Computational and mathematical methods in brain atlasing.

Image segmentation and image denoising are two important and fundamental topics in the field of image processing. Geometric active contour model based on level set method can deal with the problem of image segmentation, but it does not consider the problem of image denoising. In this paper, a new diffusion equation model for noisy image segmentation is proposed by incorporating some classical diffusion equation denoising models into the segmental process. An assumption about the connection between the image intensity and level set function is given firstly. Some classical denoising models are employed to describe the evolution of level set function secondly. The final nonlinear diffusion equation model for noisy image segmentation is built thirdly. Then image segmentation and image denoising are combined in a united framework. The segmental results can be presented by level set function. Experimental results show that the new model has the advantage of noise resistance and is superior to traditional segmentation model.

This research focuses on theorems governing computational methods. Computational methods are a group of techniques that acts on big content with data to get outcomes with the prospect of obtaining a decision-making process. The theorems considered in this research are mathematical methods. The predictive techniques covered consist of mathematical analysis of solving problems, which are computational methods. These theorems encompass predictive values, which come about being considered. These methods are based on these computational methods. The major objective of this research is to utilize quantitative techniques in solving complex challenges. The techniques are enumerated in this research. The evaluation of these methods is also investigated. The technique that is more accurate and reliable is identified and selected when tested on data.

Accurate mapping of structural faults and stratigraphic sequences is essential to the success of subsurface interpretation, geologic modeling, reservoir characterization, stress history analysis, and resource recovery estimation. In the past decades, manual interpretation assisted by computational tools — i.e., seismic attribute analysis — has been commonly used to deliver the most reliable seismic interpretation. Because of the dramatic increase in seismic data size, the efficiency of this process is challenged. The process has also become overly time-intensive and subject to bias from seismic interpreters. In this study, we implement deep convolutional neural networks (CNNs) for automating the interpretation of faults and stratigraphies on the Opunake-3D seismic data set over the Taranaki Basin of New Zealand. In general, both the fault and stratigraphy interpretation are formulated as problems of image segmentation, and each workflow integrates two deep CNNs. Their specific implementation varies in the following three aspects. First, the fault detection is binary, whereas the stratigraphy interpretation targets multiple classes depending on the sequences of interest to seismic interpreters. Second, while the fault CNN utilizes only the seismic amplitude for its learning, the stratigraphy CNN additionally utilizes the fault probability to serve as a structural constraint on the near-fault zones. Third and more innovatively, for enhancing the lateral consistency and reducing artifacts of machine prediction, the fault workflow incorporates a component of horizontal fault grouping, while the stratigraphy workflow incorporates a component of feature self-learning of a seismic data set. With seven of 765 inlines and 23 of 2233 crosslines manually annotated, which is only about 1% of the available seismic data, the fault and four sequences are well interpreted throughout the entire seismic survey. The results not only match the seismic images, but more importantly they support the graben structure as documented in the Taranaki Basin.

Image segmentation consists of dividing an image domain into disjoint regions according to a characterization of the image within or in-between the regions. Therefore, segmenting an image is to divide its domain into relevant components. The efficient solution of the key problems in image segmentation promises to enable a rich array of useful applications. The current major application areas include robotics, medical image analysis, remote sensing, scene understanding, and image database retrieval. The subject of this book is image segmentation by variational methods with a focus on formulations which use closed regular plane curves to define the segmentation regions and on a level set implementation of the corresponding active curve evolution algorithms. Each method is developed from an objective functional which embeds constraints on both the image domain partition of the segmentation and the image data within or in-between the partition regions. The necessary conditions to optimize the objective functional are then derived and solved numerically. The book covers, within the active curve and level set formalism, the basic two-region segmentation methods, multiregion extensions, region merging, image modeling, and motion based segmentation. To treat various important classes of images, modeling investigates several parametric distributions such as the Gaussian, Gamma, Weibull, and Wishart. It also investigates non-parametric models. In motion segmentation, both optical flow and the movement of real three-dimensional objects are studied.

