A system-based approach to modeling the ultrasound signal backscattered by red blood cells

Ultrasound normalized cumulative residual entropy imaging: Theory, methodology, and application

BACKGROUND AND OBJECTIVE

Ultrasound information entropy imaging is an emerging quantitative ultrasound technique for characterizing local tissue scatterer concentrations and arrangements. However, the commonly used ultrasound Shannon entropy imaging based on histogram-derived discrete probability estimation suffers from the drawbacks of histogram settings dependence and unknown estimator performance. In this paper, we introduced the information-theoretic cumulative residual entropy (CRE) defined in a continuous distribution of cumulative distribution functions as a new entropy measure of ultrasound backscatter envelope uncertainty or complexity, and proposed ultrasound CRE imaging for tissue characterization.

METHODS

We theoretically analyzed the CRE for Rayleigh and Nakagami distributions and proposed a normalized CRE for characterizing scatterer distribution patterns. We proposed a method based on an empirical cumulative distribution function estimator and a trapezoidal numerical integration for estimating the normalized CRE from ultrasound backscatter envelope signals. We presented an ultrasound normalized CRE imaging scheme based on the normalized CRE estimator and the parallel computation technique. We also conducted theoretical analysis of the differential entropy which is an extension of the Shannon entropy to a continuous distribution, and introduced a method for ultrasound differential entropy estimation and imaging. Monte-Carlo simulation experiments were performed to evaluate the estimation accuracy of the normalized CRE and differential entropy estimators. Phantom simulation and clinical experiments were conducted to evaluate the performance of the proposed normalized CRE imaging in characterizing scatterer concentrations and hepatic steatosis (n = 204), respectively.

RESULTS

The theoretical normalized CRE for the Rayleigh distribution was π/4, corresponding to the case where there were ≥10 randomly distributed scatterers within the resolution cell of an ultrasound transducer. The theoretical normalized CRE for the Nakagami distribution decreased as the Nakagami parameter m increased, corresponding to that the ultrasound backscattered statistics varied from pre-Rayleigh to Rayleigh and to post-Rayleigh distributions. Monte-Carlo simulation experiments showed that the proposed normalized CRE and differential entropy estimators can produce a satisfying estimation accuracy even when the size of the test samples is small. Phantom simulation experiments showed that the proposed normalized CRE and differential entropy imaging can characterize scatterer concentrations. Clinical experiments showed that the proposed ultrasound normalized CRE imaging is capable to quantitatively characterize hepatic steatosis, outperforming ultrasound differential entropy imaging and being comparable to ultrasound Shannon entropy and Nakagami imaging.

CONCLUSION

This study sheds light on the theory and methodology of ultrasound normalized CRE. The proposed ultrasound normalized CRE can serve as a new, flexible quantitative ultrasound envelope statistics parameter. The proposed ultrasound normalized CRE imaging may find applications in quantified characterization of biological tissues. Our code will be made available publicly at https://github.com/zhouzhuhuang.

Transfontanelle photoacoustic imaging of intraventricular brain hemorrhages in live sheep

Intraventricular (IVH) and periventricular (PVH) hemorrhages in preterm neonates are common because the periventricular blood vessels are still developing up to 36 weeks and are fragile. Currently, transfontanelle ultrasound (US) imaging is utilized for screening for IVH and PVH, largely through the anterior fontanelle. However for mild hemorrhages, inconclusive diagnoses are common, leading to failure to detect IVH/PVH or, when other clinical symptoms are present, use of second stage neuroimaging modalities requiring transport of vulnerable patients. Yet even mild IVH/PVH increases the risk of moderate-severe neurodevelopmental impairment. Here, we demonstrate the capability of transfontanelle photoacoustic imaging (TFPAI) to detect IVH and PVH in-vivo in a large animal model. TFPAI was able to detect IVH/PVH as small as 0.3 mL in volume in the brain (p < 0.05). By contrast, US was able to detect hemorrhages as small as 0.5 mL. These preliminary results suggest TFPAI could be translated into a portable bedside imaging probe for improved diagnosis of clinically relevant brain hemorrhages in neonates.

Extracting Quantitative Ultrasonic Parameters from the Backscatter Coefficient

The ultrasonic backscatter coefficient (BSC) is a fundamental quantitative ultrasound (QUS) parameter that contains rich information about the underlying tissue. Deriving parameters from the BSC is essential for fully utilizing the information contained in BSC for tissue characterization. In this chapter, we review two primary approaches for extracting parameters from the BSC versus frequency curve: the model-based approach and the model-free approach, focusing on the model-based approach, where a scattering model is fit to the observed BSC to yield model parameters. For this approach, we will attempt to unite commonly used models under a coherent theoretical framework. We will focus on the underlying assumptions and conditions for various BSC models. Computer code is provided to facilitate the use of some of the models. The strengths and weaknesses of various models are also discussed.

Ultrasound simulation of blood with different red blood cell aggregations and concentrations

BACKGROUND

Considerable progress of ultrasound simulation on blood has enhanced the characterizing of red blood cell (RBC) aggregation.

OBJECTIVE

A novel simulation method aims at modeling the blood with different RBC aggregations and concentrations is proposed.

METHODS

The modeling process is as follows: (i) A three-dimensional scatterer model is first built by a mapping with a Hilbert space-filling curve from the one-dimensional scatterer distribution. (ii) To illustrate the relationship between the model parameters and the RBC aggregation level, a variety of blood samples are prepared and scanned to acquire their radiofrequency signals in-vitro. (iii) The model parameters are determined by matching the Nakagami-distribution characteristics of envelope signals simulated from the model with those measured from the blood samples.

RESULTS

Nakagami metrics m estimated from 15 kinds of blood samples (hematocrits of 20%, 40%, 60% and plasma concentrations of 15%, 30%, 45%, 60%, 75%) are compared with metrics estimated by their corresponding models (each with different eligible parameters). Results show that for the three hematocrit levels, the mean and standard deviation of the root-mean-squared deviations of m are 0.27 ± 0.0026, 0.16 ± 0.0021, 0.12 ± 0.0018 respectively.

CONCLUSION

The proposed simulation model provides a viable data source to evaluate the performance of the ultrasound-based methods for quantifying RBC aggregation.

Containerless Bioorganic Reactions in a Floating Droplet by Levitation Technique Using an Ultrasonic Wave

To ensure sustainable consumption and production patterns, alternative process design without plastics for chemical and biological reactions will benefit future generations. Reaction flasks used in chemical and biological laboratories have been made from glass, metals, and plastics so far. If containerless processing can be realized, researchers will have a next-generation reaction process, which will be reactor and plastic-free, and without risks of unforeseen issues induced by contact with reactions flasks, including contamination and alteration of the reactants. Here, polymerization, click chemistry, and enzymatic reactions can proceed effectively in a floating droplet at a node of standing wave generated by ultrasonic levitation. These results demonstrate that floating droplets levitated by acoustic waves can represent a revolutionary containerless reactor for performing various reactions in the fields of chemistry and biology.

