Effects of a sudden flow reduction on red blood cell rouleau formation and orientation using RF backscattered power

The variational multiscale formulation for the fully-implicit log-morphology equation as a tensor-based blood damage model

We derive a variational multiscale (VMS) finite element formulation for a viscoelastic, tensor-based blood damage model. The tensor equation is numerically stabilized by a logarithmic shape tensor description that prevents unphysical, negative eigenvalues. The resulting VMS stabilization terms for this so-called log-morph equation are presented together with their special numerical treatment. Results for a 2D rotating stirrer test case obtained from log-morph simulations with both SUPG and VMS stabilization show significantly improved numerical behavior if compared with Galerkin/least squares (GLS) stabilized untransformed morphology simulation results. The newly proposed method is also successfully applied to a state-of-the-art centrifugal ventricular assist device (VAD), and clear advantages of the VMS stabilization compared with the SUPG-stabilized formulation are presented.

In vitro photoacoustic spectroscopy of pulsatile blood flow: Probing the interrelationship between red blood cell aggregation and oxygen saturation

We investigate the optical wavelength dependence in quantitative photoacoustic (QPA) assessment of red blood cell (RBC) aggregation and oxygen saturation (sO₂ ) during pulsatile blood flow. Experimentally, the pulsatile flow was imaged with a 700 to 900 nm laser using the VevoLAZR. Theoretically, the photoacoustic (PA) signals were computed based on a Green's function integrated with a Monte Carlo simulation of radiant fluence. The pulsatile flow created periodic conditions of RBC aggregation/nonaggregation, altering the aggregate size, and, in turn, the sO₂ . The dynamic range, DR (a metric of change in PA power) from 700 to 900 nm for nonaggregated RBCs, was 5 dB for both experiment and theory. A significant difference in the DR for aggregated RBCs was 1.5 dB between experiment and theory. Comparing the DR at different wavelengths, the DR from nonaggregated to aggregated RBCs at 700 nm was significantly smaller than that at 900 nm for both experiment (4.0 dB < 7.1 dB) and theory (5.3 dB < 9.0 dB). These results demonstrate that RBC aggregation simultaneously affects the absorber size and the absorption coefficient in photoacoustic imaging (PAI) of pulsatile blood flow. This investigation elucidates how QPA spectroscopy can be used for probing hemodynamics and oxygen transport by PAI of blood flow.

Neuromuscular electrical stimulation reduces sludge in the popliteal vein

BACKGROUND

The common peroneal nerve stimulator (CPNS) is a UK-approved device for reducing venous thromboembolism (VTE) risk. It resembles a wrist watch and is placed over the common peroneal nerve, discharging electricity at a rate of 1 impulse/s. It has been presumed that as blood flow slows, erythrocytes aggregate into ultrasound-detectable echogenic particles, described as venous sludge. The aim of the study was to determine whether the CPNS reduces venous sludge by using an ultrasound-derived gray-scale (0-255) venous sludge index (VSI).

METHODS

Twenty-five healthy volunteers had their right popliteal vein video recorded using B-mode ultrasound at 22 frames/s in longitudinal and transverse views, standing and lying. This was performed first with the CPNS off and then with the CPNS on. The CPNS impulse intensity used was set from 1 to 7 for each individual, and the level was sufficient to cause an outward jerking movement of the foot. A single frame of the possible 154 frames, lasting 7 seconds, was selected using a random number generator for the image analysis. The "brightness" of the erythrocyte aggregates (pixels) within a circular sampling area was quantified using the VSI. The brighter the sample, the greater the sludge.

RESULTS

Values are expressed as median (interquartile range). On standing with the device off, there was a significantly higher VSI (P < .0005) compared with lying (longitudinal view, 27.7 [18.8-41.4] vs 11.7 [5.5-17.5]; transverse view, 20.7 [13.6-32.2] vs 11.4 [6.3-15.9]). Activation of the CPNS significantly reduced all the VSI values (P < .0005) shown (longitudinal view, 2 [1.1-3.2] and 1.5 [0.5-3.1]; transverse view, 1.1 [0.6-2.7] and 0.8 [0.5-2.1]).

