Size determination of red blood cell aggregates induced by dextran using ultrasound backscattering phenomenon

Classification of red blood cell aggregation using empirical wavelet transform analysis of ultrasonic radiofrequency echo signals

Grading red blood cell (RBC) aggregation is important for the early diagnosis and prevention of related diseases such as ischemic cardio-cerebrovascular disease, type II diabetes, deep vein thrombosis, and sickle cell disease. In this study, a machine learning technique based on an adaptive analysis of ultrasonic radiofrequency (RF) echo signals in blood is proposed, and its feasibility for classifying RBC aggregation is explored. Using an adaptive empirical wavelet transform (EWT) analysis, the ultrasonic RF signals are decomposed into a series of empirical mode functions (EMFs); then, dominant empirical mode functions (DEMFs) are selected from the series. Six statistical characteristics, including the mean, variance, median, kurtosis, root mean square (RMS), and skewness are calculated for the locally normalized DEMFs, aiming to form primary feature vectors. Random forest (RDF) and support vector machine (SVM) classifiers are trained with the given feature vectors to obtain prediction models for RBC classification. Ultrasonic RF echo signals are acquired from five groups of six types of porcine blood samples with average numbers of aggregated RBCs of 1.04, 1.20, 1.83, 2.31, 2.72, and 4.28, respectively, to test the classification performance of the proposed method. The best subset with regard to the variance, kurtosis, and RMS is determined according to the maximum accuracy based on the RDF and SVM classifiers. The classification accuracies are 84.03 ± 3.13% for the RDF classifier, and 85.88 ± 2.99% for the SVM classifier. The mean classification accuracy of the SVM classifier is 1.85% better than that of the RDF classifier. In conclusion, the machine learning method is useful for the discrimination of varying degrees of RBC aggregation, and has potential for use in characterizing and monitoring the RBC aggregation in vessels.

Rapid determination of erythrocyte sedimentation rate (ESR) by an electrically driven blood droplet biosensor

In healthcare practice, the sedimentation rate of red blood cells (erythrocytes) is a widely used clinical parameter for screening of several ailments such as stroke, infectious diseases, and malignancy. In a traditional pathological setting, the total time taken for evaluating this parameter varies typically from 1 to 2 h. Furthermore, the volume of human blood to be drawn for each test, following a gold standard laboratory technique (alternatively known as the Westergren method), varies from 4 to 5 ml. Circumventing the above constraints, here we propose a rapid (∼1 min) and highly energy efficient method for the simultaneous determination of hematocrit and erythrocyte sedimentation rate (ESR) on a microfluidic chip, deploying electrically driven spreading of a tiny drop of blood sample (∼8 μl). Our unique approach estimates these parameters by correlating the same with the time taken by the droplet to spread over a given radius, reproducing the results from more elaborate laboratory settings to a satisfactory extent. Our novel methodology is equally applicable for determining higher ranges of ESR such as high concentration of bilirubin and samples corresponding to patients with anemia and patients with some severe inflammation. Furthermore, the minimal fabrication steps involved in the process, along with the rapidity and inexpensiveness of the test, render the suitability of the strategy in extreme point-of-care settings.

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.

Influence of erythrocyte aggregation on radial migration of platelet-sized spherical particles in shear flow

