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

Learning and Production of Movement Sequences: Behavioral, Neurophysiological, and Modeling Perspectives

A growing wave of behavioral studies, using a wide variety of paradigms that were introduced or greatly refined in recent years, has generated a new wealth of parametric observations about serial order behavior. What was a mere trickle of neurophysiological studies has grown to a more steady stream of probes of neural sites and mechanisms underlying sequential behavior. Moreover, simulation models of serial behavior generation have begun to open a channel to link cellular dynamics with cognitive and behavioral dynamics. Here we summarize the major results from prominent sequence learning and performance tasks, namely immediate serial recall, typing, 2XN, discrete sequence production, and serial reaction time. These populate a continuum from higher to lower degrees of internal control of sequential organization. The main movement classes covered are speech and keypressing, both involving small amplitude movements that are very amenable to parametric study. A brief synopsis of classes of serial order models, vis-à-vis the detailing of major effects found in the behavioral data, leads to a focus on competitive queuing (CQ) models. Recently, the many behavioral predictive successes of CQ models have been joined by successful prediction of distinctively patterend electrophysiological recordings in prefrontal cortex, wherein parallel activation dynamics of multiple neural ensembles strikingly matches the parallel dynamics predicted by CQ theory. An extended CQ simulation model-the N-STREAMS neural network model-is then examined to highlight issues in ongoing attemptes to accomodate a broader range of behavioral and neurophysiological data within a CQ-consistent theory. Important contemporary issues such as the nature of working memory representations for sequential behavior, and the development and role of chunks in hierarchial control are prominent throughout.

Spiking Dynamics during Perceptual Grouping in the Laminar Circuits of Visual Cortex

Grouping of collinear boundary contours is a fundamental process during visual perception. Illusory contour completion vividly illustrates how stable perceptual boundaries interpolate between pairs of contour inducers, but do not extrapolate from a single inducer. Neural models have simulated how perceptual grouping occurs in laminar visual cortical circuits. These models predicted the existence of grouping cells that obey a bipole property whereby grouping can occur inwardly between pairs or greater numbers of similarly oriented and co-axial inducers, but not outwardly from individual inducers. These models have not, however, incorporated spiking dynamics. Perceptual grouping is a challenge for spiking cells because its properties of collinear facilitation and analog sensitivity to inducer configurations occur despite irregularities in spike timing across all the interacting cells. Other models have demonstrated spiking dynamics in laminar neocortical circuits, but not how perceptual grouping occurs. The current model begins to unify these two modeling streams by implementing a laminar cortical network of spiking cells whose intracellular temporal dynamics interact with recurrent intercellular spiking interactions to quantitatively simulate data from neurophysiological experiments about perceptual grouping, the structure of non-classical visual receptive fields, and gamma oscillations.