PARAMETERS AFFECTING THE IMAGING AND DETECTION OF MICROBUBBLES IN BLOOD

Stabilized micron-sized bubbles, known as contrast agents, are often injected into the body to enhance ultrasound imaging of blood flow. The ability to detect such bubbles in blood depends on the relative magnitude of the acoustic power backscattered from the microbubbles (‘signal’) to the power backscattered from the red blood cells (‘noise’). Erythrocytes are acoustically small (Rayleigh regime), weak scatterers, and therefore the backscatter coefficient (BSC) of blood increases as the fourth power of frequency throughout the diagnostic frequency range. Microbubbles, on the other hand, are either resonant or super-resonant in the range 5-30 MHz. Above resonance, their total scattering cross-section remains constant with increasing frequency. In the present thesis, a theoretical model of the BSC of a suspension of red blood cells is presented and compared to the BSC of Optison® contrast agent microbubbles. It is predicted that, as the frequency increases, the BSC of red blood cell suspensions eventually exceeds the BSC of the strong scattering microbubbles, leading to a dramatic reduction in signal-to-noise ratio (SNR). This decrease in SNR with increasing frequency was also confirmed experimentally by use of an active cavitation detector for different concentrations of Optison® microbubbles in erythrocyte suspensions of different hematocrits. The magnitude of the observed decrease in SNR correlated well with theoretical predictions in most cases, except for very dense suspensions of red blood cells, where it is hypothesized that the close proximity of erythrocytes inhibits the acoustic response of the microbubbles.

QUANTITATIVE THREE DIMENSIONAL ELASTICITY IMAGING

Neoplastic tissue is typically highly vascularized, contains abnormal concentrations of extracellular proteins (e.g. collagen, proteoglycans) and has a high interstitial fluid pres- sure compared to most normal tissues. These changes result in an overall stiffening typical of most solid tumors. Elasticity Imaging (EI) is a technique which uses imaging systems to measure relative tissue deformation and thus noninvasively infer its mechanical stiffness. Stiffness is recovered from measured deformation by using an appropriate mathematical model and solving an inverse problem. The integration of EI with existing imaging modal- ities can improve their diagnostic and research capabilities. The aim of this work is to develop and evaluate techniques to image and quantify the mechanical properties of soft tissues in three dimensions (3D). To that end, this thesis presents and validates a method by which three dimensional ultrasound images can be used to image and quantify the shear modulus distribution of tissue mimicking phantoms. This work is presented to motivate and justify the use of this elasticity imaging technique in a clinical breast cancer screening study. The imaging methodologies discussed are intended to improve the specificity of mammography practices in general. During the development of these techniques, several issues concerning the accuracy and uniqueness of the result were elucidated. Two new algorithms for 3D EI are designed and characterized in this thesis. The first provides three dimensional motion estimates from ultrasound images of the deforming ma- terial. The novel features include finite element interpolation of the displacement field, inclusion of prior information and the ability to enforce physical constraints. The roles of regularization, mesh resolution and an incompressibility constraint on the accuracy of the measured deformation is quantified. The estimated signal to noise ratio of the measured displacement fields are approximately 1800, 21 and 41 for the axial, lateral and eleva- tional components, respectively. The second algorithm recovers the shear elastic modulus distribution of the deforming material by efficiently solving the three dimensional inverse problem as an optimization problem. This method utilizes finite element interpolations, the adjoint method to evaluate the gradient and a quasi-Newton BFGS method for optimiza- tion. Its novel features include the use of the adjoint method and TVD regularization with piece-wise constant interpolation. A source of non-uniqueness in this inverse problem is identified theoretically, demonstrated computationally, explained physically and overcome practically. Both algorithms were test on ultrasound data of independently characterized tissue mimicking phantoms. The recovered elastic modulus was in all cases within 35% of the reference elastic contrast. Finally, the preliminary application of these techniques to tomosynthesis images showed the feasiblity of imaging an elastic inclusion.