A computational approach is essential whenever the complexity of the process under study is such that direct theoretical or experimental approaches are not viable. This is the case for protein folding, for which a significant amount of data are being collected. This paper reports on the essential role of in silico methods and the unprecedented interplay of computational and theoretical approaches, which is a defining point of the interdisciplinary investigations of the protein folding process. Besides giving an overview of the available computational methods and tools, we argue that computation plays not merely an ancillary role but has a more constructive function in that computational work may precede theory and experiments. More precisely, computation can provide the primary conceptual clues to inspire subsequent theoretical and experimental work even in a case where no preexisting evidence or theoretical frameworks are available. This is cogently manifested in the application of machine learning methods to come to grips with the folding dynamics. These close relationships suggested complementing the review of computational methods within the appropriate theoretical context to provide a self-contained outlook of the basic concepts that have converged into a unified description of folding and have grown in a synergic relationship with their computational counterpart. Finally, the advantages and limitations of current computational methodologies are discussed to show how the smart analysis of large amounts of data and the development of more effective algorithms can improve our understanding of protein folding.

COVID-19 is a global catastrophe affecting over 200 nations worldwide. The RT-PCR and antibody based detection assay are considered as a standard diagnostic method and are expensive, time-consuming with low sensitivity (40–80%) making it imperative to look for alternatives. COVID-19 patients display severe lung damage which can be spotted in chest X-ray and CT scan which can be analyzed by computational methods for confirmation of the disease. Apart from above techniques, we have discussed battery of computational intelligence tools like docking, molecular dynamics and quantum mechanics (QM), the novel biosensor based diagnostic tool has been developed. The biosensor involves hybridization of SARS-CoV-2 RNA with cDNA to form RNA (viral)–cDNA (probe) hybrid, with intercalation of transition metal Osmium-Ruthenium (II) redox probe that release electrons. The electrons generated by redox metal measured by respective electrodes and detect even miniscule quantities of viral-RNA in the sample. The computational methods support efficient measurement of interaction of redox probe with viral genetic material and intercalation of the Osmium-Ruthenium (II) redox probe between RNA-cDNA hybrid. The computational docking offers proof of concept with better sensitivity, speed and accuracy, by presenting stronger interaction of RNA–DNA hybrid with Osmium (II) redox probe as compared DNA-DNA hybrid in RT-PCR.KeywordsRT-PCRCOVID-19SARS-CoV-2RNA–DNA hybridMolecular docking and dynamics and quantum mechanics (QM)

This issue marks a transition and a changing of the guard for Computational and Mathematical Methods in Medicine (CMMM). It is with some nostalgia that we look back on our long and illustrious association with Taylor and Francis; however, at the same time we look to the future with optimism and hope as Hindawi takes the helm and converts CMMM to the community-based, open access model that they have so successfully championed. The Hindawi Publishing Corporation is one of the fastest growing academic publishers worldwide with over 200 academic journals in their portfolio and a commitment to the highest levels of peer review and excellence. Reflecting on the genesis and evolution of CMMM, it is clear that Brian Sleeman, the founding Editor-in-Chief, showed great foresight in creating a journal that brought together the disparate disciplines of mathematics and medicine and that continues to play a major role in the development of mathematical medicine. He worked passionately to develop and promote the journal through some difficult times, with the insight and courage to bring together both biomedical/clinical scientists and mathematical scientists onto a single editorial board (a practice that has become more commonplace in subsequent journals in the field). The success that the journal has enjoyed thus far is a clear testament to his hard work, dedication, and vision. The journal has continued to provide a unique forum for the dissemination of interdisciplinary research resulting from collaborations between clinicians/experimentalists and theoreticians. CMMM has also continued to evolve rapidly, reflecting the increased focus on systems and interdisciplinary collaborative efforts across the breadth of biomedical, clinical, and translational research areas. The past year also saw the result of much hard work, with the inclusion of the journal in PubMed/Medline and the Science Citation Index Expanded. This was a great development for the journal since it not only has had an enormous impact on the general awareness and profile of the journal but has also resulted in increased submissions and downloads from the journal website over the past year. It has been exciting and rewarding to see the journal develop and evolve in this manner, and we look forward to increased success following this higher profile. The future looks extremely bright for the field of mathematical medicine as it emerges from its period of infancy and takes its place as a legitimate and central field of research and enquiry. Our sincere hope and wish is that CMMM continues from strength to strength and fulfills its role and promise as envisioned originally by its founding editor. Pamela Jones Sivabal Sivaloganathan

