Surface Smoothing: A Way Back in Early Brain

Abstract. In this article we propose to investigate the analogy between early cortical folding process and cortical smoothing by mean curvature flow. First, we introduce a one-parameter model that is able to fit a developmental trajectory as represented in a Volume-Area plot and we propose an efficient optimization strategy for parameter estimation. Second, we validate the model on forty cortical surfaces of preterm newborns by comparing global geometrical indices and trajectories of central sulcus along developmental and simulation time.

Statistical shape analysis of neuroanatomical structures based on spherical wavelet transformation

Thesis (Ph. D.)--Harvard-MIT Division of Health Sciences and Technology, 2008.Includes bibliographical references.Evidence suggests that morphological changes of neuroanatomical structures may reflect abnormalities in neurodevelopment, or relate to a variety of disorders, such as schizophrenia and Alzheimer's disease (AD). Advances in high-resolution Magnetic Resonance Imaging (MRI) techniques allow us to study these alterations of brain structures in vivo. Previous work in studying the shape variations of brain structures has provided additional localized information compared with traditional volume-based study. However, challenges remain in finding an accurate shape presentation and conducting shape analysis with sound statistical principles. In this work, we develop methods for automatically extracting localized and multi-scale shape features and conducting statistical shape analysis of neuroanatomical structures obtained from MR images. We first develop a procedure to extract multi-scale shape features of brain structures using biorthogonal spherical wavelets. Using this wavelet-based shape representation, we build multi-scale shape models and study the localized cortical folding variations in a normal population using Principal Component Analysis (PCA). We then build a shape-based classification framework for detecting pathological changes of cortical surfaces using advanced classification methods, such as predictive Automatic Relevance Determination (pred-ARD), and demonstrate promising results in patient/control group comparison studies. Thirdly, we develop a nonlinear temporal model for studying the temporal order and regional difference of cortical folding development based on this shape representation. Furthermore, we develop a shape-guided segmentation method to improve the segmentation of sub-cortical structures, such as hippocampus, by using shape constraints obtained in the wavelet domain.(cont.) Finally, we improve upon the proposed wavelet-based shape representation by adopting a newly developed over-complete spherical wavelet transformation and demonstrate its utility in improving the accuracy and stability of shape representations. By using these shape representations and statistical analysis methods, we have demonstrated promising results in localizing shape changes of neuroanatomical structures related to aging, neurological diseases, and neurodevelopment at multiple spatial scales. Identification of these shape changes could potentially lead to more accurate diagnoses and improved understanding of neurodevelopment and neurological diseases.by Peng Yu.Ph.D

Efficient Computation of Slepian Functions for Arbitrary Regions on the Sphere

In this paper, we develop a new method for the fast and memory-efficient computation of Slepian functions on the sphere. Slepian functions, which arise as the solution of the Slepian concentration problem on the sphere, have desirable properties for applications where measurements are only available within a spatially limited region on the sphere and/or a function is required to be analyzed over the spatially limited region. Slepian functions are currently not easily computed for large band-limits for an arbitrary spatial region due to high computational and large memory storage requirements. For the special case of a polar cap, the symmetry of the region enables the decomposition of the Slepian concentration problem into smaller subproblems and consequently the efficient computation of Slepian functions for large band-limits. By exploiting the efficient computation of Slepian functions for the polar cap region on the sphere, we develop a formulation, supported by a fast algorithm, for the approximate computation of Slepian functions for an arbitrary spatial region to enable the analysis of modern datasets that support large band-limits. For the proposed algorithm, we carry out accuracy analysis of the approximation, computational complexity analysis, and review of memory storage requirements. We illustrate, through numerical experiments, that the proposed method enables faster computation, and has smaller storage requirements, while allowing for sufficiently accurate computation of the Slepian functions.Alice P. Bates is supported by the Australian Research Council’s Discovery Projects funding scheme (Project no. DP150101011). Rodney A. Kennedy is supported by the Australian Research Council’s Discovery Projects funding scheme (Project no. DP170101897)

Hippocampal shape analysis in Alzheimer’s disease using Functional Data Analysis

The hippocampus is one of the first affected regions in Alzheimer's disease. The left hippocampi of control subjects, patients with mild cognitive impairment and patients with Alzheimer's disease are represented by spherical harmonics. Functional data analysis is used in the hippocampal shape analysis. Functional principal component analysis and functional independent component analysis are defined for multivariate functions with two arguments. A functional linear discriminant function is also defined. Comparisons with other approaches are carried out. Our functional approach gives promising results, especially in shape classification. Copyright © 2013 John Wiley & Sons, Ltd

SignReLU neural network and its approximation ability

Deep neural networks (DNNs) have garnered significant attention in various fields of science and technology in recent years. Activation functions define how neurons in DNNs process incoming signals for them. They are essential for learning non-linear transformations and for performing diverse computations among successive neuron layers. In the last few years, researchers have investigated the approximation ability of DNNs to explain their power and success. In this paper, we explore the approximation ability of DNNs using a different activation function, called SignReLU. Our theoretical results demonstrate that SignReLU networks outperform rational and ReLU networks in terms of approximation performance. Numerical experiments are conducted comparing SignReLU with the existing activations such as ReLU, Leaky ReLU, and ELU, which illustrate the competitive practical performance of SignReLU

