Characterization of Retinal Ganglion Cell Responses to Electrical Stimulation Using White Noise

Retinitis pigmentosa and age-related macular degeneration are two leading causes of degenerative blindness. While there is still not a definitive course of treatment for either of these diseases, there is currently the world over, many different treatment strategies being explored. Of these various strategies, one of the most successful has been retinal implants. Retinal implants are microelectrode or photodiode arrays, that are implanted in the eye of a patient, to electrically stimulate the degenerating retina. Clinical trials have shown that many patients implanted with such a device, are able to regain a certain degree of functional vision. However, while the results of these ongoing clinical trials have been promising, there are still many technical challenges that need to be overcome. One of the biggest challenges facing present implants is the inability to preferentially stimulate different retinal pathways. This is because retinal implants use large-amplitude current or voltage pulses. This in turn leads to the indiscriminate activation of multiple classes of retinal ganglion cells (RGCs), and therefore, an overall reduction in the restored visual acuity. To tackle this issue, we decided to explore a novel stimulus paradigm, in which we present to the retina, a stream of smaller-amplitude subthreshold voltage pulses. By then correlating the retinal spikes to the stimuli preceding them, we calculate temporal input filters for various classes of RGCs, using a technique called spike-triggered averaging (STA). In doing this, we found that ON and OFF RGCs have electrical filters, which are very distinct from each other. This finding creates the possibility for the selective activation of the retina through the use of STA-based waveforms. Finally, using statistical models, we verify how well these temporal filters can predict RGC responses to novel electrical stimuli. In a broad sense, our work represents the successful application of systems engineering tools to retinal prosthetics, in an attempt to answer one of the field’s most difficult questions, namely selective stimulation of the retina

Characterizing Retinal Ganglion Cell Responses to Electrical Stimulation Using Generalized Linear Models

The ability to preferentially stimulate different retinal pathways is an important area of research for improving visual prosthetics. Recent work has shown that different classes of retinal ganglion cells (RGCs) have distinct linear electrical input filters for low-amplitude white noise stimulation. The aim of this study is to provide a statistical framework for characterizing how RGCs respond to white-noise electrical stimulation. We used a nested family of Generalized Linear Models (GLMs) to partition neural responses into different components-progressively adding covariates to the GLM which captured non-stationarity in neural activity, a linear dependence on the stimulus, and any remaining non-linear interactions. We found that each of these components resulted in increased model performance, but that even the non-linear model left a substantial fraction of neural variability unexplained. The broad goal of this paper is to provide a much-needed theoretical framework to objectively quantify stimulus paradigms in terms of the types of neural responses that they elicit (linear vs. non-linear vs. stimulus-independent variability). In turn, this aids the prosthetic community in the search for optimal stimulus parameters that avoid indiscriminate retinal activation and adaptation caused by excessively large stimulus pulses, and avoid low fidelity responses (low signal-to-noise ratio) caused by excessively weak stimulus pulses

Energetics Based Spike Generation of a Single Neuron: Simulation Results and Analysis

Existing current based models that capture spike activity, though useful in studying information processing capabilities of neurons, fail to throw light on their internal functioning. It is imperative to develop a model that captures the spike train of a neuron as a function of its intracellular parameters for non-invasive diagnosis of diseased neurons. This is the first ever article to present such an integrated model that quantifies the inter-dependency between spike activity and intracellular energetics. The generated spike trains from our integrated model will throw greater light on the intracellular energetics than existing current models. Now, an abnormality in the spike of a diseased neuron can be linked and hence effectively analyzed at the energetics level. The spectral analysis of the generated spike trains in a time–frequency domain will help identify abnormalities in the internals of a neuron. As a case study, the parameters of our model are tuned for Alzheimer’s disease and its resultant spike trains are studied and presented. This massive initiative ultimately aims to encompass the entire molecular signaling pathways of the neuronal bioenergetics linking it to the voltage spike initiation and propagation; due to the lack of experimental data quantifying the inter dependencies among the parameters, the model at this stage adopts a particular level of functionality and is shown as an approach to study and perform disease modeling at the spike train and the mitochondrial bioenergetics level

FRI SAMPLING AND RECONSTRUCTION OF ASYMMETRIC PULSES

We consider the problem of modelling asymmetric pulse trains as finite-rate-of-innovation (FRI) signals. In particular, we show that the sum of amplitude-scaled and time-shifted pulses with different asymmetry factors is an FRI signal. Such signals frequently arise in applications such as ultrasound and radio detection and ranging (RADAR) where the received signal has skewed pulses. In this paper, we model the asymmetric component of a pulse using its derivative. A sampling kernel with a sum-of-sincs frequency response is used to measure the samples, and a modified annihilating filter method is applied on the samples to estimate the parameters of the FRI signal. We show accurate reconstruction for signals containing asymmetric Gaussian, Cauchy-Lorentz, and sinc pulses. Analysis of the proposed scheme in the presence of noise shows that the error in the estimated parameters decreases by oversampling the signal

Asymmetric Pulse Modeling for FRI Sampling

We consider sampling and reconstruction of finite-rate-of-innovation (FRI) signals such as a train of pulses, where the pulses have varying degrees of asymmetry. We address the problem of asymmetry modeling starting from a given symmetric prototype. We show that among the class of unitary operators that are linear and invariant to translation and scale, the fractional Hilbert (FrH) operator is unique for parametrically modeling pulse asymmetry. The FrH operator is obtained by a trigonometric interpolation between the standard Hilbert and identity operators, where the interpolation weights are determined by the degree of asymmetry. The FrH operators are also steerable, which allows for estimation of the asymmetry factors, in addition to the delays and amplitudes, using the high-resolution spectral estimation techniques that are used for solving standard FRI problems. We also develop the discrete counterpart using discrete FrH operators and show that all the desirable properties carry over smoothly to the discrete setting as well. We derive closed-form expressions for the Cramer-Rao bounds and Hammersley-Chapman-Robbins bound, on the variances of the estimators for continuous and discrete parameters, respectively. Experimental results show that the proposed estimators have variances that meet the lower bounds. We demonstrate an application of the proposed discrete FrH methodology on real electrocardiogram (ECG) signals in the presence of noise. Specifically, we show how the asymmetry of QRS complexes in various channels of an ECG signal could be modeled accurately