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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
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Affiliations:
1 Laboratory of Biorheology and Medical Ultrasonics, University of Montreal Hospital Research Center, Pavilion J.A. de Sève (Room Y-1619), 2099 Alexandre de Sève, Montréal, Québec, H2L 2W5, Canada
a) Electronic mail: francois.yu@polymtl.ca
b) Electronic mail: guy.cloutier@umontreal.ca
J. Acoust. Soc. Am. 122, 645 (2007)
/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

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. ], the second-order Taylor model with and [Eq. ], and H6 experimental data obtained by using nonfocused transducers (Refs. ) 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 ). Standard deviations are not shown for clarity.

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 ). Results are expressed as means s.d. over three experiments.

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.

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. are also displayed. The standard deviations are not shown for clarity.

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 .

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. .

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.

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.

FIG. 9.

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

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 .

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

TABLE I.

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

TABLE II.

Labeling of the different types of blood samples studied.

TABLE III.

Characteristics of each transducer used to collect rf US data.

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. .

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.

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. (RS0, ) at corresponding times were used for comparison.

/content/asa/journal/jasa/122/1/10.1121/1.2735805
2007-07-01
2014-04-24

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