Defining optimal axial and lateral resolution for estimating scatterer properties from volumes using ultrasound backscatter

The rf signals used to construct conventional ultrasound B-mode images contain frequency-dependent information that can be examined through the backscattered power spectrum. Typically, the backscattered power spectrum is calculated from a region of interest (ROI) within some larger volume. The dimensions of the ROI are defined axially by the spatial length corresponding to the time gate and laterally by the number of scan lines included in the ROI. Averaging the backscattered power spectra from several independent scan lines can reduce the presence of noise caused by electronics and by the random scatterer spacings, but also decreases the lateral resolution of the interrogation region. Furthermore, larger axial gate lengths can be used to reduce the effects of noise and improve the precision and accuracy of scatterer property estimates but also decreases the axial resolution. A trade-off exists between the size of the ROI (the number of scan lines used, the separation distance between each scan line, the axial gate length) and the accuracy and precision of scatterer property estimates. A series of simulations and measurements from physical phantoms were employed to examine these trade-offs. The simulations and phantom measurements indicated the optimal lateral and axial sizes of the ROI, where estimate accuracy and precision were better than 10% and 5%, respectively, occurred at 4 to 5 beamwidths laterally and 15 to 20 spatial pulse lengths axially.     

A theoretical comparison of attenuation measurement techniques from backscattered ultrasound echoes

Accurate characterization of tissue pathologies using ultrasonic attenuation is strongly dependent on the accuracy of the algorithm that is used to obtain the attenuation coefficient estimates. In this paper, computer simulations were used to compare the accuracy and the precision of the three methods that are commonly used to estimate the local ultrasonic attenuation within a region of interest (ROI) in tissue; namely, the spectral log difference method, the spectral difference method, and the hybrid method. The effects of the inhomgeneities within the ROI on the accuracy of the three algorithms were studied, and the optimal ROI size (the number of independent echoes laterally and the number of pulse lengths axially) was quantified for each method. The three algorithms were tested for when the ROI was homogeneous, the ROI had variations in scatterer number density, and the ROI had variations in effective scatterer size. The results showed that when the ROI was homogeneous, the spectral difference method had the highest accuracy and precision followed by the spectral log difference method and the hybrid method, respectively. Also, when the scatterer number density varied, the spectral difference method completely failed, while the log difference method and hybrid method still gave good results. Lastly, when the scatterer size varied, all of the methods failed.     

Attenuation measurement uncertainties caused by speckle statistics

Attenuation measurements can be derived from the decay of backscattered signal with depth in an inhomogeneous material. In cases such as liver tissue, where many small inhomogeneities are likely to be included in sample volumes defined by pulse and beam widths, Rayleigh statistics describe the random nature of the magnitude of backscattered pressure. The statistics of speckle underlie the uncertainties in estimates of attenuation at discrete frequencies, and of the magnitude and frequency dependence of attenuation over a bandwidth. This paper derives expressions for the standard deviations of attenuation magnitude and frequency dependence in terms of parameters such as the dimensions of the region of interest, and the bandwidth of the ultrasonic system. Practical examples are given using published data, and comparisons to other techniques which measure "attenuation slope" are made. The analysis yields insights into trade-offs among variables such as the dimensions and shape of regions of interest, and the segmenting of data in time and frequency domain.     

Nonlinear propagation effects on broadband attenuation measurements and its implications for ultrasonic tissue characterization.

A study is presented in which the influence of the pressure amplitude of the incident pulse on the estimated frequency dependency of the attenuation coefficient is shown. First, the effect is demonstrated with a simple theoretical model for both transmission and reflection measurements. Simulations show that for both measurement techniques a high-amplitude incident pulse results in a biased estimate of the attenuation coefficient due to nonlinear interaction of the different frequency components of the incident pulse. It is shown that in transmission and reflection measurements the biases have opposite signs. The effect of bandwidth, central frequency, and phase of the incident pulse on this bias is investigated. Second, the effect is demonstrated both in vitro, using a broadband through-transmission substitution technique on a tissue mimicking gelatine phantom, and in vivo, using reflection measurements with standard clinical equipment. The experimental results agree well with the theoretical model. The relevance of this study for ultrasonic tissue characterization is shown.     