CONCLUSIONS

The CPNS device significantly reduces venous sludge within the popliteal vein irrespective of whether the subject is standing or lying down or of the longitudinal or transverse position of the ultrasound transducer. The principal mode of action of the device in the claim that it may reduce venous thromboembolism risk may be through a reduction of venous sludge. However, the relationship between erythrocyte aggregation, venous stasis, and venous thromboembolism risk requires more investigation.

Red cells' dynamic morphologies govern blood shear thinning under microcirculatory flow conditions

Blood viscosity decreases with shear stress, a property essential for an efficient perfusion of the vascular tree. Shear thinning is intimately related to the dynamics and mutual interactions of RBCs, the major component of blood. Because of the lack of knowledge about the behavior of RBCs under physiological conditions, the link between RBC dynamics and blood rheology remains unsettled. We performed experiments and simulations in microcirculatory flow conditions of viscosity, shear rates, and volume fractions, and our study reveals rich RBC dynamics that govern shear thinning. In contrast to the current paradigm, which assumes that RBCs align steadily around the flow direction while their membranes and cytoplasm circulate, we show that RBCs successively tumble, roll, deform into rolling stomatocytes, and, finally, adopt highly deformed polylobed shapes for increasing shear stresses, even for semidilute volume fractions of the microcirculation. Our results suggest that any pathological change in plasma composition, RBC cytosol viscosity, or membrane mechanical properties will affect the onset of these morphological transitions and should play a central role in pathological blood rheology and flow behavior.

Dynamic and rheological properties of soft biological cell suspensions

Quantifying dynamic and rheological properties of suspensions of soft biological particles such as vesicles, capsules, and red blood cells (RBCs) is fundamentally important in computational biology and biomedical engineering. In this review, recent studies on dynamic and rheological behavior of soft biological cell suspensions by computer simulations are presented, considering both unbounded and confined shear flow. Furthermore, the hemodynamic and hemorheological characteristics of RBCs in diseases such as malaria and sickle cell anemia are highlighted.

In vivo observation of the hypo-echoic "black hole" phenomenon in rat arterial bloodstream: a preliminary Study

The "black hole," a hypo-echoic hole at the center of the bloodstream surrounded by a hyper-echoic zone in cross-sectional views, has been observed in ultrasound backscattering measurements of blood with red blood cell aggregation in in vitro studies. We investigated whether the phenomenon occurs in the in vivo arterial bloodstream of rats using a high-frequency ultrasound imaging system. Longitudinal and cross-sectional ultrasound images of the rat common carotid artery (CCA) and abdominal aorta were obtained using a 40-MHz ultrasound system. A high-frame-rate retrospective imaging mode was employed to precisely examine the dynamic changes in blood echogenicity in the arteries. When the imaging was performed with non-invasive scanning, blood echogenicity was very low in the CCA as compared with the surrounding tissues, exhibiting no hypo-echoic zone at the center of the vessel. Invasive imaging of the CCA by incising the skin and subcutaneous tissues at the imaging area provided clearer and brighter blood echo images, showing the "black hole" phenomenon near the center of the vessel in longitudinal view. The "black hole" was also observed in the abdominal aorta under direct imaging after laparotomy. The aortic "black hole" was clearly observed in both longitudinal and cross-sectional views. Although the "black hole" was always observed near the center of the arteries during the diastolic phase, it dissipated or was off-center along with the asymmetric arterial wall dilation at systole. In conclusion, we report the first in vivo observation of the hypo-echoic "black hole" caused by the radial variation of red blood cell aggregation in arterial bloodstream.