On Factors Affecting Subharmonic-aided Pressure Estimation (SHAPE)

Subharmonic-aided pressure estimation (SHAPE) estimates hydrostatic pressure using the inverse relationship with subharmonic amplitude variations of ultrasound contrast agents (UCAs). We studied the impact of varying incident acoustic outputs (IAO), UCA concentration, and hematocrit on SHAPE. A Logiq 9 scanner with a 4C curvilinear probe (GE, Milwaukee, Wisconsin) was used with Sonazoid (GE Healthcare, Oslo, Norway) transmitting at 2.5 MHz and receiving at 1.25 MHz. An improved IAO selection algorithm provided improved correlations ( r from -0.85 to -0.95 vs. -0.39 to -0.98). There was no significant change in SHAPE gradient as the pressure increased from 10 to 40 mmHg and hematocrit concentration was tripled from 1.8 to 4.5 mL/L (Δ0.00-0.01 dB, p = 0.18), and as UCA concentration was increased from 0.2 to 1.2 mL/L (Δ0.02-0.05 dB, p = 0.75). The results for the correlation between the SHAPE gradient and hematocrit values for patients ( N = 100) in an ongoing clinical trial were also calculated showing a poor correlation value of 0.14. Overall, the SHAPE gradient is independent of hematocrit and UCA concentration. An improved algorithm for IAO selection will make SHAPE more accurate.

Quantitative Measurement of Erythrocyte Aggregation as a Systemic Inflammatory Marker by Ultrasound Imaging: A Systematic Review

This systematic review is aimed at answering two questions: (i) Is erythrocyte aggregation a useful biomarker in assessing systemic inflammation? (ii) Does quantitative ultrasound imaging provide the non-invasive option to measure erythrocyte aggregation in real time? The search was executed through bibliographic electronic databases CINAHL, EMB Review, EMBASE, MEDLINE, PubMed and the grey literature. The majority of studies correlated elevated erythrocyte aggregation with inflammatory blood markers for several pathologic states. Some studies used "erythrocyte aggregation" as an established marker of systemic inflammation. There were limited but promising articles regarding the use of quantitative ultrasound spectroscopy to monitor erythrocyte aggregation. Similarly, there were limited studies that used other ultrasound techniques to measure systemic inflammation. The quantitative measurement of erythrocyte aggregation has the potential to be a routine clinical marker of inflammation as it can reflect the cumulative inflammatory dynamics in vivo, is relatively simple to measure, is cost-effective and has a rapid turnaround time. Technologies like quantitative ultrasound spectroscopy that can measure erythrocyte aggregation non-invasively and in real time may offer the advantage of continuous monitoring of the inflammation state and, thus, may help in rapid decision making in a critical care setup.

A Method for Stereological Determination of the Structure Function From Histological Sections of Isotropic Scattering Media

The frequency-dependent ultrasonic backscatter coefficient (BSC) from tissues, a fundamental parameter estimated by quantitative ultrasound (QUS) techniques, contains microstructure information useful for tissue characterization. To extract the microstructure information from the BSC, the tissue under investigation is often modeled as a collection of discrete scatterers embedded in a homogeneous background. From a discrete scatterer point of view, the BSC is dependent on not only the properties of individual scatterers relative to the background but also the scatterer spatial arrangement [described by the structure function (SF)]. Recently, the 2-D SF was computed from histological tissue sections, and was shown to be related to the volumetric SF extracted from QUS measurements. In this paper, a stereological method is proposed to extract the volumetric (3-D) SF from 2-D histological tissue sections. Simulations and experimental cell pellet biophantom studies were conducted to evaluate the proposed method. Simulation results verified the proposed method. Experimental results showed that the volumetric SF extracted using the proposed method had a significantly better agreement with the QUS-extracted SF than did the 2-D SF extracted in the previous study. The proposed stereological approach provides a useful tool for predicting the SF from histology.

Effects of the container on structure function with impedance map analysis of dense scattering media

Quantitative ultrasound (QUS) can be used to estimate acoustic properties of tissue microstructure. In one approach to QUS, the backscatter coefficient (BSC) is utilized to quantify and classify tissue state. From the BSC, parametric models can be constructed to relate the frequency-dependent BSC to geometrical properties of the underlying tissue. However, most of these parametric models are based on analytic expressions (e.g., Gaussian function) and not on actual tissue morphology. Impedance map analysis has been proposed to help identify sources of ultrasonic scattering in tissues and to develop improved models of scattering. Previously, two-dimensional impedance maps (2DZMs) were demonstrated to provide tissue models of three-dimensional (3D) structures for sparse scattering media. In the current study, 2DZMs analysis of dense scatterer media combining the structure function with impedance map analysis was studied through a series of simulations. The simulation analysis demonstrated that the correlation coefficient and power spectrum could be estimated for a dense collection of spheres using 2DZMs. The current finding implies that 2DZMs can capture information about the 3D spatial positions of scatterers in addition to information about the size and shape of the scatterers for a dense scattering media, which is expected to be encountered in many tissues.

Quantitative Analysis of Helical Flow with Accuracy Using Ultrasound Speckle Image Velocimetry: In Vitro and in Vivo Feasibility Studies

Venous valve dysfunction and induced secondary abnormal flows are closely associated with venous diseases. Thus, detailed analysis of venous valvular flow is invaluable from biological and medical perspectives. However, most of the previous studies on venous perivalvular flows were based on qualitative analysis. On the contrary, quantitative analysis of perivalvular flows has not been fully understood. In this study, we used the ultrasound speckle image velocimetry (SIV) technique, which utilizes the speckle patterns of red blood cells (RBCs) created by ultrasound waves to measure 3-D valvular flows quantitatively. The flow structures obtained with the proposed SIV technique for an in vitro model were compared with those obtained by numerical simulation and the color Doppler method to validate the measurement accuracy of the ultrasound SIV technique. Blood flow in the human great saphenous vein was then measured at various distances from the valve with and without exercise. 3-D valvular flow was analyzed in accordance with the dimensionless index, helical intensity. The results obtained by the proposed method matched well with those obtained by numerical simulation and the color Doppler method. The hemodynamic characteristics of 3-D valvular helical flow which were analyzed experimentally using the SIV method would be used for quantitative diagnosis of venous valvular diseases.

