Steering Toward Normative Wide-Dynamic-Range Neuron Activity in Nerve-Injured Rats With Closed-Loop Peripheral Nerve Stimulation.

OBJECTIVES: Chronic pain is primarily treated with pharmaceuticals, but the effects remain unsatisfactory. A promising alternative therapy is peripheral nerve stimulation (PNS), but it has been associated with suboptimal efficacy because its modulation mechanisms are not clear and the current therapies are primarily open loop (ie, manually adjusting the stimulation parameters). In this study, we developed a proof-of-concept computational modeling as the first step toward implementing closed-loop PNS in future biological studies. When developing new pain therapies, a useful pain biomarker is the wide-dynamic-range (WDR) neuron activity in the dorsal horn. In healthy animals, the WDR neuron activity occurs in a stereotyped manner; however, this response profile can vary widely after nerve injury to create a chronic pain condition. We hypothesized that if injury-induced changes of neuronal response can be normalized to resemble those of a healthy condition, the pathological aspects of pain may be treated while maintaining protective physiological nociception. MATERIALS AND METHODS: Using an in vivo electrophysiology data set of WDR neuron recordings obtained in nerve-injured rats and naïve rats, we constructed sets of linear phenomenologic models of WDR firing rate during windup stimulation for both conditions. Then, we applied robust control systems techniques to identify a closed-loop PNS controller, which can drive the dynamics of WDR neuron response in neuropathic pain model into ranges associated with normal physiological pain. RESULTS: The sets of identified linear models can accurately predict, in silico, nonlinear neural responses to electrical stimulation of the peripheral nerve. In addition, we showed that continuous closed-loop control of PNS can be used to normalize WDR neuron firing responses in three injured cases. CONCLUSIONS: In this proof-of-concept study, we show how tractable, linear mathematical models of pain-related neurotransmission can be used to inform the development of closed-loop PNS. This new application of robust control to neurotechnology may also be expanded and applied across other neuromodulation applications.

Towards Robust Control of PNS for Chronic Pain: Modeling Spinal Cord Wide-Dynamic Range Neurons with Structured Uncertainty.

Pain is a protective physiological system essential for survival. However, it can malfunction and create a debilitating disease known as chronic pain (CP), which is primarily treated with drugs that can produce negative side effects (e.g., opioid addiction). Peripheral nerve stimulation (PNS) is a promising alternative therapy; it has fewer negative side effects but has been associated with suboptimal efficacy since its mechanisms are unclear, and the current therapies are primarily open-loop (i.e. manual adjustment). To adapt to the needs of the user, the next step in advancing PNS therapies is to "close the loop" by using feedback to adjust the stimulation in real-time. A critical step in developing closed-loop PNS treatment is a deeper understanding of pain processing in the dorsal horn (DH) of the spinal cord, which is the first central relay station on the pain pathway. Mechanistic models of the DH have been developed to investigate modulation mechanisms but are non-linear, high-dimensional, and thus difficult to analyze. In this paper, we propose a novel application of structured uncertainty to model and analyze the nonlinear dynamical nature of the DH, and provide the foundation for developing robust PNS controllers using µ-synthesis. Using electrophysiological DH recordings from both naive and nerve-injured rats during windup stimulation, we build two separate models, which contains a linear time-invariant nominal (average) model, and structured uncertainty to quantify the nonlinear deviations in response from the nominal model. Using the structured uncertainty, we analyze the naive and injured models to discover underlying DH dynamics not identifiable using traditional methods, such as spike counting.

Predicting Wide-Dynamic Range Neuron Activity from Peripheral Nerve Stimulation using Linear Parameter Varying Models.

Neuromodulation treatments for chronic pain are programmed with limited knowledge of how electrical stimulation of nerve fibers affects the dynamic response of pain-processing neurons in the spinal cord and the brain. By modeling these effects with tractable representations, we may be able to improve efficacy of stimulation therapy. However, pain transmitting neurons in the dorsal horn of the spinal cord, the first pain relay station in the nervous system, have complex responses to peripheral nerve stimulation (PNS) with nonlinearities and history effects. Wide-dynamic range (WDR) neurons are well studied in pain models and respond to peripheral noxious and non-noxious stimuli. We propose to use linear parameter varying (LPV) models to capture PNS responses of WDR neurons of the deep lamina in the dorsal horn in the spinal cord. Here we show that LPV models perform better than a single linear time-invariant (LTI) model in representing the responses of the WDR neurons to widely varying amplitudes of PNS current. In the future, we can use these models alongside LPV control techniques to design closed-loop PNS stimulation that may accomplish optimal pain treatment goals.Clinical Relevance- Electrical nerve stimulation as a therapy for chronic pain is in need of a more informed approach to programming. By describing the effects of stimulation on the pain system with tractable mathematical models, we may be able to titrate the stimulation to more effectively treat chronic pain.

