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 t _s; 2) a stationary final phase beginning at time t _f; 3) a growing intermediate phase characterized by its duration t _f-t _s. 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 t _s, t _f and the maximum slope s of the curve during the intermediate phase, determined with the model, allows a means to study RBC aggregate growth.