Protocol for Robust In Vivo Measurements of Erythrocyte Aggregation Using Ultrasound Spectroscopy

Erythrocyte aggregation is a non-specific marker of acute and chronic inflammation. Although it is usual to evaluate this phenomenon from blood samples analyzed in laboratory instruments, in vivo real-time assessment of aggregation is possible with spectral ultrasound techniques. However, variable blood flow can affect the interpretation of acoustic measures. Therefore, flow standardization is required. Two techniques of flow standardization were evaluated with porcine and equine blood samples in Couette flow. These techniques consisted in either stopping the flow or reducing it. Then, the sensibility and repeatability of the retained method were evaluated in 11 human volunteers. We observed that stopping the flow compromised interpretation and repeatability. Conversely, maintaining a low flow provided repeatable measures and could distinguish between normal and high extents of erythrocyte aggregation. Agreement was observed between in vivo and ex vivo measures of the phenomenon (R² = 82.7%, p value < 0.0001). These results support the feasibility of assessing in vivo erythrocyte aggregation in humans by quantitative ultrasound means.

Spectrum analysis for assessing red blood cell aggregation using high-frequency ultrasound array transducer

The purpose of this study is to investigate a spectrum analysis technique for detecting and monitoring red blood cell (RBC) aggregation using a high-frequency array transducer. To assess the feasibility of this approach, the backscattered radio-frequency signal from non-aggregated and aggregated RBC samples with two hematocrit levels were acquired by using a 30-MHz linear array transducer and analyzed in frequency domain. Three parameters such as spectral slope, midband fit and Y intercept were extracted in a static condition. Fresh porcine blood was used and degrees of aggregation were changed by diluting plasma concentration. From the experiments, it was demonstrated that the spectral slope related to a size of scatterer progressively declined as the level of aggregation increased; its mean values at hematocrit of 40% were 1.10 and -0.22 dB/MHz for RBCs suspended in isotonic phosphate buffered saline and solution with 70% plasma concentrations, respectively. For the midband fit and Y intercept, the mean values were increased by 9.1 and 46.4 dB, respectively. These results indicated that the spectrum analysis technique is useful for monitoring RBC aggregation and can be potentially developed for assessing aggregation in clinical applications.

Detecting changes in ultrasound backscattered statistics by using Nakagami parameters: Comparisons of moment-based and maximum likelihood estimators

The Nakagami distribution is an approximation useful to the statistics of ultrasound backscattered signals for tissue characterization. Various estimators may affect the Nakagami parameter in the detection of changes in backscattered statistics. In particular, the moment-based estimator (MBE) and maximum likelihood estimator (MLE) are two primary methods used to estimate the Nakagami parameters of ultrasound signals. This study explored the effects of the MBE and different MLE approximations on Nakagami parameter estimations. Ultrasound backscattered signals of different scatterer number densities were generated using a simulation model, and phantom experiments and measurements of human liver tissues were also conducted to acquire real backscattered echoes. Envelope signals were employed to estimate the Nakagami parameters by using the MBE, first- and second-order approximations of MLE (MLE₁ and MLE₂, respectively), and Greenwood approximation (MLE_gw) for comparisons. The simulation results demonstrated that, compared with the MBE and MLE₁, the MLE₂ and MLE_gw enabled more stable parameter estimations with small sample sizes. Notably, the required data length of the envelope signal was 3.6 times the pulse length. The phantom and tissue measurement results also showed that the Nakagami parameters estimated using the MLE₂ and MLE_gw could simultaneously differentiate various scatterer concentrations with lower standard deviations and reliably reflect physical meanings associated with the backscattered statistics. Therefore, the MLE₂ and MLE_gw are suggested as estimators for the development of Nakagami-based methodologies for ultrasound tissue characterization.

Structure Function Estimated From Histological Tissue Sections

Ultrasonic scattering is determined by not only the properties of individual scatterers but also the correlation among scatterer positions. The role of scatterer spatial correlation is significant for dense medium, but has not been fully understood. The effect of scatterer spatial correlation may be modeled by the structure function as a frequency-dependent factor in the backscatter coefficient (BSC) expression. The structure function has been previously estimated from the BSC data. The aim of this study is to estimate the structure function from histology to test if the acoustically estimated structure function is indeed caused by the scatterer spatial distribution. Hematoxylin and eosin stained histological sections from dense cell pellet biophantoms were digitized. The scatterer positions were determined manually from the histological images. The structure function was calculated from the extracted scatterer positions. The structure function obtained from histology showed reasonable agreement in the shape but not in the amplitude, compared with the structure function previously estimated from the backscattered data. Fitting a polydisperse structure function model to the histologically estimated structure function yielded relatively accurate cell radius estimates ([Formula: see text]). Furthermore, two types of mouse tumors that have similar cell size and shape but distinct cell spatial distributions were studied, where the backscattered data were shown to be related to the cell spatial distribution through the structure function estimated from histology. In conclusion, the agreement between acoustically estimated and histologically estimated structure functions suggests that the acoustically estimated structure function is related to the scatterer spatial distribution.

Multidimensional spectral analysis of the ultrasonic radiofrequency signal for characterization of media

The importance of the analysis of the radiofrequency signal is by now recognized in the field of tissue characterization via ultrasound. The RF signal contains a wealth of information and structural details that are usually lost in the B-Mode representation. The HyperSPACE (Hyper SPectral Analysis for Characterization in Echography) algorithm presented by the authors in previous papers for clinical applications is based on the radiofrequency ultrasonic signal. The present work describes the method in detail and evaluates its performance in a repeatable and standardized manner, by using two test objects: a commercial test object that simulates the human parenchyma, and a laboratory-made test object consisting of human blood at different dilution values. In particular, the sensitivity and specificity in discriminating different density levels were estimated. In addition, the robustness of the algorithm with respect to the signal-to-noise ratio was also evaluated.

Experimental application of ultrafast imaging to spectral tissue characterization

Ultrasound ultrafast imaging (UI) allows acquisition of thousands of frames per second with a sustained image quality at any depth in the field of view. Therefore, it would be ideally suited to obtain good statistical sampling of fast-moving tissues using spectral-based techniques to derive the backscatter coefficient (BSC) and associated quantitative parameters. In UI, an image is formed by insonifying the medium with plane waves steered at different angles, beamforming them and compounding the resulting radiofrequency images. We aimed at validating, experimentally, the effect of these beamforming protocols on the BSC, under both isotropic and anisotropic conditions. Using UI techniques with a linear array transducer (5-14 MHz), we estimated the BSCs of tissue-mimicking phantoms and flowing porcine blood at depths up to 35 mm with a frame rate reaching 514 Hz. UI-based data were compared with those obtained using single-element transducers and conventional focusing imaging. Results revealed that UI compounded images can produce valid estimates of BSCs and effective scatterer size (errors less than 2.2 ± 0.8 and 0.26 ± 0.2 dB for blood and phantom experiments, respectively). This work also describes the use of pre-compounded UI images (i.e., steered images) to assess the angular dependency of circulating red blood cells. We have concluded that UI data sets can be used for BSC spectral tissue analysis and anisotropy characterization.

