Electrical Stimulation of Distal Tibial Nerve During Stance Phase of Walking May Reverse Effects of Unilateral Paw Pad Anesthesia in the Cat

Cutaneous feedback from feet is involved in regulation of muscle activity during locomotion, and the lack of this feedback results in motor deficits. We tested the hypothesis that locomotor changes caused by local unilateral anesthesia of paw pads in the cat could be reduced/reversed by electrical stimulation of cutaneous and proprioceptive afferents in the distal tibial nerve during stance. Several split-belt conditions were investigated in four adult female cats. In addition, we investigated the effects of similar distal tibial nerve stimulation on overground walking of one male cat that had a transtibial, bone-anchored prosthesis for 29 months and, thus, had no cutaneous/proprioceptive feedback from the foot. In all treadmill conditions, cats walked with intact cutaneous feedback (control), with right fore- and hindpaw pads anesthetized by lidocaine injections, and with a combination of anesthesia and electrical stimulation of the ipsilateral distal tibial nerve during the stance phase at 1.2× threshold of afferent activation. Electrical stimulation of the distal tibial nerve during the stance phase of walking with anesthetized ipsilateral paw pads reversed or significantly reduced the effects of paw pad anesthesia on several kinematic variables, including lateral center of mass shift, cycle and swing durations, and duty factor. We also found that stimulation of the residual distal tibial nerve in the prosthetic hindlimb often had different effects on kinematics compared with stimulation of the intact hindlimb with paw anesthetized. We suggest that stimulation of cutaneous and proprioceptive afferents in the distal tibial nerve provides functionally meaningful motion-dependent sensory feedback, and stimulation responses depend on limb conditions.

Analyzing the Effects of Parameters for Tremor Modulation via Phase-Locked Electrical Stimulation on a Peripheral Nerve

(1) Background: Non-invasive neuromodulation is a promising alternative to medication or deep-brain stimulation treatment for Parkinson's Disease or essential tremor. In previous work, we developed and tested a wearable system that modulates tremor via the non-invasive, electrical stimulation of peripheral nerves. In this article, we examine the proper range and the effects of various stimulation parameters for phase-locked stimulation. (2) Methods: We recruited nine participants with essential tremor. The subjects performed a bean-transfer task that mimics an eating activity to elicit kinetic tremor while using the wearable stimulation system. We examined the effects of stimulation with a fixed duty cycle, at different stimulation amplitudes and frequencies. The epochs of stimulation were locked to one of four phase positions of ongoing tremor, as measured with an accelerometer. We analyzed stimulation-evoked changes of the frequency and amplitude of tremor. (3) Results: We found that the higher tremor amplitude group experienced a higher rate of tremor power reduction (up to 65%) with a higher amplitude of stimulation when the stimulation was applied at the ±peak of tremor phase. (4) Conclusions: The stimulation parameter can be adjusted to optimize tremor reduction, and this study lays the foundation for future large-scale parameter optimization experiments for personalized peripheral nerve stimulation.

Fitts Law-Based Performance Metrics to Quantify Tremor in Individuals with Essential Tremor

Current methods of evaluating essential tremor (ET) either rely on subjective ratings or use limited tremor metrics (i.e., severity/amplitude and frequency). In this study, we explored performance metrics from Fitts law tasks that replicate and expand existing tremor metrics, to enable low-cost, home-based tremor quantification and analyze the cursor movements of individuals using a 3D mouse while performing a collection of drawing tasks. We analyzed the 3D mouse cursor movements of 11 patients with ET and three controls, on three computer-based tasksa spiral navigation (SPN) task, a rectangular track navigation (RTN) task, and multi-directional tapping/clicking (MDT)with several performance metrics (i.e., outside area (OA), throughput (TP in Fitts law), path efficiency (PE), and completion time (CT)). Using an accelerometer and scores from the Essential Tremor Rating Assessment Scale (TETRAS), we correlated the proposed performance metrics with the baseline tremor metrics and found that the OA of the SPN and RTN tasks were strongly correlated with baseline tremor severity (R²=0.57 and R²=0.83). We also found that the TP in the MDT tasks were strongly correlated with tremor frequency (R²=0.70). In addition, as the OA of the SPN and RTN tasks was correlated with tremor severity and frequency, it may represent an independent metric that increases the dimensionality of the characterization of an individuals tremor. Thus, this pilot study of the analysis of those with ET-associated tremor performing Fitts law tasks demonstrates the feasibility of introducing a new tremor metric that can be expanded for repeatable multi-dimensional data analyses.

