Chemistry Reference
In-Depth Information
30
25
20
15
10
0
0
0
20
40
60
80
100
Haematocrit (%)
Fig. 3.4
The plot of the backscattering coefficient versus haematocrit for porcine red
blood cells suspended in saline (
). The smooth curve represents the Percus-Yevick theory
for the packing of hard spheres. (Results from Mo et al., 1994.)
is possible. In blood flow, it is assumed that the red blood cells (erythro-
cytes) far outnumber the other possible scatterers both in quantity and
volume (Shung
et al.
, 1976) and are thereby the main source of scat-
tering in blood. A theoretical analysis of scattering by Angelsen (1980)
was based on the assumption that blood is an isotropic continuum and
that the scattering arises from fluctuations in the compressibility and
mass density of the continuum. This explains the development of the
backscattering coefficient as a function of the haematocrit, shown in
Fig. 3.4. Until about 20% haematocrit, the backscattering coefficient
increases with the concentration of the scatterers. Above this, if the
concentration is high enough, the waves scattered by the individual par-
ticles will interfere, which leads to phase cancellation. This is why the
overall scattering depends on the configuration of the set of scatterers.
The more regular is the distribution (higher isotropy), the lower is the
backscattering coefficient. So, towards the maximum packing density,
the backscattering coefficient reaches its minimum. Also, the flow itself
influences the particle fluctuation and therefore the backscattering prop-
erties (Sigel
et al.
, 1983; Shung
et al.
, 1984; Cloutier and Shung, 1993;
Cloutier and Qin, 1997; Lin and Shung, 1999; Rouffiac
et al.
, 2004).
The models of Angelsen (1980) and Twersky (1988) were further
developed independently by Mo
et al.
(1994) and Bascom and Cobbold
(1995) by combining them with the voxel model. A voxel refers to an el-
emental volume that is small enough so that the incident ultrasonic wave
may be assumed to arrive with the same phase at every scatterer located
within it. Another model for the scattering in tissues was developed by
Jensen (1991) in which effects of flow disturbance and haematocrit on
