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.

The Sensor Network Workbench: Towards Functional Specification, Verification and Deployment of Constrained Distributed Systems

As the commoditization of sensing, actuation and communication hardware increases, so does the potential for dynamically tasked sense and respond networked systems (i.e., Sensor Networks or SNs) to replace existing disjoint and inflexible special-purpose deployments (closed-circuit security video, anti-theft sensors, etc.). While various solutions have emerged to many individual SN-centric challenges (e.g., power management, communication protocols, role assignment), perhaps the largest remaining obstacle to widespread SN deployment is that those who wish to deploy, utilize, and maintain a programmable Sensor Network lack the programming and systems expertise to do so. The contributions of this thesis centers on the design, development and deployment of the SN Workbench (snBench). snBench embodies an accessible, modular programming platform coupled with a flexible and extensible run-time system that, together, support the entire life-cycle of distributed sensory services. As it is impossible to find a one-size-fits-all programming interface, this work advocates the use of tiered layers of abstraction that enable a variety of high-level, domain specific languages to be compiled to a common (thin-waist) tasking language; this common tasking language is statically verified and can be subsequently re-translated, if needed, for execution on a wide variety of hardware platforms. snBench provides: (1) a common sensory tasking language (Instruction Set Architecture) powerful enough to express complex SN services, yet simple enough to be executed by highly constrained resources with soft, real-time constraints, (2) a prototype high-level language (and corresponding compiler) to illustrate the utility of the common tasking language and the tiered programming approach in this domain, (3) an execution environment and a run-time support infrastructure that abstract a collection of heterogeneous resources into a single virtual Sensor Network, tasked via this common tasking language, and (4) novel formal methods (i.e., static analysis techniques) that verify safety properties and infer implicit resource constraints to facilitate resource allocation for new services. This thesis presents these components in detail, as well as two specific case-studies: the use of snBench to integrate physical and wireless network security, and the use of snBench as the foundation for semester-long student projects in a graduate-level Software Engineering course.