Effects of Estimators on Ultrasound Nakagami Imaging in Visualizing the Change in the Backscattered Statistics from a Rayleigh Distribution to a Pre-Rayleigh Distribution

Ultrasound Nakagami imaging has recently attracted interest as an imaging technique for analyzing envelope statistics. Because the presence of structures has a strong effect on estimation of the Nakagami parameter, previous studies have indicated that Nakagami imaging should be used specifically for characterization of soft tissues with fewer structures, such as liver tissues. Typically, changes in the properties of the liver parenchyma cause the backscattered statistics to transform from a Rayleigh distribution to a pre-Rayleigh distribution, and this transformation can be visualized using a Nakagami imaging technique. However, different estimators result in different estimated values; thus, the performance of a Nakagami image may depend on the type of estimator used. This study explored the effects of various estimators on ultrasound Nakagami imaging to describe the backscattered statistics as they change from a Rayleigh distribution to a pre-Rayleigh distribution. Simulations and clinical measurements involving patients with liver fibrosis (n = 85) yielded image data that were used to construct B-mode and conventional Nakagami images based on the moment estimator (denoted as mINV images) and maximum-likelihood estimator (denoted as mML images). In addition, novel window-modulated compounding Nakagami images based on the moment estimator (denoted as mWMC images) were also obtained. The means and standard deviations of the Nakagami parameters were examined as a function of the backscattered statistics. The experimental results indicate that the mINV, mML and mWMC images enabled quantitative visualization of the change in backscattered statistics from a Rayleigh distribution to a pre-Rayleigh distribution. Importantly, the mWMC image is superior to both mINV and mML images because it simultaneously realizes sensitive detection of the backscattered statistics and a reduction of estimation variance for image smoothness improvement. We therefore recommend using mWMC image as a novel strategy in Nakagami imaging technique for liver tissue characterization.

Optical properties of tissues quantified using morphological granulometry from phase-contrast images of thin tissue samples

A method combining morphological granulometry with Mie theory to determine optical scattering in biological tissues was proposed. Otsu's method was applied to binarize phase-contrast images. Binary morphological granulometry was used to estimate size density distribution of the tissue samples based on the binary phase-contrast images. Our results showed that the optical parameters associated with light scattering in tissue could be quantitatively determined by combining size density distribution with Mie theory. It was suggested that this unique method could be used to characterize biological tissues for disease diagnosis.

Entropic imaging of cataract lens: an in vitro study

Phacoemulsification is a common surgical method for treating advanced cataracts. Determining the optimal phacoemulsification energy depends on the hardness of the lens involved. Previous studies have shown that it is possible to evaluate lens hardness via ultrasound parametric imaging based on statistical models that require data to follow a specific distribution. To make the method more system-adaptive, nonmodel-based imaging approach may be necessary in the visualization of lens hardness. This study investigated the feasibility of applying an information theory derived parameter - Shannon entropy from ultrasound backscatter to quantify lens hardness. To determine the physical significance of entropy, we performed computer simulations to investigate the relationship between the signal-to-noise ratio (SNR) based on the Rayleigh distribution and Shannon entropy. Young's modulus was measured in porcine lenses, in which cataracts had been artificially induced by the immersion in formalin solution in vitro. A 35-MHz ultrasound transducer was used to scan the cataract lenses for entropy imaging. The results showed that the entropy is 4.8 when the backscatter data form a Rayleigh distribution corresponding to an SNR of 1.91. The Young's modulus of the lens increased from approximately 8 to 100 kPa when we increased the immersion time from 40 to 160 min (correlation coefficient r = 0.99). Furthermore, the results indicated that entropy imaging seemed to facilitate visualizing different degrees of lens hardening. The mean entropy value increased from 2.7 to 4.0 as the Young's modulus increased from 8 to 100 kPa (r = 0.85), suggesting that entropy imaging may have greater potential than that of conventional statistical parametric imaging in determining the optimal energy to apply during phacoemulsification.

Probing red blood cell morphology using high-frequency photoacoustics

A method that can rapidly quantify variations in the morphology of single red blood cells (RBCs) using light and sound is presented. When irradiated with a laser pulse, an RBC absorbs the optical energy and emits an ultrasonic pressure wave called a photoacoustic wave. The power spectrum of the resulting photoacoustic wave contains distinctive features that can be used to identify the RBC size and morphology. When particles 5-10 μm in diameter (such as RBCs) are probed with high-frequency photoacoustics, unique periodically varying minima and maxima occur throughout the photoacoustic signal power spectrum at frequencies >100 MHz. The location and distance between spectral minima scale with the size and morphology of the RBC; these shifts can be used to quantify small changes in the morphology of RBCs. Morphological deviations from the normal biconcave RBC shape are commonly associated with disease or infection. Using a single wide-bandwidth transducer sensitive to frequencies between 100 and 500 MHz, we were able to differentiate healthy RBCs from irregularly shaped RBCs (such as echinocytes, spherocytes, and swollen RBCs) with high confidence using a sample size of just 21 RBCs. As each measurement takes only seconds, these methods could eventually be translated to an automated device for rapid characterization of RBC morphology and deployed in a clinical setting to help diagnose RBC pathology.

Comparison of three scattering models for ultrasound blood characterization

Ultrasonic backscattered signals from blood contain frequency-dependent information that can be used to obtain quantitative parameters reflecting the aggregation level of red blood cells (RBCs). The approach is based on estimating structural aggregate parameters by fitting the spectrum of the backscattered radio-frequency echoes from blood to an estimated spectrum considering a theoretical scattering model. In this study, three scattering models were examined: a new implementation of the Gaussian model (GM), the structure factor size estimator (SFSE), and the new effective medium theory combined with the structure factor model (EMTSFM). The accuracy of the three scattering models in determining mean aggregate size and compactness was compared by 2-D and 3-D computer simulations in which RBC structural parameters were controlled. Two clustering conditions were studied: 1) the aggregate size varied and the aggregate compactness was fixed in both 2-D and 3-D cases, and 2) the aggregate size was fixed and the aggregate compactness varied in the 2-D case. For both clustering conditions, the EMTSFM was found to be more suitable than GM and SFSE for characterizing RBC aggregation.

Real-time GPU-based ultrasound simulation using deformable mesh models

This paper presents a real-time capable graphics processing unit (GPU)-based ultrasound simulator suitable for medical education. The main focus of the simulator is to synthesize realistic looking ultrasound images in real-time including artifacts, which are essential for the interpretation of this data. The simulation is based on a convolution-enhanced ray-tracing approach and uses a deformable mesh model. Deformations of the mesh model are calculated using the PhysX engine. Our method advances the state of the art for real-time capable ultrasound simulators by following the path of the ultrasound pulse, which enables better simulation of ultrasound-specific artifacts. An evaluation of our proposed method in comparison with recent generative slicing-based strategies as well as real ultrasound images is performed. Hereby, a gelatin ultrasound phantom containing syringes filled with different media is scanned with a real transducer. The obtained images are then compared to images which are simulated using a slicing-based technique and our proposed method. The particular benefit of our method is the accurate simulation of ultrasound-specific artifacts, like range distortion, refraction and acoustic shadowing. Several test scenarios are evaluated regarding simulation time, to show the performance and the bottleneck of our method. While being computationally more intensive than slicing techniques, our simulator is able to produce high-quality images in real-time, tracing over 5000 rays through mesh models with more than 2 000 000 triangles of which up to 200 000 may be deformed each frame.