Blood platelets when activated are involved in the mechanisms of hemostasis and thrombosis, and their migration toward injured vascular endothelium necessitates interaction with red blood cells (RBCs). Rheology co-factors such as a high hematocrit and a high shear rate are known to promote platelet mass transport toward the vessel wall. Hemodynamic conditions promoting RBC aggregation may also favor platelet migration, particularly in the venous system at low shear rates. The aim of this study was to confirm experimentally the impact of RBC aggregation on platelet-sized micro particle migration in a Couette flow apparatus. Biotin coated micro particles were mixed with saline or blood with different aggregation tendencies, at two shear rates of 2 and 10s^-1 and three hematocrits ranging from 20 to 60%. Streptavidin membranes were respectively positioned on the Couette static and rotating cylinders upon which the number of adhered fluorescent particles was quantified. The platelet-sized particle adhesion on both walls was progressively enhanced by increasing the hematocrit (p<0.001), reducing the shear rate (p<0.001), and rising the aggregation of RBCs (p<0.001). Particle count was minimum on the stationary cylinder when suspended in saline at 2s^-1 (57±33), and maximum on the rotating cylinder at 60% hematocrit, 2s^-1 and the maximum dextran-induced RBC aggregation (2840±152). This fundamental study is confirming recent hypotheses on the role of RBC aggregation on venous thrombosis, and may guide molecular imaging protocols requiring injecting active labeled micro particles in the venous flow system to probe human diseases.

A portable microfluidic system for rapid measurement of the erythrocyte sedimentation rate

The erythrocyte sedimentation rate (ESR) is a frequently used 30 min or 60 min clinical test for screening of several inflammatory conditions, infections, trauma, and malignant diseases, as well as non-inflammatory conditions including prostate cancer and stroke. Erythrocyte aggregation (EA) is a physiological process where erythrocytes form face-to-face linear structures, called rouleaux, at stasis or low shear rates. In this work, we proposed a method for ESR measurement from EA. We developed a microfluidic opto-electro-mechanical system, using which we experimentally showed a significant correlation (R² = 0.86) between ESR and EA. The microfluidic system was shown to measure ESR from EA using fingerprick blood in 2 min. 40 μl of whole blood is filled in a disposable polycarbonate cartridge which is illuminated with a near infrared emitting diode. Erythrocytes were disaggregated under the effect of a mechanical shear force using a solenoid pinch valve. Following complete disaggregation, transmitted light through the cartridge was measured using a photodetector for 1.5 min. The intensity level is at its lowest at complete disaggregation and highest at complete aggregation. We calculated ESR from the transmitted signal profile. We also developed another microfluidic cartridge specifically for monitoring the EA process in real-time during ESR measurement. The presented system is suitable for ultrafast, low-cost, and low-sample volume measurement of ESR at the point-of-care.

Polyvalent choline phosphate as a universal biomembrane adhesive

Phospholipids in the cell membranes of all eukaryotic cells contain phosphatidyl choline (PC) as the headgroup. Here we show that hyperbranched polyglycerols (HPGs) decorated with the 'PC-inverse' choline phosphate (CP) in a polyvalent fashion can electrostatically bind to a variety of cell membranes and to PC-containing liposomes, the binding strength depending on the number density of CP groups per macromolecule. We also show that HPG-CPs can cause cells to adhere with varying affinity to other cells, and that binding can be reversed by subsequent exposure to low molecular weight HPGs carrying small numbers of PCs. Moreover, PC-rich membranes adsorb and rapidly internalize fluorescent HPG-CP but not HPG-PC molecules, which suggests that HPG-CPs could be used as drug-delivery agents. CP-decorated polymers should find broad use, for instance as tissue sealants and in the self-assembly of lipid nanostructures.

Ultrasonic backscatter from rat blood in aggregating media under in vitro rotational flow

Ultrasonic backscatter from flowing and static rat red blood cells (RBCs) in autologous plasma and in 360 kDa polyvinylpyrrolidone (PVP 360) solution was measured as a function of hematocrit. The flow speed was varied by a stirring magnet in a cylindrical chamber. The radio-frequency (RF) signals backscattered by RBC samples were measured over 5 min in a pulse-echo setup with a 5 MHz focused transducer. Although the intact rat blood has poor RBC aggregability, RBC aggregation of rat blood was enhanced by replacing its plasma with a higher molecular weight polymer solution. The experimental results showed that the nonlinear relationship between hematocrit and ultrasonic backscatter from rat RBCs in plasma and aggregating media is affected by flow speed, which may provide a unified insight into hematocrit dependence of RBC aggregation under flowing and static conditions.

