The PBS Nova Documentary Fractals: Hunting for the Hidden Dimension was very interesting. Applying mathematics to abstract truths that we see every day in the world is fascinating. Near the end of the documentary there was a short section that touches on fractal geometry and the eye. I was thinking about this right before the documentary had gotten to this point, and thought about the iris, not only for human identification, but also in the diagnosis and treatment of glaucoma and the trabecular meshwork in the anterior chamber of the eye. I was also curious about retinal imaging that I have done, and the possibility of fractal geometry being used to restore vision in patients with retinal disorders. The implications of fractal geometry in the human body will surely be used to treat conditions that can currently not be treated due to the lack of technology to work on a microscopic level in the body, but this technology is being developed as we speak and the future of medicine is definitely more concrete than construal due to physics and abstract mathematics such as fractals.
I found an article by Iranian professors that discusses using fractal geometry to determine the individuality of iris structure in comparison to fingerprints and retinal imaging (M. Jampour). They determined that the iris is likely more accurate to identify individuals than fingerprints or handwriting analyses. I was not able to find any information on the trabecular meshwork (drainage canals in the iris for the aqueous humor to pass through the anterior chamber of the eye), which leads me to believe there has not been much research in this area, or no correlation with the structure of the iris and its pigment having anything to do with the actual drainage. This seems unlikely; however, because the effectiveness laser surgery to treat glaucoma is directly affected by the amount of pigment in the iris.
This video also got me thinking about the other structures in the eye. I have worked in ophthalmology for thirteen years, and in that time I have seen many retinal conditions but the most severe and devastating is retinitis pigmentosa. It is a genetic condition where pigmentation cells attack the retina and flood the tissue, essentially, with pigment or a giant mole that overtakes the retina, destroys the rod and cone cells, and blinds the patient (The Foundation). This disease starts in the late teens or early twenties and by age forty the patient is usually completely blind. There are no current treatments for this condition, and as medical professionals we diagnose and give a prognosis, and then watch the patient deteriorate. It is so sad for me to see these people who never in their life would have thought that they would be blind all of the sudden start to lose their sight.
Fractal geometry and the concept of reconstruction of rod and cone cells, or removing pigmentation in fractal patterns seems to me like an experimental treatment that could possibly create cures for conditions like retinitis pigmentosa or macular degeneration. The layout of the retinal cells looks very similar to a fractal pattern, and I think that with 3D printing technology done with organic-material-medium could revolutionize treatments. 3D printing on a cellular level with a CAD system under a microscope could give hope in printing new retinas for these patients. The printed pseudo-organic “retina” could theoretically be surgically attached to the posterior chamber of the eye. This sounds far-fetched, but retinal specialists complete membrane peels of retinal layers all of the time for surface wrinkling retinopathy and other scar tissue producing conditions. Only certain layers of the retina can have this procedure done without destroying the rod and cone cells, for a patient that is completely blind, to peel the entire retina and replace it with organic tissue with similar capabilities of truly organic rod and cone cells seems like it could be theoretically possible, especially when the vascular structures of the retina are also able to calculated with fractal geometry (Kansas University).
In my current profession using these relatively new concepts to think more creatively about specific problems in the world is extremely important. There have been studies that have discussed fractal geometry and retinal vessel structure, but as I was searching I did not find anything about the cellular components (University Kansas). I am sure as technology increasing and the possibilities of microscopic surgeries develop there will be more published about this in medical journals. I am leaving my current career in ophthalmic medicine, but this will be something that I keep in the back of my mind as my career in politics develops in terms of funding and research. Blindness will someday very soon be a thing of the past, as may paralyses and other ailments that effect human beings on a microscopic level causing catastrophic disability. In order for treatments for disabling conditions to be developed, researchers need to be taken seriously, and sometimes as in the case of Benoit Mandelbrot it takes decades for their research to be taken seriously.
References
Extract and Classification of Iris Images by Fractal Dimension and Efficient Color of Iris
Mahdi Jampour and others March 2011
Retinitis Pigmentosa
The Foundation Fighting Blindness
http://www.blindness.org/retinitis-pigmentosa
The fractal properties of retinal vessels: embryological and clinical implications.
Department of Ophthalmology, Kansas University Medical Center, Kansas City