Experimental assessment of four ultrasound scattering models for characterizing concentrated tissue-mimicking phantoms

Tissue-mimicking phantoms with high scatterer concentrations were examined using quantitative ultrasound techniques based on four scattering models: The Gaussian model (GM), the Faran model (FM), the structure factor model (SFM), and the particle model (PM). Experiments were conducted using 10- and 17.5-MHz focused transducers on tissue-mimicking phantoms with scatterer concentrations ranging from 1% to 25%. Theoretical backscatter coefficients (BSCs) were first compared with the experimentally measured BSCs in the forward problem framework. The measured BSC versus scatterer concentration relationship was predicted satisfactorily by the SFM and the PM. The FM and the PM overestimated the BSC magnitude at actual concentrations greater than 2.5% and 10%, respectively. The SFM was the model that better matched the BSC magnitude at all the scatterer concentrations tested. Second, the four scattering models were compared in the inverse problem framework to estimate the scatterer size and concentration from the experimentally measured BSCs. The FM did not predict the concentration accurately at actual concentrations greater than 12.5%. The SFM and PM need to be associated with another quantitative parameter to differentiate between low and high concentrations. In that case, the SFM predicted the concentration satisfactorily with relative errors below 38% at actual concentrations ranging from 10% to 25%.

Correlation functions and power spectra of Doppler response signals in ultrasonic medical applications

Ultrasound Doppler methods are widely used in clinical practice as prospective investigational tool to study the vascular system and soft biological tissues. Meanwhile, the most general relationship between the power Doppler spectra, spectral characteristics of the scattering fluctuations and the probing ultrasound field parameters for some clinical implementations are still unexplored. Based upon the continuum model of scattering inhomogeneities, a set of the closed-form expressions for the correlation functions and the spectra of Doppler response of soft tissues and blood have been derived. The influence of the correlation among inhomogeneities and the diffusion processes on the Doppler power spectra formed by stationary flows have been examined. Computer simulations of Doppler spectra were performed for different values of correlation radius and diffusion coefficient. With simulation results the effects of the correlation among inhomogeneities and the diffusion processes on the spectral width and mean frequency are established and discussed in respect to turbulent flows. Closed-form expressions for correlation functions and Doppler spectra for the vibrational sonoelastography technique for visualizing malignant tumors in tissues have been derived. Based on the peculiarities of the obtained Doppler spectra, it is shown that the differentiation of soft tissues with respect to the amplitude value of constrained oscillations is feasible. The expressions were derived for the cases of non-stationary accelerated blood movement. It has been found that the frequency dependence reveals solely at a finite time of observation and depends on the initial phase of the accelerated movement.

Minimum requirement of artificial noise level for using noise-assisted correlation algorithm to suppress artifacts in ultrasonic Nakagami images

The Nakagami image is a complementary imaging mode for pulse-echo ultrasound B-scan to characterize tissues. White noise in anechoic areas induces artifacts in the Nakagami image. Recently, we proposed a noise-assisted correlation algorithm (NCA) for suppressing the Nakagami artifact. In the NCA, artificial white noise is intentionally added twice to backscattered signals to produce two noisy data, which are used to establish a correlation profile for rejecting noise. This study explored the effects of artificial noise level on the NCA to suppress the artifact of the Nakagami image. Simulations were conducted to produce B-mode images of anechoic regions under signal-to-noise ratios (SNRs) of 20, 10 and 5 dB. Various artificial noise levels ranging from 0.1- to 1-fold of the intrinsic noise amplitude were used in the NCA for constructing the Nakagami images. Phantom experiments were conducted to validate the performance of using the optimal artificial noise level suggested by the simulation results to suppress the Nakagami artifacts by the NCA. The simulation results indicated that the artifacts of the Nakagami image in the anechoic regions can be gradually suppressed by increasing the artificial noise level used in the NCA to improve the image contrast-to-noise ratio (CNR). The CNR of the Nakagami image reached 20 dB when the artificial noise level was 0.7-fold of the intrinsic noise amplitude. This criterion was demonstrated by the phantom results to provide the NCA with an excellent ability to obtain artifact-free Nakagami images.

Forward problem study of an effective medium model for ultrasound blood characterization

The structure factor model (SFM) is a scattering model developed to simulate the backscattering coefficient (BSC) of aggregated red blood cells (RBCs). However, the SFM can hardly be implemented to estimate the structural aggregate parameters in the framework of an inverse problem formulation. A scattering model called the effective medium theory combined with the SFM (EMTSFM) is thus proposed to approximate the SFM. The EMTSFM assumes that aggregates of RBCs can be treated as individual homogeneous scatterers, which have effective properties determined by the acoustical characteristics and concentration of RBCs within aggregates. The EMTSFM parameterizes the BSC by three indices: the aggregate radius, the concentration of RBCs with- in aggregates (the aggregate compactness), and the systemic hematocrit. The goodness of fit of the EMTSFM approximation in comparison with the SFM was then examined. Based on a 2-D study, the EMTSFM was found to approximate the SFM with relative errors less than 30% for a product of the wavenumber times the mean aggregate radius krΛκ <; 1.32. The main contribution of this work is the parameterization of the BSC with the RBC aggregate compactness, which is of relevance in clinical hemorheology because it reflects the binding energy between RBCs.

Assessment of accuracy of the structure-factor-size-estimator method in determining red blood cell aggregate size from ultrasound spectral backscatter coefficient

A computer simulation study to produce ultrasonic backscatter coefficients (BSCs) from red blood cell (RBC) clusters is discussed. The simulation algorithm is suitable for generating non-overlapping, isotropic, and fairly identical RBC clusters. RBCs were stacked following the hexagonal close packing (HCP) structure to form a compact spherical aggregate. Such an aggregate was repeated and placed randomly under non-overlapping condition in the three-dimensional space to mimic an aggregated blood sample. BSCs were computed between 750 KHz and 200 MHz for samples of various cluster sizes at different hematocrits. Magnitudes of BSCs increased with mean aggregate sizes at low frequencies (<20 MHz). The accuracy of the structure-factor-size-estimator (SFSE) method in determining mean aggregate size and packing factor was also examined. A good correlation (R(2) ≥ 0.94) between the mean size of aggregates predicted by the SFSE and true size was found for each hematocrit. This study shows that for spherical aggregates there exists a region for each hematocrit where SFSE works most accurately. Typically, error of SFSE in estimating mean cluster size was <20% for dimensions between 14 and 17 μm at 40% hematocrit. This study suggests that the theoretical framework of SFSE is valid under the assumption of isotropic aggregates.

