"Abstract Conventional ultrasound imaging systems use array transducers for focusing and beam steering, to improve lateral resolution and permit real-time imaging. This thesis research investigates a different use of array transducers, where the acoustic field and the receiver characteristics are designed such that the energy of the output signal from targets of a specified geometry is maximized. The output signal is the sum of the received signals obtained using all the possible combinations of transducer array elements as transmitter and receiver. This work is based on annular array transducers, but is applicable for any array configuration. The first step is the development of software for the efficient modeling of the wave interaction between transmitted field and target, and between the transducer and receiver field. Using this software, we have calculated the received signal for each combination of an array element as transmitter and the same or another array element as receiver, leading to an N x N received signal matrix for an N element array transducer. A waveform optimization algorithm is then implemented for the purpose of determining the set of delays for the individual array elements, which maximizes the energy of the sum of the received signals. In one implementation of this algorithm, the received signal with the maximum energy is considered as a reference signal, and specific delays are applied to the other signals so that any two signals produce a maximum correlation. This leads to an N x N delay matrix, which, however, is not readily implemented in a practical real-time system, which uses all the elements in an array transducer simultaneously to customize acoustic fields. Hence, the values in this delay matrix are fed into a linear programming optimizer tool to obtain a set of delay values, which makes its implementation practical. The optimized set of delays thus obtained is used to maximize the energy of the received signal for a given transducer and target geometry and hence to enhance the reflectivity of that target. It is also important to check the robustness of the optimized set of delays obtained above, for a given target geometry. Robustness refers to the sensitivity of the optimization to variation in target geometry. This aspect is also evaluated as a part of this thesis work."

In this dissertation, a novel fast modeling technique called peri-ultrasound that can model both linear and nonlinear ultrasonic behavior of materials is developed and implemented. Nonlinear ultrasonic response can detect even very small material non- linearity. Quantification of the material nonlinearity at the early stages of damage is important to avoid catastrophic failure and reduce repair costs. The developed model uses the nonlocal continuum-based peridynamic theory which was found to be a good simulation tool for handling crack propagation modeling, in particular when multiple cracks grow simultaneously. The developed peri-ultrasound modeling tool has been used to model the ultrasonic response at the interface of two materials in presence of an interface crack. Also, the stress wave propagation in a half-space (or half-plane for a 2-dimensional problem) with boundary loading is investigated using peri-ultrasound modeling. In another simulation, well-established two-dimensional Lamb's problem is investigated where the results are verified against available analytical solution. Also, the interaction between the surface wave and a surface breaking crack is studied.

In this thesis, two algorithms are introduced for use in ultrasound elastography. Ultrasound elastography is a technique developed in the last 20 years by which anomalous regions in soft tissue are located and diagnosed without the need for biopsy. Due to this, the relativity cheap cost of ultrasound imaging and the high level of accuracy in the methods, ultrasound elastography methods have shown great potential for the diagnosis of cancer in soft tissues. The algorithms introduced in this thesis represent an advance in this field. The first algorithm is a two-step iteration procedure consisting of two minimization problems - displacement estimation and elastic parameter calculation that allow for diagnosis of any anomalous regions within soft tissue. The algorithm represents an improvement on existing methods in several ways. A weighting factor is introduced for each different point in the tissue dependent on the confidence in the accuracy of the data at that point, an exponential substitution is made for the elasticity modulus, an adjoint method is used for efficient calculation of the gradient vector and a total variation regularization technique is used. Most importantly, an adaptive mesh refinement strategy is introduced that allows highly efficient calculation of the elasticity distribution of the tissue though using a number of degrees of freedom several orders lower than methods that use a uniform mesh refinement strategy. Results are presented that show the algorithm is robust even in the presence of significant noise and that it can locate a tumour of 4mm in diameter within a 5cm square region of tissue. Also, the algorithm is extended into 3 dimensions and results are presented that show that it can calculate a 3 dimensional elasticity distribution efficiently. This extension into 3-d is a significant advance in the field. The second algorithm is a one-step algorithm that seeks to combine the two problems of elasticity distribution and displacement calculation into one. As in the two-step algorithm, a weighting factor, exponential substitution for the elasticity parameter, adjoint method for calculation of the gradient vector, total variation regularization and adaptive mesh refinement strategy are incorporated. Results are presented that show that this original approach can locate tumours of varying sizes and shapes in the presence of varying levels of added artificial noise and that it can determine the presence of a tumour in images taken from breast tissue in vivo.