**4.2. Iso-surface viewing**

36 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

**Figure 17.** Sliced View of *RMS|E|* [dB] (only in agar phantom, colormap hot, jet, alpha 0.7)

**Figure 18.** Surface View of RMS|E| in [dB] (transparency of tumour region set to 1 – opaque,

Through this method we can produce much more intricate visualizations of results which are unseen in commercial EM simulators. For example we can mask results in uninteresting regions (immediate vicinity of power source etc.) almost entirely, semi-mask results in exposed tissue and left results in tumour unmasked, vital organs and other key regions of simulation domain. Note that masking results with transparency matrix does not alter

This may pose a problem when values around a power source are extreme and render the rest of results unclear. For this purpose you may consider utilizing simmilar approach as presented in Figure 7. Instead of finding values lower than some value you may find values

Many more possibilities are offered thanks to post processing of EM results in Matlab. As mentioned before, the greatest advantage is that it is extremely flexible and can meet very specific requirements which can arrise with various applications of EM field. In the following section we shall demonstrate some results obtained during our primary research of EM field of microtubules (nanostructures in living cells which serve as a crude frame of a

transparency of other regions set to 0.5 – semi-transparent; colormap – jet and lines)

higher than some reasonable value and lower all higher values to this level.

cell and have other important roles in life cycle of a cell).

presented values.

In this section we are going to show several results of EM field around microtubule. This structure is generally consisting of protofilaments which are polymerized tubulin heterodimers. Thirteen protofilaments bound together form a microtubule structure which resembles a long hollow tube (see Fig. 20).

**Figure 20.** Microtubule Structure Visualization

Tubulin heterodimers (i.e. basic building block of microtubules) are highly polar structures and provided some form of external energy (movement of microtubules, mechanical vibrations etc.) they may produce EM field around themselves (Pohl, 1981; Fröhlich, 1978).

In our work EM field simulations of microtubule model were entirely conducted using Matlab. Tubulin heterodimers were represented as vibrating elementary electrical dipoles (EED) and EM field was determined for each of these EEDs. Combining the results led to unravelling the EM field produced by these complicated structures at whole (Havelka, 2009).

For the purpose of this text we shall look at visualization of these results we used to present obtained EM field. Because microtubules are symmetrical structures we have found out that representing its field by iso-surface view is very clear and easy to interpret.

**Figure 21.** Sliced Semi-transparent View of Electric Field around Microtubule (see 4.1)

In the figure 23. you can see part of the code used to generate such visualization. More information on isosurface can be found in the Product Help of Matlab. In this particular example we wanted to view results in the form of several iso-surfaces. First of all we determined the range of data obtained through Matlab analysis of EM field around our sample microtubule.

Then we need to choose which values we want to be visualized as iso-surfaces (in this case, values range is extremely wide therefore we choose only exponents – 7, 5, 2). Then we need to find which positions at colour scale are lower than our actually viewed value (we generate the colour scale using function jet(length of colour scale)). Then we simply use function patch (to build 3D wire model of locations with desired values – i.e. 1e2, 1e5, 1e7) and we set its colour which we choose accordingly from our generated colour scheme.

Additionally you can choose lighting (particularly useful in this case is gouraud lighting which does not produce any glances on multiple iso-surfaces). It is also beneficial to use alpha which is lowered with each loop (to retain clarity of the visualization).

**Figure 22.** Iso-surface View of Electric Field around Microtubule [-] (A – rough data, B – iso-surface view from above, C – iso-surface view from enface, D – iso-surface view – general angle)

Last part is generating tiny triangle which is concealed in the middle of viewed data and contains the minimum and the maximum values which allows us to show colorbar appropriately for all the iso-surfaces .
