Two new methods of measuring a multidimensional displacement vector using an instantaneous ultrasound signal phase are described, i.e., the multidimensional autocorrelation method (MAM) and multidimensional Doppler method (MDM). A high measurement accuracy is achieved by combining either method with the lateral Gaussian envelope cosine modulation method (LGECMM) or multidirectional synthetic aperture method (MDSAM). Measurement accuracy is evaluated using simulated noisy echo data. Both methods yield accurate measurements comparable to that of our previously developed cross-spectrum phase gradient method (MCSPGM); however, they require less computational time (the order, MDM < MAM approximate, equals MCSPGM) and would provide realtime measurements. Moreover, comparisons of LGECMM and MDSAM performed by geometrical evaluations clarifies that LGECMM has potentials to yield more accurate measurements with less computational time. Both MAM and MDM can be applied to the measurement of tissue strain, blood flow, sonar data, and other target motions.

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In order to obtain noninvasively quantitative static mechanical properties of living tissue, we propose a new type of inverse problem by which the spatial distribution of the relative elastic modulus of the tissue can be estimated only from the deformation or strain measurement. The living tissue is modeled as a linear isotropic incompressible elastic medium which has the spatial distribution of the shear modulus, and the deformation or strain is supposedly measured ultrasonically. Assuming that there is no mechanical source in the region of interest, we derive a set of linear equations in which unknowns are the spatial derivatives of the relative shear modulus, and the coefficients are the strain and its spatial derivatives. By solving these equations, the spatial derivatives of the relative shear modulus are determined throughout the region, from which the spatial distribution of the relative shear modulus is obtained by spatial integration. The feasibility of this method was demonstrated using the simulated deformation data of the simple inclusion problem. The proposed method seems promising for the quantitative differential diagnosis on the lesion in the tissue in vivo.

High accuracy in measuring target motions can be realized by combined use of our previously developed lateral Gaussian envelope cosine modulation method (LGECMM) and displacement vector measurement methods that enable simultaneous axial and lateral displacement measurements, such as the multidimensional autocorrelation method (MAM). In this paper, LGECMM is improved by using parabolic functions and Hanning windows instead of Gaussian functions in the apodization function, i.e., parabolic apodization and Hanning apodization. The new modulations enable decreases in effective aperture length (i.e., channels) and yield more accurate displacement vector measurements than LGECMM due to increased echo signal-to-noise ratio and lateral spatial resolution. That is, on the basis of a priori knowledge about ultrasound propagation using the focusing scheme and shape of the apodization function, we stopped using Fraunhofer approximation. As practical applications of the modulations, for an agar phantom that is deformed in a lateral direction, stable and accurate 2-D shear modulus reconstructions are performed using our previously developed direct inversion approach together with 2-D strain tensor measurements using MAM.

To non-invasively quantify elasticity of soft tissue, we previously developed the iterative two-dimensional (2-D) rf-echo phase matching method for accurately measuring a 2-D displacement vector field generated in vivo in soft tissue during acquisition of two successive rf-echo data frames. We also developed a stable method for uniquely reconstructing a shear modulus distribution using strains derived from the measurement data. However, as in our measurement method a displacement is determined by using the phase characteristics of the finite local echo data as the index to iteratively search for the corresponding local data, change of the local phase characteristics due to tissue deformation deteriorates the accuracy of the determination. Thus, we improve the previous method such that, in principle, the displacement can be determined using an infinitesimal phase characteristics. That is, we incorporate an effective mechanism into the previous iterative phase matching scheme: the local size is made suitably smaller during the iterative phase matching. The demonstrated ability of measurement and reconstruction in simulation, and experiments on in vitro in pork rib and in vivo in breast tissue, shows this refinement allows not only better spatial resolution of the shear modulus image but also improved accuracy, and indicates that the improved method has a high potential to be applied for various soft tissues.