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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.

In this report, we present the regularization results of displacement vector measurement by the multidimensional cross-spectrum phase gradient method (MCSPGM), multidimensional autocorrelation method (MAM), and multidimensional Doppler method (MDM) without lateral modulation. In addition to the results of spatially variant regularization in displacement vector measurement using displacement variances, the results of displacement component-dependent regularization are presented. That is, according to the measurement accuracy of displacement components, the regularization is properly applied to the respective displacement components. For instance, only the regularization on the lateral displacement is effective. That is, for the lateral nonmodulation case, the accuracies and stabilities of lateral/elevational displacement measurements significantly increase. In conjunction, the convergence speed of phase matching also increases. The demonstrated measurements of the displacement vector distributions in experiments using inhomogeneous shear modulus agar phantoms confirm that displacement-componentdependent regularization enables better strain tensor measurement and shear modulus reconstruction from the viewpoints of accuracy and stability. The contrast-to-noise ratio (CNR) is useful to set regularization parameters properly for the displacement regularization, whereas the CNR is useless for shear modulus regularization in the sense that the accuracy of reconstruction value cannot be evaluated.

An effective setting method (that is, a method using the variances of strain tensor component measurements) is described for the properly spatially varied regularization parameters for our shear modulus reconstruction. At each position, the respective strain variances can be experimentally evaluated using plural field measurements or single field measurement, for example, when using all crosscorrelation- based methods, by using the Ziv-Zakai Lower Bound (ZZLB). The demonstrated regularization by the single field measurement using the cross-spectrum phase gradient method (MCSPGM) in experiments confirms that the use of the axial strain variance estimated by the echo signal-to-noise ratio and correlations (the combined SNRc) effectively stabilizes the 1-D reconstruction on an agar phantom and a human in vivo liver carcinoma during interstitial microwave thermal treatment. The regularization yields a spatially uniform stability in reconstruction.

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.

An axial strain measurement technique and a one-dimensional (1D) shear modulus reconstruction technique were developed previously by using the multidimensional radio-frequency (RF) echo phase matching method and an axial strain ratio, respectively. In this study, these techniques have been applied using a conventional ultrasound (US) imaging system with the constraint that the tissue deforms predominantly in the lateral direction, orthogonal to the ultrasound beam axis. Conventionally, axial strain measurement and axial strain ratio are used when the tissue deforms predominantly in the axial direction by extracorporeally applied pressure or vibration. In any case, an axial strain can be accurately measured using the multidimensional RF-echo phase matching method; such a measurement will be useful and will enable a simple reconstruction in a lateral deformation case. The usefulness of these techniques is demonstrated by agar phantom experiments; several problems related to their use in cases such as accuracy, bias error and detectability of inhomogeneity (contrast-to-noise ratio) are addressed. These techniques will be effective for deep regions-of-interest (ROIs) such as liver tissues, which are inaccessible from the body surface and normally deformed by heart motion or pulsation. Moreover, such techniques will enable the evaluation of the elasticity of various tissues under normal motion such as the arm and leg muscles during exercise.

As a differential diagnosis technique for living soft tissues, we are developing ultrasonic-strain-measurement-based shear modulus reconstruction methods. Previously, we reported three-dimensional (3-D) and 2-D reconstruction methods utilizing a typical Poisson's ratio very close to 0.5 (nearly-incompressible). However, because a decrease in the accuracy of the reconstructed value was confirmed to be due to the difference between the original value and the set value, we proposed 3-D and 2-D methods of reconstructing Poisson's ratio as well. Furthermore, we proposed methods of reconstructing density and dealing with dynamic deformation. However, due to tissue incompressibility, the reconstructions of shear modulus, Poisson's ratio, and density became unstable. In this report, to obtain stable, unique reconstructions, we describe a new reconstruction method using mean normal stress approximated by the product of one of Lame's constants X and volume strain epsilon alpha alpha as an unknown. Regularization is simultaneously applied to the respective distributions to decrease the instability of the reconstructions due to measurement errors of the deformation. This method also enables stable, unique reconstructions of shear modulus and density under the condition that the mean normal stress remains unknown. We also verify the effectiveness of this method through 3-D simulations, while showing erroneous artifacts occurring when 2-D and 1-D reconstructions are performed.

We previously reported an ultrasonic strain measurement-based one-dimensional (1-D) shear modulus reconstruction technique using a regularization method for differential diagnosis of malignancies on human superficial tissues (e.g., breast tissues). Here, ultrasonic strain measurement-based 2-D and 3-D shear modulus reconstruction techniques are described, and the 1-D technique is reviewed and subsequently applied to various human in vivo tissues, including deeply situated tissues (e.g., liver). Because soft tissues are deformed in 3-D space by externally situated arbitrary mechanical sources, the accuracy of the low-dimensional (i.e., 1-D or 2-D) reconstructions is lower to that of 3-D reconstruction due to occurrence of erroneous reconstruction artifacts (i.e., the reconstructed modulus is different than reality). These artifacts are confirmed on simulated inhomogeneous cubic phantoms containing a spherical homogenous inclusion using numerically calculated deformation data. The superiority of quasi-real-time imaging of the shear modulus is then demonstrated by comparing it with conventional B-mode imaging and strain imaging from the standpoints of monitoring the effectiveness of minimally invasive thermal therapy as well as differential diagnosis. Because the 2-D and 3-D techniques require special ultrasonic (US) equipment, the 1-D technique using conventional US imaging equipment is used, even though erroneous artifacts will occur. Specifically, the 1-D technique is applied as a diagnostic tool for differentiating malignancies in human in vivo liver and breast tissue, and a monitoring technique for determining the effectiveness of interstitial electromagnetic wave (micro and rf) thermal therapy on human in vivo liver and calf in vitro liver. Even when using the 1-D technique, reconstructed shear moduli were confirmed to be a suitable measure for monitoring thermal treatment as well as differential diagnosis. These results are encouraging in that they will promote use of 2-D and 3-D reconstruction techniques.