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.

Supporting Predicate Routing in DTN over MANET

We consider a Delay Tolerant Network (DTN) whose users (nodes) are connected by an underlying Mobile Ad hoc Network (MANET) substrate. Users can declaratively express high-level policy constraints on how "content" should be routed. For example, content may be diverted through an intermediary DTN node for the purposes of preprocessing, authentication, etc. To support such capability, we implement Predicate Routing [7] where high-level constraints of DTN nodes are mapped into low-level routing predicates at the MANET level. Our testbed uses a Linux system architecture and leverages User Mode Linux [2] to emulate every node running a DTN Reference Implementation code [5]. In our initial prototype, we use the On Demand Distance Vector (AODV) MANET routing protocol. We use the network simulator ns-2 (ns-emulation version) to simulate the mobility and wireless connectivity of both DTN and MANET nodes. We show preliminary throughput results showing the efficient and correct operation of propagating routing predicates, and as a side effect, the performance benefit of content re-routing that dynamically (on-demand) breaks the underlying end-to-end TCP connection into shorter-length TCP connections.

PreDA: Predicate Routing for DTN Architectures over MANET

We consider a Delay Tolerant Network (DTN) whose users (nodes) are connected by an underlying Mobile Ad hoc Network (MANET) substrate. Users can declaratively express high-level policy constraints on how “content” should be routed. For example, content can be directed through an intermediary DTN node for the purposes of preprocessing, authentication, etc., or content from a malicious MANET node can be dropped. To support such content routing at the DTN level, we implement Predicate Routing [1] where high-level constraints of DTN nodes are mapped into low-level routing predicates within the MANET nodes. Our testbed [2] uses a Linux system architecture with User Mode Linux [3] to emulate every DTN node with a DTN Reference Implementation code [4]. In our initial architecture prototype, we use the On Demand Distance Vector (AODV) routing protocol at the MANET level. We use the network simulator ns-2 (ns-emulation version) to simulate the wireless connectivity of both DTN and MANET nodes. Preliminary results show the efficient and correct operation of propagating routing predicates. For the application of content re-routing through an intermediary, as a side effect, results demonstrate the performance benefit of content re-routing that dynamically (on-demand) breaks the underlying end-to-end TCP connections into shorter-length TCP connections.