In vivo ultrasonic attenuation slope estimates for detecting cervical ripening in rats: Preliminary results

To effectively postpone preterm birth, cervical ripening needs to be detected and delayed. As the cervix ripens, the spacing between the collagen fibers increases and fills with water, hyaluronan, decorin, and enzymes suggesting that the ultrasonic attenuation of the cervix should decrease. The decrease in ultrasonic attenuation may be detectable, leading to an effective means of detecting cervical ripening. Herein, the traditional attenuation slope-estimation algorithm based on measuring the downshift in center frequency of the ultrasonic backscattered signal with propagation depth was modified and applied to the cervix of rats. The modified algorithm was verified using computer simulations and an ex vivo tissue sample before being evaluated in in vivo animal studies. Spherically-focused f/3 transducers with 33-MHz center frequencies and with 9-mm focal lengths were used in both the simulations and experiments. The accuracy was better than 15% in the simulations, and the attenuation slope of the cervix in the ex vivo experiment was 2.6+/-0.6 dB/cm-MHz, which is comparable to 2.5+/-0.4 dB/cm-MHz measured using a through-transmission insertion loss technique. For the in vivo experiments, a statistically significant effect of ultrasonic attenuation with gestational age was not observed. The large variances in the in vivo results were most likely due to the natural variation in attenuation for biological tissue between animals.     

Time and frequency parameters of bottlenose dolphin whistles as predictors of surface behavior in the Mississippi Sound

In this study, an algorithm previously developed for estimating the total ultrasonic attenuation along the propagation path from the surface of the transducer to a region of interest (ROI) in tissue, was modified to make it more practical for use in clinical settings. Specifically, the algorithm was re-derived for when a tissue mimicking phantom rather than a planar reflector is used to obtain the reference power spectrum. The reference power spectrum is needed to compensate for the transfer function of the transmitted pulse, the transfer function of transducer, and the diffraction effects that result from focusing/beam forming. The modified algorithm was tested on simulated radio frequency (RF) echo lines obtained from two samples that have different scatterer sizes and different attenuation coefficient slopes, one of which was used as a reference. The mean and standard deviation of the percent errors in the attenuation coefficient estimates (ACEs) were less than 5% and 10%, respectively, for ROIs that contain more than 10 pulse lengths and more than 25 independent echo lines. The proposed algorithm was also tested on two tissue mimicking phantoms that have attenuation coefficient slopes of 0.7 dB/cm-MHz and 0.5 dB/cm-MHz respectively, the latter being the reference phantom. When a single element spherically focused source was used, the mean and standard deviation of the percent errors in the ACEs were less than 5% and 10% respectively for windows that contain more than 10 pulse lengths and more than 17 independent echo lines. When a clinical array transducer was used, the mean and standard deviation of the percent errors in the ACEs were less than 5% and 25%, respectively, for windows that contain more than 12 pulse lengths and more than 45 independent echo lines.     

Identifying ultrasonic scattering sites from three-dimensional impedance maps

Ultrasonic backscattered signals contain frequency-dependent information that is usually discarded to produce conventional B-mode images. It is hypothesized that parametrization of the quantitative ultrasound frequency-dependent information (i.e., estimating scatterer size and acoustic concentration) may be related to discrete scattering anatomic structures in tissues. Thus, an estimation technique is proposed to extract scatterer size and acoustic concentration from the power spectrum derived from a three-dimensional impedance map (3DZM) of a tissue volume. The 3DZM can be viewed as a computational phantom and is produced from a 3D histologic data set. The 3D histologic data set is constructed from tissue sections that have been appropriately stained to highlight specific tissue features. These tissue features are assigned acoustic impedance values to yield a 3DZM. From the power spectrum, scatterer size and acoustic concentration estimates were obtained by optimization. The 3DZM technique was validated by simulations that showed relative errors of less than 3% for all estimated parameters. Estimates using the 3DZM technique were obtained and compared against published ultrasonically derived estimates for two mammary tumors, a rat fibroadenoma and a 4T1 mouse mammary carcinoma. For both tumors, the relative difference between ultrasonic and 3DZM estimates was less than 10% for the average scatterer size.     

