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Recent studies reveal that Allee effect may play important roles in the growth of tumor. We present one of the first mathematical models of avascular tumor that incorporates the weak Allee effect. The model considers the densities of tumor cells in three stages: proliferating cells, quiescent cells, and necrotic cells. We investigate how Allee effect impacts the growth of the avascular tumor. We also investigate the effect of apoptosis of proliferating cells and necrosis of quiescent cells. The system is numerically solved in 2D using different sets of parameters. We show that Allee effect and apoptosis play important roles in the growth of tumor and the formation of necrotic core.

The geometry of uranium components is one of the key characteristics and strictly confidential. The geometry identification of metal uranium components was studied using 252Cf source-driven correlation measurement method. For the 3 uranium samples with the same mass and enrichment, there are subtle differences in neutron signals. Even worse, the correlation functions were disturbed by scatter neutrons and include “accidental” coincidence, which is not conductive to the geometry identification. In this paper, we proposed an identification method combining principal component analysis and least-square support vector machine (PCA-LSSVM). The results based on PCA-LSSVM showed that the training precision was 100% and the test precision was 95.83% of the identification model. The total precision of the identification model was 98.41%, which indicated that the identification model was an effective way to identify the geometry properties with the correlation functions.

For the large-scale operations of unmanned aerial vehicle (UAV) swarm and the large number of UAVs, this paper proposes a two-layer task and resource assignment algorithm based on feature weight clustering. According to the numbers and types of task resources of each UAV and the distances between different UAVs, the UAV swarm is divided into multiple UAV clusters, and the large-scale allocation problem is transformed into several related small-scale problems. A two-layer task assignment algorithm based on the consensus-based bundle algorithm (CBBA) is proposed, and this algorithm uses different consensus rules between clusters and within clusters, which ensures that the UAV swarm gets a conflict-free task assignment solution in real time. The simulation results show that the algorithm can assign tasks effectively and efficiently when the number of UAVs and targets is large.

Compressive Sensing (CS) theory has great potential for reconstructing Computed Tomography (CT) images from sparse-views projection data and Total Variation- (TV-) based CT reconstruction method is very popular. However, it does not directly incorporate prior images into the reconstruction. To improve the quality of reconstructed images, this paper proposed an improved TV minimization method using prior images and Split-Bregman method in CT reconstruction, which uses prior images to obtain valuable previous information and promote the subsequent imaging process. The images obtained asynchronously were registered via Locally Linear Embedding (LLE). To validate the method, two studies were performed. Numerical simulation using an abdomen phantom has been used to demonstrate that the proposed method enables accurate reconstruction of image objects under sparse projection data. A real dataset was used to further validate the method.

The study has investigated the effect of isoflavone attenuates the caspase-1 and caspase-3 level in cell model of Parkinsonism. The subjects were PC12 cells. They were randomly divided into six groups: control, MPP+(250 μmol/L), isoflavone (10 μM), isoflavone (10 μM) + MPP+(250 μmol/L), Z-YVAD-CHO (10 nM) + MPP+group, and Z-DEVD-CHO (10 nM) + MPP+group. Cell viability was measured by MTT methods; the content of tyrosine hydroxylase was measured by immunocytochemistry method of avidinbiotin peroxidase complex; apoptosis ratio was measured by flow cytometry. The results showed that cell viability in the MPP+group was lower than in all other five groups. There was no difference in cell viability between isoflavone + MPP+and control group. Optical density of TH positive cells in isoflavone group was higher than in control, isoflavone + MPP+, and MPP+only groups. The apoptosis ratio in the isoflavone + MPP+group and control group and the Z-YVAD-CHO + MPP+and Z-DEVD-CHO + MPP+group was similar, which was lower than in the MPP+group. The lowest apoptosis ratio was found in the isoflavone only group.

Currently industrial X-CT system is designed according to characteristics of test objects, and test objects determine industrial X-CT system structure, X-ray detector/sensor property, scanning mode, and so forth. So there are no uniform standards for the geometry size of scintillation crystals of detector. Moreover, scintillation crystals are usually mixed with some highly toxic impurity elements, such as Tl and Cd. Thus, it is indispensable for establishing guidelines of engineering practice to simulate X-ray detection performances of different scintillation crystals. This paper focuses on how to achieve high efficient X-ray detection in industrial X-CT system which used Monte Carlo (MC) method to study X-ray energy straggling characteristics, full energy peak efficiency, and conversion efficiency of some scintillation crystals (e.g., CsI(Tl), NaI(Tl), and CdWO4) after X-ray interacted with these scintillation crystals. Our experimental results demonstrate that CsI(Tl) scintillation crystal has the advantages of conversion efficiency, spectral matching, manufacturing process, and full energy peak efficiency; it is an ideal choice for high efficient X-ray detection in industrial X-CT system.