Cyclic changes in blood echogenicity under pulsatile flow are frequency dependent

Previous in vivo and in vitro studies have demonstrated that blood echogenicity varies under pulsatile flow, but such changes could not always be measured at physiological stroke rates. The apparent contradiction between these studies could be a result of the use of different ultrasound frequencies. Backscattered signals from porcine blood were measured in a pulsatile Couette flow apparatus. Cyclic changes in shear rate for stroke rates of 20 to 70 beats per minute (BPM) were applied to the Couette system, and different blood samples were analyzed (normal blood and blood with hyperaggregating erythrocytes promoted with dextran). To confirm that cyclic echogenicity variations were observable, spectral analysis was performed to verify if changes in echo-amplitude corresponded to the stroke rate applied to the flow. Echogenicity was measured with two single-element transducers at 10 and 35 MHz. At 35 MHz, cyclic variations in backscatter were observed from 20 to 70 BPM. However at 10 MHz, they were detected only at 20 BPM. For all cases except for hyperaggregating red blood cells (RBCs) at 20 BPM, the magnitude of the cyclic variations were higher at 35 MHz. We conclude that cyclic variations in RBC aggregation exist at physiological stroke rates, unlike what has been demonstrated in previous in-vitro studies at frequencies of 10 MHz. The increased sensitivity at 35 MHz to small changes in aggregate size might be the explanation for the better characterization of RBC aggregation at high stroke rates. Our results corroborate in-vivo observations of cyclic blood echogenicity variations in patients using a 30-MHz intravascular ultrasound catheter.

Rheology and ultrasound scattering from aggregated red cell suspensions in shear flow

The shear flow dynamics of reversible red cell aggregates in dense suspensions were investigated by ultrasound scattering, to study the shear disruption processes of Rayleigh clusters and examine the effective mean field approximation used in microrheological models. In a first section, a rheo-acoustical model, in the Rayleigh scattering regime, is proposed to describe the shear stress dependence of the low frequency scattered power in relation to structural parameters. The fractal scattering regime characterizing the anisotropic scattering from flocs of size larger than the ultrasound wavelength is further discussed. In the second section, we report flow-dependent changes in the low-frequency scattering coefficient in a plane-plane flow geometry to analyze the shear disruption processes of hardened or deformable red cell aggregates in neutral dextran polymer solution. Rheo-acoustical experiments are examined on the basis of the rheo-acoustical model and the effective medium approximation. The ability of ultrasound scattering technique to determine the critical disaggregation shear stress and to give quantitative information on particle surface adhesive energy is analyzed. Lastly, the shear-thinning behavior of weakly aggregated hardened or deformable red cells is described.

Aggregate formation of erythrocytes in postcapillary venules

The purpose of the present study was to obtain information on erythrocyte aggregate formation in vivo. The movements of erythrocytes in postcapillary venules of the rat spinotrapezius muscle at various flow rates were recorded with a high-speed video camera before and after infusion of dextran 500. To distinguish aggregates, the following criteria were used: 1) a fixed distance (4 microm) between the center points of two adjacent cells, 2) lack of visible separation between the adjacent cells, and 3) movement of the adjacent cells in the same direction. Without dextran 500 infusion, 11 and 5% of erythrocytes formed aggregates in low (33.2 +/- 28.3 s) and high pseudoshear (144.2 +/- 58.3 s) conditions, respectively, based on the above criteria. After dextran 500 infusion, 53% of erythrocytes satisfied the criteria in the low pseudoshear condition (26.5 +/- 17.0 s) and 13% of erythrocytes met the criteria in the high pseudoshear condition (240.0 +/- 85.9 s), indicating erythrocyte aggregation is strongly associated with shear rate. Approximately 90% of aggregate formation occurred in a short time period (0.15-0.30 s after entering the venule) in a region 15 to 30 microm from the entrance. The time delay may reflect rheological entrance conditions in the venule.