Improved scatterer property estimates from ultrasound backscatter for small gate lengths using a gate-edge correction factor

Backscattered rf signals used to construct conventional ultrasound B-mode images contain frequency-dependent information that can be examined through the backscattered power spectrum. The backscattered power spectrum is found by taking the magnitude squared of the Fourier transform of a gated time segment corresponding to a region in the scattering volume. When a time segment is gated, the edges of the gated regions change the frequency content of the backscattered power spectrum due to truncating of the waveform. Tapered windows, like the Hanning window, and longer gate lengths reduce the relative contribution of the gate-edge effects. A new gate-edge correction factor was developed that partially accounted for the edge effects. The gate-edge correction factor gave more accurate estimates of scatterer properties at small gate lengths compared to conventional windowing functions. The gate-edge correction factor gave estimates of scatterer properties within 5% of actual values at very small gate lengths (less than 5 spatial pulse lengths) in both simulations and from measurements on glass-bead phantoms. While the gate-edge correction factor gave higher accuracy of estimates at smaller gate lengths, the precision of estimates was not improved at small gate lengths over conventional windowing functions.     

A novel power spectrum calculation method using phase-compensation and weighted averaging for the estimation of ultrasound attenuation

An estimation of ultrasound attenuation in soft tissues is critical in the quantitative ultrasound analysis since it is not only related to the estimations of other ultrasound parameters, such as speed of sound, integrated scatterers, or scatterer size, but also provides pathological information of the scanned tissue. However, estimation performances of ultrasound attenuation are intimately tied to the accurate extraction of spectral information from the backscattered radiofrequency (RF) signals. In this paper, we propose two novel techniques for calculating a block power spectrum from the backscattered ultrasound signals. These are based on the phase-compensation of each RF segment using the normalized cross-correlation to minimize estimation errors due to phase variations, and the weighted averaging technique to maximize the signal-to-noise ratio (SNR). The simulation results with uniform numerical phantoms demonstrate that the proposed method estimates local attenuation coefficients within 1.57% of the actual values while the conventional methods estimate those within 2.96%. The proposed method is especially effective when we deal with the signal reflected from the deeper depth where the SNR level is lower or when the gated window contains a small number of signal samples. Experimental results, performed at 5 MHz, were obtained with a one-dimensional 128 elements array, using the tissue-mimicking phantoms also show that the proposed method provides better estimation results (within 3.04% of the actual value) with smaller estimation variances compared to the conventional methods (within 5.93%) for all cases considered.     

Estimate of the attenuation coefficient using a clinical array transducer for the detection of cervical ripening in human pregnancy

Premature delivery is the leading cause of infant mortality in the United States. Currently, premature delivery cannot be prevented and new treatments are difficult to develop due to the inability to diagnose symptoms prior to uterine contractions. Cervical ripening is a long period that precedes the active phase of uterine contractions and cervical dilation. The changes in the microstructure of the cervix during cervical ripening suggest that the ultrasonic attenuation should decrease. The objective of this study is to use the reference phantom algorithm to estimate the ultrasonic attenuation in the cervix of pregnant human patients. Prior to applying the algorithm to in vivo human data, two homogeneous phantoms with known attenuation coefficients were used to validate the algorithm and to find the length and the width of the region of interest (ROI) that achieves the smallest error in the attenuation coefficient estimates. In the phantom data, we found that the errors in the attenuation coefficients estimates are less than 12% for ROIs that contain 40 wavelengths or more axially and 30 echo lines or more laterally. The reference phantom algorithm was then used to obtain attenuation maps of the echoes from two human pregnant cervices at different gestational ages. It was observed that the mean of the attenuation coefficient estimates in the cervix of the patient at a more advanced gestational age is smaller than the mean of the attenuation coefficient estimates in the cervix of the patient at an earlier gestational age which suggests that ultrasonic attenuation decreases with increasing gestational age. We also observed a large variance between the attenuation coefficient estimates in the different regions of the cervix due to the natural variation in tissue micro-structures across the cervix. The preliminary results indicate that the algorithm could potentially provide an important diagnostic tool for diagnosing the risk of premature delivery.     