Towards extra-luminal blood detection from intravascular ultrasound radio frequency data

Recent evidence has suggested that the presence and proliferation of vasa vasorum (VV) in the plaque is correlated to an increase in plaque inflammation and destabilization, leading to acute coronary events (e.g., heart attacks). Therefore, the detection and quantification of VV in plaque (i.e., extra luminal blood perfusion) is an important problem since it may enable the development of an index of plaque vulnerability. In this paper, we explore the feasibility of a method that employs a physics-based model of the scattered intravascular ultrasound (IVUS) radio frequency signal for the detection of blood. We evaluate our method using synthetic data and validate it using six 40 MHz pullback sequences acquired with three different IVUS systems from different arteries of rabbits and swines. Our experimental results are very promising and indicate the feasibility of our method for the computation of a feature that leads to automatic extra-luminal blood detection which may be an indication of plaque inflammation.

An inverse scattering algorithm for the segmentation of the luminal border on intravascular ultrasound data

Intravascular ultrasound (IVUS) is a catheter-based medical imaging technique that produces cross-sectional images of blood vessels and is particularly useful for studying atherosclerosis. In this paper, we present a novel method for segmentation of the luminal border on IVUS images using the radio frequency (RF) raw signal based on a scattering model and an inversion scheme. The scattering model is based on a random distribution of point scatterers in the vessel. The per-scatterer signal uses a differential backscatter cross-section coefficient (DBC) that depends on the tissue type. Segmentation requires two inversions: a calibration inversion and a reconstruction inversion. In the calibration step, we use a single manually segmented frame and then solve an inverse problem to recover the DBC for the lumen and vessel wall (kappa(l) and kappa(w), respectively) and the width of the impulse signal theta. In the reconstruction step, we use the parameters from the calibration step to solve a new inverse problem: for each angle theta(i) of the IVUS data, we reconstruct the lumen-vessel wall interface. We evaluated our method using three 40MHz IVUS sequences by comparing with manual segmentations. Our preliminary results indicate that it is possible to segment the luminal border by solving an inverse problem using the IVUS RF raw signal with the scatterer model.

Approaching artery rigid dynamics in IVUS

Tissue biomechanical properties (like strain and stress) are playing an increasing role in diagnosis and long-term treatment of intravascular coronary diseases. Their assessment strongly relies on estimation of vessel wall deformation. Since intravascular ultrasound (IVUS) sequences allow visualizing vessel morphology and reflect its dynamics, this technique represents a useful tool for evaluation of tissue mechanical properties. Image misalignment introduced by vessel-catheter motion is a major artifact for a proper tracking of tissue deformation. In this work, we focus on compensating and assessing IVUS rigid in-plane motion due to heart beating. Motion parameters are computed by considering both the vessel geometry and its appearance in the image. Continuum mechanics laws serve to introduce a novel score measuring motion reduction in in vivo sequences. Synthetic experiments validate the proposed score as measure of motion parameters accuracy; whereas results in in vivo pullbacks show the reliability of the presented methodologies in clinical cases.

Monte Carlo study on ultrasound backscattering by three-dimensional distributions of red blood cells

A Monte Carlo study on ultrasound backscattering by red blood cells (RBCs) is presented for three-dimensional (3D) distributions of particles. The cells were treated as classical spherical particles and accordingly, the Boltzmann distribution was considered to describe probability distribution of energy states of a system composed of such particles. The well-known Metropolis algorithm can generate configurations according to that probability distribution and therefore, was employed in this study to simulate some realizations of both nonaggregating and aggregating RBCs. The study of nonaggregating particles was motivated to compare simulations with existing experimental results and consequently, to validate the model. In the case of aggregating RBCs, the interaction potential between cells was modeled with the Morse potential and the frequency-dependent backscattering coefficient (BSC) was investigated at different hematocrits (H, particle volume fractions). The impact of aggregation potential on the spectral slope (SS) was also evaluated. It is shown that BSC increased as the magnitude of aggregating potential was raised and the effect was more pronounced at higher hematocrits. Moreover, spectral slopes at nonaggregating and low aggregating conditions were found to be around 4, which is consistent with the Rayleigh scattering theory. However, it had diminished significantly, particularly at higher hematocrits as the magnitude of the attractive potential energy was raised. For instance, at H=40% SS dropped from 4.04 for nonaggregating particles to 3.62 at the highest aggregating potential considered in this study. Our results suggest that this 3D model is capable of reflecting the effects of RBC aggregation on BSC and SS.

Feasibility exploration of blood flow estimation by contrast-assisted Nakagami imaging

The microbubble contrast agent destruction/replenishment technique has been widely applied to ultrasound-based blood flow estimation. The rate of increase of the time-intensity curve (TIC) due to microbubbles flowing into the region of interest as measured from B-mode images closely reflects the flow velocity. In this study, we monitored microbubble replenishment by a proposed new approach called the time-Nakagami-parameter curve (TNC) obtained from Nakagami-parameter images for quantifying the flow velocity. The feasibility of using the TNC to estimate the flow was evaluated in computer simulations of the TIC and TNC for flow velocities from 10 to 30 cm/s under an ultrasound frequency of 5 MHz. The clutter effects on the TIC and TNC were explored in amore realistic situation by carrying out phantom measurements of 25 MHz. The rates of increase of the TIC and TNC were expressed by the rate constants beta1 and betaN of a monoexponential model, respectively. The average beta1 increased from 38 to 110 s(-1) as the flow velocity increased from 10 to 30 cm/s (r = 0.98), and the average betaN increased from approximately 40 to 120 s(-1) for the same increase in flow velocity (r = 0.98). The p-value between the results of beta1 and betaN as a function of flow velocity was 0.77. These results represent that betaN quantifies the flow velocity similarly to the conventional beta1. In particular, both the simulation and experimental results revealed that the TNC method conditionally tolerates the presence of nonperfused areas (e.g., surrounding tissues or vessel walls) in the region of interest without requiring application of an additional wall filter to cancel the influences of clutter echoes on the flow estimation. These findings suggest that the TNC-based technique may be a potential method as a complementary tool for the conventional TIC technique to improve the estimation of blood flow.

