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.
Search WWH ::




Custom Search