An integrated functional mapping and source localization platform for brain research

The premise of this dissertation is to create a highly integrated platform that combines the most current recording technologies for brain research through the development of new algorithms for three-dimensional (3D) functional mapping and 3D source localization. The recording modalities that were integrated include: Electroencephalography (EEG), Optical Topographic Maps (OTM), Magnetic Resonance Imaging (MRI), and Diffusion Tensor Imaging (DTI). This work can be divided into two parts: The first part involves the integration of OTM with MRI, where the topographic maps are mapped to both the skull and cortical surface of the brain. This integration process is made possible through the development of new algorithms that determine the probes location on the MRI head model and warping the 2D topographic maps onto the 3D MRI head/brain model. Dynamic changes of the brain activation can be visualized on the MRI head model through a graphical user interface. The second part of this research involves augmenting a fiber tracking system, by adding the ability to integrate the source localization results generated by commercial software named Curry. This task involved registering the EEG electrodes and the dipole results to the MRI data. Such Integration will allow the visualization of fiber tracts, along with the source of the EEG, in a 3D transparent brain structure. The research findings of this dissertation were tested and validated through the participation of patients from Miami Children Hospital (MCH). Such an integrated platform presented to the medical professionals in the form of a user-friendly graphical interface is viewed as a major contribution of this dissertation. It should be emphasized that there are two main aspects to this research endeavor: (1) if a dipole could be situated in time at its different positions, its trajectory may reveal additional information on the extent and nature of the brain malfunction; (2) situating such a dipole trajectory with respect to the fiber tracks could ensure the preservation of these fiber tracks (axons) during surgical interventions, preserving as a consequence these parts of the brain that are responsible for information transmission.

Reduced-parameter model of head-related transfer functions for synthesized spatial audio

Digital systems can generate left and right audio channels that create the effect of virtual sound source placement (spatialization) by processing an audio signal through pairs of Head-Related Transfer Functions (HRTFs) or, equivalently, Head-Related Impulse Responses (HRIRs). The spatialization effect is better when individually-measured HRTFs or HRIRs are used than when generic ones (e.g., from a mannequin) are used. However, the measurement process is not available to the majority of users. There is ongoing interest to find mechanisms to customize HRTFs or HRIRs to a specific user, in order to achieve an improved spatialization effect for that subject. Unfortunately, the current models used for HRTFs and HRIRs contain over a hundred parameters and none of those parameters can be easily related to the characteristics of the subject. This dissertation proposes an alternative model for the representation of HRTFs, which contains at most 30 parameters, all of which have a defined functional significance. It also presents methods to obtain the value of parameters in the model to make it approximately equivalent to an individually-measured HRTF. This conversion is achieved by the systematic deconstruction of HRIR sequences through an augmented version of the Hankel Total Least Squares (HTLS) decomposition approach. An average 95% match (fit) was observed between the original HRIRs and those re-constructed from the Damped and Delayed Sinusoids (DDSs) found by the decomposition process, for ipsilateral source locations. The dissertation also introduces and evaluates an HRIR customization procedure, based on a multilinear model implemented through a 3-mode tensor, for mapping of anatomical data from the subjects to the HRIR sequences at different sound source locations. This model uses the Higher-Order Singular Value Decomposition (HOSVD) method to represent the HRIRs and is capable of generating customized HRIRs from easily attainable anatomical measurements of a new intended user of the system. Listening tests were performed to compare the spatialization performance of customized, generic and individually-measured HRIRs when they are used for synthesized spatial audio. Statistical analysis of the results confirms that the type of HRIRs used for spatialization is a significant factor in the spatialization success, with the customized HRIRs yielding better results than generic HRIRs.

Structure-based modeling of head -related transfer functions towards interactive customization of binaural sound systems

One of the most popular techniques for creating spatialized virtual sounds is based on the use of Head-Related Transfer Functions (HRTFs). HRTFs are signal processing models that represent the modifications undergone by the acoustic signal as it travels from a sound source to each of the listener's eardrums. These modifications are due to the interaction of the acoustic waves with the listener's torso, shoulders, head and pinnae, or outer ears. As such, HRTFs are somewhat different for each listener. For a listener to perceive synthesized 3-D sound cues correctly, the synthesized cues must be similar to the listener's own HRTFs. ^ One can measure individual HRTFs using specialized recording systems, however, these systems are prohibitively expensive and restrict the portability of the 3-D sound system. HRTF-based systems also face several computational challenges. This dissertation presents an alternative method for the synthesis of binaural spatialized sounds. The sound entering the pinna undergoes several reflective, diffractive and resonant phenomena, which determine the HRTF. Using signal processing tools, such as Prony's signal modeling method, an appropriate set of time delays and a resonant frequency were used to approximate the measured Head-Related Impulse Responses (HRIRs). Statistical analysis was used to find out empirical equations describing how the reflections and resonances are determined by the shape and size of the pinna features obtained from 3D images of 15 experimental subjects modeled in the project. These equations were used to yield “Model HRTFs” that can create elevation effects. ^ Listening tests conducted on 10 subjects show that these model HRTFs are 5% more effective than generic HRTFs when it comes to localizing sounds in the frontal plane. The number of reversals (perception of sound source above the horizontal plane when actually it is below the plane and vice versa) was also reduced by 5.7%, showing the perceptual effectiveness of this approach. The model is simple, yet versatile because it relies on easy to measure parameters to create an individualized HRTF. This low-order parameterized model also reduces the computational and storage demands, while maintaining a sufficient number of perceptually relevant spectral cues. ^

Investigation of spatial patterns of ground-water exchange with lakes, using a three-dimensional numerical model

Hydrogeologic variables controlling groundwater exchange with inflow and flow-through lakes were simulated using a three-dimensional numerical model (MODFLOW) to investigate and quantify spatial patterns of lake bed seepage and hydraulic head distributions in the porous medium surrounding the lakes. Also, the total annual inflow and outflow were calculated as a percentage of lake volume for flow-through lake simulations. The general exponential decline of seepage rates with distance offshore was best demonstrated at lower anisotropy ratio (i.e., Kh/Kv = 1, 10), with increasing deviation from the exponential pattern as anisotropy was increased to 100 and 1000. 2-D vertical section models constructed for comparison with 3-D models showed that groundwater heads and seepages were higher in 3-D simulations. Addition of low conductivity lake sediments decreased seepage rates nearshore and increased seepage rates offshore in inflow lakes, and increased the area of groundwater inseepage on the beds of flow-through lakes. Introduction of heterogeneity into the medium decreased the water table and seepage ratesnearshore, and increased seepage rates offshore in inflow lakes. A laterally restricted aquifer located at the downgradient side of the flow-through lake increased the area of outseepage. Recharge rate, lake depth and lake bed slope had relatively little effect on the spatial patterns of seepage rates and groundwater exchange with lakes.