An optimized technique for backscatter attenuation measurements in optical fibres

A technique which gives maximum range and sensitivity for estimating fibre attenuation from the backscattered light has been evolved. With this technique stability problems in the source and receiver are overcome by taking two different time samples for each pulse launched into the fibre, the attenuation being derived from the ratio of the two samples. An analysis indicates that an optimum operating strategy exists in terms of the choice of system parameters such that the range over which attenuation can be measured is maximized. Results indicate that local loss measurements can be performed on fibre sections which are remote from the source by a distance corresponding to a fibre attenuation of 27 dB. Furthermore, preliminary experimental results are presented to demonstrate the viability of the technique.     

Frequency dependence of acoustic parameters of freshly excised tissues of Sprague Dawley rats

A modified version of the pulse echo technique was used to measure the velocity of propagation and attenuation of ultrasound in excised tissue of young-adult Sprague-Dawley rats. The measurements were made at ultrasonic frequencies of 1.0, 2.25, 5.0, 7.5 and 10.0 MHz. The temperature of the tissues was monitored continuously to within ± 0.1°C of the ambient temperature. The acoustic parameters were measured in the liver, kidney, cardiac muscle and gastrocnemius muscle. All measurements were carried out in the near field region of the ultrasonic beam. It was observed that the velocity of propagation in tissues showed a slight dispersion with frequency. The attenuation in tissues increased with increasing frequency.     

Ultrasonic spectrum characterization of pig''''s pathological liver tissues

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Impact of local attenuation approximations when estimating correlation length from backscattered ultrasound echoes

Estimating the characteristic correlation length of tissue microstructure from the backscattered power spectrum could improve the diagnostic capability of medical ultrasound. Previously, size estimates were obtained after compensating for source focusing, the frequency-dependent attenuation along the propagation path (total attenuation), and the frequency-dependent attenuation in the scattering region (local attenuation). In this study, the impact of approximations of the local attenuation on the scatterer size estimate was determined using computer simulations and theoretical analysis. The simulations used Gaussian impedance distributions with an effective radius of 25 microm randomly positioned in a homogeneous half-space sonified by a spherically focused source (f/1 to f/4). The approximations of the local attenuation that were assessed neglected local attenuation (i.e., assume 0 dB/cm-MHz) neglected frequency dependence of the local attenuation, and assumed a finite frequency dependence (i.e., 0.5 dB/cm-MHz) independent of the true attenuation of the medium. Errors in the scatterer size estimate due to the local attenuation approximations increased with increasing window length, increasing true local attenuation and increasing f number. The most robust estimates were obtained when the local attenuation was approximated by a tissue-independent attenuation value that was greater than 70% of the largest attenuation expected in the tissue region of interest.     

A numerical method to predict the effects of frequency-dependent attenuation and dispersion on speed of sound estimates in cancellous bone

Many studies have demonstrated that time-domain speed-of-sound (SOS) measurements in calcaneus are predictive of osteoporotic fracture risk. However, there is a lack of standardization for this measurement. Consequently, different investigators using different measurement systems and analysis algorithms obtain disparate quantitative values for calcaneal SOS, impairing and often precluding meaningful comparison and/or pooling of measurements. A numerical method has been developed to model the effects of frequency-dependent attenuation and dispersion on transit-time-based SOS estimates. The numerical technique is based on a previously developed linear system analytic model for Gaussian pulses propagating through linearly attenuating, weakly dispersive media. The numerical approach is somewhat more general in that it can be used to predict the effects of arbitrary pulse shapes and dispersion relationships. The numerical technique, however, utilizes several additional assumptions (compared with the analytic model) which would be required for the practical task of correcting existing clinical databases. These include a single dispersion relationship for all calcaneus samples, a simple linear model relating phase velocity to broadband ultrasonic attenuation, and a constant calcaneal thickness. Measurements on a polycarbonate plate and 30 human calcaneus samples were in good quantitative agreement with numerical predictions. In addition, the numerical approach predicts that in cancellous bone, frequency-dependent attenuation tends to be a greater contributor to variations in transit-time-based SOS estimates than dispersion. This approach may be used to adjust previously acquired individual measurements so that SOS data recorded with different devices using different algorithms may be compared in a meaningful fashion.     

