Signal Modeling and Data Reduction for Wireless Brain-Machine Interfaces

Brain-machine interfaces (BMIs) provide a uni- or bidirectional communication link between the central nervous system and the outside world. This link facilitates the studying of neuronal mechanisms underlying behavior as well as the treatment of neurological disease. Wired BMIs are limited in the sense that they restrict the mobility of the subject and they increase the risks for post-surgical complications. While wireless BMIs ideally solve these problems, their designers face the challenge of combining high information throughput with limited wireless link capacity and energy resources. Therefore, measures have to be taken to maximize the utilization of the wireless link and energy resources by designing computationally efficient and reliable data reduction techniques. The design and validation of such techniques requires the presence of well defined test data, where the true information content is known a priori. This thesis deals with both the modeling of the neural signal to provide realistic and practical means of generating test data, as well as low-complexity methods for data reduction that lead to efficient utilization of the wireless link and the energy resources at hand. The main part of the thesis is a collection of papers that address these aspects. Paper I presents the design and implementation of a simple telemetry system for the wireless transmission of neural data from four measurement channels. This paper highlights some of the design challenges that need to be considered and thereby serves as a pilot investigation for the following papers. Paper II presents a recording model and a simulation tool for generating single-channel test recordings for the validation of algorithms for spike detection and spike sorting. Having set up the geometry of the recording, each neuron is assigned a random spike waveforms from a library of experimentally obtained templates. The contribution of each neuron is generated by adding the corresponding waveform at randomly generated spike times and the spike trains are added up to form the entire recording. Spike times are modeled by a renewal process. The model is evaluated in terms of realism by comparing the power spectral density and autocorrelation of synthetic biological noise generated by the model, to noise obtained from real recordings. Paper III extends the finite spike library provided in paper II in order to provide a greater, still realistic, variation in spike waveforms. Principal component analysis and Gaussian mixture models are used to model the statistical properties of the original spike library and the statistical model can then be used to generate an arbitrary number of spike wavforms with realistic properties. The extension is shown to be usable in providing access to arbitrarily large libraries of spikes with realistic properties. Paper IV uses the models presented in papers II and III to explore the effects of sampling rate and resolution on the performance in spike detection and spike sorting at various noise levels and numbers of target neurons. Performance curves are analyzed to find sampling rate and resolution breakpoints for spike detection and spike sorting. These breakpoints serve as guidelines for selecting sampling parameters when dimensioning wireless BMIs. The paper presents methods for quantifying the accuracy in spike detection and spike sorting and provides general insight into how the performance of these processing tasks are influenced by sampling parameters, noise level and number of target units. Paper V presents a preliminary study of the characteristic relationship between physical electrode movements and movements of detected spikes in feature space, using the signal models presented in paper VI. We then model this relationship as a linear transformation between two coordinate systems and show that given that a training procedure is introduced at the time of electrode insertion, future electrode movements can be estimated directly from the feature space representation of spikes. Paper VI presents a new, computationally and memory efficient approach for modeling the extracellular signal. We use traditional compression techniques and polynomial fitting to derive a deterministic model that can be used for fast calculation of spike waveforms in arbitrary measurement points surrounding a compartment model of a neuron. Four different neuron models are derived and they are all shown to accurately predict the spike waveforms produced by the original compartment model, both in terms of spike shape and amplitude. The model is implemented into a simulation tool that efficiently and realistically synthesizes recordings with multielectrode arrays of arbitrary geometries. Paper VII addresses low-complexity methods of compressing detected spike waveforms in wireless BMIs to ensure efficient use of the wireless link and energy resources at hand. The paper shows that given the correct choice of overall system architecture and spike detector, spike waveforms can be compressed with fixed generic compression bases, derived from experimentally obtained spike libraries, without significant loss in accuracy in spike reconstruction and sorting