Encoding and processing of sensory information in neuronal spike trains

Recently, a statistical signal-processing technique has allowed the information carried by single spike trains of sensory neurons on time-varying stimuli to be characterized quantitatively in a variety of preparations. In weakly electric fish, its application to first-order sensory neurons encoding electric field amplitude (P-receptor afferents) showed that they convey accurate information on temporal modulations in a behaviorally relevant frequency range (<80 Hz). At the next stage of the electrosensory pathway (the electrosensory lateral line lobe, ELL), the information sampled by first-order neurons is used to extract upstrokes and downstrokes in the amplitude modulation waveform. By using signal-detection techniques, we determined that these temporal features are explicitly represented by short spike bursts of second-order neurons (ELL pyramidal cells). Our results suggest that the biophysical mechanism underlying this computation is of dendritic origin. We also investigated the accuracy with which upstrokes and downstrokes are encoded across two of the three somatotopic body maps of the ELL (centromedial and lateral). Pyramidal cells of the centromedial map, in particular I-cells, encode up- and downstrokes more reliably than those of the lateral map. This result correlates well with the significance of these temporal features for a particular behavior (the jamming avoidance response) as assessed by lesion experiments of the centromedial map

Simulating and optimizing electrical current flow and neuronal activation in retinal implants

© 2018 Dr Timothy Bede Esler[Abstract Withheld

Brain Microstructure: Impact of the Permeability on Diffusion MRI

Diffusion Magnetic Resonance Imaging (dMRI) enables a non invasive in-vivo characterization of the brain tissue. The disentanglement of each microstructural property reflected on the total dMRI signal is one of the hottest topics in the field. The dMRI reconstruction techniques ground on assumptions on the signal model and consider the neurons axons as impermeable cylinders. Nevertheless, interactions with the environment is characteristic of the biological life and diffusional water exchange takes place through cell membranes. Myelin wraps axons with multiple layers constitute a barrier modulating exchange between the axon and the extracellular tissue. Due to the short transverse relaxation time (T2) of water trapped between sheets, myelin contribution to the diffusion signal is often neglected. This thesis aims to explore how the exchange influences the dMRI signal and how this can be informative on myelin structure. We also aimed to explore how recent dMRI signal reconstruction techniques could be applied in clinics proposing a strategy for investigating the potential as biomarkers of the derived tissue descriptors. The first goal of the thesis was addressed performing Monte Carlo simulations of a system with three compartments: intra-axonal, spiraling myelin and extra-axonal. The experiments showed that the exchange time between intra- and extra-axonal compartments was on the sub-second level (and thus possibly observable) for geometries with small axon diameter and low number of wraps such as in the infant brain and in demyelinating diseases. The second goal of the thesis was reached by assessing the indices derived from three dimensional simple harmonics oscillator-based reconstruction and estimation (3D-SHORE) in stroke disease. The tract-based analysis involving motor networks and the region-based analysis in grey matter (GM) were performed. 3D-SHORE indices proved to be sensitive to plasticity in both white matter (WM) and GM, highlighting their viability as biomarkers in ischemic stroke. The overall study could be considered the starting point for a future investigation of the interdependence of different phenomena like exchange and relaxation related to the established dMRI indices. This is valuable for the accurate dMRI data interpretation in heterogeneous tissues and different physiological conditions

Applicability of Quantitative Functional MRI Techniques for Studies of Brain Function at Ultra-High Magnetic Field