Computational biorheology of human blood flow in health and disease

Hematologic disorders arising from infectious diseases, hereditary factors and environmental influences can lead to, and can be influenced by, significant changes in the shape, mechanical and physical properties of red blood cells (RBCs), and the biorheology of blood flow. Hence, modeling of hematologic disorders should take into account the multiphase nature of blood flow, especially in arterioles and capillaries. We present here an overview of a general computational framework based on dissipative particle dynamics (DPD) which has broad applicability in cell biophysics with implications for diagnostics, therapeutics and drug efficacy assessments for a wide variety of human diseases. This computational approach, validated by independent experimental results, is capable of modeling the biorheology of whole blood and its individual components during blood flow so as to investigate cell mechanistic processes in health and disease. DPD is a Lagrangian method that can be derived from systematic coarse-graining of molecular dynamics but can scale efficiently up to arterioles and can also be used to model RBCs down to the spectrin level. We start from experimental measurements of a single RBC to extract the relevant biophysical parameters, using single-cell measurements involving such methods as optical tweezers, atomic force microscopy and micropipette aspiration, and cell-population experiments involving microfluidic devices. We then use these validated RBC models to predict the biorheological behavior of whole blood in healthy or pathological states, and compare the simulations with experimental results involving apparent viscosity and other relevant parameters. While the approach discussed here is sufficiently general to address a broad spectrum of hematologic disorders including certain types of cancer, this paper specifically deals with results obtained using this computational framework for blood flow in malaria and sickle cell anemia.

Multiscale modeling of blood flow: from single cells to blood rheology

Mesoscale simulations of blood flow, where the red blood cells are described as deformable closed shells with a membrane characterized by bending rigidity and stretching elasticity, have made much progress in recent years to predict the flow behavior of blood cells and other components in various flows. To numerically investigate blood flow and blood-related processes in complex geometries, a highly efficient simulation technique for the plasma and solutes is essential. In this review, we focus on the behavior of single and several cells in shear and microcapillary flows, the shear-thinning behavior of blood and its relation to the blood cell structure and interactions, margination of white blood cells and platelets, and modeling hematologic diseases and disorders. Comparisons of the simulation predictions with existing experimental results are made whenever possible, and generally very satisfactory agreement is obtained.

In vivo vascular wall shear rate and circumferential strain of renal disease patients

This study measures the vascular wall shear rate at the vessel edge using decorrelation based ultrasound speckle tracking. Results for nine healthy and eight renal disease subjects are presented. Additionally, the vascular wall shear rate and circumferential strain during physiologic pressure, pressure equalization and hyperemia are compared for five healthy and three renal disease subjects. The mean and maximum wall shear rates were measured during the cardiac cycle at the top and bottom wall edges. The healthy subjects had significantly higher mean and maximum vascular wall shear rate than the renal disease subjects. The key findings of this research were that the mean vascular wall shear rates and circumferential strain changes between physiologic pressure and hyperemia that was significantly different between healthy and renal disease subjects.

Margination of white blood cells in microcapillary flow

Margination of white blood cells (WBCs) towards vessel walls is an essential precondition for their efficient adhesion to the vascular endothelium. We perform numerical simulations with a two-dimensional blood flow model to investigate the dependence of WBC margination on hydrodynamic interactions of blood cells with the vessel walls, as well as on their collective behavior and deformability. We find WBC margination to be optimal in intermediate ranges of red blood cell (RBC) volume fractions and flow rates, while, beyond these ranges, it is substantially attenuated. RBC aggregation enhances WBC margination, while WBC deformability reduces it. These results are combined in state diagrams, which identify WBC margination for a wide range of flow and cell suspension conditions.

Predicting human blood viscosity in silico

The viscosity of blood has long been used as an indicator in the understanding and treatment of disease, and the advent of modern viscometers allows its measurement with ever-improving clinical convenience. However, these advances have not been matched by theoretical developments that can yield a quantitative understanding of blood's microrheology and its possible connection to relevant biomolecules (e.g., fibrinogen). Using coarse-grained molecular dynamics and two different red blood cell models, we accurately predict the dependence of blood viscosity on shear rate and hematocrit. We explicitly represent cell-cell interactions and identify the types and sizes of reversible rouleaux structures that yield a tremendous increase of blood viscosity at low shear rates. We also present the first quantitative estimates of the magnitude of adhesive forces between red cells. In addition, our simulations support the hypothesis, previously deduced from experiments, of yield stress as an indicator of cell aggregation. This non-Newtonian behavior is analyzed and related to the suspension's microstructure, deformation, and dynamics of single red blood cells. The most complex cell dynamics occurs in the intermediate shear rate regime, where individual cells experience severe deformation and transient folded conformations. The generality of these cell models together with single-cell measurements points to the future prediction of blood-viscosity anomalies and the corresponding microstructures associated with various diseases (e.g., malaria, AIDS, and diabetes mellitus). The models can easily be adapted to tune the properties of a much wider class of complex fluids including capsule and vesicle suspensions.