Comparison of new ultrasound index with laser reference and viscosity indexes for erythrocyte aggregation quantification

We have previously established new ultrasonic indexes for erythrocyte aggregation using a Couette device, and validated them toward the Rayleigh's theory and reproducibility. Two hydrodynamic protocols were applied on various suspensions and their aggregation degrees were characterized by: 1. for the decreasing shear rates protocol: the power P(US) at the nominal frequency of the transducer used; 2. for the kinetic protocol: aggregation times (latency and half-rise times), variation between initial disaggregated state (Vo) and final aggregated state (V(inf)) and AI(US), which is the integral of the kinetic curve over time. The objective of the present study was to demonstrate the ability of these indexes to characterize the aggregation dynamics of suspensions with various levels of aggregation induced by concentrations of dextran 70 kD (Dx) of 10, 20 and 40 g/L added to washed red cells resuspended in saline solution. The results showed a maximum of backscattered power (P(US)) for Dx = 40 g/L with the decreasing shear rates protocol. We measured a final aggregation level (V(inf)), a minimal aggregation time (T(m)) and a maximal value of AI(US) for Dx = 40 g/L with the aggregation kinetics protocol. On the other hand, viscosity is increased with dextran concentration. These evolutions of the ultrasound (US) indexes and viscosity with dextran concentrations are consistent with literature reports. In addition, a particularly interesting phenomenon of US backscattering enhancement was observed for kinetics with no null final shear rate, which has never before been reported in such a precise manner. By another way, each of the dextran suspensions was tested on the laser erythroaggregometer that is presently considered as the "gold standard" method for erythrocyte characterization. The laser indexes (aggregation time T(a), aggregation indexes AI(10s) and AI(60s)), deduced from a kinetic protocol, have similar significance to the US ones. Statistical comparisons have been done between laser and ultrasonic indexes and significant correlations (0.001 < p < 0.01) were obtained. The set of results allowed us to conclude that ultrasonic indexes are suitable markers for the erythrocyte aggregation.

Depletion-mediated red blood cell aggregation in polymer solutions

Polymer-induced red blood cell (RBC) aggregation is of current basic science and clinical interest, and a depletion-mediated model for this phenomenon has been suggested; to date, however, analytical approaches to this model are lacking. An approach is thus described for calculating the interaction energy between RBC in polymer solutions. The model combines electrostatic repulsion due to RBC surface charge with osmotic attractive forces due to polymer depletion near the RBC surface. The effects of polymer concentration and polymer physicochemical properties on depletion layer thickness and on polymer penetration into the RBC glycocalyx are considered for 40 to 500 kDa dextran and for 18 to 35 kDa poly (ethylene glycol). The calculated results are in excellent agreement with literature data for cell-cell affinities and with RBC aggregation-polymer concentration relations. These findings thus lend strong support to depletion interactions as the basis for polymer-induced RBC aggregation and suggest the usefulness of this approach for exploring interactions between macromolecules and the RBC glycocalyx.

Lower limb vein enlargement and spontaneous blood flow echogenicity are normal sonographic findings during pregnancy

PURPOSE

We studied pregnancy-induced changes in lower limb venous function.

METHODS

We used plethysmography and sonography to assess the changes in venous wall distensibility, saphenous vein diameters, and spontaneous blood flow echogenicity in the common femoral veins in 190 consecutive women during and after uncomplicated pregnancies (total of 409 examinations).

RESULTS

The percentage of women with clinical symptoms and signs of venous insufficiency increased significantly during pregnancy. The mean diameters of the great and small saphenous veins also increased significantly, while occlusive venous plethysmography showed a decrease in parameters indicating vein distensibility. Spontaneous blood flow echogenicity in the common femoral veins was clearly visible or marked in 6% of cases during the first trimester of pregnancy, 63% during the second trimester, and 96% during the third trimester, versus 6% after delivery (p < 0.0001). The mean hematocrit decreased and the mean fibrinogen concentration increased during pregnancy.