Modeling Responses to Peripheral Nerve Stimulation in the Dorsal Horn.

Pain is a protective physiological system essential for survival. However, it can malfunction and create a debilitating disease known as chronic pain (CP). CP is primarily treated with drugs that can have negative side effects (e.g., opioid addiction), and lose efficacy after long-term use. Electrical stimulation of the spinal cord or peripheral nerves is an alternative therapy that has great potential to reduce the need for drugs and has fewer negative side effects; but has been associated with suboptimal efficacy because its modulation mechanisms are unknown. Critical to advancing CP treatment is a deeper understanding of how pain is processed in the superficial and deep layers of the dorsal horn (DH), which is the first central relay station for pain processing in the spinal cord. Mechanistic models of the DH have been developed to investigate modulation mechanisms but are non-linear and high-dimensional and thus difficult to analyze. In this paper, we construct a tractable computational model of the DH in rats from LFP recordings of the superficial layer network and spiking activity of WDR neurons in the deep layer. By combining a deterministic linear time-invariant model with a stochastic point process model, we can accurately predict responses of the DH circuit to electrical stimulation of the peripheral nerve. The model is computationally efficient, low-dimensional, and able to capture the stochastic nature of neuronal dynamics in the DH; and is a first step in developing new therapies for CP.

The effect of binaural beats on verbal working memory and cortical connectivity.

OBJECTIVE: Synchronization in activated regions of cortical networks affect the brain's frequency response, which has been associated with a wide range of states and abilities, including memory. A non-invasive method for manipulating cortical synchronization is binaural beats. Binaural beats take advantage of the brain's response to two pure tones, delivered independently to each ear, when those tones have a small frequency mismatch. The mismatch between the tones is interpreted as a beat frequency, which may act to synchronize cortical oscillations. Neural synchrony is particularly important for working memory processes, the system controlling online organization and retention of information for successful goal-directed behavior. Therefore, manipulation of synchrony via binaural beats provides a unique window into working memory and associated connectivity of cortical networks. APPROACH: In this study, we examined the effects of different acoustic stimulation conditions during an N-back working memory task, and we measured participant response accuracy and cortical network topology via EEG recordings. Six acoustic stimulation conditions were used: None, Pure Tone, Classical Music, 5 Hz binaural beats, 10 Hz binaural beats, and 15 Hz binaural beats. MAIN RESULTS: We determined that listening to 15 Hz binaural beats during an N-Back working memory task increased the individual participant's accuracy, modulated the cortical frequency response, and changed the cortical network connection strengths during the task. Only the 15 Hz binaural beats produced significant change in relative accuracy compared to the None condition. SIGNIFICANCE: Listening to 15 Hz binaural beats during the N-back task activated salient frequency bands and produced networks characterized by higher information transfer as compared to other auditory stimulation conditions.

The Effect of Binaural Beats on Visuospatial Working Memory and Cortical Connectivity.

Binaural beats utilize a phenomenon that occurs within the cortex when two different frequencies are presented separately to each ear. This procedure produces a third phantom binaural beat, whose frequency is equal to the difference of the two presented tones and which can be manipulated for non-invasive brain stimulation. The effects of binaural beats on working memory, the system in control of temporary retention and online organization of thoughts for successful goal directed behavior, have not been well studied. Furthermore, no studies have evaluated the effects of binaural beats on brain connectivity during working memory tasks. In this study, we determined the effects of different acoustic stimulation conditions on participant response accuracy and cortical network topology, as measured by EEG recordings, during a visuospatial working memory task. Three acoustic stimulation control conditions and three binaural beat stimulation conditions were used: None, Pure Tone, Classical Music, 5Hz binaural beats, 10Hz binaural beats, and 15Hz binaural beats. We found that listening to 15Hz binaural beats during a visuospatial working memory task not only increased the response accuracy, but also modified the strengths of the cortical networks during the task. The three auditory control conditions and the 5Hz and 10Hz binaural beats all decreased accuracy. Based on graphical network analyses, the cortical activity during 15Hz binaural beats produced networks characteristic of high information transfer with consistent connection strengths throughout the visuospatial working memory task.