This thesis describes the development, implementation and application of various quantitative functional magnetic resonance imaging (fMRI) approaches at ultra-high magnetic field including the assessment with regards to applicability and reproducibility. Functional MRI (fMRI) commonly uses the blood oxygenation level dependent (BOLD) contrast to detect functionally induced changes in the oxy-deoxyhaemoglobin composition of blood which reflect cerebral neural activity. As these blood oxygenation changes do not only occur at the activation site but also downstream in the draining veins, the spatial specificity of the BOLD signal is limited. Therefore, the focus has moved towards more quantitative fMRI approaches such as arterial spin labelling (ASL), vascular space occupancy (VASO) or calibrated fMRI which measure quantifiable physiologically and physically relevant parameters such as cerebral blood flow (CBF), cerebral blood volume (CBV) or cerebral metabolic rate of oxygen (CMRO2), respectively. In this thesis a novel MRI technique was introduced which allowed the simultaneous acquisition of multiple physiological parameters in order to beneficially utilise their spatial and temporal characteristics. The advantages of ultra-high magnetic field were utilised to achieve higher signal-to-noise and contrast-to-noise ratios compared to lower field strengths. This technique was successfully used to study the spatial and temporal characteristics of CBV, CBF and BOLD in the visual cortex. This technique is the first one that allows simultaneous acquisition of CBV, CBF and BOLD weighted fMRI signals in the human brain at 7 Tesla. Additionally, this thesis presented a calibrated fMRI technique which allowed the quantitative estimation of changes in cerebral oxygen metabolism at ultra-high field. CMRO2 reflects the amount of thermodynamic work due to neural activity and is therefore a significant physical measure in neuroscience. The calibrated fMRI approach presented in this thesis was optimised for the use at ultra-high field by adjusting the MRI parameters as well as implementing a specifically designed radio-frequency (RF) pulse. A biophysical model was used to calibrate the fMRI data based on the simultaneous acquisition of BOLD and CBF weighted MRI signals during a gas-breathing challenge. The reproducibility was assessed across multiple brain regions and compared to that of various physiologically relevant parameters. The results indicate that the degree of intra-subject variation for calibrated fMRI is lower than for the classic BOLD contrast or ASL. Consequently, calibrated fMRI is a viable alternative to classic fMRI contrasts with regards to spatial specificity as well as functional reproducibility. This calibrated fMRI approach was also compared to a novel direct calibration technique which relies on complete venous oxygenation saturation during the calibration scan via a gas-breathing challenge. This thesis introduced several reliable quantitative fMRI approaches at 7 Tesla and the results presented are a step forward to the wider application of quantitative fMRI.:1 Introduction 3 2 Background to Functional Magnetic Resonance Imaging 7 2.1 Magnetic Resonance 7 2.1.1 Quantum Mechanics 7 2.1.2 The Classical Point of View 10 2.1.3 Radio Frequency Pulses 12 2.1.4 Relaxation Effects 13 2.1.5 The Bloch Equations 15 2.2 Magnetic Resonance Imaging 16 2.2.1 Data Acquisition 16 2.2.2 Image Formation 17 2.2.2.1 Slice Selection 17 2.2.2.2 Frequency Encoding 18 2.2.2.3 Phase Encoding 19 2.2.2.4 Mathematics of Image Formation 20 2.2.2.5 Signal Formation 22 2.3 Advanced Imaging Methods 24 2.3.1 Echo-Planar Imaging (EPI) 24 2.3.2 Partial Fourier Acquisition 25 2.3.3 Generalised Autocalibrating Partially Parallel Acquisition (GRAPPA) 25 2.3.4 Inversion Recovery (IR) 26 2.3.5 Adiabatic Inversion 26 2.3.5.1 Hyperbolic Secant (HS) RF pulses 28 2.3.5.2 Time Resampled Frequency Offset Corrected Inversion (tr-FOCI) RF Pulses 28 2.4 Physiological Background 29 2.4.1 Neuronal Activity 30 2.4.2 Energy Metabolism 31 2.4.3 Physiological Changes During Brain Activation 32 2.4.4 The BOLD Contrast 34 2.4.5 Disadvantages of the BOLD Contrast 35 2.5 Arterial Spin Labelling (ASL) 35 2.5.1 Pulsed Arterial Spin Labelling 37 2.5.2 Arterial Spin Labelling at Ultra-High Field 41 2.6 Vascular Space Occupancy (VASO) 42 2.6.1 VASO at Ultra-High Field 44 2.6.2 Slice-Saturation Slab-Inversion (SS-SI) VASO 45 2.7 Calibrated Functional Magnetic Resonance Imaging 47 2.7.1 The Davis Model 47 2.7.2 The Chiarelli Model 50 2.7.3 The Generalised Calibration Model (GCM) 52 3 Materials and Methods 53 3.1 Scanner Setup 53 3.2 Gas Delivery and Physiological Monitoring System 53 3.3 MRI Sequence Developments 55 3.3.1 Tr-FOCI Adiabatic Inversion 55 3.3.2 Optimisation of the PASL FAIR QUIPSSII Sequence Parameters 60 3.3.3 Multi-TE Multi-TI EPI 64 4 Experiment I: Comparison of Direct and Modelled fMRI Calibration 68 4.1 Background Information 68 4.2 Methods 69 4.2.1 Experimental Design 69 4.2.2 Visuo-Motor Task 70 4.2.3 Gas Manipulations 71 4.2.4 Scanning Parameters 71 4.2.5 Data Analysis 72 4.2.6 M-value Modelling 72 4.2.7 Direct M-Value Estimation 73 4.3 Results 74 4.4 Discussion 79 4.4.1 M-value Estimation 79 4.4.2 BOLD Time Courses 82 4.4.3 M-Maps and Single Subject Analysis 82 4.4.4 Effects on CMRO2 Estimation 83 4.4.5 Technical Limitations and Implications for Calibrated fMRI 84 4.5 Conclusion 89 5 Experiment II: Reproducibility of BOLD, ASL and Calibrated fMRI 90 5.1 Background Information 90 5.2 Methods 91 5.2.1 Experimental Design 91 5.2.2 Data Analysis 91 5.2.3 Reproducibility 93 5.2.4 Learning and Habituation Effects 95 5.3 Results 95 5.4 Discussion 101 5.4.1 Breathing Manipulations 102 5.4.2 Functional Reproducibility 107 5.4.3 Habituation Effects on Reproducibility 109 5.4.4 Technical Considerations for Calibrated fMRI 110 5.5 Conclusion 112 6 Experiment III: Simultaneous Acquisition of BOLD, ASL and VASO Signals 113 6.1 Background Information 113 6.2 Methods 114 6.2.1 SS-SI VASO Signal Acquisition 114 6.2.2 ASL and BOLD Signal Acquisition 114 6.2.3 Experimental Design 114 6.2.4 Data Analysis 115 6.3 Results 115 6.4 Discussion 116 6.5 Conclusion 120 7 Conclusion and Outlook 12