Differential cardiovascular responses to cutaneous afferent subtypes in a nociceptive intersegmental spinal reflex

Electrical stimulation to segmental dorsal cutaneous nerves (DCNs) activates a nociceptive sensorimotor reflex and the same afferent stimulation also evokes blood pressure (BP) and heart rate (HR) responses in rats. To investigate the relationship between those cardiovascular responses and the activation of nociceptive afferents, we analyzed BP and HR responses to electrical stimulations at each DCN from T6 to L1 at 0.5 mA to activate A-fiber alone or 5 mA to activate both A- and C-fibers at different frequencies. Evoked cardiovascular responses showed a decrease and then an increase in BP and an increase and then a plateau in HR. Segmentally, both cardiovascular responses tended to be larger when evoked from the more rostral DCNs. Stimulation frequency had a larger effect on cardiovascular responses than the rostrocaudal level of the DCN input. Stimulation strength showed a large effect on BP changes dependent on C-fibers whereas HR changes were dependent on A-fibers. Additional A-fiber activation by stimulating up to 4 adjacent DCNs concurrently, but only at 0.5 mA, affected HR but not BP. These data support that cutaneous nociceptive afferent subtypes preferentially contribute to different cardiovascular responses, A-fibers to HR and C-fibers to BP, with temporal (stimulation frequency) and spatial (rostrocaudal level) dynamics.

Temporal and spatial dynamics of spinal sensorimotor processing in an intersegmental cutaneous nociceptive reflex

The cutaneus trunci muscle (CTM) reflex produces a skin "shrug" in response to pinch on a rat's back through a three-part neural circuit: 1) A-fiber and C-fiber afferents in segmental dorsal cutaneous nerves (DCNs) from lumbar to cervical levels, 2) ascending propriospinal interneurons, and 3) the CTM motoneuron pool located at the cervicothoracic junction. We recorded neurograms from a CTM nerve branch in response to electrical stimulation. The pulse trains were delivered at multiple DCNs (T₆-L₁), on both sides of the midline, at two stimulus strengths (0.5 or 5 mA, to activate Aδ fibers or Aδ and C fibers, respectively) and four stimulation frequencies (1, 2, 5, or 10 Hz) for 20 s. We quantified both the temporal dynamics (i.e., latency, sensitization, habituation, and frequency dependence) and the spatial dynamics (spinal level) of the reflex. The evoked responses were time-windowed into Early, Mid, Late, and Ongoing phases, of which the Mid phase, between the Early (Aδ fiber mediated) and Late (C fiber mediated) phases, has not been previously identified. All phases of the response varied with stimulus strength, frequency, history, and DCN level/side stimulated. In addition, we observed nociceptive characteristics like C fiber-mediated sensitization (wind-up) and habituation. Finally, the range of latencies in the ipsilateral responses were not very large rostrocaudally, suggesting a myelinated neural path within the ipsilateral spinal cord for at least the A fiber-mediated Early-phase response. Overall, these results demonstrate that the CTM reflex shares the temporal dynamics in other nociceptive reflexes and exhibits spatial (segmental and lateral) dynamics not seen in those reflexes.NEW & NOTEWORTHY We have physiologically studied an intersegmental reflex exploring detailed temporal, stimulus strength-based, stimulation history-dependent, lateral and segmental quantification of the reflex responses to cutaneous nociceptive stimulations. We found several physiological features in this reflex pathway, e.g., wind-up, latency changes, and somatotopic differences. These physiological observations allow us to understand how the anatomy of this reflex may be organized. We have also identified a new phase of this reflex, termed the "mid" response.

