length. For the healthy individuals who trained with visual feedback, the average improvement was -2.41% ± 9.54% in the walking speed and -2.84% ± 10.11% in the stride length. For the healthy individuals who trained with auditory feedback, the average improvement was 0.01% ± 7.73% in the walking speed and -2.03% ± 6.15% in the stride length. CONCLUSIONS: Training with visual and auditory feedback cues can improve gait parameters in patients with gait disorders due to cerebral palsy. This was contrasted by no improvement in age-matched healthy individuals.

Noninvertibility, chaotic coding, and chaotic multiplexity of synaptically modulated neural firing.

Widely accepted neural firing and synaptic potentiation rules specify a cross-dependence of the two processes, which, evolving on different timescales, have been separated for analytic purposes, concealing essential dynamics. Here, the morphology of the firing rates process, modulated by synaptic potentiation, is shown to be described by a discrete iteration map in the form of a thresholded polynomial. Given initial synaptic weights, a firing activity is triggered by conductance. Elementary dynamic modes are defined by fixed points, cycles, and saddles of the map, building blocks of the underlying firing code. Showing parameter-dependent multiplicity of real polynomial roots, the map is proved to be noninvertible. The incidence of chaos is then implied by the parameter-dependent existence of snap-back repellers. The highly patterned geometric and statistical structures of the associated chaotic attractors suggest that these attractors are an integral part of the neural code. It further suggests the chaotic attractor as a natural mechanism for statistical encoding and temporal multiplexing of neural information. The analytic findings are supported by simulation.

At-home training with closed-loop augmented-reality cueing device for improving gait in patients with Parkinson disease.

Shuffling and freezing while walking can impair function in patients with Parkinson disease (PD). Open-loop devices that provide fixed-velocity visual or auditory cues can improve gait but may be unreliable or exacerbate freezing of gait in some patients. We examined the efficacy of a closed-loop, accelerometer-driven, wearable, visual-auditory cueing device in 13 patients with PD with off-state gait impairment at baseline and after 2 weeks of twice daily (30 minute duration) at-home use. We measured gait velocity, stride length, and cadence using a validated electronic gait-analysis system. Subjects underwent standard motor assessment and completed a self-administered Freezing of Gait Questionnaire (FOGQ) (range 0-24; lower is better). After training, device use enhanced walking velocity (61.6 ± 20.1 cm/s to 72.6 ± 26.5 cm/s, p = 0.006) and stride length (74.3 ± 16.4 cm to 84.0 ± 18.5 cm, p = 0.004). Upon device removal, walking velocity (64.5 ± 21.4 cm/s to 75.4 ± 21.5 cm/s, p < 0.001) and stride length (79.0 ± 20.3 cm to 88.8 ± 17.7 cm, p = 0.003) exhibited a greater magnitude of change, suggesting immediate residual benefits. Also upon device removal, nearly 70 percent of subjects improved by at least 20 percent in either walking velocity, stride length, or both. An overall improvement in gait was measured by the FOGQ (14.2 ±1.9 to 12.4 ± 2.5, p = 0.02). Although issues related to compliance and response variability render a definitive interpretation of study outcome difficult, devices using closed-loop sensory feedback appear to be effective and desirable nonpharmacologic interventions to improve walking in selected individuals with PD.

Glide-symmetric locomotion reinforcement in patients with multiple sclerosis by visual feedback.

PURPOSE: To compare the effects of gait training with distinct glide-symmetric visual feedback cues, adapted to the geometry of human locomotion, to the effects of training with visual cues of no distinct symmetry, on the walking abilities of subjects with gait disorders due to multiple sclerosis (MS). METHODS: Ten patients trained with transverse lines while 11 patients trained with checkerboard tiles, both provided by a wearable virtual reality device. Baseline performance (walking speed and stride length along a 10 m straight track) was measured before device use. Following 20 min training with the device and 10 min rest, performance without the device was measured again and compared to the baseline performance. RESULTS: The average improvement in the group using the visual cue of transverse lines was 7.79% +/- 4.24% in walking speed and 7.20% +/- 3.92% in stride length. The average improvement in the group using the visual cue of checkerboard tiles was 21.09% +/- 18.39% in walking speed and 12.99% +/- 1.72% in stride length. CONCLUSIONS: Patients with gait disorders due to MS, training with a glide-symmetric visual feedback cue, showed a significantly higher improvement in their gait parameters than patients training with a visual feedback cue of no without distinct symmetry.

Auditory feedback control for improvement of gait in patients with Multiple Sclerosis.

OBJECTIVE: To study the use of auditory feedback for gait management and rehabilitation in patients with Multiple Sclerosis (MS). METHODS: An auditory feedback cue, responding to the patient's own steps in closed-loop, was produced by a wearable motion sensor and delivered to the patient through ear phones. On-line (device on) and residual short-term therapeutic effects on walking speed and stride length were measured in fourteen randomly selected patients with gait disturbances predominantly due to cerebellar ataxia. RESULTS: Patients showed an average improvement of 12.84% on-line and 18.75% residually in walking speed. Average improvement in stride length was 8.30% on-line and 9.93% residually. The improvement results are particularly noteworthy when compared with the lack of change in healthy control subjects. CONCLUSIONS: Patients with MS using auditory feedback cues showed improvement in walking abilities.

Virtual reality cues for improvement of gait in patients with multiple sclerosis.

OBJECTIVE: To study the effects of visual cues, provided through a portable visual-feedback virtual reality (VR) apparatus, on the walking abilities of patients with multiple sclerosis (MS). METHODS: On-line (display-on) and residual short-term therapeutic effects on walking speed and stride length were measured in 16 randomly selected patients with gait disturbances predominantly due to cerebellar ataxia. RESULTS: Patients whose baseline walking speed (BWS) was below the median showed an average on-line improvement of 13.46% in their walking speed, while patients whose BWS was above the median improved their speed by 1.47%. The average short-term residual therapeutic improvement in walking speed was 24.49% in patients with BWS below the median, and 9.09% in patients with BWS above the median. Similar results were obtained for improvements in stride length. These results of improved functions in patients are particularly noteworthy when compared with the lack of change in healthy control subjects. CONCLUSIONS: Patients with multiple sclerosis showed improvement in walking abilities using virtual reality visual-feedback cues.