A method has been developed which can predict the appearance and properties of B-scan images. The theoretical basis for the tissue models used, and the assumptions made in the simulation concerning the nature of pulse-echo imaging, are discussed. A key feature of the simulation is the Fourier domain synthesis of the tissue model, which permits convenient specification of some statistical properties of a randomly inhomogeneous scattering medium. Other characteristics that may be specified include the ultrasonic pulse and beam shapes, and subsequent signal processing. Both the initial tissue model and the simulated B-scan image are displayed as grey-scale pictures, allowing visual comparison in the same way that clinical B-scans are currently observed. Preliminary results of applying the simulation are shown to have a number of features in common with clinical images and with scans of a test object. A better understanding of the nature of pulse-echo images is gained and conclusions drawn regarding the range of system and tissue parameters over which these images convey information about the tissue structure. The method may also be of use to determine optimum design of equipment for imaging and tissue characterisation, and to investigate the extent to which the acoustic structure of tissues can be described in terms of simple mathematical models.

https://iopscience.iop.org/article/10.1088/0031-9155/25/3/006/pdf

Ultrasonic B-scanning: a computer simulation.

Trabecular bone plays a significant role in maintaining bone structural integrity. Its density is a significant determinant of bone strength and fracture risk, but there is still unexplained variance. It has been suggested that the ability to measure structural information will improve the estimation of bone strength and fracture risk. Quantitative ultrasound (QUS) is a mechanical wave that can be influenced by bone structure, in addition to bone mineral density (BMD). This article reviews the evidence in the literature supporting or refuting this assumption. Theoretically, the propagation of QUS is influenced by both structure and density of the medium. QUS measurement in vivo shows weak but significant association with axial BMD. However, the association becomes stronger when measured in vitro. Broadband ultrasound attenuation (BUA) exhibits a nonlinear relationship with density over a large density range. When cubes of cancellous bone are measured in the three orthogonal directions, both BUA and speed of sound (SOS) show significant anisotropy which mirrors mechanical anisotropy. QUS has also been shown to correlate significantly with structural parameters measured by histomorphometry. However, structure remains a significant predictor after adjustment for BMD mainly in bovine samples. Other studies using phantoms of bone samples have also demonstrated that QUS is dependent on structure. There is preliminary indication that fractal dimensions are significantly associated with QUS. The ultimate usefulness of structural dependence of QUS will be in its ability to improve bone strength estimation above and beyond density. There is ample evidence documenting the ability of QUS to predict bone strength in vitro. BMD is a significant predictor of bone strength and the additive value of structure in estimating bone strength is variable. Clinically, ultrasound of the calcaneus is measured in one direction (medio-lateral) and the structural variation in this direction may be limited. Nevertheless, QUS can provide useful additional information to that provided by axial BMD due in part to different precision and accuracy errors and to biological discordance. On the whole one could conclude that ultrasound attenuation is due to structural parameters and these variables are also dependent on density.

Is Quantitative Ultrasound Dependent on Bone Structure? A Reflection

Measurements are reported on the ultrasonic attenuation coefficient, the velocity of sound propagation and the differential scattering coefficient (for 180° scattering) for 3 types of freshly excised normal human tissues: liver, spleen and brain (white matter). The measurements are made as a continuous function of frequency in the range 0.7–7 MHz. The data for attenuation and scattering are consistent with a power law dependence on frequency though the latter are best described by a two-term fit. Comparison of the scattering data with theory suggests that two forms of tissue structure, with characteristic dimensions of approx. 1 and 0.02 mm, are predominantly responsible for scattering in the frequency range 0.5–5 MHz. The absolute value of backscattering for freshly excised human liver tissue at 1 MHz is 3.5 × 10 −4 cm −1 Sr −1 rising to 9.0 × 10 −4 cm −1 Sr −1 at 3 MHz. Extrapolation to total scattering suggests that the contribution of scattering to attenuation varies from approx. 2% at 1 MHz to 5.4% at 3 MHz.