Cutaneous sensory feedback from paw pads affects lateral balance control during split-belt locomotion in the cat

Cutaneous sensory feedback from the paw pads plays an important role in regulating body balance, especially in challenging environments like ladder or slope walking. Here, we investigated the contribution of cutaneous sensory feedback from the paw pads to balance control in cats stepping on a split-belt treadmill. Forepaws and hindpaws were anesthetized unilaterally using lidocaine injections. We evaluated body balance in intact and compromised cutaneous feedback conditions during split-belt locomotion with belt-speed ratios of 0.5, 1.0, 1.5 and 2.0. Measures of body balance included step width, relative duration of limb support phases, lateral bias of center of mass (CoM) and margins of static and dynamic stability. In the intact condition, static and dynamic balance declined with increasing belt-speed ratio as a result of a lateral shift of the CoM toward the borders of support on the slower moving belt. Anesthesia of the ipsilateral paws improved locomotor balance with increasing belt-speed ratios by reversing the CoM shift, decreasing the relative duration of the two-limb support phase, increasing the duration of four- or three-limb support phases, and increasing the hindlimb step width and static stability. We observed no changes in most balance measures in anesthetized conditions during tied-belt locomotion at 0.4 m s-1 CoM lateral displacements closely resembled those of the inverted pendulum and of human walking. We propose that unilaterally compromised cutaneous feedback from the paw pads is compensated for by improving lateral balance and by shifting the body toward the anesthetized paws to increase tactile sensation during the stance phase.

A Prototype of a Neural, Powered, Transtibial Prosthesis for the Cat: Benchtop Characterization

We developed a prototype of a neural, powered, transtibial prosthesis for the use in a feline model of prosthetic gait. The prosthesis was designed for attachment to a percutaneous porous titanium implant integrated with bone, skin, and residual nerves and muscles. In the benchtop testing, the prosthesis was fixed in a testing rig and subjected to rhythmic vertical displacements and interactions with the ground at a cadence corresponding to cat walking. Several prosthesis functions were evaluated. They included sensing ground contact, control of transitions between the finite states of prosthesis loading, and a closed-loop modulation of the linear actuator gain in each loading cycle. The prosthetic design parameters (prosthesis length = 55 mm, mass = 63 g, peak extension moment = 1 Nm) corresponded closely to those of the cat foot-ankle with distal shank and the peak ankle extension moment during level walking. The linear actuator operated the prosthetic ankle joint using inputs emulating myoelectric activity of residual muscles. The linear actuator gain was modulated in each cycle to minimize the difference between the peak of ground reaction forces (GRF) recorded by a ground force sensor and a target force value. The benchtop test results demonstrated a close agreement between the GRF peaks and patterns produced by the prosthesis and by cats during level walking.

Longitudinal wearable tremor measurement system with activity recognition algorithms for upper limb tremor

Assessments of tremor characteristics by movement disorder physicians are usually done at single time points in clinic settings, so that the description of the tremor does not take into account the dependence of the tremor on specific behavioral situations. Moreover, treatment-induced changes in tremor or behavior cannot be quantitatively tracked for extended periods of time. We developed a wearable tremor measurement system with tremor and activity recognition algorithms for long-term upper limb behavior tracking, to characterize tremor characteristics and treatment effects in their daily lives. In this pilot study, we collected sensor data of arm movement from three healthy participants using a wrist device that included a 3-axis accelerometer and a 3-axis gyroscope, and classified tremor and activities within scenario tasks which resembled real life situations. Our results show that the system was able to classify the tremor and activities with 89.71% and 74.48% accuracies during the scenario tasks. From this results, we expect to expand our tremor and activity measurement in longer time period.

Quantitative assessment of arm tremor in people with neurological disorders

Abnormal oscillatory movement (i.e. tremor) is usually evaluated with qualitative assessment by clinicians, and quantified with subjective scoring methods. These methods are often inaccurate. We utilized a quantitative and standardized task based on the Fitts' law to assess the performance of arm movement with tremor by controlling a gyration mouse on a computer. The experiment included the center-out tapping (COT) and rectangular track navigation (RTN) tasks. We report the results of a pilot study in which we collected the performance for healthy participants in whom tremor was simulated by imposing oscillatory movements to the arm with a vibration motor. We compared their movement speed and accuracy with and without the artificial "tremor." We found that the artificial tremor significantly affected the path efficiency for both tasks (COT: 56.8 vs. 46.2%, p <; 0.05; RTN: 94.2 vs. 67.4%, p <; 0.05), and we were able to distinguish the presence of tremor. From this result, we expect to quantify severity of tremor and the effectiveness therapy for tremor patients.

