TEARS AND THEIR FRACTAL DIMENSION
Exploring the possibility's of optically determining different types of tears.
Recently I found out that you can calculate the fractal dimension of a image by using the box counting method. This inspired me to do more research in to the technique and current methods available. The idea would be to see if is possible, to use this methode for fractal analysis on crystalline structures produced by tears, photographed trough a microscope. If so, can it possibly help to optically determine the different types of (basal, reflex and emotional) tears?
Tear fluid contains a cocktail of oils, proteins, enzymes and a large quantity of electrolytes suspended in water. These vary regarding your own unique physiology, and type of tears that are produced. Together with the different variables such as the temperature and humidity, the tear evaporation and crystallisation process will be influenced. Resulting in different and unique crystalline structures. When viewed trough a microscope, these tear crystallisations show approximate fractal shapes, that seem to repeat due to their quasi self similarity on different scales throughout the crystallisation.
In the past years, Imaginarium of Tears has imaged many tears. Our main goal was always to only visualise emotional tears and there stories. But in the past years we also got many basal and reflex tears. These tears where never discarded, altho they where of less importance to the project, time was taken to also image those tears.
These micrographs of tear crystallisations will now be used to test the proces of analysing fractal dimensions by using the box counting methode. Starting with a small dataset containing a sample size of 30 images, 10 micrographs for each of the three tear types will be selected and processed.
Altho such a small sample size will probably not yield any statistically powerful results, it would be worth a try to see what kind of information can be extracted using this method. From there on, we can maybe classify a new sample size count, which in the future would give more insights into the possibilities of optically determining tears under a microscope by their fractal dimension.
Calculating fractal dimension by using ImageJ:
To calculate the fractal dimensions, the program ImageJ together with the plugin FracLac (Fractal Dimension and Lacunarity) will be used to analyse the micrographs containing tear crystallisation's.
To start I needed to figure out how to work with FracLac, ImageJ was already familiar, only working and setting up FracLac was a bit more complicated and difficult then expected, but I got lucky! Big thanks to @Agustín Bassó for helping me out in this part of the process.
Image 1: shows the micrograph of a tear crystallisation. With this image I will show my process of analysing and calculating the fractal dimension by using the the box counting method in the FracLac plugin of ImageJ.
Step 1:
Convert the original image into 8bit.
* image/type/8bit.
Step 2:
Apply threshold to extract the tear crystallisation from the background.
* image/Threshold/Adjust. Press auto, uncheck dark background and press apply.
Step 3:
Clean up the image by removing al black specs and outer ring of the crystallisation. This to get beter accuracy in our calculations of the inner fractal shapes.
* Select the brush tool in the menu.
The final result of the pre-process micrograph, which is now ready to be analysed in FracLac.
Step 5:
Starting and configuration the FracLac plugin.
* Go to Menu > Plugins >Fractal Analysis > FracLac. Once its menu is open press te BC button. This opens the configuration panel where you can setup the needed variables. (see image)
Once done, press OK. Answer the additional popup questions. Once back at the FracLac menu press SCAN.
Now the process will start calculating the fractal dimension of the micrograph, by using the box counting method. Once finished many overlay windows will be shown, all these windows contain the data sets of the different types of calculations done on that specific micrograph, and the values related to them. To get the fractal dimension value I checked collum number 6 and wrote down its value.
Results:
Quite a time and labour intensive process, but it shows that it is indeed possible to analyse tear crystallisations with the box counting methode and calculate their fractal dimension. Next up would be to process all other 29 tears, with the same settings as described above. Starting with the other 9 emotional tears to complete the set of 10 tears for this group. Each of the emotional tears has their own background story.
Next up will be the “second group” of 10 basal tears. All these basal tears where created by letting the person sit in front of a big fan, stimulating the production of basal tears. The results of these tears can be found below.
At last the “third group” the reflex teas where processed. Like the other two groups these also contain 10 tears. This group consists out of persons that used different stimuli like; eating peppers, cutting onions or by using menthol oil to induce reflex tears.
So can we use this method for optically determining different types of tears? Well I honestly I don’t know, since I’m not an expert on this front. This test was purely out of genuine interest into fractals and fractal dimensions.
So I asked @Agustín Bassó again to help out with the statistical part.
Kurskal Wallis Test
Calculation Summary
H = (12/(N(N+1)) * (∑T2/n) — 3(N+1)
H = 0.013 * 7371.65–93
H = 2.1181
The verdict at this time is that the limited and small sample size of N=30 is not sufficient. So at this point in time it is not yet clear if we in the future can use the fractal dimension for the optically determination of tears under a microscope.
When a regular parametric statistical methods like ANOVA is used with this data set, to compare the fractal dimension of the tears in this experiment. We can calculate that by checking the normality of their residuals, that the minimum sample size needed to give more insights into this experiment woud be N= 60. Any higher tear samples size from that point on, would result into more statistical power, a more clear outcome of the possibility to use fractal dimension to optimally determinate tears under a microscope.
Future plans:
To continue this experiment more tear crystallisations are needed. To do this Imaginarium of Tears is looking to get support from local universities or other interested parties, that want to help and facilitate this experiment.
For each of the three tear groups, volunteers are needed to participate and donate their tears. The volunteers can choose themselves which tear type they want to donate for the experiment. The three tear groups are;
Reflex tears; induced by different stimuli; This group can be split up into three different sub groups. Each subgroup will be using a different stimuli;
subgroup 1: will cut onions, to induce tears.
subgroup 2: will be eating hot peppers, to induce tears.
subgroup 3: will be using a menthol (cry stick), to induce tears.
Basal tears; wil be induced by looking (directly) into a powerful ventilator, by exposing the eyes to a high airflow basal tears will be produced.
Emotional tears; will become a big challenge. Since crying emotionally on command is hard to force. Especially in a strange unknown environment / location. The best way to do this would be to send out a larger quantity of the Tear Collection Kits to a select group of people with extra documentation related to the experiment. Hopefully enough tears collection kits will be returned with emotional tears to process in the experiment.
Due to the knowledge that has been gathered in the past years, we also need to change our processing methods to get a better consistent workflow where al tears are processed in the same way. With the current test we have used tears that where processed in slightly different ways over the years. Not even to mention the different circumstances the tears where crystallised in.
To fix this a new standardised protocol should be thought out for the tear inducing, documenting, collecting, storing and processing & imaging. The hardest part would be the processing of tears since this will have to take place in a climate chamber so all external conditions will closely be monitored to get matching crystallisation conditions.
Creating this DIY climate chamber is something I recently posted a story on. Since both of these parts of the project are quite difficult currently I’m stumbling apron some resistance to continue, knowledge & budget wise.
So, If this story garbed your attention and interests, please help me to share it! One day I will hopefully be able trough the help of my followers to achieve this next goal. So if you have any leads and or knowledge in this field of expertise please don’t hesitate to contact me.
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Turn your own tears into a unique tangible work of art with the Tear Collection Kit:
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