4.3 Analysis of Non-Fixed Platelets
4.3.4 Further Data Analysis
The moving average of the above calculated cell area as well as ofdx(β,t),dy(β,t) and the lengths of corresponding vectors~vcell-ellipse(β,t)were calculated. By this procedure, small errors that arised, e.g. from imprecisely detected cell outlines could be minimized, while preserving the overall result. Furthermore, missing values could be interpolated.
The moving average of a variable (see above) at a frame fi was calculated by taking
xiFor this direction the line was defined asx=x(mean center of mass).
xiiDue to the pixelated nature of the cell outline rounding to the nearest natural number was neces-sary.
Chapter 4 DATA ANALYSIS is shown in black, the cell in blue, the points of inter-ception between straight represents one time point. The choice of the number of values that were averaged is discussed further in section 6.2. The sign of the vectors (~vcell-ellipse(β,t), magenta in figure 4.8) was calculated based on the moving average treated dx(β,t) and dy(β,t), i.e. the differences between cell outline and ellipse in x- and y-direction.
If the cell outline lay inside of the ellipse, the sign of~vcell-ellipse(β,t)was denoted as negative, if it lay outside of the ellipse the sign was denoted as positive. The moving average of the signed length lcell-ellipse(β,t)was plotted viaimagescas can be seen in figure 4.9.
To describe the interdependencies of the different values of~vcell-ellipse(β,t), both the variance oflcell-ellipse(β,t)between the different angles/directions at fixed time points (see figure 4.6) vardir as well as the variance of lcell-ellipse(β,t) between the different time points for a fixed angle/direction vartimewere computed. The for-mer describes the relations between,e.g. spreading over holes and on interspaces on structured substrates, the latter the dynamics along different directions. Addi-tionally, the variances vardirandvartimewere calculated based on the original,i.e.
not moving average treated values for the signed lengthslcell-ellipse(β,t). In figure
xiiiFor the first and last 10 frames the size of the interval was adjusted to the number of available frames on the site of the interval where there were fewer than 10 frames.
56
Analysis of Non-Fixed Platelets 4.3
Figure 4.9.: Plot of the moving average of the signed lengthslcell-ellipse(β,t)of the cell shown in gure 4.8.
The values for dierent angles corresponding to the dierent lines (see gure 4.6) are shown on thex-axis and the evolution over time is shown on they-axis. The signed lengthslcell-ellipse(β,t) are shown color-coded ranging from dark blue for the largest negative values, i.e. the cell outline lies inside the ellipse, to dark red for the largest positive values, i.e. the cell outline lies outside of the ellipse. A further discussion of these plots can be found in chapter 6. The missing values are shown in white.
4.10 an illustration of how the variances are calculated is shown. The area values in the last 50 images of all analyzed images were averaged for each platelet and plotted with the box-plot option in OriginPro 8.5 G (OriginLab). Furthermore, the mean values of vardir were calculated and plotted, both in OriginPro 8.5 G (OriginLab). The mean areas and the meanvardirvalues were calculated from the moving average treated data. Furthermore, the areas and variances were plotted in OriginPro 8.5 G (OriginLab).
Chapter 4 DATA ANALYSIS
Events of Retraction and Protrusion
Based on the moving average of the signed length lcell-ellipse(β,t), the spreading behavior was analyzed further by detecting events of large retraction or outgrowth.
A further discussion of the choice of the parameters chosen here to detect retrac-tions and outgrowth can be found in section 6.2.
To detect large retractions and outgrowth, the difference of each lcell-ellipse(β,t) -value in framet = fi with the corresponding value in frame t = fi+120 was com-puted. This difference is denoted asd(β,fi,fi+120) =|lcell-ellipse(β,fi)−lcell-ellipse
(β,fi+120)| in the following. If the absolute value of the above calculated differ-ence was at least 0.75µm and the differences d(β,fi, fi+x)with x lying in the in-terval [i+121 ,i+160] showed similar values asd(β,fi,fi+120),i.e. d(β,fi,fi+x)≥ d(β, fi,fi+120) − 0.1µm, this was defined as an event.xiv Furthermore, the sign of the differences d(β, fi,fi+120)and d(β,fi,fi+x) was required to stay the same. By comparinglcell-ellipse(β,t)in framet=ti withlcell-ellipse(β,t)in framet= ti+120,i.e.
180 seconds later, and ensuring that the differences were maintained for at least 40 more frames,i.e. 60 seconds, simple fluctuations were excluded. Multiple
detec-xivFor the last 160 frames no events could be detected as comparable points later in time were missing.
Figure 4.10.: Illustration of calculation of the two variances vardirandvartime. The arrows show on basis of which values the variances were calculated.
58
Analysis of Non-Fixed Platelets 4.3 tions of one event were sorted out by the condition that different events (along one
direction) had to happen at least 50 frames,i.e. 75 seconds apart in time. As time point at which the event took place, the time of frame fi+120was denoted. Further-more, it was denoted whether the event signifies a protrusion or an invagination based on whether the cell outline lay within, outside or on the ellipse in the frame fi+120. Finally, also the direction of the change was computed, i.e. whether the invagination was filled up/the protrusion grew or the invagination got larger/the protrusion retracted. These data are shown in chapter 6.
Display of Cell Outlines over Time
First, the images were rotated by the function imrotate (bilinear interpolation, bounding box: loose, see also section 4.3.3). The rotation alines the underlying rows of holes with the image borders. Then, the cell outline was found as de-scribed in section 4.2.2 by the functionsbwlabel and bwtraceboundary. Thereafter, the outline in each frame was plotted in a color-coded way ranging from dark blue for early time points to dark red for later time points. Examples for this way of presentation can be found in figure 6.5 in chapter 6.