A three-dimensional image processing program for accurate, rapid, and semi-automated segmentation of neuronal somata with dense neurite outgrowth

Three-dimensional (3-D) image analysis techniques provide a powerful means to rapidly and accurately assess complex morphological and functional interactions between neural cells. Current software-based identification methods of neural cells generally fall into two applications: (1) segmentation of cell nuclei in high-density constructs or (2) tracing of cell neurites in single cell investigations. We have developed novel methodologies to permit the systematic identification of populations of neuronal somata possessing rich morphological detail and dense neurite arborization throughout thick tissue or 3-D in vitro constructs. The image analysis incorporates several novel automated features for the discrimination of neurites and somata by initially classifying features in 2-D and merging these classifications into 3-D objects; the 3-D reconstructions automatically identify and adjust for over and under segmentation errors. Additionally, the platform provides for software-assisted error corrections to further minimize error. These features attain very accurate cell boundary identifications to handle a wide range of morphological complexities. We validated these tools using confocal z-stacks from thick 3-D neural constructs where neuronal somata had varying degrees of neurite arborization and complexity, achieving an accuracy of ≥95%. We demonstrated the robustness of these algorithms in a more complex arena through the automated segmentation of neural cells in ex vivo brain slices. These novel methods surpass previous techniques by improving the robustness and accuracy by: (1) the ability to process neurites and somata, (2) bidirectional segmentation correction, and (3) validation via software-assisted user input. This 3-D image analysis platform provides valuable tools for the unbiased analysis of neural tissue or tissue surrogates within a 3-D context, appropriate for the study of multi-dimensional cell-cell and cell-extracellular matrix interactions.

A PDMS-based integrated stretchable microelectrode array (isMEA) for neural and muscular surface interfacing

Numerous applications in neuroscience research and neural prosthetics, such as electrocorticogram (ECoG) recording and retinal prosthesis, involve electrical interactions with soft excitable tissues using a surface recording and/or stimulation approach. These applications require an interface that is capable of setting up high-throughput communications between the electrical circuit and the excitable tissue and that can dynamically conform to the shape of the soft tissue. Being a compliant material with mechanical impedance close to that of soft tissues, polydimethylsiloxane (PDMS) offers excellent potential as a substrate material for such neural interfaces. This paper describes an integrated technology for fabrication of PDMS-based stretchable microelectrode arrays (MEAs). Specifically, as an integral part of the fabrication process, a stretchable MEA is directly fabricated with a rigid substrate, such as a thin printed circuit board (PCB), through an innovative bonding technology-via-bonding-for integrated packaging. This integrated strategy overcomes the conventional challenge of high-density packaging for this type of stretchable electronics. Combined with a high-density interconnect technology developed previously, this stretchable MEA technology facilitates a high-resolution, high-density integrated system solution for neural and muscular surface interfacing. In this paper, this PDMS-based integrated stretchable MEA (isMEA) technology is demonstrated by an example design that packages a stretchable MEA with a small PCB. The resulting isMEA is assessed for its biocompatibility, surface conformability, electrode impedance spectrum, and capability to record muscle fiber activity when applied epimysially.

Enabling techniques for in vitro studies on mammalian spinal locomotor mechanisms

The neonatal rodent spinal cord maintained in vitro is a powerful model system to understand the central properties of spinal circuits generating mammalian locomotion. We describe three enabling approaches that incorporate afferent input and attached hindlimbs. (i) Sacral dorsal column stimulation recruits and strengthens ongoing locomotor-like activity, and implementation of a closed positive-feedback paradigm is shown to support its stimulation as an untapped therapeutic site for locomotor modulation. (ii) The spinal cord hindlimbs-restrained preparation allows suction electrode electromyographic recordings from many muscles. Inducible complex motor patterns resemble natural locomotion, and insights into circuit organization are demonstrated during spontaneous motor burst 'deletions', or following sensory stimuli such as tail and paw pinch. (iii) The spinal cord hindlimbs-pendant preparation produces unrestrained hindlimb stepping. It incorporates mechanical limb perturbations, kinematic analyses, ground reaction force monitoring, and the use of treadmills to study spinal circuit operation with movement-related patterns of sensory feedback while providing for stable whole-cell recordings from spinal neurons. Such techniques promise to provide important additional insights into locomotor circuit organization.