Image segmentation is the first step in many computer vision methods and serves to simplify the problem by grouping the pixels in the image in logical ways. Here we develop a new approach to deal with the problem of image segmentation in the framework of MATLAB programming environment which integrates thresholding, edge extraction and color information and shows good results when applied to some sample images. Further, we describe the merits and demerits of the proposed algorithm. In fact we can use this segmentation technique as an improvement over the in-built MATLAB 'edge detection' function.

In the first part of the paper a new theoretical approach to the problem of image segmentation is described. A method for automatic segmenting of an unknown number and unknown location of objects in an image has been proposed. This method is based on both local properties of neighbouring pixels and global image features. To allow for automated segmentation, slices are formed at different values of the threshold level, which contain spatial uniformity regions. In the second part, the image segmentation is considered as a problem of selection of slices, which should comprise regions with features satisfying the requirements desired. The selection is based on the proposed minima criterion including a volume analysis of neighbouring slices. An important characteristic of the approach is that it reflects object shapes devoid of noise, and does not use heuristic parameters such as an edge value. The results of this method are presented on several examples containing greyscale images of objects of different brightness.

Multi-agent stochastic level set method in image segmentation

The brain is a complex organ operating on multiple scales. From molecular events that inform electrical and biochemical cellular responses, the brain interconnects processes all the way up to the massive network size of billions of brain cells. This strongly coupled, nonlinear, system has been subject to research that has turned increasingly multidisciplinary. The seminal work of Hodgkin and Huxley in the 1950s made use of experimental data to derive a coherent physical model of electrical signaling in neurons, which can be solved using mathematical and computational methods, thus bringing together neuroscience, physics, mathematics, and computer science. Over the last decades numerous projects have been dedicated to modeling and simulation of specific parts of molecular dynamics, neuronal signaling, and neural network behavior. Simulators have been developed around a specific objective and scale, in order to cope with the underlying computational complexity. Often times a dimension reduction approach allows larger scale simulations, this however has the inherent drawback of losing insight into structure-function interplay at the cellular level. This paper gives an overview of the project NeuroBox that has the objective of integrating multiple brain scales and associated physical models into one unified framework. NeuroBox hosts geometry and anatomical reconstruction methods, such that detailed three-dimensional domains can be integrated into numerical simulations of models based on partial differential equations. The project further focusses on deriving numerical methods for handling complex computational domains, and to couple multiple spatial dimensions. The latter allows the user to specify in which parts of the biological problem high-dimensional representations are necessary and where low-dimensional approximations are acceptable. NeuroBox offers workflow user interfaces that are automatically generated with VRL-Studio and can be controlled by non-experts. The project further uses uG4 as the numerical backend, and therefore accesses highly advanced discretization methods as well as hierarchical and scalable numerical solvers for very large neurobiological problems.

