APPLICATION OF THE KHOKHLOV-ZABOLOTSKAYA-KUZNETSOV EQUATION TO MODELING HIGH-INTENSITY FOCUSED ULTRASOUND BEAMS

High-intensity focused ultrasound is a form of therapeutic ultrasound which uses high amplitude acoustic waves to heat and ablate tissue. HIFU employs acoustic amplitudes that are high enough that nonlinear propagation effects are important in the evolution of the sound field. A common model for HIFU beams is the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation which accounts for nonlinearity, diffraction, and absorption. The KZK equation models diffraction using the parabolic or paraxial approximation. Many HIFU sources have an aperture diameter similar to the focal length and the paraxial approximation may not be appropriate. Here, results obtained using the “Texas code,” a time-domain numerical solution to the KZK equation, were used to assess when the KZK equation can be employed. In a linear water case comparison with the O’Neil solution, the KZK equation accurately predicts the pressure field in the focal region. The KZK equation was also compared to simulations of the exact fluid dynamics equations (no paraxial approximation). The exact equations were solved using the Fourier-Continuation (FC) method to approximate derivatives in the equations. Results have been obtained for a focused HIFU source in tissue. For a low focusing gain transducer (focal length 50λ and radius 10λ), the KZK and FC models showed excellent agreement, however, as the source radius was increased to 30λ, discrepancies started to appear. Modeling was extended to the case of tissue with the appropriate power law using a relaxation model. The relaxation model resulted in a higher peak pressure and a shift in the location of the peak pressure, highlighting the importance of employing the correct attenuation model. Simulations from the code that were compared to experimental data in water showed good agreement through the focal plane.

Iterative Linearized Density Matrix Propagation for Modeling Coherent Energy Transfer in Photosynthetic Light Harvesting

We present results of calculations [1] that employ a new mixed quantum classical iterative density matrix propagation approach (ILDM , or so called Is‐Landmap) [2] to explore the survival of coherence in different photo synthetic models. Our model studies confirm the long lived quantum coherence , while conventional theoretical tools (such as Redfield equation) fail to describe these phenomenon [3,4]. Our ILDM method is a numerical exactly propagation scheme and can be served as a bench mark calculation tools[2]. Result get from ILDM and from other recent methods have been compared and show agreement with each other[4,5]. Long lived coherence plateau has been attribute to the shift of harmonic potential due to the system bath interaction, and the harvesting efficiency is a balance between the coherence and dissipation[1]. We use this approach to investigate the excitation energy transfer dynamics in various light harvesting complex include Fenna‐Matthews‐Olsen light harvesting complex[1] and Cryptophyte Phycocyanin 645 [6]. [1] P.Huo and D.F.Coker ,J. Chem. Phys. 133, 184108 (2010) . [2] E.R. Dunkel, S. Bonella, and D.F. Coker, J. Chem. Phys. 129, 114106 (2008). [3] A. Ishizaki and G.R. Fleming, J. Chem. Phys. 130, 234111 (2009). [4] A. Ishizaki and G.R. Fleming, Proc. Natl. Acad. Sci. 106, 17255 (2009). [5] G. Tao and W.H. Miller, J. Phys. Chem. Lett. 1, 891 (2010). [6] P.Huo and D.F.Coker in preparation

Improved Tracking of Multiple Humans with Trajectory Prediction and Occlusion Modeling

A combined 2D, 3D approach is presented that allows for robust tracking of moving bodies in a given environment as observed via a single, uncalibrated video camera. Tracking is robust even in the presence of occlusions. Low-level features are often insufficient for detection, segmentation, and tracking of non-rigid moving objects. Therefore, an improved mechanism is proposed that combines low-level (image processing) and mid-level (recursive trajectory estimation) information obtained during the tracking process. The resulting system can segment and maintain the tracking of moving objects before, during, and after occlusion. At each frame, the system also extracts a stabilized coordinate frame of the moving objects. This stabilized frame is used to resize and resample the moving blob so that it can be used as input to motion recognition modules. The approach enables robust tracking without constraining the system to know the shape of the objects being tracked beforehand; although, some assumptions are made about the characteristics of the shape of the objects, and how they evolve with time. Experiments in tracking moving people are described.

A Neural Model of 3D Shape-From-Texture: Multiple-Scale Filtering, Boundary Grouping, and Surface Filling-In

A neural model is presented of how cortical areas V1, V2, and V4 interact to convert a textured 2D image into a representation of curved 3D shape. Two basic problems are solved to achieve this: (1) Patterns of spatially discrete 2D texture elements are transformed into a spatially smooth surface representation of 3D shape. (2) Changes in the statistical properties of texture elements across space induce the perceived 3D shape of this surface representation. This is achieved in the model through multiple-scale filtering of a 2D image, followed by a cooperative-competitive grouping network that coherently binds texture elements into boundary webs at the appropriate depths using a scale-to-depth map and a subsequent depth competition stage. These boundary webs then gate filling-in of surface lightness signals in order to form a smooth 3D surface percept. The model quantitatively simulates challenging psychophysical data about perception of prolate ellipsoids (Todd and Akerstrom, 1987, J. Exp. Psych., 13, 242). In particular, the model represents a high degree of 3D curvature for a certain class of images, all of whose texture elements have the same degree of optical compression, in accordance with percepts of human observers. Simulations of 3D percepts of an elliptical cylinder, a slanted plane, and a photo of a golf ball are also presented.