An effective lift-off method for patterning high-density gold interconnects on an elastomeric substrate

High-resolution, high-density gold interconnects are effectively patterned on an elastomeric substrate. A 3cm cable of ten gold wires with 10μm width and 20μm pitch is achieved, successfully demonstrating density increases of more than one order of magnitude from previously established work. Many applications in the fields of stretchable electronics and conformable neural interfaces will benefit from these fabrication developments.

High-density stretchable electronics: toward an integrated multilayer composite

High-density stretchable electronics is achieved using multilayer interconnects on an elastomeric substrate. Two major challenges associated with stretchable electronics—increasing integration density and improving electrical bonding—have been addressed by our innovative multilayer via-bonding technology. The resulting multichip-module architecture provides an elastic, high-density solution for numerous potential applications.

A PDMS-based conical-well microelectrode array for surface stimulation and recording of neural tissues

A method for fabricating polydimethylsiloxane (PDMS) based microelectrode arrays (MEAs) featuring novel conical-well microelectrodes is described. The fabrication technique is reliable and efficient, and facilitates controllability over both the depth and the slope of the conical wells. Because of the high-PDMS elasticity (as compared to other MEA substrate materials), this type of compliant MEA is promising for acute and chronic implantation in applications that benefit from conformable device contact with biological tissue surfaces and from minimal tissue damage. The primary advantage of the conical-well microelectrodes--when compared to planar electrodes--is that they provide an improved contact on tissue surface, which potentially provides isolation of the electrode microenvironment for better electrical interfacing. The raised wells increase the uniformity of current density distributions at both the electrode and tissue surfaces, and they also protect the electrode material from mechanical damage (e.g., from rubbing against the tissue). Using this technique, electrodes have been fabricated with diameters as small as 10 μm and arrays have been fabricated with center-to-center electrode spacings of 60 μm. Experimental results are presented, describing electrode-profile characterization, electrode-impedance measurement, and MEA-performance evaluation on fiber bundle recruitment in spinal cord white matter.

Neuromechanical tuning of nonlinear postural control dynamics

Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.

A retrofitted neural recording system with a novel stimulation IC to monitor early neural responses from a stimulating electrode

Extracellular electrical stimulation is increasingly used for in vitro neural experimentation, including brain slices and cultured cells. Although it is desirable to record directly from the stimulating electrode, relatively high stimulation levels make it extremely difficult to record immediately after the stimulation. We have shown that this is feasible by a stimulation system (analog IC) that includes the feature of active electrode discharge. Here, we piggybacked the new IC onto an existing recording amplifier system, making it possible to record neural responses directly from the stimulating channel as early as 3 ms after the stimulation. We used the retrofitted recording system to stimulate and record from dissociated hippocampal neurons in culture. This new strategy of retrofitting an existing system is a simple but attractive approach for instrumentation designers interested in adding a new feature for extracellular recording without replacing already existing recording systems.

A lithographically-patterned, elastic multi-electrode array for surface stimulation of the spinal cord

A new, scalable process for microfabrication of a silicone-based, elastic multi-electrode array (MEA) is presented. The device is constructed by spinning poly(dimethylsiloxane) (PDMS) silicone elastomer onto a glass slide, depositing and patterning gold to construct wires and electrodes, spinning on a second PDMS layer, and then micropatterning the second PDMS layer to expose electrode contacts. The micropatterning of PDMS involves a custom reactive ion etch (RIE) process that preserves the underlying gold thin film. Once completed, the device can be removed from the glass slide for conformal interfacing with neural tissue. Prototype MEAs feature electrodes smaller than those known to be reported on silicone substrate (60 microm diameter exposed electrode area) and were capable of selectively stimulating the surface of the in vitro isolated spinal cord of the juvenile rat. Stretchable serpentine traces were also incorporated into the functional PDMS-based MEA, and their implementation and testing is described.

