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Experimental ultrasound characterization of red blood cell aggregation using the structure factor size estimator
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10.1121/1.2735805
/content/asa/journal/jasa/122/1/10.1121/1.2735805
http://aip.metastore.ingenta.com/content/asa/journal/jasa/122/1/10.1121/1.2735805

Figures

Image of FIG. 1.
FIG. 1.

(Color online) (a) Backscatter coefficient for H6 blood gently stirred in a beaker and T6 blood sheared at in the Couette flow apparatus. The theoretical Rayleigh prediction [Eq. (1) ], the second-order Taylor model with and [Eq. (10) ], and H6 experimental data obtained by using nonfocused transducers (Refs. 15 and 16 ) are also plotted. (b) Backscatter coefficient for H40 blood sheared at and T40 blood sheared at in the Couette flow apparatus. The theoretical Rayleigh prediction with and , and the second-order Taylor model with and are also plotted (see Table IV ). Standard deviations are not shown for clarity.

Image of FIG. 2.
FIG. 2.

(Color online) BSC during the kinetics of rouleaux formation for (a) T6 and (b) T40 blood at different residual shear rates of 0, 2, 10, and . A high shear rate of was first applied during the first (before ). BSC is taken as the mean value over the transducer bandwidth (see Table III ). Results are expressed as means s.d. over three experiments.

Image of FIG. 3.
FIG. 3.

(Color online) Time variations of fitted parameters and during the kinetics of RBC aggregation for experiments with (a) T6 blood and (b) T40 blood at different residual shear rates ( , 2, 10, and ). A high shear of was applied during the first of each acquisition. Results are expressed as means s.d. over three experiments.

Image of FIG. 4.
FIG. 4.

(Color online) Frequency dependencies of (a) T6 and (b) T40 blood samples sheared at different residual shear rates ( , 2, 10, and ), and corresponding fitted models. H6 experimental data taken from Refs. 15 and 16 are also displayed. The standard deviations are not shown for clarity.

Image of FIG. 5.
FIG. 5.

Columns represent typical microscopic images and image processing at a particular time during the kinetics of aggregation of a T6 sample. Rows represent grayscale images, binary images, and segmented images. Actual processed images were bigger than those represented here . Resolution is .

Image of FIG. 6.
FIG. 6.

(Color online) Histograms of the aggregate dimension in number of cells at times 0, 15, 60, and . Cell count was arbitrarily separated in 15 logarithmically spaced bins to allow better resolution for small sizes. The distributions were fitted by an exponential function of mean defined by . was determined using Eq. (13) .

Image of FIG. 7.
FIG. 7.

(Color online) Comparison of estimated with the optical and US methods. Each point is the mean over three experiments at a particular time during the kinetics of aggregation.

Image of FIG. 8.
FIG. 8.

(Color online) Spherical Gaussian form factor, exponential form factor, and the second-order Taylor expansion of the structure factor as a function of , for diluted scatterers . , the effective radius of the scatterer, is often denoted as in the literature.

Image of FIG. 9.
FIG. 9.

(Color online) Effect of increasing and on the BSC in the second-order model.

Image of FIG. 10.
FIG. 10.

(Color online) Quadratic relationship between and for all shear rates at both 6% and 40% whole blood hematocrits. The high frequency limit was fixed at .

Image of FIG. 11.
FIG. 11.

(Color online) Guinier plots extended to for T6-RS2 and T40-RS2. The linear slope transition indicates the limit of the Guinier domain.

Tables

Generic image for table
TABLE I.

Some physical properties of blood (Ref. 48 ). The density is denoted , the adiabatic compressibility , and the acoustic impedance .

Generic image for table
TABLE II.

Labeling of the different types of blood samples studied.

Generic image for table
TABLE III.

Characteristics of each transducer used to collect rf US data.

Generic image for table
TABLE IV.

Experimental and theoretical values of and for disaggregated RBCs suspended in an isotonic saline solution at 6% and 40% hematocrits. and were calculated using Eqs. (3) and (4) .

Generic image for table
TABLE V.

T6 and T40 blood fitting parameters and at different residual shear rates (averaged values were computed between and ). RS100 data were averaged between and . Results are expressed as means over three experiments.

Generic image for table
TABLE VI.

Estimations of with the optical and ultrasonic methods. Microscopic images were acquired with a time resolution of . A time resolution of was used here to reduce the size of the table. US data taken from Fig. 3 (RS0, ) at corresponding times were used for comparison.

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/content/asa/journal/jasa/122/1/10.1121/1.2735805
2007-07-01
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Experimental ultrasound characterization of red blood cell aggregation using the structure factor size estimator
http://aip.metastore.ingenta.com/content/asa/journal/jasa/122/1/10.1121/1.2735805
10.1121/1.2735805
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