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Real-time closed-loop protocol to assess neural variability in temporal coding
Alberto Ayala, Angel Lareo, Pablo Varona, Francisco B. Rodriguez
TL;DR
Temporal coding relies on spike timing, but neural codes vary with neural dynamics, complicating their detection and study. This paper evaluates a real-time closed-loop protocol that compares detected and triggering spike sequences with the Victor-Purpura distance before stimulation. In noisy Hindmarsh-Rose experiments, the protocol adapted to variability and conditioned activity toward brief-burst and regularized-burst targets, although effectiveness declined at higher noise levels.
Problem
Variable spike timing makes it challenging to determine whether different spike sequences represent the same temporal code and to study temporal coding under realistic conditions.
Method
The protocol detects discretized spike sequences in real time, uses Victor-Purpura similarity to a triggering code, and delivers predefined stimulation when the similarity criterion is met.
Results
The protocol showed high adaptability and conditioned Hindmarsh-Rose activity in both experimental paradigms, outperforming open-loop stimulation; brief-burst elicitation reached 97.45% versus 38.24%.
Takeaways & Limitations
Adaptive closed-loop stimulation supports studying temporal codes and controlling neural dynamics under variable activity, with real-time latencies meeting requirements for fast neural dynamics.
Takeaways & Limitations
Effectiveness declined as model variability increased, and biological experiments are still needed to test whether similarly detected variable spike trains are functionally equivalent codes.
Abstract
from arXiv · showhide
Understanding temporal coding in neural systems is essential for decoding brain communication and advancing knowledge of neural information processing. Neural activity often conveys information through spike sequences with stereotypical temporal structures linked to specific functions. However, these sequences are subject to variability introduced by neural dynamics. Real-time closed-loop stimulation is a powerful approach to study temporal coding through adaptive control. In this work, we evaluate how a closed-loop protocol adapts to this variability to drive neural dynamics toward a desired state. It computes the Victor-Purpura distance to quantify similarity between spike sequences generated by the neural system and a triggering pattern. If the protocol determines that a neural sequence is similar to the trigger pattern, it applies stimulation to the system. This allows for an analysis of whether the system's responses are consistent and facilitates the identification of varying spike sequences that can be considered instances of the same functional temporal code. We designed two validation experiments using the Hindmarsh-Rose model: (i) detection of a temporal code and delivery of stimulation to produce brief interspersed bursts, and (ii) detection of burst onset in chaotic activity followed by inhibitory stimulation to regularize it. Gaussian noise was progressively injected to increase variability. The protocol exhibited high degree of adaptability to variability and was effective in achieving the target dynamics. The results reported in this paper suggest that adaptive closed-loop stimulation can enhance experimental methodologies for studying neural coding under realistic variability conditions.
1. Introduction
Temporal coding links information to the precise timing structure of spike sequences, even though neural codes vary in spike number and timing. This work evaluates whether real-time closed-loop stimulation can detect variable instances of a temporal code and drive neural dynamics toward desired states.
- Motivation: Temporal coding proposes that precise spike timing carries information about neural and sensorimotor states despite intrinsic variability in spike number and interspike intervals.The paper defines a code as a temporal sequence of discrete neural spikes characterized by the relative structure of their occurrence times.
- Motivation: Biological and Hindmarsh-Rose spike sequences can form variable families that preserve a behavioral message or underlying dynamic regime.The fish examples convey the same agonistic behavioral message despite timing variability, while the model reproduces similar variability.
- Motivation: Closed-loop approaches enable real-time exploration of neural dynamics and activity-dependent stimulation linked to the system’s internal state.This complements traditional unidirectional stimulation for studying complex dynamics that are difficult to assess otherwise.
- Approach: The protocol uses Victor-Purpura distance to determine whether spike sequences remain sufficiently similar to a triggering temporal code despite spike-time jitter.Unlike approaches guided by firing rate or signal amplitude, stimulation is triggered by temporal-code similarity.
- Study design: Two Hindmarsh-Rose experiments test adaptive stimulation under progressively increasing Gaussian noise: brief-burst elicitation and chaotic-burst regularization.The study also compares closed-loop conditioning with open-loop stimulation and examines real-time latency and consistency with simulation.
- Contribution: The work extends prior research by adding chaotic-activity regularization and evaluating protocol adaptability in a real-time environment.These aspects were identified as unexplored in the earlier study addressed by the paper.
2. Methods
The protocol digitizes neural activity into temporal codes, compares detected and triggering codes with the Victor-Purpura distance, and stimulates when similarity meets a threshold. Its adaptability is tested in noisy Hindmarsh-Rose simulations and hardware-constrained experiments targeting brief bursts or regularized bursting.
- Protocol: TCDS acquires neural signals in real time and converts consecutive predefined time windows into binary bits representing spike occurrences.The bin time determines protocol resolution and should capture spike events without information loss.
- Protocol: The flowchart applies stimulation when the detected-code distance is less than or equal to threshold θ, with real-time operations executed at 10 kHz.In the illustrated example, two 10 ms shifts produce distance 1 for q = 50.
- Protocol: Victor-Purpura distance measures the minimum cost of inserting, deleting, or temporally shifting spikes to compare detected and triggering codes.The temporal-shift cost is q · |t1 − t2|, where q determines the cost of shifting a spike in time.
