Epilepsy is a neurological disorder that can negatively affect the visual, audial and motor functions of the human brain. Statistical analysis of neurophysiological recordings, such as electroencephalogram (EEG), facilitates the understanding and diagnosis of epileptic seizures. Standard statistical methods, however, do not account for topological features embedded in EEG signals. In the current study, we propose a persistent homology (PH) procedure to analyze single-trial EEG signals. The procedure denoises signals with a weighted Fourier series (WFS), and tests for topological difference between the denoised signals with a permutation test based on their PH features persistence landscapes (PL). Simulation studies show that the test effectively identifies topological difference and invariance between two signals. In an application to a single-trial multichannel seizure EEG dataset, our proposed PH procedure was able to identify the left temporal region to consistently show topological invariance, suggesting that the PH features of the Fourier decomposition during seizure is similar to the process before seizure. This finding is important because it could not be identified from a mere visual inspection of the EEG data and was in fact missed by earlier analyses of the same dataset.

Objective To provide quantitative data on the multi-planar growth of the mandible, this study derived accurate linear and angular mandible measurements using landmarks on three dimensional (3D) mandible models. This novel method was used to quantify 3D mandibular growth and characterize the emergence of sexual dimorphism. Design Cross-sectional and longitudinal imaging data were obtained from a retrospective computed tomography (CT) database for 51 typically developing individuals between the ages of one and nineteen years. The software Analyze was used to generate 104 3DCT mandible models. Eleven landmarks placed on the models defined six linear measurements (lateral condyle, gonion, and endomolare width, ramus and mental depth, and mandible length) and three angular measurements (gonion, gnathion, and lingual). A fourth degree polynomial fit quantified growth trends, its derivative quantified growth rates, and a composite growth model determined growth types (neural/cranial and somatic/skeletal). Sex differences were assessed in four age cohorts, each spanning five years, to determine the ontogenetic pattern producing sexual dimorphism of the adult mandible. Results Mandibular growth trends and growth rates were non-uniform. In general, structures in the horizontal plane displayed predominantly neural/cranial growth types, whereas structures in the vertical plane had somatic/skeletal growth types. Significant prepubertal sex differences in the inferior aspect of the mandible dissipated when growth in males began to outpace that of females at eight to ten years of age, but sexual dimorphism re-emerged during and after puberty. Conclusions This 3D analysis of mandibular growth provides preliminary normative developmental data for clinical assessment and craniofacial growth studies.

The growth patterns of different anatomic structures in the human body vary in terms of growth amount over time, growth rate and growth periods. The oral and pharyngeal structures, also known as vocal tract structures, are housed in the craniofacial complex where the cranium/brain follows a distinct neural growth pattern, and the face follows a distinct somatic or skeletal growth pattern. Thus, it is reasonable to expect the oral and pharyngeal structures to follow a combined or mixed growth pattern. Existing parametric growth models are limited in that they are mainly focused on modeling one particular type of growth pattern. In this paper, we propose a novel composite growth model using neural and somatic baseline curves to fit the combined growth pattern of select vocal tract structures. The method can also determine the overall percent contribution of each of the growth types.

Meditation practice as a non-pharmacological intervention to provide health related benefits has generated much neuroscientific interest in its effects on brain activity. Electroencephalogram (EEG), an imaging modality known for its inexpensive procedure and excellent temporal resolution, is often utilized to investigate the neuroplastic effects of meditation under various experimental conditions. In these studies, EEG signals are routinely mapped on a topographic layout of channels to visualize variations in spectral powers within certain frequency ranges. Topological data analysis (TDA) of the topographic power maps modeled as graphs can provide different insight to EEG signals than standard statistical methods. A highly effective TDA technique is persistent homology, which reveals topological characteristics of a power map by tracking feature changes throughout a filtration process on the graph structure of the map. In this paper, we propose a novel inference procedure based on filtrations induced by sublevel sets of the power maps of high-density EEG signals. We apply the pipeline to simulated and real data, where we compare the persistent homological features of topographic maps of spectral powers in high-frequency bands of EEG signals recorded on long-term meditators and meditation-naive practitioners.

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We propose a seizure detection method for electroencephalographic (EEG) epilepsy data based on a novel multi-scale topological technique called persistent homology (PH). Among several PH descriptors, persistence landscape (PL) possesses many desirable properties for rigorous statistical inference. By building PLs on EEG epilepsy signals smoothed by a weighted Fourier series (WFS) expansion, we compared the before and during phases of a seizure attack in a patient diagnosed with left temporal epilepsy and successfully identified site T3 as the origin of the seizure attack.

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