This special section of Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, on multiscale modeling in life and materials sciences, is based on a summer program with the same theme, held August 4--30, 2003, at the Universita della Svizzera Italiana in Lugano, Switzerland, and organized by the ETH Zurich Computational Laboratory (CoLab). This workshop emphasized that multiscale modeling and simulation can serve as a commonscientific language enabling cross-fertilization across disciplines and the definition of new scientific frontiers. Materials science was one of the first disciplines that emphasized the need for novel multiscaling approaches bridging continuum and atomistic models. In life sciences, the rapid growth of the role played by computational methods has led to the early realization that a multiscaling approach is necessary to tackle inherently complex phenomena involving cells, organisms, and ecosystems. This summer program provided the opportunity to scientists from these different scientific fields to exchange ideas and to pursue research in an interdisciplinary fashion using multiscale computational methods as a common language. These interactions demonstrated that research in multiscaling is a fertile breeding ground for the development of novel powerful computational tools for domains where computing is established as a tool for scientific inquiry and for the dissemination of this know-how to disciplines for which computation is an emerging form of scientific investigation. This special section of MMS is a representative sample of theoretical and computational approaches to multiscale modeling and simulation in materials and life sciences. The papers discuss multiscale coupling of physical models and time/space multiresolution techniques. The problem of coupling models across space and time scales is a fundamental issue in multiscale modeling and simulation. Multiscale approaches often require the rigorous integration of diverse physical models, such as the case of blood flow in the circulatory system (Fernandez, Milisic}, and Quarteroni). The multiscale integration of diverse physical models in nanoscale magnetic systems involves the proper coupling of quantum effects in classical descriptions (Wessel, Trebst, and Troyer). Multiscale simulations of materials with heterogeneous properties are tackled using asymptotic expansions for the case of conducting inclusions embedded in a homogeneous matrix phase (Ben Hassen and Bonnetier). A broad class of multiscale problems involves the description of macroscale systems using only the information available by suitable microscopic models. This technique is demonstrated in simulating the evolution of parabolic homogenization problems with nonlinear reactions, using as a microscopic model a partial differential equation with rapidly oscillating coefficients (Samaey, Roose, and Kevrekidis). A related work extends this concept to problems with a wide separation in time scales. Using as an application a model of bacterial chemotaxis it is shown that projective time integration of coarse variables can be carried out in time scales that are long compared to those of the microscopic dynamics (Setayeshgar, Gear, Othmer, and Kevrekidis). In problems with time-dependent, large space scale variations a new class of multiresolution particle methods enhances their inherent adaptivity and presents an alternative to grid-based methods (Bergdorf, Cottet, and Koumoutsakos). Future research in multiscale modeling would continue to rely on synergies across disciplines for the development of novel computational methods, the integration of physical models, and the formulation of new challenges. This principle will continue to guide future workshops in multiscale modeling and simulations at the CoLab and, we believe, an ever-increasing number of scientific institutions. The editors in charge would like to credit, for their hard work and dedication, those editors who helped handle the peer-review process for papers submitted to this special section. Thanks to Emily Carter, Wolfgang Hackbusch, Robert Kohn, Hans Christian Ottinger, Olivier Pironneau, and John Willis. We also wish to thank SIAM Publications Manager Mitch Chernoff for his invaluable advice and help in preparing this section.

Computational methods for constructing protein structure models from 3D electron microscopy maps

In recent years the development of human-machine interfaces for medical applications and rehabilitation medicine has rapidly increased and still continues to grow [1]. The main goals have been a novel in-patient and outpatient diagnostics and improved quality of life, especially for the people with neuromuscular impairments or diseases [2]. The research and development in this field require various novel control algorithms and computational tools to extract features from measured biosignals. Some recently developed algorithms and tools may become part of the in-house equipment for hospitals, while some advanced solutions for home applications may also enable telemedical services in the recent future [3]. Before any computation or control of human activity is possible, information on movement of body segments is required. When information from natural sensors is not accessible, external devices such as accelerometers and gyroscopes can provide sufficient information on gait, standing up, balance, or specific motion of lower or upper extremities. However, these sensors are prone to bias, integration, and temperature drift and cannot provide sufficient accuracy for closed-loop control. The use of various mathematical tools, especially extended Kalman filter, can help to partly overcome the specified problem and can assure measurement of selected parameters up to the acceptable level of accuracy [4]. Besides the Kalman filter alternative feature extraction algorithms like discrete Fourier transform, dynamic time warping, or harmonic linear dynamical system are applied [5]. In this special issue we publish an example of electrocardiogram feature extraction. The accurate and reliable sensory information is a prerequisite for the design of a closed-loop control system, especially when a human is in interaction with the machine in terms of “feeling the environment” or haptics [6]. The word haptic originates from the Greek word haptikos (ἅπτικoς) and is related to the sense of touch. This is nowadays particularly important in rehabilitation of patients suffering from stroke. In combination with virtual reality technologies, an upper extremity, and balance, grasping of hand rehabilitation devices can be designed [6]. The haptic robots serving for various rehabilitation purposes are usually complex and intended for the use in clinical environment. However, their simplified passive versions or simple rehabilitation aids equipped with inertial sensory systems are already part of the telerehabilitation systems in function in patients' homes [3] or smart homes. These premises are often well equipped with information-communication technologies and the patients can take full advantage of remote treatment and testing of various novel technologies which may lead to the significant improvement of quality of life [7]. On the other hand, a technological progress, novel computation, and control methods that enable new approaches in rehabilitation medicine require constant clinical evaluation in order to find its way to the everyday clinical practice [8]. We hope the readers of the Journal of Computational and Mathematical Methods in Medicine will find in this special issue solid theoretical and technological solutions as well as their possible applications in the rehabilitation medicine. However, we would like to encourage the readers to raise new research questions and issues which will significantly contribute to the development and rapid uptake of technologies in rehabilitation medicine. Imre Cikajlo Takashi Watanabe Strahinja Dosen

