In the following, several pre-processing steps that were needed to sort out platelets that did not spread completely or might have been influenced by a distorted sub-strate, irregular fibrinogen coating or other platelets, are described and different conditions under which platelets were excluded from analysis are shown in figure 4.2. Platelets that did not spread completely were excluded from analysis (see fig-ure 4.2 a)). Not completely spread platelets appeared darker in the phase contrast image, since they were thicker and therefore could be sorted out. Additionally, platelets lying on top of irregular fibrinogen coating were excluded from analysis.
An example of irregular fibrinogen coating is shown in figure 4.2 b). Especially on selectively coated substrates, platelets were able to distort the fibrinogen coating of the substrate. In figure 4.2 c) an image of a distorted fibrinogen layer is shown.
If any distortion of the fibrinogen layer was visible, the platelet that had distorted the layer, was excluded from analysis, since these interactions with the fibrinogen coating could have altered spread area and morphology of the platelet. Distorted substrate parts, i.e. the PDMS-layer itself is distorted, may arise,e.g., when there are remaining dust particles on the coverslip to which the substrate is transferred (see section 3.2.1) or when the substrate is stretched while being transferred to the coverslip. The distortion of a substrate can be measured based on images of the substrate coating. To ensure an undistorted substrate, it was tested in ImageJ [87]
whether simultaneous alignment of the horizontal and vertical rows of holes with the borders of the image was possible by rotation. If this simultaneous alignment was not possible, platelets lying on these parts of the substrate were omitted from analysis. A sketch of the alignment attempts is shown in figure 4.2 d). Further-more, platelets were excluded from the analysis, that were in contact or too close to other platelets. Finally, platelets that were situated on a flat part of the substrate
Chapter 4 DATA ANALYSIS
Figure 4.2.: Explanatory images for dierent cases in which platelets were not analyzed.
a) The upper image shows an inverted uorescence image of stained actin. The lower image shows the corresponding phase contrast image. The images show an example of a not completely spread cell in contrast to a spread cell. In phase contrast microscopy images not completely spread platelets appear darker due to their higher thickness and thus can be sorted out.
b) Platelets lying on top of irregular brinogen coating were excluded from analysis to prevent uncontrollable inuences due to the irregularity of the coating. An example for irregular coating can be seen in the uorescence image of labeled brinogen.
c) Especially on selectively coated substrates platelets were able to distort the brinogen layer as can be seen in the uorescence image of labeled brinogen. This distortion may in return also inuence the cell (e.g. size, outline etc.). Thus, platelets that visibly distorted the brinogen coating were excluded from analysis.
d) Distortions of the substrate itself which may, for example, arise due to small dust particles on the underlying coverslip or stretching of the substrate, were detected by verifying whether the horizontal lines of holes formed a 90◦-angle with the vertical lines. This is sketched in a uorescence image of the labeled brinogen by a white vertical line following the vertical line of holes and several horizontal lines forming a90◦-angle with the vertical line. It is visible that the horizontal lines of holes deviate from the white horizontal lines. Platelets lying on this part of the substrate were excluded from analysis.
but lay too close to the neighboring structures orvice versawere sorted out.
4.2.1 Spread Area, Perimeter and Ellipse Measurements
After the cell outline had been detected as described in section 4.1, it was filled manually in ImageJ [87] creating a mask of the cell. Afterwards, this mask was se-lected and the areaacell, as well as the perimeterpcellwere measured in ImageJ [87].
Furthermore, an ellipse (orientation, major and minor axis) that had the same area, orientation and eccentricity as the selection was calculated through the second mo-ments (compare [114]) with theMeasurefunction in ImageJ [87]. The results were
46
Analysis of Fixed Samples 4.2 saved and further processed in OriginPro 8.5G (OriginLab, Northampton,
Mas-sachusetts, USA). The perimeter of the above mentioned ellipse was calculated via following equation in OriginPro 8.5G (OriginLab):
pellipse =π·(a+b)·(1+ (3·λ2/(10+ q
(4−3·λ2)))) (4.1) λ= (a−b)/(a+b)
with a being the semi-major axis of the ellipse and b the semi-minor axis. This equation is an approximation of the perimeter of an ellipse as described in [99].
The relative perimeter of a cell was calculated in OriginPro 8.5G (OriginLab) as pcell/pellipse. This relative perimeter shows how ”rough“ the outline of the cell is, since it takes the smallest value of 1 for a perfect ellipse and gets larger the more protrusions the cell has. Histograms of spread area acell and of relative perimeter pcell/pellipse were plotted in OriginPro 8.5G (OriginLab) with binsizes of 10µm2 foracelland 0.1 forpcell/pellipse. In these histograms the percentage of values lying in a certain bin was denoted.
4.2.2 Curvature Calculation of Cell Outline
The curvature of the cell outline was analyzed in MATLAB®R2009b (MathWorks®) with a code written by Dr. Sarah Schwarz G. Henriques (PhD thesis, Institute for X-Ray Physics, University of Göttingen). The general program concept is also de-scribed in chapter VII of her doctoral thesis [88]. The exact steps of the program used for the data presented here, are described below. First, the platelets were la-beled bybwlabel(4-connected objectsi). Then, it was determined which pixels are part of the cell outline through the functionbwtraceboundary. In this function, pix-els that are part of the object have to be non-zero, while the background consists of pixels with the value zero and the connectivity was set to a 4-connected neighbor-hoodii. The found cell outline was then described through a spline, a composite of several polynomial functions each describing a part of the outline. This spline was parametrized via the arc lengths along the cell outline. Parametrization with the arc-length was necessary, since the cell outline cannot be described via a function of y(x) at all positions. A spline was calculate for each sequence of 7 points. As
iThis means that a pixel belonged to the platelet if at least one of its neighboring pixels had a value of non-zero. Neighboring pixels were those pixels directly above/below or left/right of the pixel and not the ones diagonal to it.
iiNeighboring pixels were in this case again those pixels directly above/below or left/right of the pixel and not the ones diagonal to it.
Chapter 4 DATA ANALYSIS
the curvature was only calculated for static data here, no reference start-point on the cell outline had to be defined. The curvature of the calculated spline was ob-tained by |−→c(s)| =
q
∂2x(s)
∂s2 + ∂2y(s)
∂s2 . After curvature calculation, the values were further processed in OriginPro 8.5 G (OriginLab). The curvature were sorted into bins of 0.2µm−1. The percentages of values in the different bins was determined and the differences between the curvature of the cell outline on structured and flat substrates was obtained by subtracting the values on flat substrates from those on structured substrates.