Chikayoshi Sumi

Estimation of shear modulus distribution in soft tissue from strain distribution

In order to obtain noninvasively quantitative static mechanical properties of living tissue, the authors 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, the authors 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.<<ETX>>

Displacement vector measurement using instantaneous ultrasound signal phase-multidimensional autocorrelation and Doppler methods

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 ≈ 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.

Determination of the spatial distribution of a physical parameter from the distribution of another physical variable— a differential inverse problem

We propose a new type of inverse problem, in which the spatial distribution of the relative value of a physical parameter can be determined only from the distribution of another physical variable in the region of interest if there is no source in that region. The inverse problem proposed here has two features different from conventional remote probing type problems. One is that the physical variable data are given throughout the region of interest although the number of data variables is insufficient to determine directly the physical parameter of interest, while only remote data are given in a conventional problem. The other is the mathematical structure of the inverse problem: this new inverse problem yields a spatial differential equation on the target parameter, while the conventional problem becomes an integral equation on the target parameter. To show the nature of the problem, we formulated an illustrative inverse problem on the steady‐state electric current field, in which the spatial distribution...

A robust numerical solution to reconstruct a globally relative shear modulus distribution from strain measurements

To noninvasively quantify tissue elasticity for differentiating malignancy of soft tissue, the authors previously proposed a two-dimensional (2-D) mechanical inverse problem in which simultaneous partial differential equations (PDEs) represented the target distribution globally of relative shear moduli with respect to reference shear moduli such that the relative values could be determined from strain distributions obtained by conventional ultrasound (US) or nuclear magnetic resonance (NMR) imaging-based analysis. Here, the authors further consider the analytic solution in the region of interest, subsequently demonstrating that the problem is inevitably ill-conditioned in real-world applications, i.e., noise in measurement data and improper configurations of mechanical sources/reference regions make it impossible to guarantee the existence of a stable and unique target global distribution. Next, based on clarification of the inherent problematic conditions, the authors describe a newly developed numerical-based implicit-integration approach that novelly incorporates a computationally efficient regularization method designed to solve this differential inverse problem using just low-pass filtered spectra derived from strain measurements. To evaluate method effectiveness, reconstructions of the global distribution are carried out using intentionally created ill-conditioned models. The resultant reconstructions indicate the robust solution is highly suitable, while also showing it has high potential to be applied in the development of an effective yet versatile diagnostic tool for quantifying the distribution of elasticity in various soft tissues.

Usefulness of ultrasonic strain measurement- based shear modulus reconstruction for diagnosis and thermal treatment

We previously reported an ultrasonic strain measurement-based one-dimensional (T-D) shear modulus reconstruction technique using a regularisation 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 arid 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.

Regularization of tissue shear modulus reconstruction using strain variance

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 cross- correlation-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.

An effective ultrasonic strain measurement-based shear modulus reconstruction technique for superficial tissues - demonstration on in vitro pork ribs and in vivo human breast tissues

An effective shear modulus reconstruction technique is described which uses ultrasonic strain measurements for diagnosis of superficial tissues, i.e. our previously developed ultrasonic strain measurement and shear modulus reconstruction methods are combined and enhanced. The technique realizes very low computational load, yet yields fairly high quantitativeness, high stability and spatial resolution, and large dynamic range. The suitability of the method is demonstrated on in vitro pork ribs and in vivo human breast tissues (fibroadenoma and scirrhous carcinoma).

Effective lateral modulations with applications to shear modulus reconstruction using displacement vector measurement

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.

Comparison of Parabolic and Gaussian Lateral Cosine Modulations in Ultrasound Imaging, Displacement Vector Measurement, and Elasticity Measurement

Previously, we proposed to set ultrasound (US) beam-forming parameters in order to realize the required point spread function (PSF) on the basis of optimization theory. In this report, for high quality-lateral cosine modulation (LCM) US imaging and measurements of accurate displacement vector and elasticity (i.e., strain tensor, shear modulus), after briefly reviewing our trials that broke away from the use of the Fraunhofer approximation to determine the apodization function, images and measurements obtained for an agar phantom are shown. In this study, the previously reported lateral parabolic modulation (PAM) and lateral Gaussian envelope cosine modulation (LGECM) are carried out. Comparisons of the spatial resolutions of the US images obtained and the measurement accuracies of the displacement vectors and elasticity measurements obtained using our previously developed multidimensional autocorrelation and Doppler methods (i.e., MAM and MDM) are also made. The development of next-generation US imaging systems has already begun.

Real-time adaptive cancelling of ambient noise in lung sound measurement

Ambient noise such as instrument noise and human voices often disturbs the hearing and/or measurement of lung sounds. Conventional frequency-domain filtering is usually ineffective. Noise is transmitted to the microphone that measures lung sounds through the chest wall around it, and it may be feasible to cancel out the noise by identifying this transfer function. The function, however, may vary with respect to the subject and measuring site, and therefore it should be modified dynamically. We apply an adaptive filtering technique to solve this problem. A workstation-based off-line adaptive noise canceller is developed to assess its performance in detail. Filter coefficients are controlled by a least-mean-square algorithm. Results show that the ambient noise is reduced by about 30 dB in a convergence time of several seconds. A real-time adaptive noise canceller is subsequently implemented by incorporating a digital signal processor, and a prototype electronic stethoscope is realised with high immunity to ambient noise. In a clinical application experiment in which the noise-contaminated lung souds are observed during an airway sensitivity test, satisfactory results are obtained. It is proved that the proposed method and device are effective for hearing and/or measuring lung sounds in noisy environments.