Tumor cells shed from primary tumor and circulating in peripheral blood is called circulating tumor cells (CTCs). In despite of the importance of CTCs to understand the biology of metastasis and to predict treatment response or disease progression, since CTCs are extremely rare and admixed with numerous blood cells, detection and characterization of CTCs is a major technological challenge. In this review, we focus on latest trend of development of microfluidic device to detect CTCs and report a well-type microfluidic device to detect CTCs by utilizing both immunoaffinity-based and sizebased cell separation.

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In this paper, a microfluidic device for analyzing circulating tumor cells (CTCs) at the single-cell level is presented. The device consists of a microfluidic chip made of polydimethylsiloxane (PDMS),and a glass substrate equipped with an array of interidigitated microelectrodes made of indium tin oxide (ITO) and microchamber array made of epoxy-resin fabricated on top of the electrodes. The cells introduced into the microchannel on the fluidic chip can be trapped in the microchambers using dielectric force induced by applying alternating voltage to the electrodes. The feasibility of the present device for single-cell analysis of CTC is validated through the microfluidic experiments of immunostaining and viability/apoptosis assay against DU145 cells (prostate cancer cell line) captured in the microchambers.

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We applied the residual cutting (RC) method, which has excellent converging characteristics, as the numerical solution of elliptic partial differential equations, to the coupled perturbed (CP)equation. This method also shows robust and precise converging characteristics in solving the CP equation. For small molecules, it was as effective as the Pople method. As molecule size increases, the number of steps required to achieve convergence increases. For systems with large size of molecules,this method is shown to be more advantageous than the Pople method in convergence, required memory and the amount of calculation.

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Helper T cells emerge from naive T cells via lineage commitment. Helper T cells play a pivotal role in adaptive immune response to remove antigen. Most of previous mathematical studies only consider either population dynamics of T cell clonal expansion or intracellular change of gene expression for transcription factors. In the present paper, on the other hand, we construct an individual based model which describes intra- and inter-cellular dynamics of T cell lineage commitment, and then carry out stochastic simulations to investigate how balance between two specific subsets is maintained. The method presented here can be effectively utilized to trace dynamics of a cell population such as immune cells which generically change their behavioral pattern during development.

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Blood flow simulation can be used for post-operational evaluation of a stent placement as well as for investigation of initiation and growth of cardiovascular diseases such as atherosclerosis. Since the brain hemorrhage may occurs by hyper perfusion syndrome after the stent placement, it is important to simulate post-surgery conditions.
The paper presents 1D-0D multi-scale simulation taking account of the entire circulatory system and its visualization. For patient-specific simulation, using blood vessel shape extracted by medical image and peripheral resistance estimated by measured flow rate. The simulations are conducted for a patient who had stent placement. The result show that the blood flow increase in cerebral circulation.

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For reproducing and evaluating acoustical environment in general spaces, directivity of sound source is one of important factors determining the quality of acoustics. Directivity of a sound source originates from the source’s shape and its size relative to wavelength. In order to precisely simulate a directivity of a source by wave-based numerical analysis, modeling the shape of the source geometrically in detail is the physically most appropriate. In the case of sources with complex shapes, however, geometrically precise modeling of the source shape requires small size of spatial discretization, and such a fine mesh generation results in huge computational costs and leads difficulty of practical computation. In this study, applying a basic theory of Fourier analysis in which arbitrary directivity can be constructed by linear combination of spherical harmonics, the condition of the sound source for the finite-difference time-domain method to reduce computational cost and to enable efficient analysis against a source with complex directivity characteristics was investigated. Spatial distribution of sound pressure of initial condition for respective spherical harmonic function, and correction method of spectral characteristics for the finite-difference time-domain analysis are described. The applicability of the method was validated through an application to source directivity of a head and torso simulator with a mouth simulator.

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After the Tohoku earthquake, it is becoming very important to ensure a stable energy supply because of the recent developments in renewable and decentralized energy. In order to stabilize the supply of power grids, it is useful to analyze mathematical models which describe the essence of dynamical processes of the grids. In this paper, we replicated the topology of the power grid in Eastern Japan and described power grids by phase models. We used the minimum coupling strength for global frequency synchronizationas a stability measure in power grids. Further, we identify transmission lines which contribute to a stable supply.