Adaptive Parameter Selection for Deep Brain Stimulation in Parkinson’s Disease

Each year, around 60,000 people are diagnosed with Parkinson’s disease (PD) and the economic burden of PD is at least $14.4 billion a year in the United States. Pharmaceutical costs for a Parkinson’s patient can be reduced from$12,000 to $6,000 per year with the addition of neuromodulation therapies such as Deep Brain Stimulation (DBS), transcranial Direct Current Stimulation (tDCS), Transcranial Magnetic Stimulation (TMS), etc. In neurodegenerative disorders such as PD, deep brain stimulation (DBS) is a desirable approach when the medication is less effective for treating the symptoms. DBS incorporates transferring electrical pulses to a specific tissue of the central nervous system and obtaining therapeutic results by modulating the neuronal activity of that region. The hyperkinetic symptoms of PD are associated with the ensembles of interacting oscillators that cause excess or abnormal synchronous behavior within the Basal Ganglia (BG) circuitry. Delayed feedback stimulation is a closed loop technique shown to suppress this synchronous oscillatory activity. Deep Brain Stimulation via delayed feedback is known to destabilize the complex intermittent synchronous states. Computational models of the BG network are often introduced to investigate the effect of delayed feedback high frequency stimulation on partially synchronized dynamics. In this work, we developed several computational models of four interacting nuclei of the BG as well as considering the Thalamo-Cortical local effects on the oscillatory dynamics. These models are able to capture the emergence of 34 Hz beta band oscillations seen in the Local Field Potential (LFP) recordings of the PD state. Traditional High Frequency Stimulations (HFS) has shown deficiencies such as strengthening the synchronization in case of highly fluctuating neuronal activities, increasing the energy consumed as well as the incapability of activating all neurons in a large-scale network. To overcome these drawbacks, we investigated the effects of the stimulation waveform and interphase delays on the overall efficiency and efficacy of DBS. We also propose a new feedback control variable based on the filtered and linearly delayed LFP recordings. The proposed control variable is then used to modulate the frequency of the stimulation signal rather than its amplitude. In strongly coupled networks, oscillations reoccur as soon as the amplitude of the stimulus signal declines. Therefore, we show that maintaining a fixed amplitude and modulating the frequency might ameliorate the desynchronization process, increase the battery lifespan and activate substantial regions of the administered DBS electrode. The charge balanced stimulus pulse itself is embedded with a delay period between its charges to grant robust desynchronization with lower amplitude needed. The efficiency and efficacy of the proposed Frequency Adjustment Stimulation (FAS) protocol in a delayed feedback method might contribute to further investigation of DBS modulations aspired to address a wide range of abnormal oscillatory behaviors observed in neurological disorders. Adaptive stimulation can open doors towards simultaneous stimulation with MRI recordings. We additionally propose a new pipeline to investigate the effect of Transcranial Magnetic Stimulation (TMS) on patient specific models. The pipeline allows us to generate a full head segmentation based on each individual MRI data. In the next step, the neurosurgeon can adaptively choose the proper location of stimulation and transmit accurate magnetic field with this pipeline

頭部伝達関数の空間領域特性モデリング

Tohoku University鈴木陽一課

In Vivo Human Right Ventricle Shape and Kinematic Analysis with and without Pulmonary Hypertension

Pulmonary hypertension (PH) is a severe cardio-pulmonary illness which has been commonly observed to induce substantial and ultimately deleterious changes to the human right ventricle (RV) shape and function. As such, the functional state of the RV is thought to be a major determinant of symptoms and survival rates for PH. However, there has been little success to-date to identify clinically obtainable metrics of RV shape and deformation as a means to detect the onset and progression of PH. This difficulty is largely the result of the absence of a proven approach that is generally applicable for consistent and reliable quantitative analysis of anatomical shapes, particularly the RV, between patients and over time. Therefore, a computational framework which can quantitatively analyze RV shape and deformation could be a key to assist in clinically detecting the onset and progression of PH. Statistical shape analysis techniques were developed, implemented, and assessed to analyze variations in human RV endocardial surface (RVES) shapes and kinematics from noninvasive clinical medical imaging data with respect to a spectrum of hemodynamic states. A computational framework for the quantitative analysis and statistical decomposition of sets of 3D genus-0 shapes that combines a modified harmonic mapping approach directly with proper orthogonal decomposition (DM-POD) is presented. The DM-POD approach is shown to be a robust technique for recovering inherent shape-related features through the analysis of sets of artificially generated shapes. The DM-POD approach is then applied to obtain kinematic features of the human RV based on the relative change in shape of the endocardial surface using cardiac computed tomography images. In addition, the kinematic features of the RVES obtained by the DM-POD approach are shown to be consistent and associated with intrinsically physiological components of the heart, and thus may potentially provide a more accurate means for classifying the progressive change in RV function caused by PH, in comparison to traditional clinical hemodynamic and volume-based metrics. Statistical shape analysis for the human RV is further evaluated through analysis of alternate components of the DM-POD approach, as well as through comparison of the DM-POD workflow with an alternate spherical harmonic function-based workflow (SPHARM), with respect to the aspects of surface representation, alignment, and decomposition. Additionally, different ways of utilizing the available imaging data with respect to the classification potential are investigated by considering analysis results when applying both the various DM-POD and SPHARM approaches with several different combinations of the phases captured throughout a single cardiac cycle for the patient set. Lastly, a novel statistical decomposition technique known as independent component analysis (ICA) was incorporated into the statistical shape analysis framework (i.e., DM-POD) to produce an alternative workflow (DM-ICA). Both the DM-POD and DM-ICA approaches are applied to analyze sets of artificially generated data and the human RVES datasets, and the respective results are compared. The DM-POD and DM-ICA workflows are shown to produce consistent, but substantially different results due to the various principles and views of each of the two statistical decomposition algorithms (i.e., POD and ICA). Most importantly, the results from the DM-POD and DM-ICA workflows appear to relate to RV function in unique ways, with respect to both traditional clinical metrics and each other, and have the potential to provide new metrics for better understanding of the human RV and its relationship to PH