Biomedical Engineering Reference
In-Depth Information
FIGURE 8-52
Distribution of
turbulent kinetic
energy in a pulsatile
pump. (a) During
filling. (b) During
ejection. (Okamoto,
Fukuoka et al.,
2001), copyright
Informa Healthcare,
reproduced with
permission.
The Reynolds's shear stress,
τ
, is defined as
τ
=−
ρ
u
i
¯
v
j
(8.3)
where
is the density,
u
i
is the fluctuating component of the velocity in one direction,
and
v
i
is the fluctuating component at right angles to
u
i
.
Using (8.2) and (8.3), the shear stress can be approximated by
ρ
τ
=−
2
ρ
k
(8.4)
A snapshot of the distribution of the Reynolds's shear stress through the dotted cross
sections is shown in Figure 8-52.
It has been experimentally observed that red blood cell damage in shear flow is due to
two factors acting at the same time: (1) the level of shear stress; and (2) the exposure time
of the blood cell membrane to these stresses. A basic model, developed by Wurzinger,
which relates the damage to the effects of shear stress on blood corpuscles, is
)
=
Hb
Hb
=
10
−
5
×
t
0
.
785
2
.
416
L
RBC
(
%
3
.
62
×
×
τ
(8.5)
where
L
RBC
(%) is the lysis rate for red blood cells,
Hb
is the haemoglobin content,
Hb
is the damaged hemoglobin content, and
t
is the exposure time.
To obtain accurate results, the incremental lysis rate as a blood cell travels through
the pump is determined. This is achieved by calculating a number of flow lines from the
input to the output of the pump and determining the integrated lysis rate for each.
This lysis rate, along with the total blood volume, the flow rate, and the hematocrit
(%), is then used to determine the free hemoglobin volume and ultimately the normalized
index of hemolysis.
The authors show that small changes to the shape of the pump were able to decrease
the Reynolds's stress by a significant margin with a result that the normalized index of
hemolysis was reduced significantly. The results are summarized in Table 8-3.