MR diffusion - "diffraction" phenomenon in multi-pulse-field-gradient experiments

Using pulsed-field-gradient (PFG) experiments, the sizes of the pores in ordered porous media can be estimated from the "diffraction" pattern that the signal attenuation curves exhibit. A different diffraction pattern is observed when the experiment is extended to a larger number (N) of diffusion gradient pulse pairs. Simulations to calculate signal values from arbitrary gradient waveforms are performed for diffusion in restricted geometries using a matrix operator formalism. The simulations suggest that the differences in the characteristics of the attenuation curves are expected to make it possible to measure smaller pore sizes, to improve the accuracy of pore size measurements and potentially to distinguish different pore shapes using the N-PFG technique. Moreover, when an even number of PFG pairs is used, it is possible to observe the diffraction pattern at shorter diffusion times and measure an approximation to the average pore size even when the sample contains pores with a broad distribution of sizes.     

Measurements of cloud contribution to rain millimeter wave attenuation by using a radar and radiometers

The measurement technique of cloud contribution to rain attenuation and the equipment consisted of the coherent pulse Doppler radar at wavelength =3.2 cm, the radiometers at=0.4; 0.8 and 1.35 cm and apparatus for signal recording and processing is described. The results of such measurements are given. The Doppler spectrum of the rain backscattered radar signal was used for determination of rain drop size distribution height profile then rain attenuation was calculated and cloud attenuation was determined as the difference between the total attenuation measured by using the radiometers and rain attenuation. The results of this work gave possibility to improve the known rain model of P.Misme for prediction of rain attenuation statistics for Earth-satellite links at millimeter wave.     

Estimation of light transport parameters in biological media using coherent backscattering

The suitability of using the angular peak shape of the coherent backscattered light for estimating the light transport parameters of biological media has been investigated. Milk and methylene blue doped milk were used as tissue phantoms for the measurements carried out with a He-Ne laser (632.8 nm). Results indicate that while the technique accurately estimates the transport length, it can determine the absorption coefficient only when the absorption is moderately high (α>1 cm⁻¹) for the long transport lengths typical of tissues. Further, the possibility of determining the anisotropy factor by estimating the single scattering contribution to the diffuse background is examined.     

Tunnelling rays in graded-index fibres

An analysis of the role of tunnelling rays in pulse propagation in graded-index fibres is presented. Tunnelling ray attenuation is handled by using the generalized parameter technique which allows attenuation coefficients to be dispensed with and relevant families of tunnelling rays to be identified. Results are given for impulse response pulse widths and shapes. Incorporation of tunnelling ray pulse contributions into the formalism for determining optimum refractive-index profiles is presented. For most cases, tunnelling ray effects are small, but significant corrections may be necessary when measurements are made on short lengths of fibre.     

Attenuation coefficient estimation using experimental diffraction corrections with multiple interface reflections

The ultrasonic attenuation coefficient of a fluid or solid is an acoustic parameter routinely estimated for the purpose of materials characterization and defect/disease detection. This paper describes a broadband attenuation coefficient estimation technique that combines two established estimation approaches. The key elements of these two approaches are: (1) the use of magnitude spectrum ratios of front surface, first back surface, and second back surface reflections from interfaces of materials with plate-like geometries, and (2) the use of an experimental diffraction correction approach to avoid diffraction losses. The combined estimation approach simplifies the attenuation coefficient estimation process by eliminating the need to explicitly make diffraction corrections or calculate reflection/transmission coefficients. The approach yields estimates of the attenuation coefficient, reflection coefficient, and material density. Models, experimental procedures, and signal analysis procedures, which support implementation of the approach, are presented. Attenuation coefficient and reflection coefficient estimates are presented for water and solid samples with estimates based on measurements made with multiple transducers.