Measurement of red blood cell aggregation using X-ray phase contrast imaging

When a coherent beam illuminates spatially disordered particles, speckle patterns are formed due to interference of the scattered light waves. Speckle patterns from biological tissues using synchrotron phase contrast X-ray imaging can provide functional information about micro-scale morphological structures of the tissues. In this study, we investigated the size and contrast variations of the speckles of aggregated red blood cells (RBCs) suspensions with varying the degree of RBC aggregation. Results show that the degree of RBC aggregation is a governing parameter on the change of speckle characteristics. This blood speckle analysis method can be used as a novel modality for monitoring RBC aggregation.

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.

Non-Gaussian statistics and temporal variations of the ultrasound signal backscattered by blood at frequencies between 10 and 58 MHz

Very little is known about the blood backscattering behavior and signal statistics following flow stoppage at frequencies higher than 10 MHz. Measurements of the radio frequency (rf) signals backscattered by normal human blood (hematocrit = 40%, temperature = 37 degrees C) were performed in a tube flow model at mean frequencies varying between 10 and 58 MHz. The range of increase of the backscattered power during red blood cell (RBC) rouleau formation was close to 15 dB at 10 and 36 MHz, and dropped, for the same blood samples, below 8 dB at 58 MHz. Increasing the frequency from 10 to 58 MHz raised the slope of the power changes at the beginning of the kinetics of aggregation, and could emphasize the non-Gaussian behavior of the rf signals interpreted in terms of the K and Nakagami statistical models. At 36 and 58 MHz, significant increases of the kurtosis coefficient, and significant reductions of the Nakagami parameter were noted during the first 30 s of flow stoppage. In conclusion, increasing the transducer frequency reduced the magnitude of the backscattered power changes attributed to the phenomenon of RBC aggregation, but improved the detection of rapid growth in aggregate sizes and non-Gaussian statistical behavior.

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.

Quantitative IVUS blood flow: validation in vitro, in animals and in patients

In recent years, a new method to measure transverse blood flow based on the decorrelation of the radiofrequency (RF) signals of intravascular ultrasound (IVUS) rotating single-element scanners was introduced. We report here in vitro, animal and patient testing to evaluate the correlation-based method using an IVUS array catheter. A new correlation-based method to dynamically correct the correlation coefficients for noise is implemented. The decorrelation due to noise was estimated from the correlation coefficients from flowing blood obtained at increasing time lags. First, blood flow experiments were carried out with different catheters in a tissue-mimicking flow phantom with an inner diameter ranging from 3.0 to 5.0 mm. A calibrated electromagnetic flow meter (EMF, range: 0 to 250 cc/min) was used as a reference. Good linear relationships were found between the IVUS-derived flow and the calibrated EMF (all R(2)> 0.96). The catheter position within the flow phantom and the size of the ring-down were theoretically analyzed. These elements, and noise in the RF signals, have an important influence on the IVUS blood flow measurements reflected by the offset and the slope of the linear relationships. By placing the IVUS catheter outside the flow phantom, parabolic blood flow profiles were also measured. Second, IVUS blood flow measurements were performed in the carotid artery of two Yorkshire pigs, which showed linear relationships (all R(2)> 0.85) between the IVUS-derived flow and the calibrated EMF. Experimentally, the offset was lower than 3 mL/min and the slope was close to 1. Third, IVUS blood flow measurements were performed in coronary arteries in patients. Preliminary results for the coronary flow reserve (CFR = high flow/baseline flow) in patients using the decorrelation method of RF signals of an array IVUS scanner were comparable with CFR based on Doppler measurements.

A new ultrasound principle for characterizing erythrocyte aggregation: in vitro reproducibility and validation

RATIONALE AND OBJECTIVES

There is no method currently available to quantify erythrocyte aggregation in vivo. In this work, using a Couette system, we defined new ultrasound indexes potentially applicable for non-invasive investigations.

