Sparse Signal Representation in Digital and Biological Systems

Theories of sparse signal representation, wherein a signal is decomposed as the sum of a small number of constituent elements, play increasing roles in both mathematical signal processing and neuroscience. This happens despite the differences between signal models in the two domains. After reviewing preliminary material on sparse signal models, I use work on compressed sensing for the electron tomography of biological structures as a target for exploring the efficacy of sparse signal reconstruction in a challenging application domain. My research in this area addresses a topic of keen interest to the biological microscopy community, and has resulted in the development of tomographic reconstruction software which is competitive with the state of the art in its field. Moving from the linear signal domain into the nonlinear dynamics of neural encoding, I explain the sparse coding hypothesis in neuroscience and its relationship with olfaction in locusts. I implement a numerical ODE model of the activity of neural populations responsible for sparse odor coding in locusts as part of a project involving offset spiking in the Kenyon cells. I also explain the validation procedures we have devised to help assess the model's similarity to the biology. The thesis concludes with the development of a new, simplified model of locust olfactory network activity, which seeks with some success to explain statistical properties of the sparse coding processes carried out in the network.

INTEGRATED THRESHOLD-ACTIVATED FEEDBACK MICROSYSTEM FOR REAL-TIME CHARACTERIZATION, SENSING AND TREATMENT OF BACTERIAL BIOFILMS

Biofilms are the primary cause of clinical bacterial infections and are impervious to typical amounts of antibiotics, necessitating very high doses for treatment. Therefore, it is highly desirable to develop new alternate methods of treatment that can complement or replace existing approaches using significantly lower doses of antibiotics. Current standards for studying biofilms are based on end-point studies that are invasive and destroy the biofilm during characterization. This dissertation presents the development of a novel real-time sensing and treatment technology to aid in the non-invasive characterization, monitoring and treatment of bacterial biofilms. The technology is demonstrated through the use of a high-throughput bifurcation based microfluidic reactor that enables simulation of flow conditions similar to indwelling medical devices. The integrated microsystem developed in this work incorporates the advantages of previous in vitro platforms while attempting to overcome some of their limitations. Biofilm formation is extremely sensitive to various growth parameters that cause large variability in biofilms between repeated experiments. In this work we investigate the use of microfluidic bifurcations for the reduction in biofilm growth variance. The microfluidic flow cell designed here spatially sections a single biofilm into multiple channels using microfluidic flow bifurcation. Biofilms grown in the bifurcated device were evaluated and verified for reduced biofilm growth variance using standard techniques like confocal microscopy. This uniformity in biofilm growth allows for reliable comparison and evaluation of new treatments with integrated controls on a single device. Biofilm partitioning was demonstrated using the bifurcation device by exposing three of the four channels to various treatments. We studied a novel bacterial biofilm treatment independent of traditional antibiotics using only small molecule inhibitors of bacterial quorum sensing (analogs) in combination with low electric fields. Studies using the bifurcation-based microfluidic flow cell integrated with real-time transduction methods and macro-scale end-point testing of the combination treatment showed a significant decrease in biomass compared to the untreated controls and well-known treatments such as antibiotics. To understand the possible mechanism of action of electric field-based treatments, fundamental treatment efficacy studies focusing on the effect of the energy of the applied electrical signal were performed. It was shown that the total energy and not the type of the applied electrical signal affects the effectiveness of the treatment. The linear dependence of the treatment efficacy on the applied electrical energy was also demonstrated. The integrated bifurcation-based microfluidic platform is the first microsystem that enables biofilm growth with reduced variance, as well as continuous real-time threshold-activated feedback monitoring and treatment using low electric fields. The sensors detect biofilm growth by monitoring the change in impedance across the interdigitated electrodes. Using the measured impedance change and user inputs provided through a convenient and simple graphical interface, a custom-built MATLAB control module intelligently switches the system into and out of treatment mode. Using this self-governing microsystem, in situ biofilm treatment based on the principles of the bioelectric effect was demonstrated by exposing two of the channels of the integrated bifurcation device to low doses of antibiotics.