Segmentation is a low-level processing aimed at the partition of an image in disjoint regions, each one homogeneous with respect to some properties like intensity, texture, shape, etc. Such a task is needed in many high-level processing and applications in such diverse fields as remote-sensing, medical imaging, video coding, and industrial automation, just to name a few. In this work of thesis, we first deal with the problem of color based image segmentation, that is based on some form of homogeneity in the color/spectral properties of the image, and then move to the more complex task of texture based segmentation, where the aim is to recognize complex structures in the image which are typically non homogeneous in terms of spectral properties. Concerning color based segmentation, we focus on a specific class of Markov Random Field (MRF) probability models, namely the Tree-Structured Markov Random Fields (TS-MRF), recently proposed to provide a hierarchical multiscale description of images. Based on such a model, the unsupervised image segmentation is carried out by means of a sequence of nested class splits, where each class is modeled as a local binary MRF. As a first contribution, we first extend the model to generic tree structures removing the unnecessary binary constraint, and then devise a new TS-MRF unsupervised segmentation technique which improves upon the original algorithm by selecting a better tree structure and eliminating spurious classes. Such results are obtained by using the Mean-Shift procedure to estimate the number of pdf modes at each node, and to obtain a more reliable initial clustering for subsequent MRF optimization. To this end, we devise a new reliable and fast clustering algorithm based on the Mean-Shift technique, which makes use of a variable-bandwidth strategy based on the k-Nearest Neighbors (k-NN) technique, and is implemented with a speed-up strategy that cuts significantly the computational complexity. Experimental results on synthetic data and real life images from the remote sensing domain prove the potential of the proposed method. Turning to texture based segmentation, we present a novel multiscale texture model, and a related algorithm for the unsupervised segmentation of color images. Elementary textures are characterized by their spatial interactions with neighboring regions along selected directions. Such interactions are modeled in turn by means of a set of Markov chains, one for each direction, whose parameters are collected in a feature vector that synthetically describes the texture. Based on the feature vectors, the texture are then recursively merged, giving rise to larger and more complex textures, which appear at different scales of observation: accordingly, the model is named Hierarchical Multiple Markov Chain (H-MMC). The Texture Fragmentation and Reconstruction (TFR) algorithm, addresses the unsupervised segmentation problem based on the H-MMC model. The ``fragmentation'' step allows one to find the elementary textures of the model, while the ``reconstruction'' step defines the hierarchical image segmentation based on a probabilistic measure (texture score) which takes into account both region scale and inter-region interactions. The performance of the proposed method was assessed through the Prague segmentation benchmark, based on mosaics of real natural textures, and also tested on real-world natural images from the Berkeley dataset. Finally, an application of the TFR algorithm for the unsupervised segmentation of multiresolution remotely sensed images is proposed, based on the significant presence of textural content in last generation high-resolution satellite images. The obtained results further assess the potential of the proposed method for such real life applications.