CONCLUSIONS

The increase in lower limb venous pressure seen during pregnancy leads to venous overdistention and worsens blood stasis. Decreased venous flow velocity and rheological alterations result in increased red cell aggregation, giving rise to spontaneous blood flow echogenicity. Spontaneous blood flow echogenicity is therefore a normal finding during pregnancy and should not be mistaken for venous thrombosis.

Rheo-acoustical study of the shear disruption of reversible aggregates. Ultrasound scattering from concentrated suspensions of red cell aggregates

Shear-induced disruption of reversible aggregates or clusters in a concentrated suspension is investigated by ultrasound backscattering in the low shear regime. Fractal aggregates are considered as non-Brownian scatterers much smaller than the wavelength with acoustic properties close to those of the surrounding liquid, so that the attenuation of the coherent field is weak and multiple scattering can be neglected. The concept of variance in local particle volume fraction is used to deduce a first-order expression of the ultrasound scattering cross section per unit volume for Rayleigh scatterers in a dense suspension. On the basis of a scaling law for the shear-induced disruption of aggregates, the shear stress dependence of the ultrasonic scattered intensity from a dense suspension of clusters is derived. In a second part, the shear breakup of hardened red blood cell aggregates is investigated in plane-plane flow geometry by ultrasound scattering. Rheo-acoustical experiments are analyzed within the framework of the self-consistent field approximation and the scaling laws currently used in microrheological models. Finally, the ability of ultrasonic, light reflectometry and viscometry methods to provide quantitative information about red blood cell aggregation and membrane adhesiveness is discussed.

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.

Kinetic model for erythrocyte aggregation

It is well known that light transmission through blood is the most widely utilized method for the study of erythrocyte aggregation. The curves obtained had been considered empirically as exponential functions. In consequence, the process becomes characterized by an only parameter that varies with all the process factors without discrimination. In the present paper a mathematical model for RBC aggregation process is deduced in accordance with von Smoluchowski's theory about the kinetics of colloidal particles agglomeration. The equation fitted the experimental pattern of the RBC suspension optical transmittance closely and contained two parameters that estimate the most important characteristics of the aggregation process separately, i.e., (1) average size of rouleaux at equilibrium and (2) aggregation rate. The evaluation of the method was assessed by some factors affecting erythrocyte aggregation, such as temperature, plasma dilutions, Dextran 500, Dextran 70 and PVP 360, at different media concentrations, cellular membrane alteration by the alkylating agent TCEA, and decrease of medium osmolarity. Results were interpreted considering the process characteristics estimated by the parameters, and there were also compared with similar studies carried out by other authors with other methods. This analysis allowed us to conclude that the equation proposed is reliable and useful to study erythrocyte aggregation.

Characterization of red blood cell aggregate formation using an analytical model of the ultrasonic backscattering coefficient

Ultrasound backscattering is well adapted to study the red blood cell (RBC) aggregation phenomenon and growth of RBC aggregates since the backscattered ultrasonic intensity depends on the sixth power of the mean radius of the scattering centers when considered as spherical. Thus, small variations of aggregate size induce large variations of the backscattered intensity. From measurements of the ultrasonic backscattering coefficient (ultrasonic backscattering cross section per unit volume of suspension), an analytical model describing its variation versus time, for human aggregated red blood cells in sedimentation, is proposed. Results given by the model allow to define three phases in the phenomenon: 1) a starting phase characterized by a duration ts; 2) a stationary final phase beginning at time tf; 3) a growing intermediate phase characterized by its duration tf - ts. The analytical model has been applied to describe RBC aggregation in dextran 70,000 dalton of different concentrations, and at various hematocrits. Knowledge of the durations ts, tf and the maximum slope s of the curve during the intermediate phase, determined with the model, allows a means to study RBC aggregate growth.