Spectral/multienergy CT employing the state-of-the-art energy-discriminative photon-counting detector can identify absorption features in the multiple ranges of photon energies and has the potential to distinguish different materials based on K-edge characteristics. K-edge characteristics involve the sudden attenuation increase in the attenuation profile of a relatively high atomic number material. Hence, spectral CT can utilize material K-edge characteristics (sudden attenuation increase) to capture images in available energy bins (levels/windows) to distinguish different material components. In this paper, we propose an imaging model based on K-edge characteristics for maximum material discrimination with spectral CT. The wider the energy bin width is, the lower the noise level is, but the poorer the reconstructed image contrast is. Here, we introduce the contrast-to-noise ratio (CNR) criterion to optimize the energy bin width after the K-edge jump for the maximum CNR. In the simulation, we analyze the reconstructed image quality in different energy bins and demonstrate that our proposed optimization approach can maximize CNR between target region and background region in reconstructed image.

The last quarter century has witnessed major advancements that have brought biomedical imaging to a paramount status in life sciences. Generally speaking, the scope of biomedical imaging covers data acquisition, image reconstruction, and image analysis, involving theories, methods, systems, and applications. While many kinds of imaging modalities, such as X-ray computed tomography (CT) and magnetic resonance imaging (MRI), become increasingly sophisticated, the mathematical methods involved in these modalities play more and more critical roles in further improving their performance in anatomical, functional, cellular, and molecular applications. The overall goal of this issue is to promote research and development of biomedical imaging by publishing high-quality research articles in this rapidly growing interdisciplinary field. Due to the time limit, this special issue mainly focused on 4 kinds of biomedical imaging modalities: CT, MRI, ultrasound, and fluorescence imaging; several biomedical image processing methods were also involved. Each paper published in this special issue was reviewed by at least two reviewers and revised according to reviewer's comments. For CT imaging, A. Cai et al. developed an efficient iterative image reconstruction (IIR) algorithm, using cone beam CT reconstruction that is based on total-variation (TV) minimization to overcome the computational complexity of IIR scheme in cone beam CT reconstruction; L.-z. Deng et al. proposed a hybrid reconstruction method combining TV and nonaliasing contourlet transform (NACT) and using the Split-Bregman method to solve the optimization problem. This algorithm utilized the geometrical information of CT image and got a sparser representation compared with wavelet and gradient operator. For MRI imaging, in order to reduce time consuming in MRI image reconstruction, Q. Li et al. proposed a parallel computing method which was based on a novel patch-based nonlocal operator (PANO). Simulation results demonstrated that this method can accelerate PANO-based MRI reconstruction several times compared with original one. W. He et al. introduced a direct nonconvex Lp norm algorithm for MRI phase unwrapping which leaded to faithful phase correction. Also analytical high order tensor decomposition was introduced into crossing fibers detection in diffusion MRI by T. Megherbi et al., which provided a better angular resolution and accuracy than the classical maxima localization method. For biomedical image processing, R. Jaramillo et al. used a wavelet domain filter to improve the performance of the Prony method. In this work, MRI images were considered to be affected only by Rician noise, and a new wavelet domain bilateral filtering process was implemented to reduce the noise in the images. X. Wang et al. proposed a model that allows robustness to noise as well for handling the intensity inhomogeneity and weak boundary problems in medical image segmentation using region-scalable discriminant and fitting energy for image segmentation. Also, a region-based active contour model which introduced a total energy as a penalty function in medical image segmentation is proposed by T. Liu et al. Another active contours based segmentation method was proposed by F. Akram et al. for intensity inhomogeneous MRI images to enable boundaries detection of the homogenous regions. Not only CT and MRI but also other medical imaging modalities, such as ultrasound and fluorescence imaging, are included in this special issue. S.-K. Ueng et al. designed a special filter aiming at suppressing speckles and enhancing features in the ultrasound images. In this method, diffusion tensor of intensity at each pixel was represented in the form of a Hessian matrix which was used to compute eigen values at each pixel. The eigen values were used in detection and classifying the underlying structure and a refinement strategy was followed to improve the classification. Then, based on the computed structure types, feasible filters were selected from a filter pool to suppress speckles and enhance features. X. Lin et al. used three-dimensional fluorescent spectra imaging to investigate whether and how Tubeimoside 1 (TBMS 1) can affect HepG2 cells, which indicated that fluorescent spectra method is a promising substitute for flow cytometry in cancer research. A computational model to estimate fluence rate for a biological medium with inclusion was developed by M. Gantri. In this work, the entire setting of the medium was treated to have spatially and stochastically varying refractive index to match practical applications and Legendre integral transform technique is incorporated to solve the radiative transfer equation. These papers represent an insightful observation into the state of the art, as well as future topics in this biomedical imaging field. We hope that this special issue would attract a wide attention of the peers and provide a chance to share the latest research work. Peng Feng Kumar Durai Fenglin Liu Xiaobo Qu

