Quantitative ultrasound brain imaging with multiscale deconvolutional waveform inversion

High-resolution images of human brain are critical for monitoring the neurological conditions in a portable and safe manner. Sound speed mapping of brain tissues provides unique information for such a purpose. In addition, it is particularly important for building digital human acoustic models, which form a reference for future ultrasound research. Conventional ultrasound modalities can hardly image the human brain at high spatial resolution inside the skull due to the strong impedance contrast between hard tissue and soft tissue. We carry out numerical experiments to demonstrate that the time-domain waveform inversion technique, originating from the geophysics community, is promising to deliver quantitative images of human brains within the skull at a sub-millimeter level by using ultra-sound signals. The successful implementation of such an approach to brain imaging requires the following items: signals of sub-megahertz frequencies transmitting across the inside of skull, an accurate numerical wave equation solver simulating the wave propagation, and well-designed inversion schemes to reconstruct the physical parameters of targeted model based on the optimization theory. Here we propose an innovative modality of multiscale deconvolutional waveform inversion that improves ultrasound imaging resolution, by evaluating the similarity between synthetic data and observed data through using limited length Wiener filter. We implement the proposed approach to iteratively update the parametric models of the human brain. The quantitative imaging method paves the way for building the accurate acoustic brain model to diagnose associated diseases, in a potentially more portable, more dynamic and safer way than magnetic resonance imaging and x-ray computed tomography.     

运动车辆横向振动半车模型分析

通过半车模型, 数值研究平滑路面上运动车辆车体的前两阶横向振动频率. 将车体模型化为两端自由的Euler-Bernoulli梁, 半车模型的车轮模型化为两个弹性不等的弹簧. 建立半车模型的数学模型描述车体的横向振动. 以两端自由的静态梁的模态为试函数和权函数, 通过高阶Galerkin截断计算车体横向振动的频率, 并研究车辆运行速度、车体刚度、弹簧刚度等参数对车体振动频率的影响.     

ON ALMOST PERIODIC SOLUTIONS FOR A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS

ＯＮＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＷａｎｇＺｈｅｎ（王震）＆ＬｕｏＹｉ（骆毅）（ＡｎｈｕｉＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒ...     

Stability for the equilibrium state manifold of relativistic Birkhoffian systems

In this paper, the stability of equilibrium state manifold for relativistic Birkhoffian systems in studied. The equilibrium state equations, the disturbance equations and their first approximation are presented. The criteria of stability for the equilibrium state manifold are obtained. The relationship between the stability of the equilibrium-state manifold of relativistic Birkhoffian systems and that of classical Birkhoffian systems is discussed. An example is given to illustrate the results.