Power Doppler ultrasound evaluation of the shear rate and shear stress dependences of red blood cell aggregation

The use of power Doppler ultrasound at 10 MHz is evaluated as a method to study the shear rate and the shear stress dependences of red blood cell aggregation. This evaluation was based on six in vitro experiments conducted in a 1.27-cm diameter tube under steady flow conditions. Porcine whole blood was circulated in the flow model at flow rates ranging between 125 to 1500 ml/min (mean shear rate across the tube ranging between 6 and 74 s-1). For each flow condition, the variation of the Doppler power across the tube and the velocity profile were measured by moving the Doppler sample volume across the tube diameter. For each radial position, the shear rate within the Doppler sample volume was also determined by considering the radial power pattern of the ultrasound beam. To estimate the shear stress within the Doppler sample volume, the apparent viscosity of blood samples withdrawn from the flow model was measured for each experiment. The variation of the Doppler power as a function of the shear rate within the sample volume showed a rapid reduction of the power between 1 and 5 s-1, a transition region between 5 and 10 s-1, and a very slow reduction beyond 10 s-1. Little variation of the Doppler power was measured for shear stress higher than 2 dyn/cm2. The maximum Doppler power for all flow rates was usually found near the center of the tube. Based on the ultrasonic scattering models, which predict that the Doppler power is related to the volume square of the scatterers, the method described in the present study showed a very high sensitivity to the presence of red blood cell aggregation for shear rates below 10 s-1.

Ultrasound backscatter at 30 MHz from human blood: influence of rouleau size affected by blood modification and shear rate

High frequency intravascular ultrasound may show a high intensity backscatter from blood which hampers the discrimination between lumen and arterial wall. In this study, the acoustic behaviour of blood at 30 MHz in relation to rouleau size was analyzed. In a Couette viscometer, high frequency (20-40 MHz) backscatter data from normal and modified blood samples from eight volunteers were obtained at shear rates from 0 to 1000 s-1. The acoustic behaviour of blood was quantified by the integrated backscatter power and the spectral slope of the backscatter coefficient. Backscatter from blood depended on rouleau size. At a shear rate of zero, both whole blood and rouleau-enhanced blood showed a 11-dB-higher integrated backscatter power than rouleau-suppressed blood, which itself was 10 dB higher than that of hemolysed blood, the latter showing a 6-dB-higher backscatter than saline. Platelets did not contribute to the backscatter power. Plasma and saline produced no detectable integrated backscatter power other than noise. The spectral slope of whole and rouleau-enhanced blood was small (1 and 0.5, respectively), whereas rouleau-suppressed blood and hemolysed blood (both with a slope of 3.3) behaved almost like a Rayleigh scattering medium (slope = 4). The backscatter from rouleau-suppressed blood showed no shear rate dependence. At low shear rates ( < 0.8 s-1 for integrated backscatter power and < 0.2 s-1 for the spectral slope), whole blood and rouleau-enhanced blood tended to the results from the static situation (no shear). At high shear rates ( > 80 s-1 for integrated backscatter power and >11 s-1 for spectral slope), these samples tended to the results of rouleau-suppressed blood. Ultrasound backscatter at 30 MHz from human blood is only caused by red blood cells. With increasing aggregate (rouleau) size, the integrated backscatter power increased by 11 dB, and the spectral slope decreased from 3.3 to 1.

A unified approach to modeling the backscattered Doppler ultrasound from blood

A unified approach to modeling the backscattered Doppler ultrasound signal from blood is presented. The approach consists of summing the contributions from elemental acoustic voxels each containing many red blood cells (RBC's). For an insonified region that is large compared to a wavelength, it is shown that the Doppler signal is a Gaussian random process that arises from fluctuation scattering, which implies that the backscattered power is proportional to the variance of local RBC concentrations. As a result, some common misconceptions about the relationship between the backscattering coefficient and hematocrit can be readily resolved. The unified approach was also used to derive a Doppler signal simulation model which shows that, regardless of flow condition, the power in the Doppler frequency spectrum is governed by the exponential distribution. For finite beamwidth and paraxial flow, it is further shown that the digitized Doppler signal can be modeled by a moving average random process whose order is determined by the signal sampling rate as well as the flow velocity profile.