Biomedical Engineering Reference
In-Depth Information
Biological fluids are typically non-Newtonian. Blood plasma is Newtonian and is very
similar in physical properties to water. Whole blood behaves as a Bingham plastic, whereby
a nonzero shear stress, denoted yield stress t
0
, is required before this fluid begins to flow.
Blood is often characterized by a power law function, of the form
g
n
t
¼
k
_
ð
4
:
57
Þ
where
k
and
n
are constants derived from a straight-line fit of ln t plotted as a function of
ln
g, since
_
ln t
¼
ln
k
þ
n
ln
g
_
Another common description of blood's viscosity is the Casson equation:
1
2
0
t
2
g
2
Þ
From a Casson plot, the yield stress t
0
can be measured. Rheology, the study of deforma-
tion and flow of fluids, focuses on these often complex viscous properties of fluids. Text-
books with rheological data for biofluids include
¼
t
þ
k
_
ð
4
:
58
Basic Transport Phenomena in Biomedical
Engineering
by Fournier [9] and
Biofluid Mechanics
by Chandran and colleagues [4].
EXAMPLE PROBLEM 4.13
The following rheological data were measured on a blood sample:
Shear Strain Rate [s
1
]
Shear Stress [dyne/cm
2
]
1.5
12.5
2.0
16.0
3.2
25.2
6.5
40.0
11.5
62.0
16.0
80.5
25.0
120
50.0
240
100
475
Fit the data to a power law function using a MATLAB m-file.
Solution
% Power Law Fit of Blood Data
%
% Store shear strain rate and stress data in arrays
alpha
¼
[1.5,2,3.2,6.5,11.5,16,25,50,100];
T
[12.5,16,25.2,40,62,80.5,120,240,475];
% Take natural logs of both
x
¼
¼
log(alpha);
y
¼
log(T);