Experimental ultrasound characterization of red blood cell aggregation using the structure factor size estimator

The frequency dependence of the ultrasonic backscattering coefficient (BSC) was studied to assess the level of red blood cell (RBC) aggregation. Three monoelement focused wideband transducers were used to insonify porcine blood sheared in a Couette flow from 9 to 30 MHz. A high shear rate was first applied to promote disaggregation. Different residual shear rates were then used to promote formation of RBC aggregates. The structure factor size estimator (SFSE), a second-order data reduction model based on the structure factor, was applied to the frequency-dependent BSC. Two parameters were extracted from the model to describe the level of aggregation at 6% and 40% hematocrits: W, the packing factor, and D the aggregate diameter, expressed in number of RBCs. Both parameters closely matched theoretical values for nonaggregated RBCs. W and D increased during aggregation with stabilized values modulated by the applied residual shear rate. Furthermore, parameter D during the kinetics of aggregation at 6% hematocrit under static conditions correlated with an optical RBC aggregate size estimation from microscopic images (r(2)=0.76). To conclude, the SFSE presents an interesting framework for tissue characterization of partially correlated dense tissues such as aggregated RBCs.

Imaging local scatterer concentrations by the Nakagami statistical model

The ultrasonic B-mode image is an important clinical tool used to examine the internal structures of the biological tissue. Due to the fact that the conventional B-scans cannot fully reflect the nature of the tissue, some useful quantitative parameters have been applied to quantify the properties of the tissue. Among various possibilities, the Nakagami parameter was demonstrated to have an outstanding ability to detect the variation of the scatterer concentration. This study is aimed to develop a scatterer concentration image based on the Nakagami parameter map to assist in the B-mode image for tissue characterization. In particular, computer simulations are carried out to generate phantoms of different scatterer concentrations and echogenicity coefficients and their B-mode and Nakagami parametric images are compared to evaluate the performance of the Nakagami image in differentiating the properties of the scatterers. The simulated results show that the B-mode image would be affected by the system settings and user operations, whereas the Nakagami parametric image provides a comparatively consistent image result when different diagnosticians use different dynamic ranges and system gains. This is largely because the Nakagami image formation is only based on the backscattered statistics of the ultrasonic signals in local tissues. Such an imaging principle allows the Nakagami image to quantify the local scatterer concentrations in the tissue and to extract the backscattering information from the regions of the weaker echoes that may be lost in the B-mode image. These findings suggest that the Nakagami image can be combined with the use of the B-mode image simultaneously to visualize the tissue structures and the scatterer properties for a better medical diagnosis.

The effect of logarithmic compression on estimation of the Nakagami parameter for ultrasonic tissue characterization: a simulation study

Previous studies have demonstrated that the Nakagami parameter estimated using the envelopes of backscattered ultrasound is useful in detecting variations in the concentration of scatterers in tissues. The signal processing in those studies was linear, whereas nonlinear logarithmic compression is routinely employed in existing ultrasonic scanners. We therefore explored the effect of the logarithmic compression on the estimation of the Nakagami parameter in this study. Computer simulations were used to produce backscattered signals of various scatterer concentrations for the estimation of the Nakagami parameters before and after applying the logarithmic compression on the backscattered envelopes. The simulated results showed that the logarithmic compression would move the statistics of the backscattered envelopes towards post-Rayleigh distributions for most scatterer concentrations. Moreover, the Nakagami parameter calculated using compressed backscattered envelopes is more sensitive than that calculated using uncompressed envelopes in differentiating variations in the scatterer concentration, making the former better at quantifying the scatterer concentration in biological tissues.

Effect of red cell clustering and anisotropy on ultrasound blood backscatter: a Monte Carlo study

When flowing at a low shear rate, blood appears hyperechogenic on ultrasound B-scans. The formation of red blood cell (RBC) aggregates that also alters blood viscosity is the microscopic mechanism explaining this acoustical phenomenon. In this study, Monte Carlo simulations were performed to predict how RBC clustering increases ultrasound scattering by blood. A bidimensional Gibbs-Markov random point process parameterized by the adhesion energy epsilon and an anisotropy index nu was used to describe RBC positions for a hematocrit H = 40%. The frequency dependence of the backscattering coefficient chi(f) was computed using Born approximation. The backscattering coefficient chi0 at 5 MHz and the spectral slopes n(x) and n(y) (chi alpha f(nx) or f(ny)) measured, respectively, when the insonification is parallel and perpendicular with the RBC cluster axis were then extracted. Under isotropic conditions, chi0 increased up to 7 dB with epsilon and n(x) = n(y) decreased from 4.2 to 3.4. Under anisotropic conditions, the backscattering was stronger perpendicularly to aggregate axis, resulting in n(x) < n(y). The anisotropy in scattering appeared more pronounced when epsilon or nu increased. These two dimensional results generally predict that low-frequency blood backscatter is related to cluster dimension, and higher-frequency properties are affected by finer morphological features as anisotropy. This numerically establishes that ultrasound backscatter spectroscopy on a large frequency range is pertinent to characterize in situ hemorheology.

The effect of transducer characteristics on the estimation of Nakagami paramater as a function of scatterer concentration

The effect of transducer characteristics on the sensitivity of the Nakagami parameter to detect the variation of scatterer concentrations was studied. The rationale for this study stems from our pilot results which showed that the Nakagami parameters, estimated using a nonfocused transducer were not as sensitive as those of measurements using a commercial ultrasonic scanner in previous reports. This discrepancy may be attributed to the effects of transducer characteristics relative to the size of the resolution cell as verified by measurements of phantoms and 2-D computer simulations. The Nakagami parameter as a function of scatterer concentration was calculated using backscattered signals acquired from the scattering medium of different scatterer concentrations ranging from 2 to 32 scatterers/mm(3) using both 5 MHz nonfocused and focused transducers. Experimental and simulation results obtained from the nonfocused transducer represent that their respective Nakagami parameters increased from 1.17 to 1.31 and from 0.82 to 1.01 corresponding to the increase of scatterer concentrations. For the results obtained from the focused transducer, their average Nakagami parameters increased from 0.27 to 0.72 and from 0.33 to 0.81. These consistent results demonstrated that Nakagami parameter estimated using a focused transducer tends to be more sensitive than that by a nonfocused transducer to detect the variation of low scatterer concentration. This difference is fully due to the effect of transducer characteristics associated with the effective number of scatterers in the resolution cell.

Modeling the frequency dependence (5-120 MHz) of ultrasound backscattering by red cell aggregates in shear flow at a normal hematocrit

The frequency dependence of the ultrasound signal backscattered by blood in shear flow was studied using a simulation model. The ultrasound backscattered signal was computed with a linear model that considers the characteristics of the ultrasound system and tissue acoustic properties. The tissue scattering properties were related to the position and shape of the red blood cells (RBCs). A 2D microrheological model simulated the RBC dynamics in a Couette shear flow system. This iterative model, described earlier [Biophys. J. 82, 1696-1710 (2002)], integrates the hydrodynamic effect of the flow, as well as adhesive and repulsive forces between RBCs. RBC aggregation was simulated at 40% hematocrit and shear rates of 0.05-2 s(-1). The RBC aggregate sizes ranged, on average, from 3.3 RBCs at 2 s(-1) to 33.5 cells at 0.05 s(-1). The ultrasound backscattered power was studied at frequencies between 5-120 MHz and insonification angles between 0-180 degrees. At frequencies below approximately 30 MHz, the ultrasound backscattered power increased as the shear rate was decreased and the size of the aggregates was raised. A totally different scattering behavior was noted above 30 MHz. Typical spectral slopes of the backscattered power (log-log scale) between 5-25 MHz equaled 3.8, whereas slopes down to 0.6 were measured at 0.05 s(-1), between 40-60 MHz. The ultrasound backscattered power was shown to be angle dependent at low frequencies (5-25 MHz). The anisotropy persisted at high frequencies (>25 MHz) for small aggregates (at 2 s(-1)). In conclusion, this study sheds some light on the blood backscattering behavior with an emphasis on the non-Rayleigh regime. Additional experimental studies may be necessary to validate the simulation results, and to fully understand the relation between the ultrasound backscattered power, level of RBC aggregation, shear rate, frequency, and insonification angle.