Three projects in applied mathematics: discovering underlying features amid large, noisy data

In many scientific fields, we are faced with extremely large, noisy datasets. Features of interest in these datasets may be difficult to explicitly define, obscured by noise, or simply lost in the magnitude of the dataset. Uncovering these features often necessitates the development of novel mathematical and statistical modeling approaches, and the utilization of powerful analysis tools. In this work, we present three distinct projects, all of which develop specific mathematical and statistical analysis to find features of interest amid large, noisy data. The first project measures cross-frequency coupling (CFC), i.e., the extent to which signals in different frequency bands interact, amid large, noisy neural voltage recordings. We use generalized linear models (GLMs) to define an accurate measure with confidence intervals and significance values. We show in simulation how this measure improves upon existing approaches, and apply this measure to analyze CFC during a human seizure. The second project develops a fully-automated detector of spike ripples, a powerful biomarker of epilepsy, which occur sparingly in long duration neural voltage recordings. The method applies convolutional neural networks (CNNs) to spectrogram data, and performs comparably to gold-standard expert classifications. We apply this measure to a population of patients with childhood epilepsy, and effectively separate them into high and low seizure risk groups. The final project studies the COVID-19 epidemic, modeling infections and deaths over time from large quantities of noisy, incomplete state-level observations. We use a statistical, data-driven analysis to estimate the basic reproduction number (R0), and use this estimate in multiple compartmental models, fitting unknown parameters for death and recovery rates using an ensemble Markov chain Monte Carlo (MCMC) method. We show consistent estimates of dynamics and parameters across multiple compartmental models, in alignment with our current epidemiological understanding of the disease. In all projects, we are able to uncover key features of interest amid the large, noisy data, providing key insights backed by mathematical and statistical rigor

Stochastic resonance and finite resolution in a network of leaky integrate-and-fire neurons.

This thesis is a study of stochastic resonance (SR) in a discrete implementation of a leaky integrate-and-fire (LIF) neuron network. The aim was to determine if SR can be realised in limited precision discrete systems implemented on digital hardware. How neuronal modelling connects with SR is discussed. Analysis techniques for noisy spike trains are described, ranging from rate coding, statistical measures, and signal processing measures like power spectrum and signal-to-noise ratio (SNR). The main problem in computing spike train power spectra is how to get equi-spaced sample amplitudes given the short duration of spikes relative to their frequency. Three different methods of computing the SNR of a spike train given its power spectrum are described. The main problem is how to separate the power at the frequencies of interest from the noise power as the spike train encodes both noise and the signal of interest. Two models of the LIF neuron were developed, one continuous and one discrete, and the results compared. The discrete model allowed variation of the precision of the simulation values allowing investigation of the effect of precision limitation on SR. The main difference between the two models lies in the evolution of the membrane potential. When both models are allowed to decay from a high start value in the absence of input, the discrete model does not completely discharge while the continuous model discharges to almost zero. The results of simulating the discrete model on an FPGA and the continuous model on a PC showed that SR can be realised in discrete low resolution digital systems. SR was found to be sensitive to the precision of the values in the simulations. For a single neuron, we find that SR increases between 10 bits and 12 bits resolution after which it saturates. For a feed-forward network with multiple input neurons and one output neuron, SR is stronger with more than 6 input neurons and it saturates at a higher resolution. We conclude that stochastic resonance can manifest in discrete systems though to a lesser extent compared to continuous systems