Biomedical Engineering Reference
In-Depth Information
% Use MATLAB's polyfit function to do linear curve fit
coeff
¼
polyfit(x,y,1)
% Write curve fit coefficients as a new x-y function for plotting
x1
¼
[0;0.01;5]
¼
y1
polyval(coeff,x1)
% Plot the original data as 'o' points
plot(x,y,'o')
hold on
% Overlay a plot of the curve-fit line
plot(x1,y1)
grid on
title('Power Law Function')
xlabel('ln Strain Rate [ln(1/s)]')
ylabel('ln Shear Stress [ln dyne/cm2]')
%
The resulting plot appears in Figure 4.36.
Power Law Function
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
ln Strain Rate [ln(1/s)]
FIGURE 4.36
The power law curve-fit using MATLAB of the rheological blood data in Example Problem
4.13.
When subjected to very low shear rates, blood's apparent viscosity is higher than expected.
This is due to the aggregation of red blood cells, called rouleaux. Such low shear rates are
lower than those typically occurring in major blood vessels or in medical devices. In small
tubes of less than 1 mm diameter, blood's apparent viscosity at high shear rates is smaller
than in larger tubes. This Fahraeus-Lindquist effect arises from plasma-red blood cell dynam-
ics. Beyond these two special cases, blood behaves as a Newtonian fluid and is widely
accepted as such. We shall see that the assumption of Newtonian fluid greatly simplifies
mechanical description of the circulation.