METHODS

Two ultrasound protocols were developed: (1) a protocol in which decreasing shear rates ranging from 200 to 1 s-1 were applied to solutions; and (2) a protocol in which a 200 s-1 shear rate was initially applied followed by stoppage of flow (a kinetics protocol). New ultrasound indexes were defined as: the power PUS at the nominal frequency of each transducer, Rayleigh's slope (tangent of the curve PUS = f(log(F)) through the 3.5 to 15 MHz frequency bandwidth) and kinetic indexes characterizing the aggregation/aggregability of the suspension.

RESULTS

Using washed erythrocytes resuspended in saline, it was shown that the ultrasound intensity is dependent at 3.54 +/- 5.9% (NS) to the power of the frequency (theoretical value = 4). Using 10 total blood samples extracted from a single pig, good reproducibility for all indexes (5%) was demonstrated.

CONCLUSIONS

A suitable and reproducible methodology was developed and validated for studying erythrocyte aggregation in calibrated in vitro conditions.

Decorrelation characteristics of transverse blood flow along an intravascular array catheter: effects of aggregation of red blood cells

A method to measure transverse blood flow, based on the correlation between consecutive radiofrequency (RF) signals, has been introduced. This method was validated for an intravascular (IVUS) rotating single element catheter. Currently, we are implementing the method for an IVUS array transducer catheter. The decorrelation characteristics during transverse blood flow using the IVUS array catheter were investigated using computer modeling. Before this, blood was simulated as a collection of randomly located point scatterers and, by moving this scattering medium transversely across the acoustical beam, blood flow was simulated. This paper presents a more realistic scattering media by simulating aggregates of red blood cells (RBCs) as strings of point scatterers. Three configurations of aggregates of RBCs were simulated. First, aggregates of RBCs were strings with different lengths and parallel to the catheter axis. Second, the strings were with a fixed length and angles of plus or minus 45 degrees with respect to the catheter axis. Third, the strings were with different lengths and random angles ranging from -45 degrees to + 45 degrees. The decorrelation characteristics for these configurations of aggregates of RBCs were investigated and compared with point scatterers. For the aggregates of RBCs parallel to the catheter axis, the decorrelation rate became slower when the aggregate length was increased. RBC aggregations with fixed and random lengths and angles resulted in a decorrelation rate that approaches the decorrelation pattern from point scatterers. Results suggests that the presence of aggregates of RBCs will probably not affect the measurements of transverse blood flow using a decorrelation-based method and an IVUS array catheter.

Power Doppler ultrasound scan imaging of the level of red blood cell aggregation: an in vitro study

PURPOSE

The purpose of this study was to evaluate the effect of the shear rate on red blood cell (RBC) aggregation with power Doppler ultrasound scanning (PDU), pulsed-wave Doppler scanning, and color Doppler flow imaging.

METHODS

Equine and porcine blood were circulated with a steady flow in a phantom with a diameter of 9.52 mm. The color Doppler flow imaging mode was used to estimate the velocity profile and the shear rate across the tube. A transfer function that related the Doppler scan power, measured in gray level with the PDU method, to the power, measured in decibels with the pulsed-wave Doppler scan technique, was used to estimate the echogenicity of blood and the level of aggregation.

RESULTS

For the four experiments reported, the power peaked at low shear rates probably because of increased RBC collisions and aggregation and then decreased thereafter because of disaggregation. The largest power variations were measured at shear rates of less than 40 seconds -1. At flow rates that varied between 75 and 500 mL/min, the echogenicity was low near the wall of the tube, increased toward the middle, and decreased at the tube center. The Doppler scan power was uniform across the tube at flow rates of 750 and 1000 mL/min.

CONCLUSION

PDU is reliable to quantify the echogenicity of blood and the level of RBC aggregation. In comparison with other methods proposed to measure RBC aggregation, ultrasound scanning is applicable in vivo and may help to improve our basic understanding of the relationship between the hemodynamic of the circulation and RBC aggregation in human vessels.