Biomedical imaging is a rapidly growing field to provide a state-of-the-art tool for preclinical biomedical research and clinical applications, in view of its ability to noninvasively reveal subtle structural variations of biological tissues and visualize in vivo physiological and pathological processes at the cellular and molecular levels. Mathematical methods are involved with imaging theories, models, and reconstruction algorithms in biomedical imaging. X-ray computed tomography (CT) was a successful application of mathematical method in medical imaging. The CT mathematical model can be reduced to a Radon transform. The inverse transform of Radon transform is invented by Radon in 1917. Magnetic resonance imaging (MRI) is a versatile medical imaging modality. MRI can provide more diagnostic information than any of the existing imaging techniques. It does not involve the use of ionizing radiation, hence free from associated harmful effects. Inverse Fast Fourier Transform (IFFT) is a standard method of image reconstruction in MRI from uniformly sampled K-space data. From nonuniform K-space data, iterative algorithms can improve image quality of image reconstruction for MRI. In the optical molecular imaging, the radiative transport equation (RTE) is the fundamental equation to describe photon propagation in biological tissues. The forward solution predicts photon propagation in the optical molecular imaging. The inverse solution can reconstruct molecular probe distribution in a small animal for providing unique insights into disease pathogenesis, drug development, and responses of therapy. The solutions for RTE usually involve analytical methods, Monte Carlo (MC) method, diffusion approximation (DA) method, simplified spherical harmonics method, and some numerical methods. In this special issue, each paper was reviewed by at least two reviewers and revised according to review comments. This special issue covered most of common biomedical imaging models and various image processing methods, such as registration, segmentation, and so forth, were involved. For Positron Emission Tomography (PET) imaging model, two attenuation correction methods based on X-rays CT (CTAC method) and segmentation of emission images (SE-AC method) were simulated with Monte Carlo method and compared. For synchrotron Micro-CT imaging model, a semiautomatic segmentation algorithm for extracting the complete structure of acini has been proposed. For ultrasound imaging model, a common carotid artery segmentation scheme based on active shape model can get better result and promote the translation of carotid 3D US to clinical care for the monitoring of the atherosclerotic disease progression and regression. For MRI model, a mesh-deformation constraints based image registration algorithm was carefully investigated. Also the development of image segmentation for intracranial aneurysms and rotation covariant image processing method for biomedical applications are summarized. Furthermore, in order to accelerate the parallel imaging, a sparse constrained reconstruction approach with variable splitting methods was proposed and verified: total variation (TV)-minimization interior tomography algorithm, dynamic and robust blind watermarking scheme to resist against common distortions, modified global and modified linear contrast stretching techniques for identification of various stages and species of malaria, a 3D surface-based deformable model as guidance for nonrigid 3D medical image registration and fusion, mathematical or computational modeling for oncogene inactivation, a group factor analysis model for neuroimaging applications by assigning separate factor patterns to control and patient groups yielding more reasonable factor scores and patterns, different MISO Volterra methods to model simulated ultrasound contrast agents signals, an automated process that determines whether an aortic object in a slice is a candidate for aortic dissection or PAU based on contrast enhanced CT data, image-based computational techniques to quantify the severity and directionality of individual scratches and scrapes, combination of genetic algorithm and closed loop to obtain optimal ternary command which maximized the contrast to tissue ratio, and magnetoacoustic tomography with magnetic induction (MAT-MI) for generating electrical conductivity images of biological tissues with high spatial resolution. An acceleration strategy for fluorescence molecular tomography (FMT) with early photons is proposed using graphics processing units (GPUs). The fluorescence molecular tomography (FMT) with early photons can efficiently improve the spatial resolution and fidelity of the reconstructed results. An efficient compressed sensing-based algorithm is proposed for CT image reconstruction from few-view data to suppress the streak artifact. The compressed sensing (CS) algorithm shows the potential to accurately recover images from highly undersampled data. The discriminant analysis techniques are discussed using MRI to identify the correlative pattern of brain changes for differentiating parkinsonian syndromes. A hybrid multiscale and multilevel image fusion algorithm for green fluorescent protein (GFP) image and phase contrast image of Arabidopsis cell is proposed. This algorithm uses different fusion strategies for different detailed subbands, which include neighborhood consistency measurement (NCM) that can adaptively find balance between color background and gray structure. A detrended fluctuation analysis (DFA) method is applied to image analysis to investigate the characteristic of different type of simulated and lymphoma image. A method is presented to estimate the tilt and decentration of intraocular lens (IOL) more accurately. The Bayesian hierarchical model for the analysis of categorical longitudinal data is investigated from sedation measurement for MRI and CT. In vivo MRI of local drug delivery is discussed to visualize and quantify the time resolved distribution of MRI contrast agents. These papers represent an insightful observation into the state of the art, as well as future topics in this biomedical imaging field. We hope that this special issue would attract a wide attention of the peers. Wenxiang Cong Kumar Durairaj Peng Feng