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    Studying the Patterns of Electromagnetic and Acoustic Waves in and around the Human Head

    Leszek Demkowicz
    Title Associate Professor, Department of Aerospace Engineering and Engineering Mechanics, Texas Institute for Computational and Applied Mathematics, University of Texas at Austin

    Sounds and electronic signals travel in the form of waves, traveling around and through objects in their path. The path that sound waves follow around the human head and into the ears helps a person locate the source of a sound. Electromagnetic waves, which have much greater energy than acoustic waves, often travel through the head, bouncing off the skull and brain. To study how the waves of sound and electronic signals interact with the irregular shape of the human head, Leszek Demkowicz and colleagues at the University of Texas are creating programs to track the path of these waves through a model of the human head and other objects.

    Whether it's a human head or a piece of silicon, a mathematical model of an object is constructed of building blocks--hundreds or thousands of elements assembled into the shape of the object being studied. A simulation, in general terms, computes how waves or other changes move from element to element through the object.





    The results of such simulations depend heavily on how the elements are assembled into the final shape, or mesh. Coming up with a better mesh may result in a better answer, and adaptive methods automate the process of constructing a more accurate mesh. Demkowicz, a professor in the Department of Aerospace Engineering and Engineering Mechanics and the Texas Institute for Computational and Applied Mathematics (TICAM) has built his career on studying adaptive methods.

    Adaptive methods can be applied to many types of problems, and Demkowicz's efforts have ranged from the pattern that electromagnetic waves make when hitting the human head to the acoustics of submarines. There are two adaptations these methods can implement--changing the mesh size and changing the order of approximation. The mesh size is usually referred to by the variable h, and the order of approximation with the variable p, so these methods are usually called h-adaptive and p-adaptive, respectively.

    A typical adaptive method simulation begins with an initial mesh on which the computer solves the problem. Next, an error estimate is calculated--finding the right error calculation is a subject of research in its own right--and the error distribution is estimated for the entire mesh. Finally, the mesh is modified by either changing the size of the mesh or by changing the order of approximation, and the process is repeated.

    However, certain common types of engineering problems--specifically problems with singular solutions--require methods that automatically vary both the size and order of approximation--called hp-adaptive methods. Under the leadership of Tinsley Oden, TICAM's director, Demkowicz and colleagues wrote the first codes to implement hp-adaptive methods. The codes eventually resulted in PHLEX, the first hp-adaptive finite element commercial software, developed at the Computational Mechanics Company. Applications included a variety of complex problems in solid and fluid mechanics, focusing especially around supersonic compressible flows.

    In the early 1990s, Oden and Demkowicz began working on wave propagation problems. The U.S. Navy, for example, funded acoustics studies of submarines using hp-adaptive techniques. By 1996, the acoustics work had progressed far enough for the team to begin looking at electromagnetics--a harder problem because solving Maxwell's equations is computationally more complex. "With a little luck, we proposed a method that has so far been very successful," Demkowicz said.

    With the electromagnetics codes available, DARPA funded studies of integrated circuits and how electromagnetic waves interfered with the circuitry of combined digital and analog chips. In another project, the Air Force supports studies of antenna problems and large 3-D scattering (radar) simulations.

    Figure 1: An Adaptive Mesh

    Adaptive meshes are required to capture singular solutions. This mesh shows a solution of a microstrip problem--a component of the larger problem of simulating electric fields.


    Motorola, however, funded the study that has remained at the center of Demkowicz's research--estimating the effects of radiation from cellular phones on the human head. Cell phones use frequencies of between one and two gigahertz, the same frequencies as a microwave oven. Even though the overall energy is small, a potential concern arises regarding local energy concentrations caused by the irregularities in the density and shape of the human head.

    Studies showed that cell phones do not pose a significant danger to the human head; however, the hp-adaptive methods remain essential for accurately capturing the effects of singularities of the electromagnetic fields in the human head. As part of NPACI, Demkowicz and colleagues at TICAM--Waldek Rachowicz, Andrzej Bajer, Timothy Walsh, and Satish Chavva--are creating a general code for solving 3-D electromagnetics wave propagation problems, using the hp-adaptive methods. To parallelize their code, they are collaborating with James Demmel at UC Berkeley of NPACI's Programming Tools and Environments thrust area and researchers at the Texas Advanced Computing Center.

    "I am an engineer, not a computer scientist," Demkowicz said. "Having a running code is more important to me than having an optimal code. We are parallelizing the methods on the CRAY T3E at Texas, and this is an excellent starting point for our NPACI efforts to create a better implementation."

    The codes will be applied to two variants of the head problem. In an emerging effort with Rich Charles of SDSC, Demkowicz's codes will be used to simulate how a sound propagates from a source through the outer, middle, and inner ear until the nerves pick up the signal. Charles intends to model a baseline for normal hearing, particularly the contributions of the outer ear for localizing sound.

    "The shape of the pinna and the ear canal help us locate sound," Charles said. "Hearing aids don't take advantage of those contributions, and that's why hearing aid wearers have trouble finding the source of a sound." By modeling the normal hearing process, hearing aids would be able to incorporate more sophisticated cues.


    Figure 2: The Head Problem

    To study electromagnetic scattering and absorption in the human head, Demkowicz's team at the University of Texas created boundary and finite element domain models of the human head (left) and simulated electric fields, visualized with stream tubes shown within the head (right).


    The head problem also comes into play in a collaboration between Demkowicz's team, Chandra Bajaj from TICAM, and researchers at the University of Texas Medical Center at San Antonio led by Jack Lancaster. Lancaster's group is performing a medical study in which an electromagnetic field is used to stimulate brain cells. To determine the effectiveness of this procedure, the physicians want to simulate the distribution of the field in a patient, a process similar to the Motorola study, with one key difference.

    To analyze the effects on a patient, the researchers must run Demkowicz's electromagnetic wave simulations on the patient's own head, not a hypothetical head. The first step therefore is to reconstruct the mesh representing a patient's head from magnetic resonance imaging (MRI) scans. Once these meshes are created, they can be reused for other simulations, such as Charles's acoustics study.

    With the mesh of the patient's brain, Demkowicz then performs the electromagnetic wave simulation to analyze the scattering and absorption patterns in the patient's brain. "We believe our methods are perfectly suited for this effort," Demkowicz said. "It requires simulating regions with different dielectric constants, and the interface between regions causes discontinuities in the electromagnetic field. Our methods can handle these."

    While they currently work with one MRI data set at a time, the size of the data--a typical MRI scan is about one gigabyte--introduces possible complications for the future if they wish to handle several scans simultaneously. Demkowicz plans to collaborate with investigators from NPACI's Data-intensive Computing thrust area to address these issues.

    "We have never solved a large 3-D problem in this context," Demkowicz said. "The techniques and codes have been there for small problems on workstations. The challenge that we are addressing through NPACI is to do large problems in parallel." --DH