- Model: The Hindmarsh-Rose model represents membrane potential, recovery dynamics, and slow ionic-current adaptation, with Gaussian noise injected as an external current.Regular bursting uses Ireg = 1.9, whereas chaotic bursting uses Ireg = 3.281.
- Brief-burst experiment: The brief-burst experiment increases noise from 0% to 26%, uses 10 trials per level, detects complete bursts, and applies positive-ramp stimulation to elicit 2-3-spike bursts.The same target is evaluated against open-loop stimulation, including in a hardware-constrained electronic-neuron implementation with adjusted parameters.
- Results: Closed-loop stimulation elicited brief bursts in up to 97.45% of stimuli, compared with 38.24% for open-loop stimulation under 3% noise.Both sessions delivered ramp stimuli at the same time points.
- Regularization experiment: The regularization experiment detects burst onset during chaotic bursting and applies inhibitory stimulation to produce bursts with a regular period.At 0.45% noise, closed-loop stimulation consistently regularizes activity, whereas open-loop stimulation is less robust.
3. Results
Across simulated and hardware-constrained experiments, closed-loop stimulation adapted to noise-induced variability while conditioning Hindmarsh–Rose activity toward brief bursts or regular bursting. Performance generally exceeded open-loop stimulation, although effectiveness declined at high noise.
- Brief-burst elicitation: Closed-loop stimulation generated brief bursts more robustly than open-loop stimulation across tested real-time noise levels.Closed-loop percentages were 97.27%, 97.45%, and 68.56%, compared with 41.78%, 38.24%, and 24.26% for open-loop stimulation at corresponding noise conditions.
- Brief-burst elicitation: Victor-Purpura distances showed that closed-loop pre-stimulation codes consistently resembled the triggering temporal code at 3% noise.At 25% noise, detected-code diversity increased and some triggering sequences failed to produce brief bursts.
- Brief-burst elicitation: PCA of recurrence features showed clustered closed-loop activity and more dispersed open-loop activity, with greater closed-loop dispersion at 25% noise.Silhouette coefficients were 0.288 without noise, 0.274 at 3% noise, and 0.099 at 25% noise.
- Real-time performance: At 10 kHz, maximum and average real-time latencies remained below the 100 µs system period across experiments.This met the temporal requirements for studying temporal coding in the tested system.
- Chaotic-burst regularization: Closed-loop stimulation regularized chaotic bursting more robustly than open-loop stimulation at noise levels below 1.5%.Under closed-loop stimulation, mean period deviation remained close to zero, while open-loop variability increased when noise was introduced.
- Chaotic-burst regularization: In hardware-constrained regularization experiments, closed-loop stimulation remained consistent at 0.45% noise, whereas both methods failed at 5% noise.With no noise and identical initial conditions, both methods achieved the same regularization results.
4. Discussion
The discussion positions adaptive closed-loop stimulation as a flexible approach for real-time activity-dependent study of temporal coding. The protocol is not tied to the Hindmarsh–Rose model, but similarity-based detection has reduced performance under extreme variability.
- Scope: The protocol’s detection–metric–stimulation chain remains applicable beyond the Hindmarsh–Rose model when systems produce discretizable temporal patterns.The Hindmarsh–Rose model was used as a dynamically versatile case study rather than as a protocol-specific requirement.
- Limitations: Performance decreased at high noise levels, revealing a limitation of similarity-based detection under extreme variability.At such variability, detected temporal-code similarity becomes less effective for achieving the target dynamics.
- Metric choice: Victor-Purpura distance enabled adaptability, but other parametric and non-parametric spike-train comparison metrics could serve similar purposes.The discussion names Victor-Purpura, van Rossum, and Schreiber similarity measures as alternatives within this metric family.
- Implementation: RTXI implementation provides a standardized, disseminable, user-friendly platform whose parameters and stimuli can be modified flexibly.The authors contrast this software implementation with reliance on specialized hardware such as an FPGA.
5. Conclusions
The real-time closed-loop protocol adapted to neural variability and conditioned Hindmarsh–Rose dynamics across brief-burst and chaotic-activity experiments. Its real-time latency met requirements for studying fast neural dynamics, while increasing variability reduced effectiveness and motivates further adaptive strategies.
- The protocol robustly conditioned Hindmarsh–Rose dynamics under variability in brief-burst generation and chaotic-activity regularization.The two experiments used Gaussian noise to induce variability and compared performance with open-loop stimulation in simulated and real-time environments.
- 97.45% versus 38.24% closed- versus open-loop performance was achieved for brief-burst elicitation.
- 1.21 ms versus 20.73 ms period deviation was observed for closed- versus open-loop regularization.
- Effectiveness declined as model-activity variability increased, suggesting that adaptive parameter adjustment could improve performance.
- Observed real-time latencies met temporal requirements for studying fast neural dynamics.This supports use of the protocol for investigating temporal coding across a wide variety of biological systems.
- Future work will test whether variable spike trains detected as similar represent functionally equivalent neural codes in biological preparations.The authors also plan to explore van Rossum distance and real-time machine-learning approaches.