Nonlinear Acoustics in Underwater and Biomedical Applications: Array Performance Degradation and Time Reversal Invariance

This dissertation describes a model for acoustic propagation in inhomogeneous flu- ids, and explores the focusing by arrays onto targets under various conditions. The work explores the use of arrays, in particular the time reversal array, for underwater and biomedical applications. Aspects of propagation and phasing which can lead to reduced focusing effectiveness are described. An acoustic wave equation was derived for the propagation of finite-amplitude waves in lossy time-varying inhomogeneous fluid media. The equation was solved numerically in both Cartesian and cylindrical geometries using the finite-difference time-domain (FDTD) method. It was found that time reversal arrays are sensitive to several debilitating factors. Focusing ability was determined to be adequate in the presence of temporal jitter in the time reversed signal only up to about one-sixth of a period. Thermoviscous absorption also had a debilitating effect on focal pressure for both linear and nonlinear propagation. It was also found that nonlinearity leads to degradation of focal pressure through amplification of the received signal at the array, and enhanced absorption in the shocked waveforms. This dissertation also examined the heating effects of focused ultrasound in a tissue-like medium. The application considered is therapeutic heating for hyperther- mia. The acoustic model and a thermal model for tissue were coupled to solve for transient and steady temperature profiles in tissue-like media. The Pennes bioheat equation was solved using the FDTD method to calculate the temperature fields in tissue-like media from focused acoustic sources. It was found that the temperature-dependence of the medium's background prop- erties can play an important role in the temperature predictions. Finite-amplitude effects contributed excess heat when source conditions were provided for nonlinear ef- fects to manifest themselves. The effect of medium heterogeneity was also found to be important in redistributing the acoustic and temperature fields, creating regions with hotter and colder temperatures than the mean by local scattering and lensing action. These temperature excursions from the mean were found to increase monotonically with increasing contrast in the medium's properties.Office of Naval Research (Code 321-TS

Vascular countercurrent network for 3D triple-layered skin structure with radiation heating

Heat transfer in living tissue has become more and more attention for researchers, because high thermal radiation produced by intense fire, such as wild fires, chemical fires, accidents, warfare, terrorism, etc, is often encountered in human\u27s daily life. Living tissue is a heterogeneous organ consisting of cellular tissue and blood vessels, and heat transfer in cellular tissue and blood vessel is quite different, because the blood vessels provide channels for fast heat transfer. The metabolic heat generation, heat conduction and blood perfusion in soft tissue, convection and perfusion of the arterial-venous blood through the capillary, and interaction with the environment should be also considered in heat transfer in living tissue. To understand the effect of high thermal radiation on biological tissues, specifically, thermo-mechanical damage to the tissue, a mathematical model for skin injury induced by radiation heating has been developed by W. Dai et al. in 2008 [19], where the skin was considered to be a 3D triple-layered structure with an embedded three-level dendritic countercurrent vascular network. Since there are up to seven layers of blood vessels in the skin tissues [25], the motivation of this dissertation research is to extend the mathematical model developed by W. Dai et al. in 2008 [19] to the case that considers a seven-level dendritic countercurrent vascular network, where the dimensions and blood flow of the blood vessels are determined based on the constructal theory of multi-scale tree-shaped heat exchangers. As such, the number of the blood vessels is increased from eight to one hundred and twenty eight. This makes the computation much more complicated. To this end, blood flow oriented coordinates system was first designed, so that a simple energy equation in blood vessels can be obtained and solved using the fourth-order Runge-Kutta method. Coupled with the mathematical model and numerical schemes developed in W. Dai\u27s paper [19], the temperature distribution in a living skin tissue embedded with a seven layered dendritic countercurrent vascular network is able to be predicted, and hence the skin burn injury induced by radiation heating can also be predicted. Furthermore, the numerical scheme is proved to be unconditional stable and the Preconditioned Richardson iteration developed for the computation is convergent. Unconditional stable scheme (no restriction on mesh ratio) is particularly important in this research since the thickness of the first layer of the skin structure is small and hence the grid size in the thickness direction can be very small. The developed Precondition Richardson iteration allows us to transform a complicated solution system to a tridiagonal linear system, so that the conventional Thomas Algorithm can be easily used, and hence the computation cost can be reduced. Numerical results show that there is no difference between the current study and the previous study regarding the area of the high degree burn injury. However, the areas of the first and second degree burn injury are different from those obtained in W. Dai\u27s paper [19], because of the more complex countercurrent vascular network that is used in the present model. The obtained model and numerical method in this dissertation could be used in future studies: e.g., by considering a larger area of skin structure with complicated dendritic countercurrent multi-level blood vessels, as well as modeling such well documented effects of thermal damage as skin wrinkles and tissue shrinkage

A numerical method for obtaining an optimal temperature distribution in a three-dimensional triple-layered skin structure embedded with multi-level blood vessels

The research related to hyperthermia has stimulated a lot of interest in recent years because of its application in cancer treatment. When heating the tumor tissue, the crucial problem is keeping the temperature of the surrounding normal tissue below a certain threshold in order to avoid the damage to the normal tissue. Hence, it is important to obtain the temperature field of the entire region during the treatment. The objective of this dissertation is to develop a numerical method for obtaining an optimal temperature distribution in a 3D triple-layered skin structure embedded with multi-level blood vessels where the surface of the skin is irradiated by laser. The skin structure is composed of epidermis, dermis and subcutaneous, while the dimension and blood flow of the multi-level blood vessels are determined based on the constructal theory of multi-scale tree-shaped heat exchangers. The method determines the optimal laser intensity to obtain prespecified temperatures at the given locations of the skin after a pre-specified laser exposure time under a pre-specified laser irradiation pattern. The modified Pennes bio-heat transfer model is employed to describe the thermal behavior for tissue coupled with the convective energy balance equations for blood. The finite difference schemes for solving these equations are developed and the least squares method is used to optimize the laser power. As such, we develop an algorithm which can be used to obtain an optimal temperature distribution. Furthermore, the preconditioned Richardson iteration and Thomas algorithm are employed to speed up and simplify the computation. To demonstrate the applicability of the mathematical model and the numerical method, we test on three examples in each of which two cases are considered. The numerical examples show that the method is applicable and efficient. This research is important since the results will provide the clinician with powerful tools to improve the ability to deliver safe and effective therapy and the means to assess treatment safety, efficacy, and clinical outcome for skin, head, and neck cancer treatments