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We show as one of the significant characteristics of complex networks the fact that the adjacency matrix has huge zero eigenvalue degeneracy. These zero eigenvalues are originated from locally symmetric structures. We also show that the corresponding eigenvectors are strongly localized to the local structures. This localization is of a different class from the well-known Anderson localization.

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In order to establish a mathematical model on a given time series, we propose to minimize sum of prediction errors by LASSO (least absolute shrinkage and selection operator). In LASSO, the optimization problem can be solved efficiently due to its convex property. Furthermore, since the solution obtained by LASSO tends to be sparse, we can reduce the effective number of parameters even if we fit a high dimensional system with many parameters. The sparseness also reduces the computation time for prediction. In this report, we show that our method is able to identify the parameters of the logistic map, which is a simple example of a chaotic system, in a short computation time.

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In this paper, we introduce our studies on a traffic signal model and chaotic Boltzmann machines. As a class of hybrid systems including these models, we propose billiard spin systems. The billiard spin systems are expected to serve as a basic model for considering complex and large-scale engineering systems, and also expected to contribute to various research fields including machine learning and analog computation.

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One difficulty of model designing problems on the partially observable Markov decision process (POMDP), such as apprenticeship learning, was its high calculation cost for solving the optimal policy of many POMDP problems.　In this paper, we propose two techniques that reduce the calculation cost within such a setting, that is, transfer learning and subgradient calculation. We show that both techniques can be efficiently implemented on a policy-iteration POMDP solver.

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In this paper, we explain the Bayesian inference framework for understanding the computational principles underlying the brain's functions. We show that this framework possibly gives a unified theory for two types of information processing: input-related computation and output-related one. We also show that the two types of information processing can be mathematically formulated as probabilistic inference problems on a dynamic Bayesian network. This model provides theoretical foundation such as Bayes' theorem on output-related computation, which may be useful for realization of artificial brain-like information processing systems.

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It is not clear what kind of features the fractal analysis of electroencephalography (EEG) signals reveals. This study aims to understand the feature of fractal structure in detail by analyzing EEGs carefully from the viewpoint of fractal. We divided EEGs into each frequency band and investigated which element is the basis of fractal structure. As a result, we have found that gamma waves play an important role in forming the fractal structure. Moreover, it became possible to distinguish time intervals where the fractal structure can be generated only by gamma waves from other time intervals. An EEG model in which gamma waves are separated from other waves or mixed with other waves can be proposed.

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There are a variety of approaches to brain research. The numerical simulation of neural network using mathematical model is one of them, and it has been extensively studied until now. However, to comprehend the brain, it is necessary to take in for simulations various properties which the real brain has, and to verify the influences of them. Here we focus on the properties called "breaking of Dale’s principle" and "pre-synaptic control", then look at the effects of them on neural network's dynamics by numerical simulations. Below we show some parts of our results.

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In order to fabricate three-dimensionally reconstituted tissues, it is indispensable to use pattern formation of cells using interaction of mutual cells. However, it is unclear that what kind of mechanisms are included such self-organization. In this report, we aimed to establish a mathematical model that can emulate the behavior of cells computationally. This trial will be able to control and regulate the pattern formation.

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The electrorotation spectrum is a potential non-invasive method for monitoring the development of fish embryo, as well as, obtaining electric properties of each region in a fish embryo. In this study, the electrorotation spectrum of single Medaka egg (~φ1.0mm) was measured. The results suggested that during the developing stage of Medaka egg embryo between 20 and 30 is detectable by monitoring the specific peak frequency of electrorotation spectrum. The electric properties of each region in Medaka egg were calculated by modeling a single Medaka egg as an effective dielectric moment which is composed of 3 layered spherical shells.

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When single-crystal surfaces are prepared by cutting a single-crystal rod with a diamond wire-saw,the cut surfaces are severely damaged. A chemical-etching recipe to remove such defects, on Ag single-crystal surfaces, is developed. The etching effect was evaluated by X-ray diffraction. It turned out that the defects created on the cut surface can be removed by etching for 10 minutes at an etching rate of 8 µm/min under the irradiation of the 45kHz supersonic wave in the solution of 67wt%HNO₃ diluted with pure water at the volume ratio 1:1.

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