Biomedical Engineering Reference
In-Depth Information
end
%Determining the distribution function
imagesize
¼
size(ROInorm);
Cnorm
¼
reshape(ROInorm, imagesize(1)*imagesize(2), 1);
distribution
¼
HISTC(Cnorm, edges)/imagesize(1)/imagesize(2);
%Plotting the probability distribution function
plot(edges, distribution);
In the above example, the region of interest is selected by a mouse click as a rectangle in the displayed
image. Subsequently, probabilities for the different concentration values are calculated and plotted.
Figure 8.12
shows the typical results of the PDFs of a micromixer. In a region such as the entrance
region, where the two fluids are not mixed, two predominant concentration values of 0 and 1 exist,
resulting in two separate peaks as shown in
Fig. 8.12
(a). In a region of well-mixed fluids, the
predominant concentration is 0.5, resulting in a single peak as shown in
Fig. 8.12
(b).
For the ideal case with
s
0
¼
1 and
s
N
¼
0, the mixing index based on standard deviation is
t
1
t
1
N
X
N
N
X
N
c
i
c
I
i
I
¼
s s
N
M
s
0
s
N
¼ s ¼
¼
(8.39)
i ¼
1
i ¼
1
where
I
i
is the intensity value at a given position (pixel) of the region of interest. The mixing index
therefore varies from 1 to 0. For convenience, mixing efficiency can also be defined based on the
mixing index:
t
1
N
X
N
I
i
I
h ¼
1
MI
¼
1
(8.40)
i ¼
1
Mixing efficiency is 1 if the two fluids are fully mixed. In published literatures, mixing efficiency is
sometimes also referred to as the mixing index.
FIGURE 8.12
Probability intensity function of: (a) a not-mixed region and (b) a well-mixed region.
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