Experimental platform for the study of region specific excitation and inhibition in neural tissue

Willfully controlling the focus of an extracellular stimulus remains a significant challenge in the development of neural prosthetics and therapeutic devices. In part, this is due to the fact that experimental validation of the evoked response to stimuli is an arduous and time-consuming task. The development of a high-throughput data acquisition and analysis tool would greatly facilitate the design of spatially selective stimulation protocols. We present an automated imaging system that can optically track and identify the action potentials of individual neurons evoked by coordinated stimulus waveforms applied at multiple electrodes. This system can simultaneously provide arbitrary current waveforms to four electrodes, and it is capable of automatically monitoring the cellular responses of every neuron in a cultured network within a 1.6 x 1.6 mm area. The purpose of this platform is to develop stimulus protocols that exploit the benefits of multi-polar field shaping and temporal ion-channel manipulation to localize cellular excitation beyond the vicinity of the electrode. Preliminary single electrode experiments demonstrate that spatially selective stimulus suppression may be achieved with cathodic, depolarizing prepulses that induce a sub-threshold refractory state in neighboring neurons. Coordinated, multi-site stimuli could potentially take advantage of this refractory state to direct the stimulus focus away from the surrounding area of the electrode and into the inter-electrode spaces.

A comparison of resonance tuning with positive versus negative sensory feedback

We used a computational model of rhythmic movement to analyze how the connectivity of sensory feedback affects the tuning of a closed-loop neuromechanical system to the mechanical resonant frequency (omega(r)). Our model includes a Matsuoka half-center oscillator for a central pattern generator (CPG) and a linear, one-degree-of-freedom system for a mechanical component. Using both an open-loop frequency response analysis and closed-loop simulations, we compared resonance tuning with four different feedback configurations as the mechanical resonant frequency, feedback gain, and mechanical damping varied. The feedback configurations consisted of two negative and two positive feedback connectivity schemes. We found that with negative feedback, resonance tuning predominantly occurred when omega(r) was higher than the CPG's endogenous frequency (omega(CPG)). In contrast, with the two positive feedback configurations, resonance tuning only occurred if omega(r) was lower than omega(CPG). Moreover, the differences in resonance tuning between the two positive (negative) feedback configurations increased with increasing feedback gain and with decreasing mechanical damping. Our results indicate that resonance tuning can be achieved with positive feedback. Furthermore, we have shown that the feedback configuration affects the parameter space over which the endogenous frequency of the CPG or resonant frequency the mechanical dynamics dominates the frequency of a rhythmic movement.

A parameter-space search algorithm tested on a Hodgkin-Huxley model

We demonstrate a parameter-space search algorithm using a computational model of a single-compartment neuron with conductance-based Hodgkin-Huxley dynamics. To classify bursting (the desired behavior), we use a simple cost function whose inputs are derived from the frequency content of the neural output. Our method involves the repeated use of a stochastic gradient descent-type algorithm to locate parameter values that allow the neural model to produce bursting within a specified tolerance. We demonstrate good results, including those showing that the utility of our algorithm improves as the pre-defined allowable parameter ranges increase and that the initial approach to our method is computationally efficient.

Functional consequences of model complexity in rhythmic systems: I. Systematic reduction of a bursting neuron model

Neural models are increasingly being used as design components of physical systems. In order to most effectively utilize neuronal models in these novel contexts, we need to develop design rules for neuronal systems that relate how model design affects overall system performance. In this paper and a companion article, we investigate how the complexity of a neural model affects the performance of a two-cell oscillator built from the model. In this paper, we create a series of related neuron models with different mathematical complexity. Starting with a complex mechanistic model of a bursting neuron, we use a variety of techniques to create a series of simplified neuron models. These three reduced models produce bursting activity that is qualitatively very similar to the original model. In the following companion article, we investigate the functional performance of oscillators built from these models.

Functional consequences of model complexity in rhythmic systems: II. Systems performance of model and hybrid oscillators

Neural models are increasingly being used as design components of physical systems. In order to best use models in these novel contexts, we must develop design rules that describe how decisions in model construction relate to the functional performance of the resulting system. In the accompanying paper, we described a series of related neuron models of varying complexity. Here, we use these models to build several half-center oscillators, and investigate how model complexity influences the robustness and flexibility of these oscillators. Our results indicate that model complexity has a significant effect on the robustness and flexibility of systems that incorporate neural models.