Simulation of ultrasound backscattering by red cell aggregates: effect of shear rate and anisotropy

Tissue characterization using ultrasound (US) scattering allows extraction of relevant cellular biophysical information noninvasively. Characterization of the level of red blood cell (RBC) aggregation is one of the proposed application. In the current paper, it is hypothesized that the microstructure of the RBCs is a main determinant of the US backscattered power. A simulation model was developed to study the effect of various RBC configurations on the backscattered power. It is an iterative dynamical model that considers the effect of the adhesive and repulsive forces between RBCs, and the effect of the flow. The method is shown to be efficient to model polydispersity in size, shape, and orientation of the aggregates due to the flow, and to relate these variations to the US backscattering properties. Three levels of aggregability at shear rates varying between 0.05 and 10 s(-1) were modeled at 40% hematocrit. The simulated backscattered power increased with a decrease in the shear rate or an increase in the RBC aggregability. Angular dependence of the backscattered power was observed. It is the first attempt to model the US power backscattered by RBC aggregates polydisperse in size and shape due to the shearing of the flow.

Blind deconvolution of ultrasound sequences using nonparametric local polynomial estimates of the pulse

The problem of reconstructing the reflectivity of a biological tissue is examined by means of blind deconvolution of the echo ultrasound signals. It is shown that the quality of the reconstruction procedure can be significantly improved when initially the ultrasonic pulse is accurately estimated. A new approach to the estimation of the ultrasound pulse echo sequences is proposed, using local polynomial approximation, which is closely related to the wavelet transform theory. This approach can be viewed as a modification of homomorphic deconvolution, by using bases different from the Fourier basis of the space of square-integrable functions L2. The bases used here are the orthogonal compactly supported wavelet bases. It is shown that the locality of the estimate can be extremely useful in number of cases of practical interest, resulting in estimates with smaller root-mean squared (rms) errors, as compared with estimates employing the Fourier basis. This approach is applied to ultrasound signals, for estimation of the ultrasound pulse log-spectrum from the log-spectrum of radio-frequency (RF) sequences. It is shown, conceptually and experimentally, that the proposed approach can provide robust and rapidly computed estimates of the ultrasound pulses from the RF-sequences, as obtained in the process of tissue scanning. The pulse phase was recovered using the minimum-phase assumption, which was found to hold for the transducers in use. The obtained pulse estimates are used for the deconvolution of the RF-sequences, which result in stable estimates of the tissue reflectivity function, fairly independent of the properties of the imaging system. Simulated data, data obtained from several phantoms and from in vitro experiments have been processed and the results seem to be quite promising.

A point process approach to assess the frequency dependence of ultrasound backscattering by aggregating red blood cells

To study the shear-thinning rheological behavior of blood, an acoustical measurement of the erythrocyte aggregation level can be obtained by analyzing the frequency dependence of ultrasonic backscattering from blood. However, the relation that exists among the variables describing the aggregation level and the backscattering coefficient needs to be better clarified. To achieve this purpose, a three-dimensional random model, the Neyman-Scott point process, is proposed to simulate red cell clustering in aggregative conditions at a low hematocrit (H<5%). The frequency dependence of the backscattering coefficient of blood, in non-Rayleigh conditions, is analytically derived from the model, as a function of the size distribution of the aggregates and of their mass fractal dimension. Quantitative predictions of the backscatter increase due to red cell aggregation are given. The parametric model of backscatter enables two descriptive indices of red cell aggregation to be extracted from experimental data, the packing factor W and the size factor delta. Previously published backscatter measurements from porcine whole blood at 4.5% hematocrit, in the frequency range of 3.5 MHz-12.5 MHz, are used to study the shear-rate dependence of these two indices.

Influence of boundary conditions on a one-dimensional ultrasound backscattering model of blood

A simulation model of one-dimensional (1-D) ultrasound (US) propagation in blood was used to study the relation between the backscattering coefficient and hematocrit. In this model, an ultrasonic plane wave was propagated in plasma normal to randomly placed slabs of constant thickness whose acoustical properties are the same as red blood cells, and the corresponding intensity reflection coefficient was calculated. The simulation results were compared to the 1-D Percus-Yevick (P-Y) theory as presented in the literature. Previous investigators have reported a close agreement over a limited range of simulation parameters between their results and the P-Y theory. However, a more careful investigation using a wider range of parameters has revealed major discrepancies. It is shown that these arise from an inappropriate choice of boundary conditions. By averaging the material properties beyond the boundaries of the simulation, as suggested by earlier theoretical work, the results are now in excellent agreement with the P-Y theory over a wide range of simulation parameters.

Modeling and analysis of ultrasound backscattering by spherical aggregates and rouleaux of red blood cells

The present study concerns the modeling and analysis of ultrasound backscattering by red blood cell (RBC) aggregates, which under pathological conditions play a significant role in the rheology of blood within human vessels. A theoretical model based on the convolution between a tissue matrix and a point spread function, representing, respectively, the RBC aggregates and the characteristics of the ultrasound system, was used to examine the influence of the scatterer shape and size on the backscattered power. Both scatterers in the form of clumps of RBC aggregates and rouleaux were modeled. For all simulations, the hematocrit was kept constant at 10%, the ultrasound frequency was 10 MHz, the insonification angle was varied from 0 to 90 degrees , and the scatterer size (diameter for clumps and length for rouleaux) ranged from 4 mum to 120 mum. Under Rayleigh scattering by assuming a Poisson distribution of scatterers in space, the ultrasound backscattered power increased linearly with the particle volume. For non-Rayleigh scatterers, the intensity of the echoes diminished as the scatterer volume increased, with the exception of rouleaux at an angle of 90 degrees . As expected, the backscattered power was angularly dependent for anisotropic particles (rouleaux). The ultrasound backscattered power did not always increase with the size of the aggregates, especially when they were no longer Rayleigh scatterers. In the case of rouleaux, the anisotropy of the backscattered power is emphasized in the non-Rayleigh region.