Evaluation of backscattering coefficients for excised human tissues: results, interpretation and associated measurements

The advent of real-time B-scanning has led to interest in the diagnostic value of the dynamic properties of soft tissue. Present ultrasonic techniques for investigating motion cannot measure the motion of homogeneous tissues. A technique has been developed which uses the correlation coefficient between A-scans to measure the amplitude and frequency of their motion, both in water tank experiments and in vivo. The success of the technique, which is digitally implemented, supports the validity of stochastic models for the acoustic structure of soft tissues. The motion pattern observed in vivo can be correlated with the arterial pressure pulse.

Measurement of soft tissue motion using correlation between A-scans

Speckle in ultrasonic imaging

Two ultrasonic scattering models for human tissue are suggested, one in which the homogeneities are discrete and the other an inhomogeneous continuum. After discussing relevant functions, the results of the literature on the two models are considered in the context of diagnosis. The results point to the parameters relevant to a description of the scattering process, emphasizing the need for more physical information about human tissue.

The scattering of ultrasound by human tissues—Some theoretical models

A ray tracing model for ultrasonic propagation through the human eye, including the lens, has been developed on the assumptions of lossless media and non-reflecting interfaces. Measurement of the distribution of an ultrasonic beam before and after traversing specimens of human eyes in vitro, and of the velocity of ultrasound in the various dissected media, has permitted some comparison of the predictions of the model with experiment. The agreement is good although there are significant limitations involved and these are discussed. For imaging systems the effect of the eye arises largely from the lens which acts as a defocussing lens of focal length approx. 13.5 cm. Although the experiments were performed at approx. 4 MHz, the validity of the ray tracing model is largely frequency independent and will be appropriate at the higher frequencies commonly used in ophthalmology.

Investigation of ultrasound axially traversing the human eye

Terminology in ultrasonic tissue characterization

Discussions of the phase and amplitude fluctuations of waves travelling through inhomogeneous media have previously considered only fluctuations caused by the variation of sound velocity in the medium, density variations being ignored since in water and air they can be shown to be small. In biological tissues this assumption cannot be made, and this paper derives the fluctuation dependence on velocity and density variations of characteristic dimension large compared to the wavelength. Previous discussions have shown a more appropriate formulation to be that of the fluctuation dependence on bulk modulus and density variations and this analysis is presented for the first time. The form of the solutions is shown to be simplified for extreme values of the wave parameter, but formulae for comparison with experiment require the specification of the analytical form of the correlation coefficients of the parameter variations. The fluctuations for correlation coefficients of the form exp (−r2/a2) are evaluated both for the general case, and for extreme values of the wave parameter. It is found that the density variations contribute to the fluctuations only insofar as they are cross-correlated with the velocity fluctuations (for velocity and density variations); while the amplitude fluctuations, for small values of the wave parameter and the specific form of correlation coefficients used, are independent of frequency.

Phase and amplitude fluctuations in the propagation of acoustic waves in lossless inhomogeneous continua with velocity, density and bulk modulus variations.

Ultrasonic tissue models have been suggested in the literature as a means of helping elucidate the physical mechanism of the tissue: ultrasound interaction, thus permitting optimization of the techniques of tissue characterization under intense study at the present time. A common requirement is that the fluid matrix of a model should have specified acoustic characteristics (e.g. density or sound velocity). This brief communication describes a simple diagrammatic aid for the selection of suitable components which also provides a close estimate of the relative proportions needed.

R.C. Chivers

Papers

The scattering of ultrasound by human tissues—Some theoretical models

Investigation of ultrasound axially traversing the human eye

Terminology in ultrasonic tissue characterization

Phase and amplitude fluctuations in the propagation of acoustic waves in lossless inhomogeneous continua with velocity, density and bulk modulus variations.

An aid to making liquid mixtures with specified acoustic characteristics