Multielectrode impedance tuning: reducing noise and improving stimulation efficacy

Multielectrode arrays (MEAs) have emerged as a leading technology for extracellular, electrophysiological investigations of neuronal networks. The study of biological neural networks is a difficult task that is further confounded by mismatches in electrode impedance. Electrode impedance plays an important role in shaping incoming signals, determining thermal noise, and influencing the efficacy of stimulation. Our approach to optimally reduce thermal noise and improving the reliability of stimulation is twofold minimize the impedance and match it across all electrodes. To this aim, we have fabricated a device that allows for the automated, impedance-controlled electroplating of micro-electrodes. This device is capable of rapidly (minutes) producing uniformly low impedances across all electrodes in an MEA. The need for uniformly low impedances is important for controlled studies of neuronal networks; this need will increase in the future as MEA technology scales from tens of electrodes to thousands.

A comparative analysis of multi-conductance neuronal models in silico

We demonstrate that a previously presented flexible silicon-neuron architecture can implement three disparate conductance-based neuron models with both fast and slow dynamics. By exploiting the real-time nature of this physical implementation, we mapped the model dynamics across a large region of parameter space. We also found that two of these dynamically different models represent points in a contiguous bursting space that spans between the two models. By systematically varying the model parameters, we also found that multiple, diverse trajectories in parameter space connected the two canonical bursting points. In addition, we found that the combination of parameter values keeps the neuron in the bursting region. These findings demonstrate the usefulness of the silicon-neuron architecture as a neural-modeling tool and illustrate its versatility as a platform for a multi-behavioral neuron that resembles its living analog.

Sensory Feedback in a Half-Center Oscillator Model

We hypothesize that one role of sensorimotor feedback for rhythmic movements in biological organisms is to synchronize the frequency of movements to the mechanical resonance of the body. Our hypothesis is based on recent studies that have shown the advantage of moving at mechanical resonance and how such synchronization may be possible in biology. We test our hypothesis by developing a physical system that consists of a silicon-neuron central pattern generator (CPG), which controls the motion of a beam, and position sensors that provide feedback information to the CPG. The silicon neurons that we use are integrated circuits that generate neural signals based on the Hodgkin-Huxley dynamics. We use this physical system to develop a model of the interaction between the sensory feedback and the complex dynamics of the neurons to create the closed-loop system behavior. This model is then used to describe the conditions under which our hypothesis is valid and the general effects of sensorimotor feedback on the rhythmic movements of this system.

Two-dimensional variation of bursting properties in a silicon-neuron half-center oscillator

We are developing hardware models of central pattern generators (CPGs) to enhance neural prostheses, create biologically based controllers for autonomous machines, and to better understand how biology creates stable and robust movements. Previously, we designed and implemented an analog integrated circuit model of a neuron with Hodgkin-Huxley like dynamics, the silicon neuron. In this work, we use silicon neurons to implement a half-center oscillator and show that the underlying dynamics of this CPG produce bursting behaviors that are well matched to the biological counterpart on which our model is based. In addition, we demonstrate the robustness of the bursting behavior by systematically varying two parameters in each silicon neuron and mapping the corresponding effects on the bursting.

An algorithmic method for reducing conductance-based neuron models

Although conductance-based neural models provide a realistic depiction of neuronal activity, their complexity often limits effective implementation and analysis. Neuronal model reduction methods provide a means to reduce model complexity while retaining the original model's realism and relevance. Such methods, however, typically include ad hoc components that require that the modeler already be intimately familiar with the dynamics of the original model. We present an automated, algorithmic method for reducing conductance-based neuron models using the method of equivalent potentials (Kelper et al., Biol Cybern 66(5):381-387, 1992) Our results demonstrate that this algorithm is able to reduce the complexity of the original model with minimal performance loss, and requires minimal prior knowledge of the model's dynamics. Furthermore, by utilizing a cost function based on the contribution of each state variable to the total conductance of the model, the performance of the algorithm can be significantly improved.

