| Condition A | Condition B | ||||
 Figure 1  Figure 2  Figure 3 dominant direciton is 7.0o  Figure 4 dominant direction is 30.0o  Figure 5 ratio estimation is about 1.04  Figure 6 ratio estimation is about 1.86 |
Studies have demonstrated that vascular endothelial cells change their shape when subjected to fluid shear stress. This morphological accomodation reflects the ability of cells to respond to external forces. A statistical measurement system was developed to quantify the cell shape and its change, including the time history of relaxation process. By assuming the cell has an ellipsoidal shape, the system uses two variables, namely alignment direction and eccentricity (elongation ratio), to characterize this morphological change. A directional representation is first obtained, using four quadrature filters which extract the orientation of each pixel relative to its neighborhood (local region). Then the probability function of direction distribution is estimated and the maximum peak of the distribution is identified as the dominant direction of the cells. This direction is also the major axis direction if a cell is assumed ellipsoidal and its perpendicular direction is the minor axis direction. The elongation is evaluated by comparing the cell lengths along the major and minor axes. The cell lengths are statistically measured from the line segments that each cell contains along the major and minor axes, respectively.
The important theory behind such statistical measurement is that we believe the characteristic information will build up over the population and will dominate statistically. Thus, the measurements only reflect the behavior of the overall population, not individual cells.
Compared to other methods such as one that fits an ellipse to each cell, the proposed system gives more reliable results and is significantly faster.
To demonstrate the system, an example is examined and explained as follows.
Figures 1&2 exhibit cells before and after subjected to shear stress.
Figures 3&4 show the corresponding distribution of directions and its estimation (in red).
(click here to see their color-coded directional representation images). In situation A,
the distribution of directions is quite flat, which is the true because free cells are
oriented randomly. But, in situation B, the alignment direction becomes dominant.
Figures 5&6 depict the distribution of cell lengths along the major and minor axes and their
estimation (in red). The ratio is the eccentricity, defined as
major_length / minor_length. From situation A to B, the ratio changes from 1.04
to 1.86, which gives an accurate quantitative measure of the elongation due to the applied
shear stress.
| Condition A | Condition B | ||||
Figure 1 Figure 2 Figure 3 dominant direciton is 7.0o Figure 4 dominant direction is 30.0o Figure 5 ratio estimation is about 1.04 Figure 6 ratio estimation is about 1.86 |