Passive dynamics of a hybrid neuromechanical joint incorporating living muscle

We have developed a hybrid neuromechanical joint to investigate the nonlinear properties of muscle in a physiologically relevant context. We constructed the hybrid system by connecting a live frog gastrocnemius muscle to a joint which is simulated as an inverted pendulum. We first tested this hybrid system with a spring as the actuator to ensure that the perturbation-response trajectories using living muscle would accurately describe the mechanical properties of the muscle. This hybrid neuromechanical system, with muscle as the actuator, responded to impulse torque perturbations with stable damped oscillations. Joint settling times to perturbations were measured while the joint mass and the initial muscle length were varied. Passive muscle alone stabilized small perturbations. With heavier joint masses and shorter initial muscle lengths the system became increasingly unstable. We found that the hybrid neuromechanical joint is an accurate tool to study the neuromuscular system.

Mechanical trauma induces immediate changes in neuronal network activity

During a traumatic insult to the brain, tissue is subjected to large stresses at high rates which often surpass cellular thresholds leading to cell dysfunction or death. The acute response of neurons to a mechanical trauma, however, is poorly understood. Plasma membrane disruption may be the earliest cellular outcome from a mechanical trauma. The increase in membrane permeability due to such disruptions may therefore play an important role in the initiation of deleterious cascades following brain injury. The immediate consequences of an increase in plasma membrane permeability on the electrophysiological behavior of a neuronal network exposed to the trauma have not been elucidated. We have developed an in vitro model of traumatic brain injury (TBI) that utilizes a novel device capable of applying stress at high rates to neuronal cells cultured on a microelectrode array. The mechanical insult produced by the device caused a transient increase in neuronal plasma membrane permeability, which subsided after 10 min. We were able to monitor acute spontaneous electrophysiological activity of injured cultures for at least 10 min following the insult. Firing frequency, average burst interval and spikes within burst were assessed before and after injury. The electrophysiological responses to the insult were heterogeneous, although an increase in burst intervals and in the variability of the assessed parameters were common. This study provides a multi-faceted approach to elucidate the role of neuronal plasma membrane disruptions in TBI and its functional consequences.

A multiconductance silicon neuron with biologically matched dynamics

We have designed, fabricated, and tested an analog integrated-circuit architecture to implement the conductance-based dynamics that model the electrical activity of neurons. The dynamics of this architecture are in accordance with the Hodgkin-Huxley formalism, a widely exploited, biophysically plausible model of the dynamics of living neurons. Furthermore the architecture is modular and compact in size so that we can implement networks of silicon neurons, each of desired complexity, on a single integrated circuit. We present in this paper a six-conductance silicon-neuron implementation, and characterize it in relation to the Hodgkin-Huxley formalism. This silicon neuron incorporates both fast and slow ionic conductances, which are required to model complex oscillatory behaviors (spiking, bursting, subthreshold oscillations).

An integrated circuit implementation of the Huxley sarcomere model

We have developed an integrated circuit to simulate the mechanical behavior demonstrated by sarcomeres found in skeletal muscle. The circuit is based upon the mathematical description of the attachment and detachment dynamics of crossbridge populations and the force generated by the crossbridges, originally formulated by A. F. Huxley. We describe the process of designing the circuit model from the mathematical model, present the sarcomere circuit implementation, and demonstrate the transient and steady-state behaviors that the fabricated circuit produces. Comparison of our results to published mechanical behavior of skeletal muscle shows qualitative similarities. We conclude that the circuit muscle model exhibits the potential for real-time simulation of muscle contractions and could be used to give engineered systems muscle-like properties.

Modeling alternation to synchrony with inhibitory coupling: a neuromorphic VLSI approach

We developed an analog very large-scale integrated system of two mutually inhibitory silicon neurons that display several different stable oscillations. For example, oscillations can be synchronous with weak inhibitory coupling and alternating with relatively strong inhibitory coupling. All oscillations observed experimentally were predicted by bifurcation analysis of a corresponding mathematical model. The synchronous oscillations do not require special synaptic properties and are apparently robust enough to survive the variability and constraints inherent in this physical system. In biological experiments with oscillatory neuronal networks, blockade of inhibitory synaptic coupling can sometimes lead to synchronous oscillations. An example of this phenomenon is the transition from alternating to synchronous bursting in the swimming central pattern generator of lamprey when synaptic inhibition is blocked by strychnine. Our results suggest a simple explanation for the observed oscillatory transitions in the lamprey central pattern generator network: that inhibitory connectivity alone is sufficient to produce the observed transition.